![2 High-Speed Devices and Circuits with THz Applications
From optics and photonics, optical communication, light-emitting diode (LED)
lamp, endoscope, etc., have been produced.
The terahertz (THz, 1012 Hz) frequency region is located in between the microwave
region and the visible light region (Figure 1.1). This region was merely studied by a
small number of researchers in limited fields, such as chemical spectroscopy, astron-
omy, and solid-state physics. However, THz technology is nowadays in strong demand
in a large variety of fields, ranging from basic science such as biochemical spectros-
copy, astronomy, and materials science to practical science such as environmental
science, medicine, agriculture, and security [1, 2]. What is the reason why the THz
wave has attracted so much interest? The advantageous properties of the THz wave
are that it can be transmitted through objects opaque to visible light and that the corre-
sponding photon energy, 1–100 meV, is in the important energy spectrum for various
materials and biomolecules. These features allow various applications of imaging and
spectroscopy in this frequency band. Figure 1.2 displays several
examples of applica-
tions of the THz waves. The measurements shown here
illuminate the THz waves
onto objects and map intensity distributions of reflected or transmitted THz waves.
In some situations, by simultaneously measuring frequency spectra, one is able to
identify the contents and characterize their physical/chemical properties. The tech-
nique therefore can be used as nondestructive inspection, which is based on the fact
that the THz wave is much safer and does not do much
damage, compared to the x-ray.
In addition to industrial and medical applications, THz
technology is also of much
importance in basic sciences. For example, in astronomy, materials science, and bio-
chemistry, the detection of very weak THz radiation from interstellar matter in space,
electrons in materials, and biomolecules is expected to unlock mysteries behind the
generation of the universe, quantum effect in materials, and life activity, respectively.
In the THz region, however, even basic components like detector and source have
not been fully established, compared to the technically mature, other frequency
regions. This is because the frequency of the THz wave is too high to be handled
with conventional high-frequency semiconductor technology. In addition, the photon
energy of the THz wave is much lower than band gap energy of semiconductors.
100
Example
industries:
Radio
communications
Radar ??? Optical
communications
Frequency (Hz)
Medical
imaging
Astrophysics
103
kilo mega giga tera peta exa zetta
106
Microwaves
Electronics Photonics
THz
Visible X-ray γ-ray
MF, HF, VHF, UHF, SHF, EHF
109
1012
1015
1018
1021
FIGURE 1.1 Chart of the electromagnetic wave spectrum. (Adapted from the THz Science &
Technology Network [http://thznetwork.net/].)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-23-320.jpg)
![4 High-Speed Devices and Circuits with THz Applications
the detection speed becomes low (a typical time constant is of the order of ms below 4 K).
The detected signal is mostly resistance change arising from the rise in the crystal
temperature due to the THz absorption. There is another type of readout
mechanism:
measuring gas pressure via thermal expansion (Golay cell detector). Since all the detec-
torsbasedonbolometricdetectionrespondtoelectromagneticwavesinawide-frequency
region, one needs a frequency cutoff filter. Wei et al. [3] recently reported a nanoscaled
superconductor bolometer with the ability of a single THz photon detection.
1.2.1.2 Wave Detection
This detector senses the THz electromagnetic wave as a high-frequency wave.
A
representative device is a Schottky barrier diode detector. The advantages of
this detector are high-speed detection (time constant of ~ns) and room temperature
operation. This detector is often used in sub-THz regions, because the sensitivity
becomes low with increasing the frequency of the incident THz wave.
1.2.1.3 Quantum Detection
In contrast to wave detection, this type of detector senses photons of the THz
electromagnetic wave. Solid-state devices based on materials like superconductors
and semiconductors usually have energy level spacing corresponding to the THz pho-
ton energy (1–100 meV), for example, energy gap of superconductor, impurity level
of semiconductor, and energy level spacing due to quantum electron confinement
of semiconductor quantum structure. It follows that excess carriers are
generated
in the devices, when these devices absorb the THz waves. One can detect the THz
wave by recording electric signals produced by the carriers. THz detectors based on
a nanoscale island connected to electrodes, such as superconductor junctions [4] and
semiconductor quantum dots [5, 6], have been presented and demonstrated to exhibit
ultra-high sensitivity, including the level of single-photon detection. However, the
operation of the superconductor and semiconductor detectors needs a very low tem-
perature environment (<0.3 K). This situation forces one to use a dilution refrigerator
or a 3He refrigerator, restricting the range of practical uses.
1.2.1.4 Others
THz time-domain spectroscopy (TDS) is nowadays widely employed in THz research
fields. As detectors, the photoconductive antenna and the electro-optic device are
used. This measurement allows real-time observation of the oscillatory electric field
of the THz wave, providing information on both amplitude and phase of the THz
electric field. Though these detectors work under room temperature, their operation
requires an expensive femtosecond pulse laser.
Another type is a frequency mixer using a supercomputer in which a beat signal
corresponding to the frequency difference with a local oscillator is measured. This
type of detector is often used in the fields of astronomy and environmental science.
1.2.2 CNT-Based THz Detector
The carbon nanotube (CNT) is expected to be used as a building block for
future nano-electronics, nano-photonics, and nano-mechanics owing to its unique](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-25-320.jpg)
![5
Terahertz Technology Based on Nano-Electronic Devices
one-dimensional structure [7]. From the viewpoint of application to the THz detector,
the CNT also has been regarded as a promising candidate. In fact, near-infrared
sensors using the CNT transistor have been successfully developed [8, 9]. In the THz
region, although there are several reports [10, 11], much higher performance has not
been achieved to date, compared to other existing detectors.
In the following, I will introduce our recent development in CNT-based THz
detectors [12, 13]. We have created a highly sensitive and frequency-tunable THz
photon detector using the CNT and GaAs/AlGaAs transistors. This detector has
two detection mechanisms: photon-assisted tunneling (PAT) [12] and current-
peak shift [13]. For the latter, THz irradiation causes a peak shift of CNT cur-
rents
relative to gate voltage, leading to the realization of ultra-high sensitivity:
THz photon detection.
1.2.2.1 Photon-Assisted Tunneling in CNT
In 1963, Tien and Gordon proposed a theory on the interaction of a nanoscale island
with an electromagnetic wave [14]. The essence of their discussion is that new energy
bands, the so-called photon sidebands, are formed by the AC electric potential of
the electromagnetic wave at intervals of nhf (n, integer number; h, Planck constant;
f, frequency of the electromagnetic wave).
A quantum dot (QD) structure connected to source, drain, and gate electrodes is
a promising device for examining their model, because the QD with the
electrodes
works like a single-electron transistor (SET). By sweeping either the gate
voltage
or the source-drain voltage and measuring the resulting source-drain current,
spectroscopic information about energy states in the QD can be directly obtained.
The photon sidebands in the QD can thus be observed as new current signals are
generated via the inelastic electron tunnel when electrons exchange photons. This
phenomenon is known as PAT (Figure 1.3(a)). With microwave irradiation of super-
conductor tunneling devices [14–16] and semiconductor QDs [17, 18], the PAT has
been successfully observed.
Compared to conventional QDs based on superconductors and semiconduc-
tors, a QD using a CNT has the following unique properties: its characteristic
energy, or charging energy, and energy level spacing due to quantum
electron
confinement typically reach ~10 meV, corresponding to a THz frequency
(~2.4 THz). This energy range is larger by a factor of 10 than that of the conven-
tional QDs. These advantageous properties potentially lead to device applications
of CNT-QDs in the THz region. In this view, we have studied the THz response
of the CNT-QDs [12].
Figure 1.3(b) schematically displays the CNT-QD structure. The CNT-QD was
fabricated as follows: First, CNTs were dispersed on a semiconductor (GaAs/
AlGaAs) wafer, whose surface was covered with a SiO2 film of ~100 nm thickness.
We mapped topography of the device surface with an atomic force microscope,
and specified locations of single-wall CNTs with a diameter of ~1 nm. Based on
the images obtained, source and drain electrodes with an interval of ~600 nm and
side-gate electrodes were patterned with electron-beam lithography. In this device,
electrons are confined to a very small area of l × 600 nm2, forming a QD. Metallic
CNTs were used.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-26-320.jpg)
![7
Terahertz Technology Based on Nano-Electronic Devices
the original peak and the satellite peaks as a function of the photon energy, hf, of the
THz wave. From the measurement of the differential conductance dISD/dVSD as a func-
tion of source-drain voltage VSD and gate voltage VG (Coulomb diamond
measurement),
we derived the conversion factor, κ = 0.18, which is defined as the conversion ratio of
VG into energy. The data clearly show good agreement between κΔVG and hf, providing
evidence for the THz-PAT in the CNT-QD. It is thus demonstrated that the CNT-QD
works as a THz detector with frequency tunability by the application of the gate voltage.
It should be noted that the satellite current is only observed on the positive VG side
with respect to the original peak. The occurrence of the satellite current corresponds
to the electron tunneling from the QD to the drain lead (the right side panel of
Figure 1.3(a)). The side of VG on which the satellite current is clearly seen depends
on the sample properties. This is possibly due to tunnel barrier asymmetry between
the source and drain electrodes.
The theory by Tine and Gordon says that the tunneling rate into the photon side-
bands should follow the Bessel functions of the illuminated power [14]. In order to
–0.80
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Current
(pA)
–0.75
Gate Voltage (V)
–0.70
Without Thz irradiation
1.4 THz
1.6 THz
2.5 THz
4.2 THz
4
0
0
4
8
12
κ∆V
G
(meV)
16
20
Slope 1
8
Photon Energy (meV)
12 16 20
–0.65
VSD = 1 mV
T = 1.5 K
FIGURE 1.4 Source-drain current ISD versus gate voltage VG for the frequency of the THz
wave, f = 1.4, 1.6, 2.4, and 4.2 THz. The experimental curves for the THz irradiation are off-
set by multiples of 0.8 pA for clarity. The inset shows the energy spacing, κΔVG, between the
original peaks and the satellite peaks as a function of the photon energy, hf, of the THz wave.
The dashed line in the inset is an eye guide corresponding to κΔVG = hf. (Adapted from
Y. Kawano et al., J. Appl. Phys., 103, 034307, 2008.)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-28-320.jpg)
![8 High-Speed Devices and Circuits with THz Applications
examine this feature, we measured the THz intensity dependence of the THz-PAT in
the CNT-QD. In the measurements, we inserted THz
attenuating
filters between the
THz laser and the sample. The result is displayed in Figure 1.5. The general tendency
is as expected, but we could not get a perfect fit to the Bessel functions. We speculate
that since the single QD was used, the tunneling processes via the electrodes would
make it difficult to analyze the result
accurately with this model. We plan to study
the THz intensity dependence in more detail by using a double-coupled CNT-QD,
in which the PAT occurs as a consequence of electron transitions between two well-
defined discrete levels. In this device, we anticipate that frequency selectivity would
be improved compared to that of the single CNT-QD.
1.2.2.2 THz Photon Detection with CNT/2DEG Hybrid Device
In the CNT THz detector described in the previous section, although frequency-selective
THz detection has been achieved, the detection sensitivity is not high. This is because
in this detection mechanism, one-photon absorption generates only one electron even if
a quantum efficiency of 100% is achieved. This limits the detection sensitivity. In order
to resolve this problem, we have created a new designed device [13]: a CNT-SET is
integrated with a GaAs/AlGaAs heterostructure chip (Figure 1.6(a)). The hybrid struc-
ture is divided into two separate roles of THz absorption (2DEG) and signal readout
(CNT-SET). A basic idea of THz detection with this device is that the CNT-SET senses
electrical polarization induced by THz-excited electron-hole pairs in the 2DEG. Since
the SET works as an ultra-sensitive electrometer, the CNT/2DEG device is expected to
exhibit ultimate sensitivity in photon detection.
14
12
10
8
6
4
2
0
–520 –510
1.0
THz intensity
(arb. units)
0.93
0.70
0.56
0.51
0.28
0.09
0
–500 –490
Gate Voltage (V)
Current
(pA)
–480 –470
VSD = 0.5 mV
T = 2.5 K
f = 2.5 THz
0.0
12
8
4
0
0.4
Satellite peak
Original peak
0.8
THz Intensity (arb. units)
Current
(pA)
FIGURE 1.5 THz intensity dependence of ISD versus VG. The inset shows the THz inten-
sity dependence of the amplitudes of a satellite peak and one of an original peak. The solid
lines in the inset are fitting curves based on the square of the nth-order Bessel functions.
(Adapted from Y. Kawano et al., J. Appl. Phys., 103, 034307, 2008.)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-29-320.jpg)
![10 High-Speed Devices and Circuits with THz Applications
of the peak shift, which is characteristic of the cyclotron resonance. In addition, from
these data, the associated m* value is derived to be 0.067m0, where m0 is the free
electron mass. This value is in good agreement with the cyclotron effective mass
for a GaAs-based 2DEG [19]. These facts indicate that the current peak shift of the
CNT-SET originates from the THz absorption by the 2DEG.
Let me explain microscopic carrier dynamics associated with the THz detec-
tion. It is well known that a 2DEG has a random potential with a typical period of
20–100 nm [20]. It follows that the THz-excited electrons and holes drift in opposite
directions through the local electric field gradient due to the random potential [21]. As a
result, they are spatially separated from each other. Such separation of electron-hole
pairs generates electrical polarization in the 2DEG. This situation is equivalent to appli-
cation of an effective gate voltage to the CNT-SET, resulting in the current peak shift.
We then measured the temporal trace of the THz signal (the ISD change associated
with the current peak shift) as the THz irradiation was cycled on and off. We here
used cyclotron radiation [22] from another 2DEG in a different GaAs/AlGaAs chip.
The intensity of this THz source can be continuously changed by altering the current
Source-drain
Current
(pA)
Source-drain
Current
(pA)
Gate Voltage (mV)
–160
80 120
100
80
60
40
20
0
70
60
50
40
30
20
10
0
–140 –160 –140
Gate Voltage (mV)
(a) (b)
0 (THz off)
7.85
7.20
6.55
5.90
5.25
4.60
×10
–12
3.95
3.25
2.60
1.95
1.30
0.65
0
f =1.6 THz f =2.5 THz
B(T) B(T)
0 (THz off)
7.85
7.20
6.55
6.13
5.25
4.60
3.95
3.25
2.60
1.95
1.30
0.65
0
FIGURE 1.7 Magnetic field dependence of source-drain current ISD versus gate voltage VG
of the CNT under THz irradiation. The magnetic field B was applied to the detector perpen-
dicular to the 2DEG plane, and the B values in units of Tesla (T) are given on the right-hand
side of the figures. The data with the THz irradiation are offset for clarity. (Adapted from
Y. Kawano, T. Uchida, and K. Ishibashi, Appl. Phys. Lett., 95, 083123, 2009.)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-31-320.jpg)
![11
Terahertz Technology Based on Nano-Electronic Devices
to the 2DEG of the THz source. We reduced its intensity to an extremely low level, on
the order of 0.1 fW. We mounted, face to face, the sample and the 2DEG-based THz
source in the same superconducting magnet so that the 2DEGs of the sample and the
source were both in cyclotron resonance condition. Figure 1.8 displays time response
of ISD for an on/off sequence of the THz irradiation at VG = –169 mV, VSD = 1.5 mV,
B = 3.95 T, and f = 1.6 THz. This result shows that the CNT-SET current was stable
when the THz radiation was off, whereas it repeatedly switched during the THz
irradiation. This behavior means that the CNT-SET senses temporal processes of
excitation and recombination of THz-excited carriers in the 2DEG.
I note that the CNT-2DEG distance is 120 nm, the relative dielectric constant of
GaAs is 13, and the separation length of excited electron-hole pairs is 20–100 nm
[20, 21]. Based on these values, the potential change caused by the polarization of a
single electron-hole pair is estimated to be 0.4 ~ 10 meV. This value is comparable
to the width of the current peak of the CNT-SET (~3 meV). This shows that single-
carrier charging via single THz photon absorption in a 2DEG can generate an observ-
able current peak shift and resulting current switching. The data of Figure 1.8 thus
demonstrate that the CNT/2DEG device is capable of detecting a few THz photons.
The power of 0.1 fW at 1.6 THz is equivalent to about 105 photons per second.
This means that the detector does not sense all incident THz photons, which is due
to the much smaller detection area than the wavelength of the incident THz wave.
I expect that this problem will be resolved by fabricating a device having appropriate
antenna-shaped electrodes for the CNT-SET.
The present detector can work at 6 ~ 7 K. This performance eliminates the use of
a dilution or 3He refrigerator with low cooling capacity and complex systems. The
device can therefore be used in a standard 4He refrigerator or a compact cryo-free
mechanical refrigerator with much higher cooling capacity and much greater ease
of use. This advantageous capability makes it possible to extend the usable range of
ultra-sensitive THz measurements.
Source-drain
Current
(pA)
4.8
3.6
2.4
1.2
0
T = 2.5 K
f = 1.6 THz
B = 3.95 T
VSD = 1.5 mV
VG = –169 mV
Time (s)
0 10 20 30 40 50 60 70 80 90 100
THz on THz on
THz off
THz off
FIGURE 1.8 Time trace of the THz-detected signal (the CNT-SET current ISD) as the THz
irradiation is cycled on and off. In this measurement, THz cyclotron radiation emitted from
another 2DEG was used with a very low intensity of ~0.1 fW. (Adapted from Y. Kawano,
T. Uchida, and K. Ishibashi, Appl. Phys. Lett., 95, 083123, 2009.)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-32-320.jpg)
![12 High-Speed Devices and Circuits with THz Applications
1.3 THz IMAGING
Enhancing spatial resolution of THz imaging is one of the central issues in THz
technology. Nevertheless, this is a formidable task, because basic components neces-
sary for obtaining high resolution, such as high-transmission wave line and a highly
sensitive detector, have not been well established compared to other frequency regions.
There are generally two methods for realizing high resolution in optical imaging:
solid immersion lens and near-field imaging technique. I explain the applications of
the techniques in the THz imaging below.
1.3.1 Solid Immersion Lens
In a standard optical imaging system like the use of a lens, spatial resolution of
an optical image is proportional to a wavelength of the light. The solid immersion
lens utilizes the fact that a wavelength in a material with high dielectric constant is
reduced compared to that in vacuum. Therefore, a lens with a large refractive index
leads to high resolution.
Figure 1.9 depicts an example of THz imaging based on the solid immersion
lens [23]. A hyperhemispherical lens made of Si is in contact with the back surface
of a sample. The sample is a 2DEG in a GaAs/AlGaAs heterostructure. A THz emis-
sion from the 2DEG is radiated as a consequence of inter-Landau-level transitions
of electrons under magnetic field, i.e., cyclotron emission (CE) [22]. The focal point
of the lens is designed to be on the 2DEG layer of the sample. The CE from the
focal point is collimated via the lens and is guided through a metallic light pipe to
a THz detector. Off-axis light is filtered by a black polyethylene pipe. The sample
is scanned relative to the lens by use of an X-Y translation stage, while the optical
system including the detector is stationary. The relatively large refractive index of
GaAs and Si (n ~ 3.4) allows a resolution much higher than that obtained with a
remote lens system.
Kawano and Komiyama [23] reported that for the solid immersion lens system, the
resolution is about 50 µm at 130 µm, the wavelength of CE in vacuum. This value is
improved by a factor of 6, compared to the resolution (300 µm) for the remote Si lens.
B
Si-lens
2DEG (THz emitter)
2DEG (THz detector)
THz absorber
FIGURE 1.9 THz microscope based on a solid immersion lens.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-33-320.jpg)
![13
Terahertz Technology Based on Nano-Electronic Devices
1.3.2 Near-Field Imaging
Though the solid immersion lens system enables relatively high resolution, the
resolution is still determined by the diffraction limit. A powerful technique for over-
coming the diffraction limit is near-field imaging [24]. When an electromagnetic wave
is illuminated onto an aperture smaller than a wavelength, a localized evanescent field
(near field) is generated just behind the aperture. The size of the evanescent field is
determined by the aperture size and not the wavelength. By illuminating or detecting
the evanescent field, it is possible to get a resolution beyond the diffraction limit.
Conventionalsystemsfornear-fieldimaginghaveanaperturetypeandanaperture-
less (scattering) type. In the visible and near-infrared regions, either a tapered,
metal-coated optical fiber (aperture type) [25] or a metal tip (aperture-less type) [26]
is used. In the microwave region, either a sharpened waveguide (aperture type) [27]
or a coaxial cable (aperture-less type) [28] is used. Since the intensity of the evanes-
cent field is very weak, the realization of near-field imaging needs a highly sensi-
tive detection scheme, such as a high-transmission wave line and highly sensitive
detector.
1.3.2.1 Near-Field Imaging in the THz Region
Several methods for near-field imaging in the THz region have been presented. In the
aperture type, a metal hole was used to obtain a resolution better than λ/4 [29]. This
method, however, has the drawback of low wave transmission through the small
aperture, which requires detecting very weak waves. Moreover, the spatial resolution
is not so high. As the aperture-less type, a sharpened antenna [30], a metal tip [31],
and a cantilever [32] were reported. Although the aperture-less technique allows
high spatial resolution, it has the problem of separation from a far-field component of
an incident wave, which generates a large background signal. For this reason, in most
instances the probe position is modulated and synchronously detected signal is mea-
sured. However, this scheme makes the whole system and its operation complicated.
At present stage, near-field THz imaging has not been fully established, and
several other techniques are proposed and attempted. This is still an ongoing issue.
1.3.2.2 Near-Field THz Imaging on One Chip
I here explain unique near-field THz imaging—on-chip THz imaging with an
integrated semiconductor device [33, 34]. The problems of other techniques were low
efficiency of near-field detection and complicated systems. The new integrated device
enables near-field THz imaging in a much simpler manner. As shown in Figure 1.10,
an aperture with an 8 µm diameter and a planar probe were deposited on a surface
of a GaAs/AlGaAs heterostructure chip. The aperture and the probe are insulated by
a 50 nm thick SiO2 layer. The GaAs chip has an electron mobility of 18 m2/Vs and a
sheet electron density of 4.4 × 10 m–2 at 77 K. The two ohmic contacts were extended
to the side surfaces of the chip, to each of which an electrical wire was attached.
A 2DEG, located 60 nm below the chip surface, works as a THz detector. In this
device structure, all components—an aperture, a probe, and a detector—are inte-
grated on one GaAs/AlGaAs chip. This scheme eliminates any optical and mechani-
cal
alignments between each component, leading to an easy-to-use and robust system.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-34-320.jpg)
![15
Terahertz Technology Based on Nano-Electronic Devices
The decay curves of Figure 1.12(b) show that the near-field THz device has a
spatial resolution of 9 µm. The important points of the data are that the
resolution
does not depend on the wavelength of the THz wave, and that it is far beyond the
diffraction limit λ/2 (107.3 µm) for the wavelength of λ = 214.6 µm. These
features
are characteristic of the near-field effect. The present device hence properly functions
as a near-field THz imaging detector. Using this device, a
high-resolution image of
THz CE distribution in another 2DEG has been obtained [35].
In general, when one improves spatial resolution, one encounters the problem
that it is necessary to largely enhance detection sensitivity. This is because the
intensity of the wave to be detected is strongly reduced as the sensing area becomes
small. This situation compels one to produce a scheme of highly sensitive detection
in a tiny region. I expect that one promising approach for tackling this problem
in the THz region will be to use the CNT/2DEG THz detector [13], described in
the previous section. Compared to the 2DEG detector, the CNT/2DEG detector
exhibits much higher sensitivity in a much smaller sensing area of
submicrometer.
When this detector is integrated with an aperture and a probe as shown in
Figure 1.10, the device will enable THz imaging with ultra-high sensitivity and a
sub-µm resolution.
Aperture
Aperture Alone
Aperture
Probe
0.0489
0.0428
0.0367
0.0306
0.0245
0.0183
0.0122
0.00611
0
Aperture + Probe
FIGURE 1.11 Calculations of THz electric field distributions in the vicinity of the aperture
for the device with the aperture and probe (upper panel) and for the device with the aperture
alone (lower panel).](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-36-320.jpg)
![17
Terahertz Technology Based on Nano-Electronic Devices
1.4 THz APPLICATION
1.4.1 Applications to Materials Researches
The photon energy and the period of the THz wave with 1 THz are about 4 meV
and 1 ps, respectively. In these energy and time regions, there are many
important
materials and their physical properties, such as energy gap of superconductor, impu-
rity level of semiconductor, phonon energy, and Landau level separation. THz spec-
troscopy and imaging can thus be exploited as a powerful tool for investigating and
characterizing various materials.
There are a lot of THz applications to materials researches. Shikii et al. [36]
reported mapping of supercurrent distributions in a high-temperature superconductor
by means of the THz imaging technique. THz-TDS is a very powerful tool for
investigating electron dynamics in materials. This technique provides two kinds
of information: real-time dynamics and frequency spectra. With this method, a
lot of important information was successfully derived and the related electronic
properties were clarified. For example, reported were THz conductivity in an MgB2
superconductor [37], Bloch oscillation in a semiconductor superlattice [38], ballistic
electron motion in a CNT [39], and dynamics of a spin-density-wave gap in a quasi-
1D organic conductor [40].
1.4.2 Applications to Semiconductor
1.4.2.1 Imaging Energy Dissipation in 2DEG
When the 2DEG is subject to a perpendicular magnetic field, it exhibits dramatic
properties known as quantum Hall effect (QHE) [41, 42]. In the QHE regime, the
longitudinal resistance vanishes and the Hall resistance is precisely quantized.
The basis of the QHE is the formation of the Landau level, which originates from
the quantization of electron cyclotron motion. Studying electron distribution of an
excited Landau level (related energy-dissipation distribution) is one of the critical
issues regarding the QHE. The reason is as follows: Earlier works reported that
the electron relaxation from excited Landau level involves a slow physical
process,
the typical timescale being as long as 10–100 ns [43]. Moreover, the equilibrium
length of the excited electrons LE was shown to reach a macroscopic value of
~0.1 mm [44, 45]. This leads us to expect that spatial distribution of the excited
electrons will be strikingly different from that of the ground-state electrons and will
drastically depend on sample dimensions, in relation with LE. However, this issue
has not been satisfactorily clarified.
Several imaging techniques have been applied to obtain information on dissipation
distributions in the QHE systems. By using the fountain pressure effect of
superfluid
liquid helium, Klaß et al. demonstrated that in the QHE state, dissipation takes place
almost totally at the diagonally opposite electron entry and exit corners of the sample
(hot spots) [46]. A similar conclusion has been derived from the experiments of
Russell et al., which applied a local bolometry technique [47]. Unfortunately, since
these earlier experiments probe the lattice temperature related to Joule heating,
they do not exclusively observe the distribution within the 2DEG, i.e., the effective](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-38-320.jpg)
![18 High-Speed Devices and Circuits with THz Applications
temperature of the excited electrons. Thus, until now no
experimental techniques
were available for imaging only the dissipation distribution in the 2DEG.
In contrast, since CE is radiated with the transition of electrons from higher
Landau levels to lower Landau levels, mapping the CE intensity with the THz micro-
scope provides a direct probe of the excited electrons. In the following, I introduce
investigations on spatial properties of the 2DEGs by use of THz-CE imaging.
1.4.2.2 Separate Imaging of Ground and Excited Levels
In order to enable separate imaging of the ground-state electrons and the excited-state
electrons, we have developed a combined system of an electrometer with a THz
microscope [48]. In the electrometer technique, we are able to map voltage distribu-
tions [49, 50]. Hence, comparing the two kinds of the mapped data (voltage and CE)
allows us to distinguish the contributions of the ground-state and excited-state elec-
trons to the generation of the voltage.
Figure 1.13 depicts the setup of the combined imaging system. An electrometer
(small Hall bar) and a hyperhemisphere Si lens are in contact with the front and back
surfaces of the sample, respectively. A THz detector is mounted at the bottom of
the system. The electrometer, the sample, and the THz detector were fabricated on
GaAs/AlGaAs heterostructure wafers having the 2DEGs 0.1 µm beneath the crystal
surfaces. In imaging experiments, the sample alone was moved with an X-Y stage,
while the electrometer and the optical system were spatially fixed. The whole system
was directly immersed into liquid 4He and was subject to a perpendicular magnetic
field B.
The detection mechanism of the electrometer is as follows: As shown in
Figure 1.14, the distance between the two 2DEG layers is very short, and consequently
they are capacitively coupled. It follows that when a current Is is passed through
the sample, excess charges ΔQ are induced into the 2DEGs, according to CV(x,y)
= ΔQ. Here, V(x,y) is a local voltage in the sample right below the electrometer, and
Voltage imaging
SiO2 film
Si-lens
2DEG (Sample)
2DEG (Electrometer)
2DEG (THz detector)
B
THz imaging
THz absorber
FIGURE 1.13 Combined imaging system of the electrometer and the THz microscope.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-39-320.jpg)
![19
Terahertz Technology Based on Nano-Electronic Devices
C is the capacitance between the two 2DEG layers. The generation of ΔQ leads to
the change, ΔRE, in the longitudinal resistance of the electrometer. By translating
the electro
meter over the sample surface and measuring ΔRE × IE, we are able to
image 2D distributions of V(x,y) in the sample (IE is the bias current for the elec-
trometer). The electrometer was processed into a Hall bar geometry from a GaAs/
AlGaAs heterostructure with an electron mobility µH = 18 m2/Vs and a sheet electron
density ns = 2.2 × 10 m15 m–2 at 4.2 K. The device has a 2DEG channel with a length
L = 200 µm and a width W = 1.5 µm, and the two voltage probes with an interval of
2.3 µm. The spatial resolution of this system is about 2 µm, which is determined by
the sensing 2DEG area of the electrometer.
The sample studied has a Hall bar geometry with L = 2.8 mm and W = 1 mm,
which is fabricated from a GaAs/AlGaAs heterostructure with µH = 53 m2/Vs and
ns = 2.4 × 1015 m–2 at 4.2 K. In imaging measurements, the voltage V(x,y) and the CE
intensity VCE(x,y) were simultaneously obtained with two lock-in amplifiers, where
a 30 Hz rectangular-wave current alternating between zero and a given finite value
Is was passed through the sample. All measurements were performed at 4.2 K.
Figure 1.15 displays images of the longitudinal voltage Vxx and VCE at three current
levels, I = 20, 70, and 140 µA, and at B = 5.75 T (Landau level filling
factor, 1.74,
of the sample). We obtained the Vxx(x,y) data by differating V(x,y) over a
distance
of 50 µm in the direction of the length of the sample: Vxx(x,y) = V(x + Δx,y) – V(x,y)
with Δx = 50 µm. The 20 µA data show that Vxx is seen over the whole 2DEG
area, whereas CE occurs only in the two diagonally opposite corners. This directly
indicates that the observed Vxx (except at the two spots) arises from
scattering of
the ground-state electrons. It is known that the CE at the two spots takes place
via tunneling injection of nonequilibrium electrons from the source
contact and
inter-
Landau-level tunneling of electrons near the drain contact [22]. The Vxx data at
I = 70 and 140 µA show that an additional Vxx is generated around the source contact,
and with
increasing the current, the area covered by the additional Vxx expands
toward the interior 2DEG region. Comparing with the VCE data reveals that a strong
CE is radiated in the similar region, indicating that Vxx observed on the source
contact side mostly originates from scattering of the excited electrons. Vxx is also
visible over the whole 2DEG region, whereas CE remains absent (except in the two
diagonally opposite corners). This situation is similar to that observed at I = 20 µA,
showing again that Vxx associated with the ground-state electrons is generated over
IS
C
V(x, y)
IE
Electrometer
Sample
CV(x, y) = ∆Q ∆RE
∆RE
∆Q
FIGURE 1.14 Equivalent circuit of the scanning electrometer system and the detection
mechanism. (Adapted from Y. Kawano, and T. Okamoto, Phys. Rev., B 70, 081308(R), 2004.)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-40-320.jpg)
![20 High-Speed Devices and Circuits with THz Applications
the entire 2DEG area. We confirmed that the pattern of these features systematically
changes upon reversing B and I, and that they are also observed for other Landau
level filling
factors and for other samples fabricated from different wafers. This
indicates that they originate from an intrinsic nature of the 2DEG and are not due to
inhomogeneity of the electron density.
Let me explain the origin of the difference in the distributions between the
ground-state electrons and the excited electrons. The summary of the experimental
findings is that as schematically shown in Figure 1.16, the scattering distribution of
the ground-state electrons spreads over the entire 2DEG region, whereas that of the
excited electrons is localized in the two corners and around the source contact. The
result indicates a large difference in the scattering processes and their
characteristic
lengths. The equilibrium length of excited electrons was shown to be a very long scale
of 10–300 µm [44, 45]. On the other hand, although there is no clear
experimental
information about the ground-state electrons, one can think that the scattering rate
will be much higher because the scattering does not require much energy. The main
scattering mechanism of the ground-state electrons is possibly impurity scattering
originating from ionized donors in the AlGaAs layer. The characteristic scattering
length of the ground-state electrons can be regarded as a period of the ionized impu-
rities, 0.05–0.3 µm, which is much shorter than LE. This explains the contrasting
situation regarding spatial distributions of ground- and excited-state electrons. I will
discuss the electron transport process in more detail below.
20
µA
70
µA
140
µA
0 4
Vxx, VCE (arb. units)
2 6 8 10
Vxx VCE
FIGURE 1.15 Distribution images of the longitudinal voltage Vxx (left) and the CE intensity
VCE (right) at three current levels, I = 20, 70, and 140 µA. The white broken lines denote the
2DEG boundaries of the sample. In the Vxx (VCE), for clarity, the signals at I = 20 and 70 µA
are magnified, respectively, by factors of 15 (18) and 9 (3) compared to that at I = 140 µA.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-41-320.jpg)
![21
Terahertz Technology Based on Nano-Electronic Devices
1.4.2.3 Macroscopic Channel Size Effect of THz Image
The experimental data in the above showed that the macroscopically long value of
LE results in the asymmetric distribution of the excited electrons. From this fact,
the following interesting phenomenon is expected: spatial distribution of the excited
electrons will drastically depend on sample dimensions, in relation with LE. We have
addressed this issue by studying the channel size dependence of the CE distribution
by use of THz imaging [51].
The experimental setup of the THz microscope is similar to that shown inFigure 1.9.
Three samples with different widths of W = 1.2, 0.3, and 0.02 mm (length L = 4 mm)
were investigated, all of which were fabricated from the same GaAs/AlGaAs het-
erostructure crystal with µH = 62 m2/Vs and ns = 2.4 × 1015 m–2 at 4.2 K. In CE mea-
surements, the detected signal was recorded with a lock-in amplifier, where 20 Hz
rectangular-wave currents alternating between zero and a given finite value I were
transmitted through the sample. All the measurements were performed at 4.2 K.
Figure 1.17 shows comparison of the CE images for the three samples. In the wid-
est sample (W = 1.2 mm), CE takes place mostly in the two diagonally opposite cor-
ners and in a localized region near the source contact. In the data for W = 0.3 mm, CE
expands into the more interior 2DEG region. Furthermore, when W = 0.02 mm, the
CE takes place over the entire region of the interior 2DEG channel. We confirmed
that the pattern of these features systematically changed upon reversing B and I, and
that the similar CE images were also observed for other samples fabricated from
different GaAs/AlGaAs wafers.
The significant change with W observed shows the validity of the above expecta-
tion: spatial distribution of the excited electrons is considerably influenced by the
very long length scale of LE. This means that the electrons travel the macroscopic
distance LE to lead to an appreciable generation of CE. Based on this, I explain the
transport process of the excited electrons below.
In the QHE devices, it is known that high electric field is concentrated in the
two diagonally opposite corners, which are also electron entry and exit corners [52].
E
E
DOS DOS
+ –
– +
FIGURE 1.16 Sketch of scattering distributions of the ground-state electrons (left) and of
the excited-state electrons (right).](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-42-320.jpg)
![23
Terahertz Technology Based on Nano-Electronic Devices
higher, like 0.4 and 1.5 A/m in the sample with W = 1.2 mm, the area where such
excitation occurs further expands through SO toward the interior region of the 2DEG
channel. Similar excitation process takes place along the boundary of the drain
contact. In this region, on the other hand, electrons travel from the opposite corner
(DO) to the electron exit corner (DE), which is opposite to that on the side of the
source contact. As a result, though electron excitation starts around DO, CE does not
appreciably occur there and mostly occurs at DE.
In contrast, when W is smaller than LE, CE is not generated in the vicinity of
the source contact. This is because in such narrow devices, the electron excitation
can take place only as the electrons traverse the Hall bar along the length direction
of the 2DEG channel. The CE thus occurs over the whole region of the interior
2DEG channel, which is in strong contrast to the CE distribution for the devices
with W >> LE.
1.5 CONCLUSION AND OUTLOOK
In this chapter, I have presented novel THz sensing and imaging devices based on
nano-electronic materials and devices: 2D semiconductor and CNT. These detectors
enable THz wave sensing with high sensitivity and high spatial resolution. I also
introduce applications of THz measurements to materials researches. The experi-
mental data have successfully revealed spatial properties of electrons in the 2DEG,
which have not been revealed by conventional transport measurements.
The next key devices for future THz technology will be THz cameras, THz video,
and THz communication. When these devices are realized in portable size, THz
technology will widely spread into our life. For this purpose, achieving higher detec-
tion sensitivity and higher power generation will increasingly become important
tasks. The development should require further breakthroughs in materials, device
structure, operation principles, etc. I anticipate that nanotechnology will still be one
of the keys for enhancing performance of THz technology.
Regarding our next target, I plan to create a THz photon counting video, which is
a strongly desired device in many fields. When many CNT-based THz photon detec-
tors [13] are integrated in a two-dimensional configuration [53, 54], the resulting
device will work as a THz video for real-time, high-resolution THz imaging.
REFERENCES
1. B. Ferguson and X.-C. Zhang, Materials for terahertz science and technology, Nat.
Mater. 1, 26 (2002).
2. M. Tonouchi, Cutting-edge terahertz technology, Nat. Photonics 1, 97 (2007).
3. J. Wei, D. Olaya, B. S. Karasik, S. V. Pereverzev, A. V. Sergeev, and M. E. Gershenson,
Ultrasensitive hot-electron nanobolometers for terahertz astrophysics, Nat. Nanotechnol.
3, 496 (2008).
4. S. Ariyoshi, C. Otani, A. Dobroiu, H. Matsuo, H. Sato, T. Taino, K. Kawase, and
H. Shimizu, Terahertz imaging with a direct detector based on superconducting tunnel
junctions, Appl. Phys. Lett. 88, 203503 (2006).
5. S. Komiyama, O. Astafiev, V. Antonov, H. Hirai, and T. Kutsuwa, A single-photon detec-
tor in the far-infrared range, Nature 403, 405 (2000).](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-44-320.jpg)
![27
2 Ultimate Fully Depleted
(FD) SOI Multigate
MOSFETs and
Multibarrier Boosted
Gate Resonant
Tunneling FETs for a
New High-Performance
Low-Power Paradigm
Aryan Afzalian
As transistors are scaled down in the nanoscale regime, quantum effects are
playing
a crucial role in device performance and parameters. Also, scaling alone is not suf-
ficient to achieve performance improvement, and new boosters and device concepts
are needed. For instance, the trade-off between power and performance in electronics
is one of the most limiting factors to push further technology scaling and develop-
ment. With scaling, the reduction of supply voltage to keep power density under con-
trol [1–3], the rise of source and drain resistance due to film thickness reduction in
order to keep good electrostatic control [3], and finally, source-drain (SD) tunneling
CONTENTS
2.1 Simulation Algorithm......................................................................................29
2.2
Gate Coupling Optimization in Nanoscale Nanowire MOSFETs:
Electrostatic vs. Quantum Confinement.......................................................... 31
2.3 Physics of RTFET............................................................................................36
2.3.1 Influence of Barrier Width................................................................... 41
2.4 SB RT-FET...................................................................................................... 41
2.5 Conclusions......................................................................................................46
Acknowledgments.....................................................................................................47
References.................................................................................................................47](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-48-320.jpg)
![28 High-Speed Devices and Circuits with THz Applications
that degrades subthreshold slope and increases leakage of
transistors below 10 nm
[3, 4] are major roadblocks that degrade on- and off-current, and ION/IOFF ratios, and
therefore the power-delay trade-off of transistors. ION/IOFF ratios and slope character-
istics of transistors depend on the gate-to-channel coupling and carrier statistics that
dictate the way carriers are made available to drive a current when increasing VG.
By reducing film thickness and increasing the number of gates, ultra-thin film multi-
gate
silicon-on-insulator (SOI) architectures have better electrostatic control and can
achieve near-ideal subthreshold slope and improved ION/IOFF ratio over more conven-
tional bulk Si single-gate architectures. Supposing ideal gate coupling, however, when
varying the gate voltage, the current varies at a rate dictated by Fermi-Dirac statis-
tics only. This is governed by the gate-controlled single-barrier paradigm on which
present field-effect transistors (FETs) are based. In a standard transistor, there is only
one barrier from channel to source, and the density of state close to the top of the
channel barrier is about constant with VG [5]. As a result, the current increase is expo-
nential below threshold with an optimal minimal inverse subthreshold slope (SS) of
kT/q.log 10, i.e., about 60 mV/decade at T = 300 K. Above threshold, when the channel
barrier passes below the source Fermi level, EFS, enabling the source highly occupied
states to drive a significant current density, and thus good delay performance, the cur-
rent increase is much slower and the inverse slope reaches much higher values.
We have recently shown the possibility of achieving better slopes than those dic-
tatedbyFermi-Dirac,bothinsubthresholdandabovethreshold,togetherwithhighon-
current,byusingaSimultibarrierboostedcomplementarymetal-oxide-semiconductor
(CMOS) transistor, the gate modulated resonant tunneling (RT) FET [5, 6]. It is a
metal-oxide-semiconductor field-effect transistor (MOSFET) boosted with addi-
tional tunnel barriers (TBs) (i.e., barriers of a few nanometers width and less than
10 nm) near the gate edge(s) and under electrostatic control of the gate that cre-
ates additional longitudinal confinement in the device. Such TBs can be created, for
instance, in a planar technology from a local reduction, or constriction, of the device
cross section, resulting from a local oxidation that can be well controlled [7], or from
Schottky barriers and dopant segregation techniques [6, 8] in this case allowing for
steep slope and low source and drain resistance. RT-FETs have also been shown to be
immune to the source-drain tunneling problem that further degrades ION/IOFF ratios
in standard devices for channel lengths below 10 nm.
In this chapter, we investigate and compare the performances of ultimate SOI
multigate nanowire FETs with channel lengths of about 10 nm and below through
nonequilibrium Green’s function (NEGF) quantum simulations, within both
ballistic
and scattering self-consistent Born approximations. Both standard single-
barrier
devices and the new multibarrier boosted architecture are compared. In Section 2.1,
the simulation algorithm is reviewed. In Section 2.2, quantum effects and their
impact on the gate coupling optimization of ultra-scaled nanowires are described by
optimizing ION/IOFF ratios vs. the cross section size in a 10 nm gate-all-around (GAA)
nanowire. It is shown that an optimum cross section exists due to a trade-off between
electrostatic and confinement. Also, the fundamental limit of improving gate con-
trol by thinning gate oxide is shown when passing from the equivalent oxide thick-
ness (EOT) to the capacitive equivalent thickness (CET) concept. In Section 2.3,
the physics and the performance limits of the new multibarrier boosted RT-FET](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-49-320.jpg)
![29
FDSOI Multigate MOSFETs and Multibarrier Boosted RTFETs
are investigated through quantum simulations in silicon nanowires and compared
to those of a nanowire multigate SOI MOSFET. Finally, the possibility of imple-
menting RT-FET with ultra-low source-drain resistance dopant-segregated Schottky
barrier MOSFETs is investigated in Section 2.4.
2.1 SIMULATION ALGORITHM
For ultra-scaled devices with cross section dimensions smaller than 10 nm
and a gate length below a few tens of nanometers, quantum effects are play-
ing a crucial role in device performances and parameters. Hence, the need for
quantum simulations arises. Among the new simulation methods developed for
that purpose, the nonequilibrium Green’s function (NEGF) method [9–14] has
gained popularity and shows a real potential for modeling quantum effects at the
scale of a few nanometers. Computations that use this method can, however, be
time-consuming, which is the main obstacle to its use in intensive device simula-
tions. In an attempt to reduce simulation time, mode-space (MS) methods, which
can result in a simulation speed-up up to two to three orders of magnitude over
more
computationally demanding real-space methods, have been introduced.
Such an approach is assumed in the following. We note, however, that here we
do not imply from MS uncoupled mode space (that is only valid for devices with
small film thicknesses and no discontinuities in their cross section along the chan-
nel; see below) as sometimes assumed in the literature, but that the coupled mode-
space approach is also encompassed.
Our quantum simulator is based on the use of a fast coupled mode-space
(FCMS) implementation of the NEGF [7], adaptive energy, and nonuniform mesh
algorithms. Compared to a real-space NEGF algorithm, the coordinates y and z of
the cross section perpendicular to the transport direction, x, are replaced by the
mode energies E x
( )
sub
m
of the electron subbands in an MS approach. This drastically
reduces computation time, as in practice only the first few subbands are populated
by electrons and need to be taken into account [12]. A full description of our simu-
lator can be found in [7]. Here we summarize the main equations and simplifying
assumptions used by our 3D MS-NEGF simulator [15]. The main convergence loop
of the program self-consistently computes the electrostatic potential in the device,
V1, by solving for the Poisson equation and the electron concentration, n1, using
the NEGF formalism [11]. A nonlinear Poisson scheme is used to ensure fast con-
vergence. Except for the Schottky barrier case, which is treated below, Neumann
(close) boundary conditions are used for the Poisson equation at the source and
drain. In quantum simulations, indeed, the applied bias is fixed through fixing the
Fermi level at source EFS and draining (EFD = EFS – qVD). This allows for elec-
trons and potential to self-
consistently adjust for ensuring charge neutrality. The
mode-space longitudinal coupled Schrödinger equation from which the mode-space
device Hamiltonian, HMS, can be computed is given by [12]
a x
x
x E x x E x x E x
2
( ) ( ) ( ) ( ) ( ) ( ) ( )
mm
m
C
mn
n
n
sub
m m m
2 2
2
∑
−
∂
∂
ϕ − ⋅ϕ + ⋅ϕ = ϕ (2.1)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-50-320.jpg)
![30 High-Speed Devices and Circuits with THz Applications
where
a x
m y z
y z x dydz
( )
1
( , )
( , ; )
mm
x
y z
m
*
,
2
∫
= ξ (2.2)
is the inverse of the average value of the effective mass in the cross section. E x
( )
C
mn
is
a term that represents the coupling between the lateral modes m and n and depends
on the integral of the product between the transversal wave function ξm and the first
and second derivatives of ξn in the cross section but is independent of y and z [12].
In the MS method, the subband energy profile E x
( )
sub
m
and the corresponding trans-
versal wave function ξm(y,z;x) need to be calculated. This is done by solving a 2D
Schrödinger problem in the cross section of the device at each slice x = x0:
H y z x E x y z x
( , ; ) ( ) ( , ; )
D
n
sub
n n
2 0 0
ξ = ξ (2.3)
and
H
y m y z y z m y z z
U x y z
2 ( , ) 2 ( , )
( , , )
D
y z
2
2
*
2
* 0
= −
∂
∂
∂
∂
−
∂
∂
∂
∂
+ (2.4)
where U = ECB – q.V1 is the potential energy and ECB is the bulk material conduction
band edge (ECB of Si is our potential reference and has been set to 0). In
nanowires
with a small and constant cross section, it is usually assumed that the eigenfunc-
tions ξn(y,z;x) remain constant along the channel even though the eigenvalues E x
( )
sub
n
do vary. In this case the coupling term in Equation (2.3) would disappear and one
can use the fast uncoupled mode-space (FUMS) hypothesis to further fasten the
algorithm by computing ξn(y,z) and replacing U(x,y,z) by its x-averaged value in
Equation (2.6). [12]. However, here a more general but slower coupled mode-space
(CMS) approach is wanted, as in RT-FETs or Schottky barrier (SB) devices, tunnel
barriers create strong variation of the wave function shape in their vicinity and there-
fore mode coupling. However, this perturbation is very local, and by considering
coupling only in the vicinity of the barrier in the FCMS, we therefore achieve FUMS
speed with accuracy of the CMS [7].
From HMS, the mode-space device Hamiltonian, the retarded Green’s function, G,
of the active device can be defined, and from there, electron concentration and cur-
rent in the device, as well as their energy spectrum, can be calculated using the
NEGF approach [11, 12]:
G(E) = [EI − HMS − ∑S(E) − ∑1(E) − ∑2(E)]−1 (2.5)
where ∑s is the self-energy that accounts for scattering inside the device (in the bal-
listic case, ∑s is equal to zero), and ∑1(∑2) is the self-energy caused by the coupling
between the device and the source (or drain) reservoir [11].
One of the strengths of the NEGF is its ability to handle different types of
elastic or inelastic scattering as electron-phonon or surface roughness scattering
without using an averaged relaxation time approximation, as has been common](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-51-320.jpg)
![31
FDSOI Multigate MOSFETs and Multibarrier Boosted RTFETs
in semiclassical or quantum-corrected drift diffusion, in higher-order Boltzmann
moment equation, or in Monte-Carlo simulation, for instance. In the NEGF, indeed,
spectral functions like density of state DoS(x,E) or density matrixes ρ(x,x,E) are
computed self-
consistently over a discretized energy mesh. The scattering rate,
or scattering self-energy ΣS(x,x,E) matrix that depends on these spectral quanti-
ties and influences them can therefore also be calculated self-consistently at each
energy, and in turn related to the exact band structure and carrier’s population. This
is
increasingly important as transistors are scaled down and confinement makes
the latter to become a strong function of the exact device structure and bias voltages.
In the NEGF approach, the input scattering parameters are therefore not relaxation
time or mobility—these are derived parameters that can be obtained as a result after
convergence of the self-consistent loop and energy averaging— but directly the per-
turbative Hamiltonian, e.g., the electron-phonon interaction Hamiltonian for pho-
non
scattering. The degree of accuracy in the modeling of this Hamiltonian results
in a trade-off between simulation time and accuracy. We have developed such an
approach to include phonon scattering (both elastic and inelastic) based on the self-
consistent Born approximation and deformation potential theory [13, 14].
Finally, the methodology used to simulate Schottky contacts is similar to [16].
The Schottky barrier is added as a boundary condition in the source and drain poten-
tial. A potential equal to
VSB = –q*(SBH – (ECB – EF)) (2.6)
is added to the source and drain potentials, where EF is the Fermi potential related
to the doping in the Si body, and ECB and SBH are respectively the bottom of the
conduction band and the Schottky barrier height value in bulk silicon. This allows
one to take into account the increase of the SBH due to the increase of EC through
quantum confinement, which has been shown to be the dominant change in small
cross sections. Note, however, that this is a worst-case scenario, as other effects
should slightly counteract this increase of SBH [17]. We have neglected these effects,
however, due to the lack of experimental studies on the SBH values in nanoscale Si
devices and the fact that the trends should not change fundamentally with a change
of a few tens of meV, as we have observed when comparing barriers differing by
hundreds of meV [6, 8]. The conduction band edge in the Schottky metal, ECSB, is
assumed to be constant and a few 100 meV lower than the source and drain Fermi
level in order to ensure sufficient injection (and independent of the exact band edge
level of the metal) of carriers in the device.
2.2
GATE COUPLING OPTIMIZATION IN NANOSCALE
NANOWIRE MOSFETs: ELECTROSTATIC
vs. QUANTUM CONFINEMENT
Using our simulation tools, we now investigate the effects of electrostatics and
quantum confinement in order to find an optimal cross section size for 10 nm channel
length nanowires. Figure 2.1 shows the maximum film thickness that can be used vs.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-52-320.jpg)
![32 High-Speed Devices and Circuits with THz Applications
the channel length for one to four gate architectures following classical electrostatic
theories [18] and for an equivalent gate oxide thickness (EOT) of 0.5 nm. It is based
on the natural length λ that scales down with the number of gates ng:
n
t
t
t t
n
t
EOT
t EOT EOT t
1 1
si
g ox
ox si
si ox
si ox
si
g S O
S O si
si
si
S O
ox
ox
i
i i
2
2 2
λ =
ε
ε
+
ε
ε
=
ε
ε
+
ε
ε ⋅
⋅ =
ε
ε
(2.7)
For given values of Si and oxide thicknesses (tsi and tox, respectively) and permit-
tivities (εsi and εox), a minimum channel length of at least 6*λ must be taken to ensure
6 8 10 12 14 16 18 20 22 24 26
2
2.5
3
3.5
4
4.5
5
5.5
6
tsi
(nm)
Lmin = 6* λ(nm)
(a)
(b)
ngate = 1
ngate = 2
ngate = 3
ngate = 4
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
× 1038
–0.15
–0.1
–0.05
0
0.05
0.1
0.15
D(E) (/ev) in x = L/2
E
(eV)
All valleys
First lateral subband
FIGURE 2.1 (a) Maximum film thickness vs. minimal channel length for one to four gate
architectures following classical electrostatic theories and for an equivalent gate oxide thick-
ness (EOT) of 0.5 nm. It is based on the natural length λ (Equation (2.7)) that scales down
with the number of gates ng. A minimum channel length of at least 6*λ must be taken to
ensure good gate control and low short channel effects. (b) DoS vs. energy for a 4 × 4 nm2
[100] GAA nanowire. The peak structure is related to the splitting of the conduction band in
subbands due to 1D confinement.](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-53-320.jpg)
![33
FDSOI Multigate MOSFETs and Multibarrier Boosted RTFETs
good gate control and low short channel effects. As can be seen for L = 10 nm a
single gate device would require an EOT below 0.5 nm or a Si film thickness below
2 nm. Both options must, however, be discarded due to quantum effects.
Due to tunneling, a physical gate oxide thickness tox below 1.5–1 nm must be
excluded to avoid high leakage due to gate tunneling currents. As gate control does
not depend on tox alone but on tox/εox, a high-k dielectric with a significantly higher
permittivity than SiO2 can achieve an equivalent oxide thickness (EOT) lower than
this tox value. However, due to quantum confinement in film thicknesses of a few nm,
a dark space region (the electron channel is not directly at the Si-oxide interface but
at a depth td in the Si film) and a reduction of the DoS are observed [19]. Both effects
tend to reduce the intrinsic gate capacitance and therefore the gate coupling. In order
to take this effect into account, one can replace EOT by an equivalent capacitive
thickness CET in Equation (2.7). The point is that CET tends to saturate when EOT
is very small because dark space and DoS reduction does not scale down with EOT,
so that even if EOT tends to 0, a minimum value of CET is reached [19]:
CET CET EOT
t
( 0) 0.55 nm
d Sio
Si
min
2
= → =
λ
⋅
ε
ε
≈ (2.8)
Because of quantum confinement (td 0) and the low 1D DoS (λ 1), it is not
possible to have a better electrostatic control of the gate to the channel in nanowires
of small cross sections than that achieved with an SiO2 oxide of thickness CETmin,
even if one could use an “ideal” gate dielectric with infinite permittivity. The value
CETmin = 0.55 nm is obtained for Si by assuming td = 0.8 nm and λ = 0.5 at high Vg,
which compares well with our simulation results for cross sections between 2 × 2 and
4 × 4 nm2 and EOT smaller than 1 nm [19].
Concerning tsi, it is usually accepted that below 2 nm of film thickness the
dependency of bandgap, and therefore threshold voltage, with tsi related to quantum
confinement is too strong and would lead to too much variability [20]. The smaller
the cross section, the larger the bandgap mismatch is for a given diameter variation,
which would arise, for example, from process variability. This can be observed in
Figure 2.2, which shows bandgap increase extracted from our 3D-NEGF
simulations
vs. the diameter reduction Δtsi. It can be quite well explained by using a simple ana-
lytical model of the energy level of a constant potential well with infinite potential
barrier at the Si/SiO2 interface. Using the effective mass approximation (parabolic
E-k dispersion relationship) in a device with film thickness tsi and width 2si, E1, the
first level above the conduction band. EC, is then given by
E t W E
m t m w
( , )
2
parab
si si C
y si z si
1
2
*
2
*
2
− =
π
+
π
(2.9)
When the diameter of the cross section is smaller than 3 nm, however, the E-k
dispersion relationship is no longer parabolic and a correction factor has to be taken
into account in order to obtain accurate results [21], but the trend of very high band-
gap sensitivity to the exact dimension in small cross section given by Equation (2.9)](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-54-320.jpg)
![ne avanza una goccia per la estrema unzione. Bada, Curio, molti
giovani, che con le armi in mano vinsero virtuosamente gli austriaci,
si lasciarono vincere dallo sbadiglio.
— Filippo, ricordo avere letto certa sentenza in un libro, credo nella
prefazione del Pellegrinaggio del giovane Aroldo, una sentenza la
quale diceva così: «L'universo è una maniera di libro, del quale ha
letto una pagina sola chi ha visto unicamente il suo paese. Io ne ho
voltate di molte, e mi sono apparse tutte cattive; però questo esame
mi è riuscito fruttuoso, imperciocchè, odiatore prima della mia patria,
quando ebbi considerato le ribalderie dei popoli in mezzo ai quali
sono vissuto, tornai ad amarla; e se dalle mie pellegrinazioni non
avessi ricavato benefizio, eccetto questo uno, non mi lagnerei delle
spese fatte, nè delle fatiche sofferte.» Veramente se il pellegrino
venne sincero a tale conchiusione, beato lui! Per me, sia che mi pigli
gli uomini nel vecchio o me li abbia a pigliare nel nuovo mondo, mi
paiono tutti fichi degni di penzolare dall'albero di Timone; e ormai
diffido trovarne quaggiù meglio nè peggio, sicchè vorrei insalutato
hospite uscirmene da questo mondo, dove non mi trattiene più nulla.
[15]
— Nulla! Nè anche la vista di quel superbo alligatore, che steso
supino costà su i giunchi del fiume si gode la benedizione dei raggi
del sole?
— Non gode, bensì si travaglia inebetito di ripienezza a cagione della
strage menata stamani di chi sa quante creature viventi. Ma sta'
tranquillo, o coccodrillo, a te non può mancare il regno dei cieli,
perchè ti scusano la fame, lo istinto della tua conservazione e la
mancanza d'intelletto, mentre noi abbiamo visto l'uomo mosso a
malfare per vanità, per ferocia, per avarizia, insomma per colpa di
spirito viziato, non già per bisogno del corpo: noi viviamo in società
con gli uomini come i cuochi in cucina presso la stia, per avere i polli
sottomano onde arrostirli; meglio coccodrilli, che uomini.
— Ecco, vedi, Curio mio, io giudico che un divario ci corra, e grande,
perchè io piglio a cottimo, con una brava palla nel cranio ovvero
nello stomaco, di mettere a partito anche un Francesco di Modena o](https://image.slidesharecdn.com/2366358-250601223559-426fef18/85/Highspeed-Devices-And-Circuits-With-Thz-Applications-Jung-Han-Choi-78-320.jpg)
Highspeed Devices And Circuits With Thz Applications Jung Han Choi
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- 7. Devices, Circuits, and Systems Series Editor Krzysztof Iniewski CMOS Emerging Technologies Research Inc., Vancouver, British Columbia, Canada PUBLISHED TITLES: Atomic Nanoscale Technology in the Nuclear Industry Taeho Woo Biological and Medical Sensor Technologies Krzysztof Iniewski Building Sensor Networks: From Design to Applications Ioanis Nikolaidis and Krzysztof Iniewski Circuits at the Nanoscale: Communications, Imaging, and Sensing Krzysztof Iniewski Electrical Solitons: Theory, Design, and Applications David Ricketts and Donhee Ham Electronics for Radiation Detection Krzysztof Iniewski Embedded and Networking Systems: Design, Software, and Implementation Gul N. Khan and Krzysztof Iniewski Energy Harvesting with Functional Materials and Microsystems Madhu Bhaskaran, Sharath Sriram, and Krzysztof Iniewski Graphene, Carbon Nanotubes, and Nanostuctures: Techniques and Applications James E. Morris and Krzysztof Iniewski High-Speed Devices and Circuits with THz Applications Jung Han Choi and Krzysztof Iniewski High-Speed Photonics Interconnects Lukas Chrostowski and Krzysztof Iniewski Integrated Microsystems: Electronics, Photonics, and Biotechnology Krzysztof Iniewski Integrated Power Devices and TCAD Simulation Yue Fu, Zhanming Li, Wai Tung Ng, and Johnny K.O. Sin Internet Networks: Wired, Wireless, and Optical Technologies Krzysztof Iniewski Low Power Emerging Wireless Technologies Reza Mahmoudi and Krzysztof Iniewski
- 8. Medical Imaging: Technology and Applications Troy Farncombe and Krzysztof Iniewski MEMS: Fundamental Technology and Applications Vikas Choudhary and Krzysztof Iniewski Microfluidics and Nanotechnology: Biosensing to the Single Molecule Limit Eric Lagally and Krzysztof Iniewski MIMO Power Line Communications: Narrow and Broadband Standards, EMC, and Advanced Processing Lars Torsten Berger, Andreas Schwager, Pascal Pagani, and Daniel Schneider Nano-Semiconductors: Devices and Technology Krzysztof Iniewski Nanoelectronic Device Applications Handbook James E. Morris and Krzysztof Iniewski Nanopatterning and Nanoscale Devices for Biological Applications Krzysztof Iniewski and Seila Šelimovic´ Nanoplasmonics: Advanced Device Applications James W. M. Chon and Krzysztof Iniewski Nanoscale Semiconductor Memories: Technology and Applications Santosh K. Kurinec and Krzysztof Iniewski Novel Advances in Microsystems Technologies and Their Applications Laurent A. Francis and Krzysztof Iniewski Optical, Acoustic, Magnetic, and Mechanical Sensor Technologies Krzysztof Iniewski Radiation Effects in Semiconductors Krzysztof Iniewski Semiconductor Radiation Detection Systems Krzysztof Iniewski Smart Grids: Clouds, Communications, Open Source, and Automation David Bakken and Krzysztof Iniewski Smart Sensors for Industrial Applications Krzysztof Iniewski Technologies for Smart Sensors and Sensor Fusion Kevin Yallup and Krzysztof Iniewski Telecommunication Networks Eugenio Iannone Testing for Small-Delay Defects in Nanoscale CMOS Integrated Circuits Sandeep K. Goel and Krishnendu Chakrabarty Wireless Technologies: Circuits, Systems, and Devices Krzysztof Iniewski PUBLISHED TITLES:
- 9. FORTHCOMING TITLES: 3D Circuit and System Design: Multicore Architecture, Thermal Management, and Reliability Rohit Sharma and Krzysztof Iniewski Circuits and Systems for Security and Privacy Farhana Sheikh and Leonel Sousa CMOS: Front-End Electronics for Radiation Sensors Angelo Rivetti Gallium Nitride (GaN): Physics, Devices, and Technology Farid Medjdoub and Krzysztof Iniewski High Frequency Communication and Sensing: Traveling-Wave Techniques Ahmet Tekin and Ahmed Emira Labs-on-Chip: Physics, Design and Technology Eugenio Iannone Laser-Based Optical Detection of Explosives Paul M. Pellegrino, Ellen L. Holthoff, and Mikella E. Farrell Metallic Spintronic Devices Xiaobin Wang Mobile Point-of-Care Monitors and Diagnostic Device Design Walter Karlen and Krzysztof Iniewski Nanoelectronics: Devices, Circuits, and Systems Nikos Konofaos Nanomaterials: A Guide to Fabrication and Applications Gordon Harling, Krzysztof Iniewski, and Sivashankar Krishnamoorthy Optical Fiber Sensors and Applications Ginu Rajan and Krzysztof Iniewski Organic Solar Cells: Materials, Devices, Interfaces, and Modeling Qiquan Qiao and Krzysztof Iniewski Power Management Integrated Circuits and Technologies Mona M. Hella and Patrick Mercier Radio Frequency Integrated Circuit Design Sebastian Magierowski Semiconductor Device Technology: Silicon and Materials Tomasz Brozek and Krzysztof Iniewski Soft Errors: From Particles to Circuits Jean-Luc Autran and Daniela Munteanu
- 10. FORTHCOMING TITLES: VLSI: Circuits for Emerging Applications Tomasz Wojcicki and Krzysztof Iniewski Wireless Transceiver Circuits: System Perspectives and Design Aspects Woogeun Rhee and Krzysztof Iniewski
- 12. CRC Press is an imprint of the Taylor & Francis Group, an informa business Boca Raton London NewYork High-Speed Devices and Circuits with THz Applications Edited by Jung Han Choi F rau nh ofer Institute, Berlin, Germany Krzysztof Iniewski Managing Editor CMOS E merging Technologies Researc h In c . Van co uver, British Columbia, Canada
- 13. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140415 International Standard Book Number-13: 978-1-4665-9012-0 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
- 14. ix Contents Preface.......................................................................................................................xi About the Editor...................................................................................................... xiii Contributors..............................................................................................................xv Chapter 1 Terahertz Technology Based on Nano-Electronic Devices...................1 Yukio Kawano Chapter 2 Ultimate Fully Depleted (FD) SOI Multigate MOSFETs and Multibarrier Boosted Gate Resonant Tunneling FETs for a New High-Performance Low-Power Paradigm................................27 Aryan Afzalian Chapter 3 SiGe BiCMOS Technology and Devices.............................................49 Edward Preisler and Marco Racanelli Chapter 4 SiGe HBT Technology and Circuits for THz Applications................67 Jae-Sung Rieh Chapter 5 Multiwavelength Sub-THz Sensor Array with Integrated Lock-In Amplifier and Signal Processing in 90 nm CMOS Technology..........................................................................................93 Péter Földesy Chapter 6 40/100 GbE Physical Layer Connectivity for Servers and Data Centers......................................................................................125 Yongmao Frank Chang Chapter 7 Equalization and Multilevel Modulation for Multi-Gbps Chip-to-Chip Links........................................................................... 177 Anthony Chan Carusone Chapter 8 25 G/40 G SerDes: Need, Architecture, and Implementation ..........199 Rohit Mittal Chapter 9 Clock and Data Recovery Circuits.................................................... 217 Jafar Savoj Index.......................................................................................................................239
- 16. xi Preface This book was motivated by the desire to explore the future perspectives of high- frequency technologies by presenting the state-of-the-art results in both new device developments and circuit implementations. It discusses issues for the circuit opera- tion beyond 100 GHz with respect to device physics, circuit implementations, and some technological bottlenecks for system implementations. Also, recent device and circuit results using SiGe technologies as an alternative to Si complementary metal-oxide-semiconductor (CMOS) devices are presented. Evolutionary device developments let people consider widening the frequency spectrum of interest up to terahertz. For example, as Si CMOS technologies evolve from 65 nm to 40 nm to 28 nm and further, the expected operation frequency of circuits correspondingly increases beyond 100 GHz. Nowadays, several universities and companies pursue developing high-frequency circuits and subsystems that could operate 60, 77, 90, 120, and 300 GHz. Furtherchallengingresearchworksonnano-electronicdeviceshavebeenreported, even enabling terahertz operations. Several research directions are challenged. New nano device developments using nanowires or carbon-based elements, e.g., graphene field effect transistors (FETs), carbon nanotubes, etc., seem to be very active research themes around the world in terms of new radio frequency (RF) directions. As the device technology continues to develop, circuit engineers could design integrated circuits (ICs) with higher operation frequencies and develop relevant new applica- tions. It seems that novel devices could lead to the creation of new applications. Also, market needs would guide the direction of future developments, e.g., lower power consumption, higher integration density, and higher speed of operations. Another exciting technical trend that we observe in the market and experience in daily life is the so-called big bang of Internet data traffic caused by handheld devices, such as laptops, tablets, and smart phones. As the amount of data traffic increases, higher-speed data transmitters and receivers play a greater role in the higher data transfer communications and now get meaningful attention from RF industries. For example, connectivity technology between high-performance computing servers in the data center becomes an important issue with respect to data transfer rates, dis- tance, power consumption, the cost of connectivity modules, and backward/ forward compatibilities with concurrent standards technologies. Several companies and research institutions exert their efforts to demonstrate next- generation connectivity technologies to customers. This book tries to put those modern topics together, e.g., novel/new nano devices, their feasible THz applications, and modern high data transfer technologies. By bring- ing those heterogeneous topics into one, engineers who work in high- frequency engineering fields or develop devices and circuits considering high-frequency appli- cations are supposed to grasp modern technical trends of nano devices, circuits, and their applications. The contributions are made by several academic institutions and relevant companies. Readers will grasp the future potential of RF products and
- 17. xii Preface research trends by reading through several chapters by the international experts in industry and academia. Chapter 1 is contributed by a researcher at the Tokyo Institute of Technology and discusses THz sensing and imaging devices based on nano devices and materials. Various devices are explained in detail, especially regarding THz imaging. Chapter 2 is written by a researcher at Université Catholique de Louvain, which investigates SOI multigate nanowire FETs. It explains theoretical aspects of nanoscale nanowire MOSFETs, simulation methods, and their results. Chapters 3 and 4 are then devoted to SiGe technologies. They thoroughly discuss the physics of the SiGe heterojunction bipolar transistor (HBT) and present commercially available SiGe HBT devices. Also, several feasible applications using those devices are addressed. Very recent experimental results over 100 GHz are presented. If readers are interested in design- ing ICs working at beyond 100 GHz, it is recommended to read through those two chapters written by SiGe device experts. Chapter 5 is also very instructive in terms of THz IC design using standard Si CMOS devices, especially for THz imaging application. The author discusses in detail experimental setups for measurements, detection methods, and so on. Chapters 6 to 9 are devoted to high-speed data rate connectivity technologies. Three chapters are contributed by industrial colleagues and one by the University of Toronto. The discussion points range from system design to IC design. Also, they are useful to understand current state-of-the-art tech- nologies in these development fields. Also, relevant standard activities and technical details behind those are addressed. One can have an outlook over these interconnec- tion technology trends by reading those chapters. It is impossible for me to express my gratitude adequately to all contributors for their sincere and passionate preparation of their chapters. I will remember their con- tributions and active exchange of their thoughts and ideas. Also, thanks should be given to Dr. Kris Iniewski for giving me an opportunity to edit this comprehensive and valuable book. Finally, I also thank my lovely wife, Mrs. Hye Won Nam, for her warm support in my completing this book. Dr. Jung Han Choi Charlottenburg, Berlin, Germany
- 18. xiii About the Editor Jung Han Choi received B.S. and M.S. degrees in electrical engineering from the Sogang University, Seoul, Korea, in 1999 and 2001, respectively, and the Dr.-Ing. degree from the Technische Universität München, Munich, Germany, in 2004. From 2001 to 2004, he was a research scientist in the Institute for High-Frequency Engineering at the Technische Universität München. During this time, he worked on high-speed device modeling, thin-film fabrication, network analyzer measure- ment, and circuit development for high-speed optical communications. From 2005 to 2011, he was with the Samsung Advanced Institute of Technology and the Samsung Digital Media & Communication Research Center, where he worked on the radio frequency (RF) biohealth sensor, nano devices, and RF/millimeter-wave circuit design, including 60 GHz Si complementary metal-oxide-semiconductor (CMOS) integrated circuits (ICs). In 2011 he joined the Fraunhofer Institute (Heinrich-Hertz Institute), Berlin, Germany. Now he is working on high-data-bit-rate transmitter and receiver circuits up to 100 Gb/s, relevant device active/passive modeling, and network analyzer measurement up to 170 GHz. In 2003, he was awarded the EEEfCOM (Electrical and Electronic Engineering for Communication) Innovation prize for his contribution to the development of the high-speed receiver circuit. His current research interests range from the active/ passive device, carbon-based nano device, and its modeling to high-frequency IC design and metamaterials.
- 20. xv Contributors Aryan Afzalian ICTEAM Institute Université Catholique de Louvain Louvain-La-Neuve, Belgium Anthony Chan Carusone Department of Electrical and Computer Engineering University of Toronto Toronto, Ontario, Canada Yongmao Frank Chang Vitesse Semiconductor Camarillo, California Jung Han Choi Fraunhofer Institute Heinrich-Hertz Institute Photonic Components Berlin, Germany Péter Földesy Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, Hungary and Faculty of Information Technology Péter Pázmány Catholic University Budapest, Hungary Yukio Kawano Department of Physical Electronics Quantum Nanoelectronics Research Center Tokyo Institute of Technology Tokyo, Japan Rohit Mittal Intel Corporation Santa Clara, California Edward Preisler Jazz Tower Newport Beach, California Marco Racanelli Jazz Tower Newport Beach, California Jae-Sung Rieh School of Electrical Engineering Korea University Seoul, Korea Jafar Savoj Xilinx San Jose, California
- 22. 1 1 Terahertz Technology Based on Nano- Electronic Devices Yukio Kawano 1.1 INTRODUCTION Since the establishment of the Maxwell equation and the discovery of the electromag- netic wave, researchers have been devoted to developing a lot of technologies based on the electromagnetic wave, bringing much change to human life. High-frequency electronics technology has provided radio, television, the cellular phone, and so on. CONTENTS 1.1 Introduction.......................................................................................................1 1.2 THz Detector.....................................................................................................3 1.2.1 Overview................................................................................................3 1.2.1.1 Bolometric (Thermal) Detection............................................3 1.2.1.2 Wave Detection.......................................................................4 1.2.1.3 Quantum Detection.................................................................4 1.2.1.4 Others......................................................................................4 1.2.2 CNT-Based THz Detector.....................................................................4 1.2.2.1 Photon-Assisted Tunneling in CNT........................................5 1.2.2.2 THz Photon Detection with CNT/2DEG Hybrid Device.......8 1.3 THz Imaging....................................................................................................12 1.3.1 Solid Immersion Lens..........................................................................12 1.3.2 Near-Field Imaging..............................................................................13 1.3.2.1 Near-Field Imaging in the THz Region................................13 1.3.2.2 Near-Field THz Imaging on One Chip.................................13 1.4 THz Application.............................................................................................. 17 1.4.1 Applications to Materials Researches................................................. 17 1.4.2 Applications to Semiconductor............................................................ 17 1.4.2.1 Imaging Energy Dissipation in 2DEG.................................. 17 1.4.2.2 Separate Imaging of Ground and Excited Levels................. 18 1.4.2.3 Macroscopic Channel Size Effect of THz Image.................21 1.5 Conclusion and Outlook..................................................................................23 References.................................................................................................................23
- 23. 2 High-Speed Devices and Circuits with THz Applications From optics and photonics, optical communication, light-emitting diode (LED) lamp, endoscope, etc., have been produced. The terahertz (THz, 1012 Hz) frequency region is located in between the microwave region and the visible light region (Figure 1.1). This region was merely studied by a small number of researchers in limited fields, such as chemical spectroscopy, astron- omy, and solid-state physics. However, THz technology is nowadays in strong demand in a large variety of fields, ranging from basic science such as biochemical spectros- copy, astronomy, and materials science to practical science such as environmental science, medicine, agriculture, and security [1, 2]. What is the reason why the THz wave has attracted so much interest? The advantageous properties of the THz wave are that it can be transmitted through objects opaque to visible light and that the corre- sponding photon energy, 1–100 meV, is in the important energy spectrum for various materials and biomolecules. These features allow various applications of imaging and spectroscopy in this frequency band. Figure 1.2 displays several examples of applica- tions of the THz waves. The measurements shown here illuminate the THz waves onto objects and map intensity distributions of reflected or transmitted THz waves. In some situations, by simultaneously measuring frequency spectra, one is able to identify the contents and characterize their physical/chemical properties. The tech- nique therefore can be used as nondestructive inspection, which is based on the fact that the THz wave is much safer and does not do much damage, compared to the x-ray. In addition to industrial and medical applications, THz technology is also of much importance in basic sciences. For example, in astronomy, materials science, and bio- chemistry, the detection of very weak THz radiation from interstellar matter in space, electrons in materials, and biomolecules is expected to unlock mysteries behind the generation of the universe, quantum effect in materials, and life activity, respectively. In the THz region, however, even basic components like detector and source have not been fully established, compared to the technically mature, other frequency regions. This is because the frequency of the THz wave is too high to be handled with conventional high-frequency semiconductor technology. In addition, the photon energy of the THz wave is much lower than band gap energy of semiconductors. 100 Example industries: Radio communications Radar ??? Optical communications Frequency (Hz) Medical imaging Astrophysics 103 kilo mega giga tera peta exa zetta 106 Microwaves Electronics Photonics THz Visible X-ray γ-ray MF, HF, VHF, UHF, SHF, EHF 109 1012 1015 1018 1021 FIGURE 1.1 Chart of the electromagnetic wave spectrum. (Adapted from the THz Science & Technology Network [http://thznetwork.net/].)
- 24. 3 Terahertz Technology Based on Nano-Electronic Devices For the above reasons, the THz wave is not easy to approach from either side of electronics and optics/photonics. In imaging technology, the THz wave also has a problem of low spatial resolution, which results from much longer wavelengths of the THz waves compared to those of visible light. The applications of nanoscale materials and devices, however, are opening up new opportunities to overcome such difficulties. Nanostructured devices based on the superconductor, semiconductor, and carbon nanotube have enabled significant improvement in detection sensitivity and spatial resolution. In this chapter, I will describe new THz sensing and imaging technology based on such nano-electronic devices. Moreover, I will show applications of cutting-edge THz measurements to materials researches, which have provided new insight into electronic properties of the materials. 1.2 THz DETECTOR 1.2.1 Overview THz detectors can be generally categorized into three types: bolometric (thermal) detection, wave detection, and quantum detection. In addition, they are also used as photoconductive antenna, electro-optic device, frequency mixer for heterodyne detection, etc. In this section, I show an overview of various THz detectors and briefly discuss their advantages and disadvantages. 1.2.1.1 Bolometric (Thermal) Detection This type of detector utilizes temperature rise via THz absorption. As the crystal temperature of the detector decreases, the detection sensitivity is improved, but Security Medicine Food IC card Agriculture Security Drug detection inside envelope Imaging of cancer cells Quality inspection Anticounterfeit technology Real-time monitoring of water content Detection of hazardous materials Ref.: Kawase (Nagoya Univ. & RIKEN) Ref.: Kawase (Nagoya Univ. & RIKEN) Ogawa (Kyoto Univ.) Ref.: THz Science & Technology Network Ref.: Terahertz Sensing & Imaging Lab., RIKEN FIGURE 1.2 Various applications of THz imaging and spectroscopy.
- 25. 4 High-Speed Devices and Circuits with THz Applications the detection speed becomes low (a typical time constant is of the order of ms below 4 K). The detected signal is mostly resistance change arising from the rise in the crystal temperature due to the THz absorption. There is another type of readout mechanism: measuring gas pressure via thermal expansion (Golay cell detector). Since all the detec- torsbasedonbolometricdetectionrespondtoelectromagneticwavesinawide-frequency region, one needs a frequency cutoff filter. Wei et al. [3] recently reported a nanoscaled superconductor bolometer with the ability of a single THz photon detection. 1.2.1.2 Wave Detection This detector senses the THz electromagnetic wave as a high-frequency wave. A representative device is a Schottky barrier diode detector. The advantages of this detector are high-speed detection (time constant of ~ns) and room temperature operation. This detector is often used in sub-THz regions, because the sensitivity becomes low with increasing the frequency of the incident THz wave. 1.2.1.3 Quantum Detection In contrast to wave detection, this type of detector senses photons of the THz electromagnetic wave. Solid-state devices based on materials like superconductors and semiconductors usually have energy level spacing corresponding to the THz pho- ton energy (1–100 meV), for example, energy gap of superconductor, impurity level of semiconductor, and energy level spacing due to quantum electron confinement of semiconductor quantum structure. It follows that excess carriers are generated in the devices, when these devices absorb the THz waves. One can detect the THz wave by recording electric signals produced by the carriers. THz detectors based on a nanoscale island connected to electrodes, such as superconductor junctions [4] and semiconductor quantum dots [5, 6], have been presented and demonstrated to exhibit ultra-high sensitivity, including the level of single-photon detection. However, the operation of the superconductor and semiconductor detectors needs a very low tem- perature environment (<0.3 K). This situation forces one to use a dilution refrigerator or a 3He refrigerator, restricting the range of practical uses. 1.2.1.4 Others THz time-domain spectroscopy (TDS) is nowadays widely employed in THz research fields. As detectors, the photoconductive antenna and the electro-optic device are used. This measurement allows real-time observation of the oscillatory electric field of the THz wave, providing information on both amplitude and phase of the THz electric field. Though these detectors work under room temperature, their operation requires an expensive femtosecond pulse laser. Another type is a frequency mixer using a supercomputer in which a beat signal corresponding to the frequency difference with a local oscillator is measured. This type of detector is often used in the fields of astronomy and environmental science. 1.2.2 CNT-Based THz Detector The carbon nanotube (CNT) is expected to be used as a building block for future nano-electronics, nano-photonics, and nano-mechanics owing to its unique
- 26. 5 Terahertz Technology Based on Nano-Electronic Devices one-dimensional structure [7]. From the viewpoint of application to the THz detector, the CNT also has been regarded as a promising candidate. In fact, near-infrared sensors using the CNT transistor have been successfully developed [8, 9]. In the THz region, although there are several reports [10, 11], much higher performance has not been achieved to date, compared to other existing detectors. In the following, I will introduce our recent development in CNT-based THz detectors [12, 13]. We have created a highly sensitive and frequency-tunable THz photon detector using the CNT and GaAs/AlGaAs transistors. This detector has two detection mechanisms: photon-assisted tunneling (PAT) [12] and current- peak shift [13]. For the latter, THz irradiation causes a peak shift of CNT cur- rents relative to gate voltage, leading to the realization of ultra-high sensitivity: THz photon detection. 1.2.2.1 Photon-Assisted Tunneling in CNT In 1963, Tien and Gordon proposed a theory on the interaction of a nanoscale island with an electromagnetic wave [14]. The essence of their discussion is that new energy bands, the so-called photon sidebands, are formed by the AC electric potential of the electromagnetic wave at intervals of nhf (n, integer number; h, Planck constant; f, frequency of the electromagnetic wave). A quantum dot (QD) structure connected to source, drain, and gate electrodes is a promising device for examining their model, because the QD with the electrodes works like a single-electron transistor (SET). By sweeping either the gate voltage or the source-drain voltage and measuring the resulting source-drain current, spectroscopic information about energy states in the QD can be directly obtained. The photon sidebands in the QD can thus be observed as new current signals are generated via the inelastic electron tunnel when electrons exchange photons. This phenomenon is known as PAT (Figure 1.3(a)). With microwave irradiation of super- conductor tunneling devices [14–16] and semiconductor QDs [17, 18], the PAT has been successfully observed. Compared to conventional QDs based on superconductors and semiconduc- tors, a QD using a CNT has the following unique properties: its characteristic energy, or charging energy, and energy level spacing due to quantum electron confinement typically reach ~10 meV, corresponding to a THz frequency (~2.4 THz). This energy range is larger by a factor of 10 than that of the conven- tional QDs. These advantageous properties potentially lead to device applications of CNT-QDs in the THz region. In this view, we have studied the THz response of the CNT-QDs [12]. Figure 1.3(b) schematically displays the CNT-QD structure. The CNT-QD was fabricated as follows: First, CNTs were dispersed on a semiconductor (GaAs/ AlGaAs) wafer, whose surface was covered with a SiO2 film of ~100 nm thickness. We mapped topography of the device surface with an atomic force microscope, and specified locations of single-wall CNTs with a diameter of ~1 nm. Based on the images obtained, source and drain electrodes with an interval of ~600 nm and side-gate electrodes were patterned with electron-beam lithography. In this device, electrons are confined to a very small area of l × 600 nm2, forming a QD. Metallic CNTs were used.
- 27. 6 High-Speed Devices and Circuits with THz Applications The CNT device was mounted in a 4He cryostat at a temperature of 1.5 K, and the device was irradiated with a THz wave through an optical window made from a Mylar sheet. As a THz illumination source, a THz gas laser pumped by a CO2 gas laser was used. Figure 1.4 shows the data on effect of THz irradiation on the CNT-QD. Differently from the black curve for the data without THz irradiation, new satellite current peaks are generated for the illumination of the THz wave. It is also seen that its position rela- tive to gate voltage shifts in the positive direction with increasing the frequency, f, of the THz wave. The inset of Figure 1.4 displays the energy spacing, kΔVG, between E N + 1 N + 1 N SiO2 N E + hf hf hf E - hf Drain Drain (a) (b) Drain Source Source –e –e –e Drain CNT THz QD Source Tunnel barrier GaAs/AlGaAs Source FIGURE 1.3 (a) Schematic diagram of electron tunneling processes in a QD under electromagnetic wave irradiation. Middle panel: When the Fermi level in the source lead aligns with a level in the QD, a source-drain current is passed via elastic tunneling. Left and right panels: When electrons interact with photons, a new current flows via inelastic tunnel- ing, i.e., photon-assisted tunneling. (b) Sketch of a carbon nanotube quantum dot (CNT-QD). (Adapted from Y. Kawano et al., J. Appl. Phys., 103, 034307, 2008.)
- 28. 7 Terahertz Technology Based on Nano-Electronic Devices the original peak and the satellite peaks as a function of the photon energy, hf, of the THz wave. From the measurement of the differential conductance dISD/dVSD as a func- tion of source-drain voltage VSD and gate voltage VG (Coulomb diamond measurement), we derived the conversion factor, κ = 0.18, which is defined as the conversion ratio of VG into energy. The data clearly show good agreement between κΔVG and hf, providing evidence for the THz-PAT in the CNT-QD. It is thus demonstrated that the CNT-QD works as a THz detector with frequency tunability by the application of the gate voltage. It should be noted that the satellite current is only observed on the positive VG side with respect to the original peak. The occurrence of the satellite current corresponds to the electron tunneling from the QD to the drain lead (the right side panel of Figure 1.3(a)). The side of VG on which the satellite current is clearly seen depends on the sample properties. This is possibly due to tunnel barrier asymmetry between the source and drain electrodes. The theory by Tine and Gordon says that the tunneling rate into the photon side- bands should follow the Bessel functions of the illuminated power [14]. In order to –0.80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Current (pA) –0.75 Gate Voltage (V) –0.70 Without Thz irradiation 1.4 THz 1.6 THz 2.5 THz 4.2 THz 4 0 0 4 8 12 κ∆V G (meV) 16 20 Slope 1 8 Photon Energy (meV) 12 16 20 –0.65 VSD = 1 mV T = 1.5 K FIGURE 1.4 Source-drain current ISD versus gate voltage VG for the frequency of the THz wave, f = 1.4, 1.6, 2.4, and 4.2 THz. The experimental curves for the THz irradiation are off- set by multiples of 0.8 pA for clarity. The inset shows the energy spacing, κΔVG, between the original peaks and the satellite peaks as a function of the photon energy, hf, of the THz wave. The dashed line in the inset is an eye guide corresponding to κΔVG = hf. (Adapted from Y. Kawano et al., J. Appl. Phys., 103, 034307, 2008.)
- 29. 8 High-Speed Devices and Circuits with THz Applications examine this feature, we measured the THz intensity dependence of the THz-PAT in the CNT-QD. In the measurements, we inserted THz attenuating filters between the THz laser and the sample. The result is displayed in Figure 1.5. The general tendency is as expected, but we could not get a perfect fit to the Bessel functions. We speculate that since the single QD was used, the tunneling processes via the electrodes would make it difficult to analyze the result accurately with this model. We plan to study the THz intensity dependence in more detail by using a double-coupled CNT-QD, in which the PAT occurs as a consequence of electron transitions between two well- defined discrete levels. In this device, we anticipate that frequency selectivity would be improved compared to that of the single CNT-QD. 1.2.2.2 THz Photon Detection with CNT/2DEG Hybrid Device In the CNT THz detector described in the previous section, although frequency-selective THz detection has been achieved, the detection sensitivity is not high. This is because in this detection mechanism, one-photon absorption generates only one electron even if a quantum efficiency of 100% is achieved. This limits the detection sensitivity. In order to resolve this problem, we have created a new designed device [13]: a CNT-SET is integrated with a GaAs/AlGaAs heterostructure chip (Figure 1.6(a)). The hybrid struc- ture is divided into two separate roles of THz absorption (2DEG) and signal readout (CNT-SET). A basic idea of THz detection with this device is that the CNT-SET senses electrical polarization induced by THz-excited electron-hole pairs in the 2DEG. Since the SET works as an ultra-sensitive electrometer, the CNT/2DEG device is expected to exhibit ultimate sensitivity in photon detection. 14 12 10 8 6 4 2 0 –520 –510 1.0 THz intensity (arb. units) 0.93 0.70 0.56 0.51 0.28 0.09 0 –500 –490 Gate Voltage (V) Current (pA) –480 –470 VSD = 0.5 mV T = 2.5 K f = 2.5 THz 0.0 12 8 4 0 0.4 Satellite peak Original peak 0.8 THz Intensity (arb. units) Current (pA) FIGURE 1.5 THz intensity dependence of ISD versus VG. The inset shows the THz inten- sity dependence of the amplitudes of a satellite peak and one of an original peak. The solid lines in the inset are fitting curves based on the square of the nth-order Bessel functions. (Adapted from Y. Kawano et al., J. Appl. Phys., 103, 034307, 2008.)
- 30. 9 Terahertz Technology Based on Nano-Electronic Devices Figure 1.6(b) shows transport properties of the CNT without THz irradiation; the data of ISD versus VG at VSD = 1.5 meV. This result shows the oscillatory behavior of ISD, indicating that the fabricated CNT device properly functions as a SET. Figure 1.7 displays the THz response of the 2DEG/CNT device and the dependence on magnetic field, B, applied perpendicular to the 2DEG plane. The experimental setup for the THz measurements shown here is similar to that for the THz-PAT in the previ- ous section. The laser intensity was reduced with a set of THz attenuating filters, and the intensity of the THz radiation applied to the sample is estimated to be 0.75 nW/mm2. The results of Figure 1.7 show that the THz irradiation caused a shift in the cur- rent peak position in the direction of positive VG. The data for the irradiation at 1.6 THz reveal that the shift was monotonically enhanced with increasing B up to 3.95 T, then decreased when B was further raised beyond B = 3.95 T. On the other hand, in case of the 2.5 THz irradiation, the B value for the maximum of the peak shift changed to 6.13 T. The physical meaning behind the features seen in Figure 1.7 is as follows: In the presence of magnetic field, the energy state of the 2DEG forms a Landau level. When the 2DEG is illuminated with a THz wave whose photon energy hf is equal to Landau level separation eB/m*, the 2DEG absorbs the THz wave (cyclotron reso- nance) well. Here, e is the elementary charge and m* is the cyclotron effective mass for the crystal used. The experimental data (B = 3.95 T for f = 1.6 THz and B = 6.13 T for f = 2.5 THz) show that the f value is proportional to the B value for the maximum (a) (b) CNT 2DEG GaAs/AlGaAs 8 6 Current (pA) 4 2 0 –250 –200 –150 Gate Voltage (mV) –100 –50 Drain Source THz THz off FIGURE 1.6 (a) THz detector using the CNT/2DEG hybrid device. (b) Source-drain current ISD as a function of gate voltage VG of the CNT-SET when the THz irradiation was off.
- 31. 10 High-Speed Devices and Circuits with THz Applications of the peak shift, which is characteristic of the cyclotron resonance. In addition, from these data, the associated m* value is derived to be 0.067m0, where m0 is the free electron mass. This value is in good agreement with the cyclotron effective mass for a GaAs-based 2DEG [19]. These facts indicate that the current peak shift of the CNT-SET originates from the THz absorption by the 2DEG. Let me explain microscopic carrier dynamics associated with the THz detec- tion. It is well known that a 2DEG has a random potential with a typical period of 20–100 nm [20]. It follows that the THz-excited electrons and holes drift in opposite directions through the local electric field gradient due to the random potential [21]. As a result, they are spatially separated from each other. Such separation of electron-hole pairs generates electrical polarization in the 2DEG. This situation is equivalent to appli- cation of an effective gate voltage to the CNT-SET, resulting in the current peak shift. We then measured the temporal trace of the THz signal (the ISD change associated with the current peak shift) as the THz irradiation was cycled on and off. We here used cyclotron radiation [22] from another 2DEG in a different GaAs/AlGaAs chip. The intensity of this THz source can be continuously changed by altering the current Source-drain Current (pA) Source-drain Current (pA) Gate Voltage (mV) –160 80 120 100 80 60 40 20 0 70 60 50 40 30 20 10 0 –140 –160 –140 Gate Voltage (mV) (a) (b) 0 (THz off) 7.85 7.20 6.55 5.90 5.25 4.60 ×10 –12 3.95 3.25 2.60 1.95 1.30 0.65 0 f =1.6 THz f =2.5 THz B(T) B(T) 0 (THz off) 7.85 7.20 6.55 6.13 5.25 4.60 3.95 3.25 2.60 1.95 1.30 0.65 0 FIGURE 1.7 Magnetic field dependence of source-drain current ISD versus gate voltage VG of the CNT under THz irradiation. The magnetic field B was applied to the detector perpen- dicular to the 2DEG plane, and the B values in units of Tesla (T) are given on the right-hand side of the figures. The data with the THz irradiation are offset for clarity. (Adapted from Y. Kawano, T. Uchida, and K. Ishibashi, Appl. Phys. Lett., 95, 083123, 2009.)
- 32. 11 Terahertz Technology Based on Nano-Electronic Devices to the 2DEG of the THz source. We reduced its intensity to an extremely low level, on the order of 0.1 fW. We mounted, face to face, the sample and the 2DEG-based THz source in the same superconducting magnet so that the 2DEGs of the sample and the source were both in cyclotron resonance condition. Figure 1.8 displays time response of ISD for an on/off sequence of the THz irradiation at VG = –169 mV, VSD = 1.5 mV, B = 3.95 T, and f = 1.6 THz. This result shows that the CNT-SET current was stable when the THz radiation was off, whereas it repeatedly switched during the THz irradiation. This behavior means that the CNT-SET senses temporal processes of excitation and recombination of THz-excited carriers in the 2DEG. I note that the CNT-2DEG distance is 120 nm, the relative dielectric constant of GaAs is 13, and the separation length of excited electron-hole pairs is 20–100 nm [20, 21]. Based on these values, the potential change caused by the polarization of a single electron-hole pair is estimated to be 0.4 ~ 10 meV. This value is comparable to the width of the current peak of the CNT-SET (~3 meV). This shows that single- carrier charging via single THz photon absorption in a 2DEG can generate an observ- able current peak shift and resulting current switching. The data of Figure 1.8 thus demonstrate that the CNT/2DEG device is capable of detecting a few THz photons. The power of 0.1 fW at 1.6 THz is equivalent to about 105 photons per second. This means that the detector does not sense all incident THz photons, which is due to the much smaller detection area than the wavelength of the incident THz wave. I expect that this problem will be resolved by fabricating a device having appropriate antenna-shaped electrodes for the CNT-SET. The present detector can work at 6 ~ 7 K. This performance eliminates the use of a dilution or 3He refrigerator with low cooling capacity and complex systems. The device can therefore be used in a standard 4He refrigerator or a compact cryo-free mechanical refrigerator with much higher cooling capacity and much greater ease of use. This advantageous capability makes it possible to extend the usable range of ultra-sensitive THz measurements. Source-drain Current (pA) 4.8 3.6 2.4 1.2 0 T = 2.5 K f = 1.6 THz B = 3.95 T VSD = 1.5 mV VG = –169 mV Time (s) 0 10 20 30 40 50 60 70 80 90 100 THz on THz on THz off THz off FIGURE 1.8 Time trace of the THz-detected signal (the CNT-SET current ISD) as the THz irradiation is cycled on and off. In this measurement, THz cyclotron radiation emitted from another 2DEG was used with a very low intensity of ~0.1 fW. (Adapted from Y. Kawano, T. Uchida, and K. Ishibashi, Appl. Phys. Lett., 95, 083123, 2009.)
- 33. 12 High-Speed Devices and Circuits with THz Applications 1.3 THz IMAGING Enhancing spatial resolution of THz imaging is one of the central issues in THz technology. Nevertheless, this is a formidable task, because basic components neces- sary for obtaining high resolution, such as high-transmission wave line and a highly sensitive detector, have not been well established compared to other frequency regions. There are generally two methods for realizing high resolution in optical imaging: solid immersion lens and near-field imaging technique. I explain the applications of the techniques in the THz imaging below. 1.3.1 Solid Immersion Lens In a standard optical imaging system like the use of a lens, spatial resolution of an optical image is proportional to a wavelength of the light. The solid immersion lens utilizes the fact that a wavelength in a material with high dielectric constant is reduced compared to that in vacuum. Therefore, a lens with a large refractive index leads to high resolution. Figure 1.9 depicts an example of THz imaging based on the solid immersion lens [23]. A hyperhemispherical lens made of Si is in contact with the back surface of a sample. The sample is a 2DEG in a GaAs/AlGaAs heterostructure. A THz emis- sion from the 2DEG is radiated as a consequence of inter-Landau-level transitions of electrons under magnetic field, i.e., cyclotron emission (CE) [22]. The focal point of the lens is designed to be on the 2DEG layer of the sample. The CE from the focal point is collimated via the lens and is guided through a metallic light pipe to a THz detector. Off-axis light is filtered by a black polyethylene pipe. The sample is scanned relative to the lens by use of an X-Y translation stage, while the optical system including the detector is stationary. The relatively large refractive index of GaAs and Si (n ~ 3.4) allows a resolution much higher than that obtained with a remote lens system. Kawano and Komiyama [23] reported that for the solid immersion lens system, the resolution is about 50 µm at 130 µm, the wavelength of CE in vacuum. This value is improved by a factor of 6, compared to the resolution (300 µm) for the remote Si lens. B Si-lens 2DEG (THz emitter) 2DEG (THz detector) THz absorber FIGURE 1.9 THz microscope based on a solid immersion lens.
- 34. 13 Terahertz Technology Based on Nano-Electronic Devices 1.3.2 Near-Field Imaging Though the solid immersion lens system enables relatively high resolution, the resolution is still determined by the diffraction limit. A powerful technique for over- coming the diffraction limit is near-field imaging [24]. When an electromagnetic wave is illuminated onto an aperture smaller than a wavelength, a localized evanescent field (near field) is generated just behind the aperture. The size of the evanescent field is determined by the aperture size and not the wavelength. By illuminating or detecting the evanescent field, it is possible to get a resolution beyond the diffraction limit. Conventionalsystemsfornear-fieldimaginghaveanaperturetypeandanaperture- less (scattering) type. In the visible and near-infrared regions, either a tapered, metal-coated optical fiber (aperture type) [25] or a metal tip (aperture-less type) [26] is used. In the microwave region, either a sharpened waveguide (aperture type) [27] or a coaxial cable (aperture-less type) [28] is used. Since the intensity of the evanes- cent field is very weak, the realization of near-field imaging needs a highly sensi- tive detection scheme, such as a high-transmission wave line and highly sensitive detector. 1.3.2.1 Near-Field Imaging in the THz Region Several methods for near-field imaging in the THz region have been presented. In the aperture type, a metal hole was used to obtain a resolution better than λ/4 [29]. This method, however, has the drawback of low wave transmission through the small aperture, which requires detecting very weak waves. Moreover, the spatial resolution is not so high. As the aperture-less type, a sharpened antenna [30], a metal tip [31], and a cantilever [32] were reported. Although the aperture-less technique allows high spatial resolution, it has the problem of separation from a far-field component of an incident wave, which generates a large background signal. For this reason, in most instances the probe position is modulated and synchronously detected signal is mea- sured. However, this scheme makes the whole system and its operation complicated. At present stage, near-field THz imaging has not been fully established, and several other techniques are proposed and attempted. This is still an ongoing issue. 1.3.2.2 Near-Field THz Imaging on One Chip I here explain unique near-field THz imaging—on-chip THz imaging with an integrated semiconductor device [33, 34]. The problems of other techniques were low efficiency of near-field detection and complicated systems. The new integrated device enables near-field THz imaging in a much simpler manner. As shown in Figure 1.10, an aperture with an 8 µm diameter and a planar probe were deposited on a surface of a GaAs/AlGaAs heterostructure chip. The aperture and the probe are insulated by a 50 nm thick SiO2 layer. The GaAs chip has an electron mobility of 18 m2/Vs and a sheet electron density of 4.4 × 10 m–2 at 77 K. The two ohmic contacts were extended to the side surfaces of the chip, to each of which an electrical wire was attached. A 2DEG, located 60 nm below the chip surface, works as a THz detector. In this device structure, all components—an aperture, a probe, and a detector—are inte- grated on one GaAs/AlGaAs chip. This scheme eliminates any optical and mechani- cal alignments between each component, leading to an easy-to-use and robust system.
- 35. 14 High-Speed Devices and Circuits with THz Applications An advantage of this device structure is that the presence of the planar probe changes the distribution of the evanescent field, enhancing the coupling of the evanescent field to the 2DEG detector. This is expected to lead to an increase in the detection sensitivity. Moreover, the 2DEG detector is not affected by the far-field wave owing to the close vicinity to the aperture and the probe, allowing the detection of the evanescent field alone. Figure 1.11 shows calculations of THz electric field distributions near the aperture using a finite element method. Compared are the device of the aperture alone and that of the aperture plus the probe, where the aperture diameters are the same. For the case of the aperture alone, the electric field is localized close to the aperture. This explains the reason why the conventional aperture-based technique suffers from low transmission through the aperture. On the other hand, when the probe is present just behind the aper- ture, the electric field extends into the interior region of the GaAs substrate. This result indicates that the presence of the probe changes the distribution profile of the evanes- cent field, enhancing the coupling between the evanescent field and the 2DEG detector. In order to confirm experimentally the above calculations, we measured the THz transmission distribution by scanning the device across a sample. In the measurements, the THz gas laser pumped by the CO2 gas laser was used as a THz source. The THz radiation was chopped at 16 Hz and the amplitude modulation of the detected signal (the voltage change of the 2DEG) was measured with a lock-in amplifier. The THz near-field device relative to the sample was scanned with a translation stage based on a piezoelectric stick-slip motion. The sample is made up of a THz transparent substrate, the surface of which is covered at regular intervals by THz opaque Au films. The widths of THz opaque and transparent regions across the scan direction are 80 and 50 µm, respectively. Two types of near-field THz devices were used: the aperture plus the probe and the aperture alone. As displayed in Figure 1.12(a), in the former case, a clear signal is visible, whereas in the latter case, no signal is observed. This feature does not depend on the wavelength of the incident THz wave. The enhancement ratio of the signal amplitude regarding comparison between the two devices was found to be 41 for λ = 118.8 µm and 67 for λ = 214.6 µm. These results clearly demonstrate that the distribution of the THz evanescent field is largely enhanced due to the presence of the probe, leading to improvement in the detection sensitivity. GaAs/AlGaAs heterostructure Near-field probe Aperture GaAs SiO2 film Au film Aperture Near-field probe 5 µm 2DEG (detector) FIGURE 1.10 Photograph of the near-field THz imaging device and its schematic view.
- 36. 15 Terahertz Technology Based on Nano-Electronic Devices The decay curves of Figure 1.12(b) show that the near-field THz device has a spatial resolution of 9 µm. The important points of the data are that the resolution does not depend on the wavelength of the THz wave, and that it is far beyond the diffraction limit λ/2 (107.3 µm) for the wavelength of λ = 214.6 µm. These features are characteristic of the near-field effect. The present device hence properly functions as a near-field THz imaging detector. Using this device, a high-resolution image of THz CE distribution in another 2DEG has been obtained [35]. In general, when one improves spatial resolution, one encounters the problem that it is necessary to largely enhance detection sensitivity. This is because the intensity of the wave to be detected is strongly reduced as the sensing area becomes small. This situation compels one to produce a scheme of highly sensitive detection in a tiny region. I expect that one promising approach for tackling this problem in the THz region will be to use the CNT/2DEG THz detector [13], described in the previous section. Compared to the 2DEG detector, the CNT/2DEG detector exhibits much higher sensitivity in a much smaller sensing area of submicrometer. When this detector is integrated with an aperture and a probe as shown in Figure 1.10, the device will enable THz imaging with ultra-high sensitivity and a sub-µm resolution. Aperture Aperture Alone Aperture Probe 0.0489 0.0428 0.0367 0.0306 0.0245 0.0183 0.0122 0.00611 0 Aperture + Probe FIGURE 1.11 Calculations of THz electric field distributions in the vicinity of the aperture for the device with the aperture and probe (upper panel) and for the device with the aperture alone (lower panel).
- 37. 16 High-Speed Devices and Circuits with THz Applications 0 0 2 4 6 8 10 100 200 THz Near-field Device Position (µm) THz Near-field Device Position (µm) THz Transmission Signal (arb. units) THz Transmission Signal (arb. units) 300 Aperture alone Aperture + Probe λ = 118.8 µm 400 500 335 340 345 350 355 0 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 THz Near-field Device Position (µm) THz Transmission Signal (arb. units) 75 80 85 90 95 0 0.1 0.2 0.3 0.4 0.5 100 200 THz Near-field Device Position (µm) (b) (a) THz Transmission Signal (arb. units) 300 Aperture alone Aperture + Probe 9 µm 9.0 ± 0.2 µm λ = 214.6 µm λ = 214.6 µm λ = 118.6 µm 400 500 FIGURE 1.12 (a) THz transmission signal versus the position of the near-field THz detector. (b) Decay curves of the signals in (a).
- 38. 17 Terahertz Technology Based on Nano-Electronic Devices 1.4 THz APPLICATION 1.4.1 Applications to Materials Researches The photon energy and the period of the THz wave with 1 THz are about 4 meV and 1 ps, respectively. In these energy and time regions, there are many important materials and their physical properties, such as energy gap of superconductor, impu- rity level of semiconductor, phonon energy, and Landau level separation. THz spec- troscopy and imaging can thus be exploited as a powerful tool for investigating and characterizing various materials. There are a lot of THz applications to materials researches. Shikii et al. [36] reported mapping of supercurrent distributions in a high-temperature superconductor by means of the THz imaging technique. THz-TDS is a very powerful tool for investigating electron dynamics in materials. This technique provides two kinds of information: real-time dynamics and frequency spectra. With this method, a lot of important information was successfully derived and the related electronic properties were clarified. For example, reported were THz conductivity in an MgB2 superconductor [37], Bloch oscillation in a semiconductor superlattice [38], ballistic electron motion in a CNT [39], and dynamics of a spin-density-wave gap in a quasi- 1D organic conductor [40]. 1.4.2 Applications to Semiconductor 1.4.2.1 Imaging Energy Dissipation in 2DEG When the 2DEG is subject to a perpendicular magnetic field, it exhibits dramatic properties known as quantum Hall effect (QHE) [41, 42]. In the QHE regime, the longitudinal resistance vanishes and the Hall resistance is precisely quantized. The basis of the QHE is the formation of the Landau level, which originates from the quantization of electron cyclotron motion. Studying electron distribution of an excited Landau level (related energy-dissipation distribution) is one of the critical issues regarding the QHE. The reason is as follows: Earlier works reported that the electron relaxation from excited Landau level involves a slow physical process, the typical timescale being as long as 10–100 ns [43]. Moreover, the equilibrium length of the excited electrons LE was shown to reach a macroscopic value of ~0.1 mm [44, 45]. This leads us to expect that spatial distribution of the excited electrons will be strikingly different from that of the ground-state electrons and will drastically depend on sample dimensions, in relation with LE. However, this issue has not been satisfactorily clarified. Several imaging techniques have been applied to obtain information on dissipation distributions in the QHE systems. By using the fountain pressure effect of superfluid liquid helium, Klaß et al. demonstrated that in the QHE state, dissipation takes place almost totally at the diagonally opposite electron entry and exit corners of the sample (hot spots) [46]. A similar conclusion has been derived from the experiments of Russell et al., which applied a local bolometry technique [47]. Unfortunately, since these earlier experiments probe the lattice temperature related to Joule heating, they do not exclusively observe the distribution within the 2DEG, i.e., the effective
- 39. 18 High-Speed Devices and Circuits with THz Applications temperature of the excited electrons. Thus, until now no experimental techniques were available for imaging only the dissipation distribution in the 2DEG. In contrast, since CE is radiated with the transition of electrons from higher Landau levels to lower Landau levels, mapping the CE intensity with the THz micro- scope provides a direct probe of the excited electrons. In the following, I introduce investigations on spatial properties of the 2DEGs by use of THz-CE imaging. 1.4.2.2 Separate Imaging of Ground and Excited Levels In order to enable separate imaging of the ground-state electrons and the excited-state electrons, we have developed a combined system of an electrometer with a THz microscope [48]. In the electrometer technique, we are able to map voltage distribu- tions [49, 50]. Hence, comparing the two kinds of the mapped data (voltage and CE) allows us to distinguish the contributions of the ground-state and excited-state elec- trons to the generation of the voltage. Figure 1.13 depicts the setup of the combined imaging system. An electrometer (small Hall bar) and a hyperhemisphere Si lens are in contact with the front and back surfaces of the sample, respectively. A THz detector is mounted at the bottom of the system. The electrometer, the sample, and the THz detector were fabricated on GaAs/AlGaAs heterostructure wafers having the 2DEGs 0.1 µm beneath the crystal surfaces. In imaging experiments, the sample alone was moved with an X-Y stage, while the electrometer and the optical system were spatially fixed. The whole system was directly immersed into liquid 4He and was subject to a perpendicular magnetic field B. The detection mechanism of the electrometer is as follows: As shown in Figure 1.14, the distance between the two 2DEG layers is very short, and consequently they are capacitively coupled. It follows that when a current Is is passed through the sample, excess charges ΔQ are induced into the 2DEGs, according to CV(x,y) = ΔQ. Here, V(x,y) is a local voltage in the sample right below the electrometer, and Voltage imaging SiO2 film Si-lens 2DEG (Sample) 2DEG (Electrometer) 2DEG (THz detector) B THz imaging THz absorber FIGURE 1.13 Combined imaging system of the electrometer and the THz microscope.
- 40. 19 Terahertz Technology Based on Nano-Electronic Devices C is the capacitance between the two 2DEG layers. The generation of ΔQ leads to the change, ΔRE, in the longitudinal resistance of the electrometer. By translating the electro meter over the sample surface and measuring ΔRE × IE, we are able to image 2D distributions of V(x,y) in the sample (IE is the bias current for the elec- trometer). The electrometer was processed into a Hall bar geometry from a GaAs/ AlGaAs heterostructure with an electron mobility µH = 18 m2/Vs and a sheet electron density ns = 2.2 × 10 m15 m–2 at 4.2 K. The device has a 2DEG channel with a length L = 200 µm and a width W = 1.5 µm, and the two voltage probes with an interval of 2.3 µm. The spatial resolution of this system is about 2 µm, which is determined by the sensing 2DEG area of the electrometer. The sample studied has a Hall bar geometry with L = 2.8 mm and W = 1 mm, which is fabricated from a GaAs/AlGaAs heterostructure with µH = 53 m2/Vs and ns = 2.4 × 1015 m–2 at 4.2 K. In imaging measurements, the voltage V(x,y) and the CE intensity VCE(x,y) were simultaneously obtained with two lock-in amplifiers, where a 30 Hz rectangular-wave current alternating between zero and a given finite value Is was passed through the sample. All measurements were performed at 4.2 K. Figure 1.15 displays images of the longitudinal voltage Vxx and VCE at three current levels, I = 20, 70, and 140 µA, and at B = 5.75 T (Landau level filling factor, 1.74, of the sample). We obtained the Vxx(x,y) data by differating V(x,y) over a distance of 50 µm in the direction of the length of the sample: Vxx(x,y) = V(x + Δx,y) – V(x,y) with Δx = 50 µm. The 20 µA data show that Vxx is seen over the whole 2DEG area, whereas CE occurs only in the two diagonally opposite corners. This directly indicates that the observed Vxx (except at the two spots) arises from scattering of the ground-state electrons. It is known that the CE at the two spots takes place via tunneling injection of nonequilibrium electrons from the source contact and inter- Landau-level tunneling of electrons near the drain contact [22]. The Vxx data at I = 70 and 140 µA show that an additional Vxx is generated around the source contact, and with increasing the current, the area covered by the additional Vxx expands toward the interior 2DEG region. Comparing with the VCE data reveals that a strong CE is radiated in the similar region, indicating that Vxx observed on the source contact side mostly originates from scattering of the excited electrons. Vxx is also visible over the whole 2DEG region, whereas CE remains absent (except in the two diagonally opposite corners). This situation is similar to that observed at I = 20 µA, showing again that Vxx associated with the ground-state electrons is generated over IS C V(x, y) IE Electrometer Sample CV(x, y) = ∆Q ∆RE ∆RE ∆Q FIGURE 1.14 Equivalent circuit of the scanning electrometer system and the detection mechanism. (Adapted from Y. Kawano, and T. Okamoto, Phys. Rev., B 70, 081308(R), 2004.)
- 41. 20 High-Speed Devices and Circuits with THz Applications the entire 2DEG area. We confirmed that the pattern of these features systematically changes upon reversing B and I, and that they are also observed for other Landau level filling factors and for other samples fabricated from different wafers. This indicates that they originate from an intrinsic nature of the 2DEG and are not due to inhomogeneity of the electron density. Let me explain the origin of the difference in the distributions between the ground-state electrons and the excited electrons. The summary of the experimental findings is that as schematically shown in Figure 1.16, the scattering distribution of the ground-state electrons spreads over the entire 2DEG region, whereas that of the excited electrons is localized in the two corners and around the source contact. The result indicates a large difference in the scattering processes and their characteristic lengths. The equilibrium length of excited electrons was shown to be a very long scale of 10–300 µm [44, 45]. On the other hand, although there is no clear experimental information about the ground-state electrons, one can think that the scattering rate will be much higher because the scattering does not require much energy. The main scattering mechanism of the ground-state electrons is possibly impurity scattering originating from ionized donors in the AlGaAs layer. The characteristic scattering length of the ground-state electrons can be regarded as a period of the ionized impu- rities, 0.05–0.3 µm, which is much shorter than LE. This explains the contrasting situation regarding spatial distributions of ground- and excited-state electrons. I will discuss the electron transport process in more detail below. 20 µA 70 µA 140 µA 0 4 Vxx, VCE (arb. units) 2 6 8 10 Vxx VCE FIGURE 1.15 Distribution images of the longitudinal voltage Vxx (left) and the CE intensity VCE (right) at three current levels, I = 20, 70, and 140 µA. The white broken lines denote the 2DEG boundaries of the sample. In the Vxx (VCE), for clarity, the signals at I = 20 and 70 µA are magnified, respectively, by factors of 15 (18) and 9 (3) compared to that at I = 140 µA.
- 42. 21 Terahertz Technology Based on Nano-Electronic Devices 1.4.2.3 Macroscopic Channel Size Effect of THz Image The experimental data in the above showed that the macroscopically long value of LE results in the asymmetric distribution of the excited electrons. From this fact, the following interesting phenomenon is expected: spatial distribution of the excited electrons will drastically depend on sample dimensions, in relation with LE. We have addressed this issue by studying the channel size dependence of the CE distribution by use of THz imaging [51]. The experimental setup of the THz microscope is similar to that shown inFigure 1.9. Three samples with different widths of W = 1.2, 0.3, and 0.02 mm (length L = 4 mm) were investigated, all of which were fabricated from the same GaAs/AlGaAs het- erostructure crystal with µH = 62 m2/Vs and ns = 2.4 × 1015 m–2 at 4.2 K. In CE mea- surements, the detected signal was recorded with a lock-in amplifier, where 20 Hz rectangular-wave currents alternating between zero and a given finite value I were transmitted through the sample. All the measurements were performed at 4.2 K. Figure 1.17 shows comparison of the CE images for the three samples. In the wid- est sample (W = 1.2 mm), CE takes place mostly in the two diagonally opposite cor- ners and in a localized region near the source contact. In the data for W = 0.3 mm, CE expands into the more interior 2DEG region. Furthermore, when W = 0.02 mm, the CE takes place over the entire region of the interior 2DEG channel. We confirmed that the pattern of these features systematically changed upon reversing B and I, and that the similar CE images were also observed for other samples fabricated from different GaAs/AlGaAs wafers. The significant change with W observed shows the validity of the above expecta- tion: spatial distribution of the excited electrons is considerably influenced by the very long length scale of LE. This means that the electrons travel the macroscopic distance LE to lead to an appreciable generation of CE. Based on this, I explain the transport process of the excited electrons below. In the QHE devices, it is known that high electric field is concentrated in the two diagonally opposite corners, which are also electron entry and exit corners [52]. E E DOS DOS + – – + FIGURE 1.16 Sketch of scattering distributions of the ground-state electrons (left) and of the excited-state electrons (right).
- 43. 22 High-Speed Devices and Circuits with THz Applications It follows that as the current increases, electron excitation into a higher Landau level starts in the vicinity of the two current contacts. On the source contact side, CE begins to take place in the electron entry corner SE (Figure 1.18). In W >> LE, though the electric field decreases away from SE, the excitation process can continue toward the opposite corner (SO) over the distance LE. As the applied electric field becomes DE + SO DE SO DO SE W < < LE W < < LE DO SE – + – FIGURE 1.18 Schematic view of trajectories (orange lines) of excited electrons in the QHE device for a wide Hall bar with W >> LE (upper panel) and a narrow Hall bar with W << LE (lower panel). 0 4 CE Intensity (arb. units) j = 0.4 A/m j = 1.5 A/m j = 0.15 A/m 2 6 8 10 FIGURE 1.17 CE images at three current densities, j = 0.15, 0.4, and 1.5 A/m, and for the three samples with different channel widths, W = 20, 300, and 1200 µm. The white solid lines denote the 2DEG boundaries of the samples. For clarity, the signals are magnified by factors of 1300 (20, 0.15), 360 (20, 0.4), 23 (20, 1.5), 70 (300, 0.15), 18 (300, 0.4), 3 (300, 1.5), 14 (1200, 0.15), and 5 (1200, 0.4), respectively, compared to that for (1200, 1.5), where (A, B) represents (W in µm, j in A/m). (Adapted from Y. Kawano, and T. Okamoto, Phys. Rev. Lett., 95, 166801, 2005.)
- 44. 23 Terahertz Technology Based on Nano-Electronic Devices higher, like 0.4 and 1.5 A/m in the sample with W = 1.2 mm, the area where such excitation occurs further expands through SO toward the interior region of the 2DEG channel. Similar excitation process takes place along the boundary of the drain contact. In this region, on the other hand, electrons travel from the opposite corner (DO) to the electron exit corner (DE), which is opposite to that on the side of the source contact. As a result, though electron excitation starts around DO, CE does not appreciably occur there and mostly occurs at DE. In contrast, when W is smaller than LE, CE is not generated in the vicinity of the source contact. This is because in such narrow devices, the electron excitation can take place only as the electrons traverse the Hall bar along the length direction of the 2DEG channel. The CE thus occurs over the whole region of the interior 2DEG channel, which is in strong contrast to the CE distribution for the devices with W >> LE. 1.5 CONCLUSION AND OUTLOOK In this chapter, I have presented novel THz sensing and imaging devices based on nano-electronic materials and devices: 2D semiconductor and CNT. These detectors enable THz wave sensing with high sensitivity and high spatial resolution. I also introduce applications of THz measurements to materials researches. The experi- mental data have successfully revealed spatial properties of electrons in the 2DEG, which have not been revealed by conventional transport measurements. The next key devices for future THz technology will be THz cameras, THz video, and THz communication. When these devices are realized in portable size, THz technology will widely spread into our life. For this purpose, achieving higher detec- tion sensitivity and higher power generation will increasingly become important tasks. The development should require further breakthroughs in materials, device structure, operation principles, etc. I anticipate that nanotechnology will still be one of the keys for enhancing performance of THz technology. Regarding our next target, I plan to create a THz photon counting video, which is a strongly desired device in many fields. When many CNT-based THz photon detec- tors [13] are integrated in a two-dimensional configuration [53, 54], the resulting device will work as a THz video for real-time, high-resolution THz imaging. REFERENCES 1. B. Ferguson and X.-C. Zhang, Materials for terahertz science and technology, Nat. Mater. 1, 26 (2002). 2. M. Tonouchi, Cutting-edge terahertz technology, Nat. Photonics 1, 97 (2007). 3. J. Wei, D. Olaya, B. S. Karasik, S. V. Pereverzev, A. V. Sergeev, and M. E. Gershenson, Ultrasensitive hot-electron nanobolometers for terahertz astrophysics, Nat. Nanotechnol. 3, 496 (2008). 4. S. Ariyoshi, C. Otani, A. Dobroiu, H. Matsuo, H. Sato, T. Taino, K. Kawase, and H. Shimizu, Terahertz imaging with a direct detector based on superconducting tunnel junctions, Appl. Phys. Lett. 88, 203503 (2006). 5. S. Komiyama, O. Astafiev, V. Antonov, H. Hirai, and T. Kutsuwa, A single-photon detec- tor in the far-infrared range, Nature 403, 405 (2000).
- 45. 24 High-Speed Devices and Circuits with THz Applications 6. P. Kleinschmidt, S. Giblin, A. Tzalenchuk, H. Hashiba, V. Antonov, and S. Komiyama, Sensitive detector for a passive terahertz imager, J. Appl. Phys. 99, 114504 (2006). 7. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical properties of carbon nano- tubes, Imperial College Press, London, 1998. 8. P. W. Barone, S. Baik, D. A. Heller, and M. S. Strano, Near-infrared optical sensors based on single-walled carbon nanotubes, Nat. Mater. 4, 86 (2005). 9. M. E. Itkis, F. Borondics, A. Yu, and R. C. Haddon, Bolometric infrared photoresponse of suspended single-walled carbon nanotube films, Science 312, 413 (2006). 10. T. Fuse,Y. Kawano, M. Suzuki,Y. Aoyagi, and K. Ishibashi, Coulomb peak shifts under terahertz-wave irradiation in carbon nanotube single-electron transistors, Appl. Phys. Lett. 90, 013119 (2007). 11. K. Fu, R. Zannoni, C. Chan, S. H. Adams, J. Nicholson, E. Polizzi, and K. S.Yngvesson, Terahertz detection in single wall carbon nanotubes, Appl. Phys. Lett. 92, 033105 (2008). 12. Y. Kawano, T. Fuse, S. Toyokawa, T. Uchida, and K. Ishibashi, Terahertz photon-assisted tunneling in carbon nanotube quantum dots, J. Appl. Phys. 103, 034307 (2008). 13. Y. Kawano, T. Uchida, and K. Ishibashi, Terahertz sensing with a carbon nanotube/two- dimensional electron gas hybrid transistor, Appl. Phys. Lett. 95, 083123 (2009). 14. P. K. Tien and J. P. Gordon, Multiphoton process observed in the interaction of micro- wave fields with the tunneling between superconductor films, Phys. Rev. 129, 647 (1963). 15. J. M. Hergenrother, M. T. Tuominena, J. G. Lua, D. C. Ralpha, and M. Tinkham, Charge transport and photon-assisted tunneling in the NSN single-electron transistor, Physica B 203, (1994) 327. 16. B. Leone, J. R. Gao, T. M. Klapwijk, B. D. Jackson, W. M. Laauwen, and G. de Lange, Electron heating by photon-assisted tunneling in niobium terahertz mixers with inte- grated niobium titanium nitride striplines, Appl. Phys. Lett. 78, 1616 (2001). 17. T. H. Oosterkamp, L. P. Kouwenhoven, A. E. A. Koolen, N. C. van der Vaart, and C. J. P. M. Harmans, Photon sidebands of the ground state and first excited state of a quantum dot, Phys. Rev. Lett. 78, 1536 (1997). 18. T. H. Oosterkamp,T. Fujisawa,W. G. van derWiel, K. Ishibashi, R.V. Hijman, S. Tarucha, and L. P. Kouwenhoven, Microwave spectroscopy of a quantum-dot molecule, Nature 395, 873 (1998). 19. F. Thiele, U. Merkt, J. P. Kotthaus, G. Lommer, F. Malcher, U. Rossler, and G. Weimann, Cyclotron masses in n-GaAs/Ga1-xAlxAs heterojunctions, Solid State Commun. 62, 841 (1987). 20. S. H. Tessmer, P. I. Glicofridis, R. C. Ashoori, L. S. Levitov, and M. R. Melloch, Subsurface charge accumulation imaging of a quantum Hall liquid, Nature 392, 51 (1998). 21. Y. Kawano, Y. Hisanaga, H. Takenouchi, and S. Komiyama, Highly sensitive and tun- able detection of far-infrared radiation by quantum Hall devices, J. Appl. Phys. 89, (2001) 4037. 22. Y. Kawano, Y. Hisanaga, and S. Komiyama, Cyclotron emission from quantized Hall devices: Injection of nonequilibrium electrons from contacts, Phys. Rev. B 59, 12537 (1999). 23. Y. Kawano and S. Komiyama, Spatial distribution of non-equilibrium electrons in quantum Hall devices: Imaging via cyclotron emission, Phys. Rev. B 68, 085328 (2003). 24. M. Ohtsu, ed., Near-field nano/atom optics and technology, Springer-Verlag, Berlin, 1998. 25. T. Saiki, S. Mononobe, M. Ohtsu, N. Saito, and J. Kusano, Tailoring a high-transmission fiber probe for photon scanning tunneling microscope, Appl. Phys. Lett. 68, 2612 (1996).
- 46. 25 Terahertz Technology Based on Nano-Electronic Devices 26. F. Zenhausern, Y. Martin, and H. K. Wickramasinghe, Scanning interferometric apertureless microscopy: Optical imaging at 10 angstrom resolution, Science 269, 1083 (1995). 27. W. C. Symons III, K. W. Whites, and R. A. Lodder, Theoretical and experimental char- acterization of a near-field scanning microwave microscope (NSMM), IEEE Trans. Microwave Theory Tech. 51, 91 (2003). 28. M. Tabib-Azar and Y. Wang, Design and fabrication of scanning near-field microwave probes compatible with atomic force microscopy to image embedded nanostructures, IEEE Trans. Microwave Theory Tech. 52, 971 (2004). 29. S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, THz near-field imaging, Opt. Commun. 150, 22 (1998). 30. N. C. J. van der Valk and P. C. M. Planken, Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip, Appl. Phys. Lett. 81, 1558 (2002). 31. H. T. Chen, R. Kersting, and G. C. Cho, Terahertz imaging with nanometer resolution, Appl. Phys. Lett. 83, 3009 (2003). 32. A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, Terahertz near- field nanoscopy of mobile carriers in single semiconductor nanodevices, Nano Lett. 8, 3766 (2008). 33. Y. Kawano and K. Ishibashi, An on-chip near-field terahertz probe and detector, Nat. Photonics 2, 618 (2008). 34. Y. Kawano, Terahertz detectors: Quantum dots enable integrated terahertz imager, Laser Focus World 45(7), 45–47, 50 (2009). 35. Y. Kawano and K. Ishibashi, On-chip near-field terahertz detection based on a two- dimensional electron gas, Physica E, 42, 1188 (2010). 36. S. Shikii, T. Kondo, M. Yamashita, M. Tonouchi, M. Hangyo, M. Tani, and K. Sakai, Observation of supercurrent distribution in YBa2Cu3C>7 – δ thin films using THz radia- tion excited with femtosecond laser pulses, Appl. Phys. Lett. 74 (1999) 1317. 37. R. A. Kaindl, M. A. Carnahan, J. Orenstein, D. S. Chemla, H. M. Christen, H.-Y. Zhai, M. Paranthaman, and D. H. Lowndes, Far-infrared optical conductivity gap in supercon- ducting MgB2 films, Phys. Rev. Lett. 88 (2001) 027003. 38. N. Sekine and K. Hirakawa, Dispersive terahertz gain of non-classical oscillator: Bloch oscillation in semiconductor superlattices, Phys. Rev. Lett. 94, 057408 (2005). 39. Z. Zhong, N. M. Gabor, J. E. Sharping, A. L. Gaeta, and P. L. McEuen, Terahertz time- domain measurement of ballistic electron resonance in a single-walled carbon nanotube, Nat. Nanotechnol. 3 (2008) 201. 40. S. Watanabe, R. Kondo, S. Kagoshima, and R. Shimano, Observation of ultrafast pho- toinduced closing and recovery of the spin-density-wave gap in (TMTSF)2PF6, Phys. Rev. B 80, 220408(R) (2009). 41. K. von Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determina- tion of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980). 42. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48, 1559 (1982). 43. B. R. A. Neves, N. Mori, P. H. Beton, L. Eaves, J. Wang, and M. Henini, Landau-level populations and slow energy relaxation of a two-dimensional electron gas probed by tunneling spectroscopy, Phys. Rev. B 52, 4666 (1995). 44. S. Komiyama,Y. Kawaguchi, T. Osada, andY. Shiraki, Evidence of nonlocal breakdown of the integer quantum Hall effect, Phys. Rev. Lett. 77, 558 (1996). 45. I. I. Kaya, G. Nachtwei, K. von Klitzing, and K. Eberl, Spatially resolved monitoring of the evolution of the breakdown of the quantum Hall effect: Direct observation of inter-Landau-level tunneling, Europhys. Lett. 46, 62 (1999).
- 47. 26 High-Speed Devices and Circuits with THz Applications 46. U. Klaß, W. Dietsche, K. von Klitzing, and K. Ploog, Imaging of the dissipation in quantum-Hall-effect experiments, Z. Phys. B 82, 351 (1991). 47. P. A. Russell, F. F. Ouali, N. P. Hewett, and L. J. Challis, Power dissipation in the quan- tum Hall regime, Surface Sci. 229, 54 (1990). 48. Y. Kawano and T. Okamoto, Imaging of intra- and inter-Landau-level scattering in quan- tum Hall systems, Phys. Rev. B 70, 081308(R) (2004). 49. Y. Kawano and T. Okamoto, Scanning electrometer using the capacitive coupling in quantum Hall effect devices, Appl. Phys. Lett. 84, 1111 (2004). 50. Y. Kawano and T. Okamoto, Noise-voltage mapping by a quantum-Hall electrometer, Appl. Phys. Lett. 87, 252108 (2005). 51. Y. Kawano and T. Okamoto, Macroscopic channel-size effect of nonequilibrium electron distributions in quantum Hall conductors, Phys. Rev. Lett. 95, 166801 (2005). 52. J. Wakabayashi and S. Kawaji, Hall effect in silicon MOS inversion layers under strong magnetic fields, J. Phys. Soc. Jpn. 44, 1839 (1978). 53. N. R. Franklin, Q. Wang, T. W. Tombler, A. Javey, M. Shim, and H. Dai, Integration of suspended carbon nanotube arrays into electronic devices and electromechanical sys- tems, Appl. Phys. Lett. 81, 913 (2002). 54. H. Tabata, M. Shimizu, and K. Ishibashi, Fabrication of single electron transistors using transfer-printed aligned single walled carbon nanotubes array, Appl. Phys. Lett. 95, 113107 (2009).
- 48. 27 2 Ultimate Fully Depleted (FD) SOI Multigate MOSFETs and Multibarrier Boosted Gate Resonant Tunneling FETs for a New High-Performance Low-Power Paradigm Aryan Afzalian As transistors are scaled down in the nanoscale regime, quantum effects are playing a crucial role in device performance and parameters. Also, scaling alone is not suf- ficient to achieve performance improvement, and new boosters and device concepts are needed. For instance, the trade-off between power and performance in electronics is one of the most limiting factors to push further technology scaling and develop- ment. With scaling, the reduction of supply voltage to keep power density under con- trol [1–3], the rise of source and drain resistance due to film thickness reduction in order to keep good electrostatic control [3], and finally, source-drain (SD) tunneling CONTENTS 2.1 Simulation Algorithm......................................................................................29 2.2 Gate Coupling Optimization in Nanoscale Nanowire MOSFETs: Electrostatic vs. Quantum Confinement.......................................................... 31 2.3 Physics of RTFET............................................................................................36 2.3.1 Influence of Barrier Width................................................................... 41 2.4 SB RT-FET...................................................................................................... 41 2.5 Conclusions......................................................................................................46 Acknowledgments.....................................................................................................47 References.................................................................................................................47
- 49. 28 High-Speed Devices and Circuits with THz Applications that degrades subthreshold slope and increases leakage of transistors below 10 nm [3, 4] are major roadblocks that degrade on- and off-current, and ION/IOFF ratios, and therefore the power-delay trade-off of transistors. ION/IOFF ratios and slope character- istics of transistors depend on the gate-to-channel coupling and carrier statistics that dictate the way carriers are made available to drive a current when increasing VG. By reducing film thickness and increasing the number of gates, ultra-thin film multi- gate silicon-on-insulator (SOI) architectures have better electrostatic control and can achieve near-ideal subthreshold slope and improved ION/IOFF ratio over more conven- tional bulk Si single-gate architectures. Supposing ideal gate coupling, however, when varying the gate voltage, the current varies at a rate dictated by Fermi-Dirac statis- tics only. This is governed by the gate-controlled single-barrier paradigm on which present field-effect transistors (FETs) are based. In a standard transistor, there is only one barrier from channel to source, and the density of state close to the top of the channel barrier is about constant with VG [5]. As a result, the current increase is expo- nential below threshold with an optimal minimal inverse subthreshold slope (SS) of kT/q.log 10, i.e., about 60 mV/decade at T = 300 K. Above threshold, when the channel barrier passes below the source Fermi level, EFS, enabling the source highly occupied states to drive a significant current density, and thus good delay performance, the cur- rent increase is much slower and the inverse slope reaches much higher values. We have recently shown the possibility of achieving better slopes than those dic- tatedbyFermi-Dirac,bothinsubthresholdandabovethreshold,togetherwithhighon- current,byusingaSimultibarrierboostedcomplementarymetal-oxide-semiconductor (CMOS) transistor, the gate modulated resonant tunneling (RT) FET [5, 6]. It is a metal-oxide-semiconductor field-effect transistor (MOSFET) boosted with addi- tional tunnel barriers (TBs) (i.e., barriers of a few nanometers width and less than 10 nm) near the gate edge(s) and under electrostatic control of the gate that cre- ates additional longitudinal confinement in the device. Such TBs can be created, for instance, in a planar technology from a local reduction, or constriction, of the device cross section, resulting from a local oxidation that can be well controlled [7], or from Schottky barriers and dopant segregation techniques [6, 8] in this case allowing for steep slope and low source and drain resistance. RT-FETs have also been shown to be immune to the source-drain tunneling problem that further degrades ION/IOFF ratios in standard devices for channel lengths below 10 nm. In this chapter, we investigate and compare the performances of ultimate SOI multigate nanowire FETs with channel lengths of about 10 nm and below through nonequilibrium Green’s function (NEGF) quantum simulations, within both ballistic and scattering self-consistent Born approximations. Both standard single- barrier devices and the new multibarrier boosted architecture are compared. In Section 2.1, the simulation algorithm is reviewed. In Section 2.2, quantum effects and their impact on the gate coupling optimization of ultra-scaled nanowires are described by optimizing ION/IOFF ratios vs. the cross section size in a 10 nm gate-all-around (GAA) nanowire. It is shown that an optimum cross section exists due to a trade-off between electrostatic and confinement. Also, the fundamental limit of improving gate con- trol by thinning gate oxide is shown when passing from the equivalent oxide thick- ness (EOT) to the capacitive equivalent thickness (CET) concept. In Section 2.3, the physics and the performance limits of the new multibarrier boosted RT-FET
- 50. 29 FDSOI Multigate MOSFETs and Multibarrier Boosted RTFETs are investigated through quantum simulations in silicon nanowires and compared to those of a nanowire multigate SOI MOSFET. Finally, the possibility of imple- menting RT-FET with ultra-low source-drain resistance dopant-segregated Schottky barrier MOSFETs is investigated in Section 2.4. 2.1 SIMULATION ALGORITHM For ultra-scaled devices with cross section dimensions smaller than 10 nm and a gate length below a few tens of nanometers, quantum effects are play- ing a crucial role in device performances and parameters. Hence, the need for quantum simulations arises. Among the new simulation methods developed for that purpose, the nonequilibrium Green’s function (NEGF) method [9–14] has gained popularity and shows a real potential for modeling quantum effects at the scale of a few nanometers. Computations that use this method can, however, be time-consuming, which is the main obstacle to its use in intensive device simula- tions. In an attempt to reduce simulation time, mode-space (MS) methods, which can result in a simulation speed-up up to two to three orders of magnitude over more computationally demanding real-space methods, have been introduced. Such an approach is assumed in the following. We note, however, that here we do not imply from MS uncoupled mode space (that is only valid for devices with small film thicknesses and no discontinuities in their cross section along the chan- nel; see below) as sometimes assumed in the literature, but that the coupled mode- space approach is also encompassed. Our quantum simulator is based on the use of a fast coupled mode-space (FCMS) implementation of the NEGF [7], adaptive energy, and nonuniform mesh algorithms. Compared to a real-space NEGF algorithm, the coordinates y and z of the cross section perpendicular to the transport direction, x, are replaced by the mode energies E x ( ) sub m of the electron subbands in an MS approach. This drastically reduces computation time, as in practice only the first few subbands are populated by electrons and need to be taken into account [12]. A full description of our simu- lator can be found in [7]. Here we summarize the main equations and simplifying assumptions used by our 3D MS-NEGF simulator [15]. The main convergence loop of the program self-consistently computes the electrostatic potential in the device, V1, by solving for the Poisson equation and the electron concentration, n1, using the NEGF formalism [11]. A nonlinear Poisson scheme is used to ensure fast con- vergence. Except for the Schottky barrier case, which is treated below, Neumann (close) boundary conditions are used for the Poisson equation at the source and drain. In quantum simulations, indeed, the applied bias is fixed through fixing the Fermi level at source EFS and draining (EFD = EFS – qVD). This allows for elec- trons and potential to self- consistently adjust for ensuring charge neutrality. The mode-space longitudinal coupled Schrödinger equation from which the mode-space device Hamiltonian, HMS, can be computed is given by [12] a x x x E x x E x x E x 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) mm m C mn n n sub m m m 2 2 2 ∑ − ∂ ∂ ϕ − ⋅ϕ + ⋅ϕ = ϕ (2.1)
- 51. 30 High-Speed Devices and Circuits with THz Applications where a x m y z y z x dydz ( ) 1 ( , ) ( , ; ) mm x y z m * , 2 ∫ = ξ (2.2) is the inverse of the average value of the effective mass in the cross section. E x ( ) C mn is a term that represents the coupling between the lateral modes m and n and depends on the integral of the product between the transversal wave function ξm and the first and second derivatives of ξn in the cross section but is independent of y and z [12]. In the MS method, the subband energy profile E x ( ) sub m and the corresponding trans- versal wave function ξm(y,z;x) need to be calculated. This is done by solving a 2D Schrödinger problem in the cross section of the device at each slice x = x0: H y z x E x y z x ( , ; ) ( ) ( , ; ) D n sub n n 2 0 0 ξ = ξ (2.3) and H y m y z y z m y z z U x y z 2 ( , ) 2 ( , ) ( , , ) D y z 2 2 * 2 * 0 = − ∂ ∂ ∂ ∂ − ∂ ∂ ∂ ∂ + (2.4) where U = ECB – q.V1 is the potential energy and ECB is the bulk material conduction band edge (ECB of Si is our potential reference and has been set to 0). In nanowires with a small and constant cross section, it is usually assumed that the eigenfunc- tions ξn(y,z;x) remain constant along the channel even though the eigenvalues E x ( ) sub n do vary. In this case the coupling term in Equation (2.3) would disappear and one can use the fast uncoupled mode-space (FUMS) hypothesis to further fasten the algorithm by computing ξn(y,z) and replacing U(x,y,z) by its x-averaged value in Equation (2.6). [12]. However, here a more general but slower coupled mode-space (CMS) approach is wanted, as in RT-FETs or Schottky barrier (SB) devices, tunnel barriers create strong variation of the wave function shape in their vicinity and there- fore mode coupling. However, this perturbation is very local, and by considering coupling only in the vicinity of the barrier in the FCMS, we therefore achieve FUMS speed with accuracy of the CMS [7]. From HMS, the mode-space device Hamiltonian, the retarded Green’s function, G, of the active device can be defined, and from there, electron concentration and cur- rent in the device, as well as their energy spectrum, can be calculated using the NEGF approach [11, 12]: G(E) = [EI − HMS − ∑S(E) − ∑1(E) − ∑2(E)]−1 (2.5) where ∑s is the self-energy that accounts for scattering inside the device (in the bal- listic case, ∑s is equal to zero), and ∑1(∑2) is the self-energy caused by the coupling between the device and the source (or drain) reservoir [11]. One of the strengths of the NEGF is its ability to handle different types of elastic or inelastic scattering as electron-phonon or surface roughness scattering without using an averaged relaxation time approximation, as has been common
- 52. 31 FDSOI Multigate MOSFETs and Multibarrier Boosted RTFETs in semiclassical or quantum-corrected drift diffusion, in higher-order Boltzmann moment equation, or in Monte-Carlo simulation, for instance. In the NEGF, indeed, spectral functions like density of state DoS(x,E) or density matrixes ρ(x,x,E) are computed self- consistently over a discretized energy mesh. The scattering rate, or scattering self-energy ΣS(x,x,E) matrix that depends on these spectral quanti- ties and influences them can therefore also be calculated self-consistently at each energy, and in turn related to the exact band structure and carrier’s population. This is increasingly important as transistors are scaled down and confinement makes the latter to become a strong function of the exact device structure and bias voltages. In the NEGF approach, the input scattering parameters are therefore not relaxation time or mobility—these are derived parameters that can be obtained as a result after convergence of the self-consistent loop and energy averaging— but directly the per- turbative Hamiltonian, e.g., the electron-phonon interaction Hamiltonian for pho- non scattering. The degree of accuracy in the modeling of this Hamiltonian results in a trade-off between simulation time and accuracy. We have developed such an approach to include phonon scattering (both elastic and inelastic) based on the self- consistent Born approximation and deformation potential theory [13, 14]. Finally, the methodology used to simulate Schottky contacts is similar to [16]. The Schottky barrier is added as a boundary condition in the source and drain poten- tial. A potential equal to VSB = –q*(SBH – (ECB – EF)) (2.6) is added to the source and drain potentials, where EF is the Fermi potential related to the doping in the Si body, and ECB and SBH are respectively the bottom of the conduction band and the Schottky barrier height value in bulk silicon. This allows one to take into account the increase of the SBH due to the increase of EC through quantum confinement, which has been shown to be the dominant change in small cross sections. Note, however, that this is a worst-case scenario, as other effects should slightly counteract this increase of SBH [17]. We have neglected these effects, however, due to the lack of experimental studies on the SBH values in nanoscale Si devices and the fact that the trends should not change fundamentally with a change of a few tens of meV, as we have observed when comparing barriers differing by hundreds of meV [6, 8]. The conduction band edge in the Schottky metal, ECSB, is assumed to be constant and a few 100 meV lower than the source and drain Fermi level in order to ensure sufficient injection (and independent of the exact band edge level of the metal) of carriers in the device. 2.2 GATE COUPLING OPTIMIZATION IN NANOSCALE NANOWIRE MOSFETs: ELECTROSTATIC vs. QUANTUM CONFINEMENT Using our simulation tools, we now investigate the effects of electrostatics and quantum confinement in order to find an optimal cross section size for 10 nm channel length nanowires. Figure 2.1 shows the maximum film thickness that can be used vs.
- 53. 32 High-Speed Devices and Circuits with THz Applications the channel length for one to four gate architectures following classical electrostatic theories [18] and for an equivalent gate oxide thickness (EOT) of 0.5 nm. It is based on the natural length λ that scales down with the number of gates ng: n t t t t n t EOT t EOT EOT t 1 1 si g ox ox si si ox si ox si g S O S O si si si S O ox ox i i i 2 2 2 λ = ε ε + ε ε = ε ε + ε ε ⋅ ⋅ = ε ε (2.7) For given values of Si and oxide thicknesses (tsi and tox, respectively) and permit- tivities (εsi and εox), a minimum channel length of at least 6*λ must be taken to ensure 6 8 10 12 14 16 18 20 22 24 26 2 2.5 3 3.5 4 4.5 5 5.5 6 tsi (nm) Lmin = 6* λ(nm) (a) (b) ngate = 1 ngate = 2 ngate = 3 ngate = 4 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 × 1038 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 D(E) (/ev) in x = L/2 E (eV) All valleys First lateral subband FIGURE 2.1 (a) Maximum film thickness vs. minimal channel length for one to four gate architectures following classical electrostatic theories and for an equivalent gate oxide thick- ness (EOT) of 0.5 nm. It is based on the natural length λ (Equation (2.7)) that scales down with the number of gates ng. A minimum channel length of at least 6*λ must be taken to ensure good gate control and low short channel effects. (b) DoS vs. energy for a 4 × 4 nm2 [100] GAA nanowire. The peak structure is related to the splitting of the conduction band in subbands due to 1D confinement.
- 54. 33 FDSOI Multigate MOSFETs and Multibarrier Boosted RTFETs good gate control and low short channel effects. As can be seen for L = 10 nm a single gate device would require an EOT below 0.5 nm or a Si film thickness below 2 nm. Both options must, however, be discarded due to quantum effects. Due to tunneling, a physical gate oxide thickness tox below 1.5–1 nm must be excluded to avoid high leakage due to gate tunneling currents. As gate control does not depend on tox alone but on tox/εox, a high-k dielectric with a significantly higher permittivity than SiO2 can achieve an equivalent oxide thickness (EOT) lower than this tox value. However, due to quantum confinement in film thicknesses of a few nm, a dark space region (the electron channel is not directly at the Si-oxide interface but at a depth td in the Si film) and a reduction of the DoS are observed [19]. Both effects tend to reduce the intrinsic gate capacitance and therefore the gate coupling. In order to take this effect into account, one can replace EOT by an equivalent capacitive thickness CET in Equation (2.7). The point is that CET tends to saturate when EOT is very small because dark space and DoS reduction does not scale down with EOT, so that even if EOT tends to 0, a minimum value of CET is reached [19]: CET CET EOT t ( 0) 0.55 nm d Sio Si min 2 = → = λ ⋅ ε ε ≈ (2.8) Because of quantum confinement (td 0) and the low 1D DoS (λ 1), it is not possible to have a better electrostatic control of the gate to the channel in nanowires of small cross sections than that achieved with an SiO2 oxide of thickness CETmin, even if one could use an “ideal” gate dielectric with infinite permittivity. The value CETmin = 0.55 nm is obtained for Si by assuming td = 0.8 nm and λ = 0.5 at high Vg, which compares well with our simulation results for cross sections between 2 × 2 and 4 × 4 nm2 and EOT smaller than 1 nm [19]. Concerning tsi, it is usually accepted that below 2 nm of film thickness the dependency of bandgap, and therefore threshold voltage, with tsi related to quantum confinement is too strong and would lead to too much variability [20]. The smaller the cross section, the larger the bandgap mismatch is for a given diameter variation, which would arise, for example, from process variability. This can be observed in Figure 2.2, which shows bandgap increase extracted from our 3D-NEGF simulations vs. the diameter reduction Δtsi. It can be quite well explained by using a simple ana- lytical model of the energy level of a constant potential well with infinite potential barrier at the Si/SiO2 interface. Using the effective mass approximation (parabolic E-k dispersion relationship) in a device with film thickness tsi and width 2si, E1, the first level above the conduction band. EC, is then given by E t W E m t m w ( , ) 2 parab si si C y si z si 1 2 * 2 * 2 − = π + π (2.9) When the diameter of the cross section is smaller than 3 nm, however, the E-k dispersion relationship is no longer parabolic and a correction factor has to be taken into account in order to obtain accurate results [21], but the trend of very high band- gap sensitivity to the exact dimension in small cross section given by Equation (2.9)
- 55. Another Random Document on Scribd Without Any Related Topics
- 56. presumendo troppo aveva ardito eziandio acconciarsi il capo, e scioltasi i capelli ci aveva passato quattro volte e sei il pettine; ma di un tratto l'era caduto, e per quanto avesse brancolato diligentemente da per tutto non l'era riuscito rinvenirlo più. Povera fanciulla! Dacchè l'era tolto di compiacersi a contemplare la sua bella chioma, sentiva tanta consolazione a pettinarsela e a palparla! Appena conobbe il rumore dei passi paterni, per non lasciargli tempo di accorgersi dello sconcio ed affliggersene, disse: — Babbo, raccatta il pettine e finisci di pettinarmi tu. E Filippo lieto ci si provò subito: assorto nel piacere di far bella la sua creatura, non pensò ad altro. Intanto che la pettinava la mise a parte di quello giudicò necessario ch'ella sapesse; ed avacciandola poi, e sovvenendola a vestirsi, quando la mirò di tutto punto, presala sotto il braccio favellò: — Andiamo via, che la signora Isabella ti aspetta. Adesso viene la volta per Filippo ad industriarsi che la figliuola si accorga men che si possa della sua disgrazia, e questo fa removendo col piede gli ostacoli che loro si parano dinanzi, ovvero sospingendo lieve col gomito la figlia, ond'ella senza accorgersene li scansi, e creda potere procedere franca come se ci vedesse. Una favilla di amore come bene e quante anime accende! La guardia della porta del Castello, quando vide la fanciulla bellissima, che veniva via pari all'angiolo che si accosta a fare aprire le porte dell'inferno, trasse tutta fuori per contemplarla e per salutarla; e il caporale, ch'era da Barberino di Mugello, bel parlatore e qualche volta dicitore in rima, le favellò: — Deh! Eufrosina, tornate presto e non ci fate aspettare; voi lo sapete, come ci lasciate ci piglia il buio ed il freddo: Quando partite voi tramonta il sole, Le chiappa il freddo e van tentoni al buio Le anime nostre desolate e sole.
- 57. — Ecco, date retta a me, disse un altro soldato, che all'accento parve siciliano, io per me proporrei che ci avessimo a collettare, e li danari deste a me per far dire una messa a santa Lucia, onde rendesse la vista degli occhi alla buona fanciulla. Parve ch'egli accendesse un fuoco d'artifizio, sicchè si udiva da più parti: — O che le avrebbe a rendere la vista dei ginocchi? — To', questa è nuova di zecca; io ho visto sempre santa Lucia dipinta cieca, o come potrebbe dare agli altri la vista che non ha per sè? — E voi altri imparate quale sarebbe il sacerdote e quale il tempio dove celebrare la messa; prete il camerata Rosolino, chiesa l'osteria del Fico. — Io vo' dire la mia, vo' dire; propongo pertanto che noi abbiamo a digiunare un giorno per uno; così si risparmia quattrini e ci troviamo la devozione bella e fatta... — . . . . . . . . ma fiorentino Mi sembri veramente quando io t'odo, interruppe un livornese: costui di fatti veniva da Firenze: — E fermi, proseguiva, mettendosi la mano in tasca; io pago il vino per tutti, e ce lo beveremo alla prossima guarigione della nostra Eufrosina piena di grazia. — Magari! risposero a coro i camerati appuntando gli sguardi nella mano del livornese, il quale, poichè ebbe rovistato un pezzo, la trasse fuori mortificato, e disse: — Maledetto vizio di portare i danari alla rinfusa! Li perdo sempre. Tanto è, finchè non ci daranno moglie, noi altri soldati avremo sempre le tasche sfondate. — Largo allo Specioso! Giusto voleva dire; il lupo perde il pelo, il vizio mai; e chi tal disse, nacque a Pisa, dove dei fumi livornesi sono piuttosto invidiosi mordaci che severi censori.
- 58. Allora Eufrosina, ridendo lietamente, incominciò: — Peccato che tanto bella concordia deva andare a monte! Quanti siete? Non risposero, compunti da pietà, però che la domanda chiarisse lo stato deplorabile della fanciulla, che dopo poco ripeteva: — Insomma, quanti siete? O che mi toccherà riscontrarvi a tasto? — Otto; col caporale nove. — Ebbene, ecco un cavurrino, che a me cieca è riuscito trovare in tasca, mentre il livornese alluminato ha fatto fiasco... — L'ha avuta! gridarono attorno i soldati uccellando il livornese, il quale con ciglio e accento severi parlò: — Signori, non mi pare buona creanza interrompere chi parla, massime quando l'oratrice è una gentil donzella. — Ora, continua Eufrosina, in questi due franchi entrano tre e più litri di vino; bevetene un bicchiere avvantaggiato per uno alla mia prossima salute. Qui ruppe tale un rombazzo di voci per applaudire Eufrosina, che il colonnello del presidio, immaginando che o qualche principe, o il re stesso si fosse fatto a visitare il castello, tirò via di uno strettone il piede dalle mani del barbiere, che gli tagliava i calli, e con una gamba calzata e l'altra scalza corse per essere primo ad ossequiare, mentre il comandante, pauroso che la rivoluzione fosse entrata in Castello, si rimpiattava sotto il letto della moglie puerpera. Eufrosina aveva operato da quella arguta giovane che era; — tanti capi, tante opinioni in Italia, così in caserma, come in mercato e in Parlamento; ed ogni dì crescono, perchè durano fatiche da cani ad insaccarci tutti nella unità dei regolamenti piemontesi e non ci riescono: unico efficace fattore della unità italiana fin qui il fiasco; Asti e Artimino, Chianti e Barbèra si riconobbero senza ostacolo di progenie latina; enotrii tutti, e si mescolarono fraternamente dentro lo stomaco dei deputati italiani.
- 59. Filippo mise la figlia nelle braccia di donna Isabella; nulla parlò; la guardò solo con uno sguardo che nè parole, nè colori valgono a dipingere; però il poeta lo tace, ed il pittore Timanto lo nascose sotto il velo, quando ebbe a effigiare Agamennone assistente al sagrifizio della figliuola Ifigenia. Ogni momento Filippo ripeteva doversene andare, ed era sempre lì; moveva verso l'uscio e poi tornava indietro; fin quando ebbe sceso mezze le scale rifece gli scalini per ribaciare la sua cara, la sua divina creatura. Nel rientrare in Castello Filippo, al caporale di guardia che gli andò incontro verso la porta, disse sentirsi rifinito, ed era vero: pel quel giorno non poteva più strascinarsi dietro le gambe, epperò avrebbe portato le sue robe alla Eufrosina alla domane per tempo, onde aver libera tutta la giornata; volesse avvertirne la guardia, perchè non gli avesse, come a caso insolito, a porre ostacolo. — Andate franco, sergente, lasciatene il pensiero a me. Tuttavia Filippo, comecchè a stento, andò a licenziare il rinforzo mandato dal comandante alle carceri, e fece in compagnia del suo secondo la visita dei prigionieri, o piuttosto la principiò, che appena ebbe trovato modo per susurrare nell'orecchio a Curio: stasera! — disse al secondo: — Io non mi reggo ritto, badate a chiudere con la solita diligenza; quando avrete finito, venite a mangiare un boccone meco, mi terrete un po' svagato, chè dall'angoscia mi sento morire. Il secondo non se lo fece ripetere due volte, e rispose: — Animo, su, sergente, dopo il tempo cattivo viene il buono, come dice l'uomo del Bosco. Pertanto, dopo tirati i chiavistelli e chiusi i lucchetti a norma dei veglianti regolamenti, egli se ne andò a trovare Filippo salendo le scale a quattro a quattro; questi, che si era buttato sul letto, scese subito e si mise a tavola col secondo; alquanto cibo gustò, al bicchiere pose appena le labbra, poi sbadigliando disse:
- 60. — Ho più voglia di dormire che di mangiare; continuate il vostro pasto, io lo ripiglierò riposato; lasciatemi la parte del pane e del companatico; il vino finitelo pure, chè di questo ce ne ho dell'altro. Veramente il secondo si era proposto non tenere lo invito, anzi aveva solennemente deliberato in cuor suo serbargli anche la metà del vino; ma sì, ciliege, bugie e bicchieri di vino vengono al mondo come Giacobbe, agguantando il piede di Esaù. Innanzi che fosse andato in fondo della boccia, il capo del secondo dondolava più della cima di un cipresso quando tira libeccio. — È meglio che anch'io me ne vada a letto, disse fra sè, ed era risoluzione piena di giudizio; peccato che la pigliava un po' tardi, perchè la seggiola, in quella ch'egli stava per alzarsi, gli scivolò di sotto, ed ei cadde lungo e disteso sul solaio. Al rumore del tracollo Filippo schiuse alquanto gli occhi, e visto il caso mormorò: — Sta bene dove sta, e voltatosi su l'altro fianco si diede in balìa del sonno. Quando si risvegliò, chè a buona caviglia aveva legato l'asino, stava per sonare l'ora della visita notturna alle carceri; bevve un bicchiere di vino, che levò da un armario per darsi un po' di fiato e poi mise mano a spogliare l'addormentato dei suoi panni, il quale voltato e rivoltato tronfiava, non però risentiva: spogliato ch'ei fu, Filippo fece delle sue vesti un fastello, ma consideratolo bene, segnò col capo tale atto da destra a sinistra, che parve mano che cancelli un rigo di su la carta; allora sciolse il fastello, ed esaminati meglio i panni gli parve avere il fatto suo; invero, essendoseli provati, trovò che sopra i suoi gli andavano a pennello, poichè il secondo fosse alquanto più atticciato di lui e quasi complesso quanto Curio. Sicuro, a chi lo aveva in pratica sarebbe parso più grosso, ma al buio non ci si bada, e poi avrebbe scansato che mettessero troppa attenzione sopra di lui; a questo fine tirò giù il lucignolo nel luminello della lanterna, tanto che mandasse un sospiro di luce, e così alla prigione il buon uomo avviossi: i passi alla lontana ei misurò in modo che al suo appressarsi la sentinella avesse trascorso oltre la porta, voltando le spalle; allora guizzò dentro l'androne dove mettevano capo talune
- 61. celle; affrettasi a quella di Curio, e aperta appena la porta gli domanda ansioso: — Sei pronto? — Si. — Aspetta, e così dicendo presto presto pon mano a spogliarsi; e poichè l'altro trasecolato esclama: — Ed ora che fai? Risponde: — Silenzio e obbedisci; mano a mano che mi spoglio io, vestiti tu. Siccome Filippo, comecchè si spogliasse, appariva sempre vestito sotto, Curio cominciò a capire. Filippo, considerando poi che la faccenda tirava troppo in lungo: — Esci, gli disse, finirai di abbigliarti fuori; rannicchiati in un canto; mentre ti vesti continuerò la visita. E come ordinò fu fatto; nel richiudere la carcere di Curio sbatacchiò gli usci con tale fragore che ne rintronarono i muri del casamento. Taluno dei prigionieri vedendo comparire Filippo solo, e rincrescendogli, però che il sotto carceriere, secondo il consueto, gli avesse promesso portargli robe vietate, si attentò domandare: — O di Pietro che n'è, che stasera non si vede venire? E Filippo, con voce e cera da Lucifero: — Che v'interessa sapere queste cose? O mirate un po' che mi bisognerà tenere in giorno i signori carcerati di quanto i superiori ordinano e disordinano? Lo so bene che a voi altri, cattivi soggetti, quando vi menano in prigione vi sembra andare in villeggiatura, e Pietro vi aiuta a bucare il regolamento: ma questa bega ha da finire... e finirà... Mortificato il prigioniere, torna chiotto chiotto a sdraiarsi sul pancaccio, e Filippo, a cui doleva sostenere la parte dell'uomo di
- 62. arme, non che per mitigare cotesta infinta asprezza, seminava sigari, conforto da carcerati. Filippo, dopo abborracciata la visita, si accosta a Curio e così gli favella sommesso: — Levati, piglia la lanterna, escirai primo, io ti terrò dietro coprendoti con la mia persona. E così fu fatto; la sentinella, la quale non aveva veduto se fossero entrati due uomini od uno, non si addò di nulla; e i nostri amici, accelerando il passo, presto si furono ridotti a casa. — Barba bene insaponata è mezzo fatta, — mormorò con lieta voce Filippo; ma per la commozione tremando, si pose a sedere sul letto asciugandosi il sudore. In breve però fu in piedi da capo e disse: — Curio, ora andiamo a fare il fagotto di Eufrosina. Mentre Curio stava per entrare nella camera di lei, incespicando nel corpo di Pietro fu ad un pelo di dare della faccia per terra. — Questo ch'è? — È Pietro spogliato per vestir te. — Vive? soggiunse Curio atterrito. Filippo, attanagliandogli con la mano destra il braccio: — So, per lo meno quanto tu, gli rispose alterato che libertà a prezzo di delitto non è libertà... dorme... ubbriaco. Empirono una balla di robe senza pigiarvele, giovando che facessero maggior volume: portando poi la balla nella prima stanza, Curio, nel rivedere Pietro steso sul solaio, osservò: — Non sarebbe meglio portarlo sul letto e coprirlo? — Lascialo stare, che sta bene. Quando ti trovi per le mani una faccenda di suprema importanza, qui intendi tutto, e non confonderti in altro: anche la pietà in mal punto può nuocere. Pietro al pancaccio ha fatto il callo; tra il pancaccio e il mattonato non ci corre un tiro di cannone, e tu l'avresti a sapere; smovendolo potrebbe urlare.
- 63. — O a mettergli adagio un guanciale sotto il capo? — No signore, tu buttati sul letto e dormi; io ho dormito tutto il giorno per vegliare. — No, vacci tu piuttosto. — Ho dormito tutto il giorno per vegliare, ti ripeto: più tardi farai a modo tuo, adesso obbedisci. Giusto nel punto in cui si apriva il Castello, Filippo si trovò alla porta con Curio dietro, portatore della balla sopra l'omero manco, celando per questo modo la faccia a chi stava fuori della porta della caserma; e secondo la promessa ci stava il caporale, che appena ebbe scorto Filippo gli andò incontro salutando: — Buon giorno, sergente. — Buon giorno, caporale. — Tanti saluti e poi tanti da parte mia alla cara Eufrosina. — Presenterò le vostre grazie: addio. — Sergente, sentite una cosa, quando tornate, mi promettete di confidarmi dove dimora adesso? — Ve lo prometto: addio. — Non crediate mica per cattivi fini; solo per mandarle di tratto in tratto i miei versi e qualche fiore. — S'intende... diavolo! addio. Senz'altro intoppo, alla fine vennero all'aperto; non si scorgendo attorno anima viva, affrettarono il passo per la via Legnano: appena giunti a un terzo, ecco occorrere loro persona che parve sbucata dal centro della terra, e rasentatili salutò: — Buon giorno e buon anno! E Filippo: — Il santo? — Santo Ambrogio da Milano, e vienmi dietro accosto al muro.
- 64. Dopo camminato un pezzo, lo sconosciuto, che precorreva, picchia con le nocche su di un portone da rimessa, che si apre, e dietro a quello sparisce. Filippo e Curio, arrivati a cotesto punto, assai sbigottirono non vedendo più alcuno, se non che a rimettere loro il cuore in corpo una voce parlò: — Buon giorno e buon anno. — Il santo? — Santo Ambrogio da Milano. — Entrate. Entrarono: l'uscio si richiuse, ed essi si trovarono dentro un fienile ingombro di legna e di strame; di corto si mostrò un uomo di faccia gioviale che li invitò a bere un bicchiere di acquavite per cacciar via la mattana, ed a mangiare un boccone di pane; finito il sobrio pasto, costui disse: — Voi altri deporrete qui la balla, e m'indicherete dove ha da essere recapitata, che noi ce la porteremo con le debite cautele, s'intende. Filippo glielo disse. — Bene, adesso spogliatevi dei vostri panni e vestite questi da barocciai; ecco due perrucche; giovanotto, giù i baffi; di biondo trasformatevi in nero; voi, vecchio, di grigio ferro vi muterete in argento schietto; ci guadagnate un tanto; tra poco arriverà qui un branco di bestie e di cristiani, e voi v'imbrancherete con gli altri; vi affideranno un baroccio; a condurre un cavallo poco ci vuole; le nostre povere bestie, affrante dalle fatiche, voi non proverete bucefali; andate dove gli altri andranno: non domandate, non rispondete; e sarà spediente che voi non vi mettiate uno dietro l'altro, lasciate tra voi quattro barocci o cinque; e addio; lavorate pulito. Dopo mezz'ora la contrada andava sossopra da un fracasso di cavalli, di barocci e di vetturali; se avessi pretensioni alla fama di storico veridico, dovrei aggiungere: e di bestemmie, perchè, io non so la cagione, la plebe tutta, ma i vetturali in particolare, hanno lite
- 65. perpetua col paradiso e con chi ci è dentro. Lascio andare l'acqua per la china, ma per me ripeto che se la plebe non crede in Dio e bestemmia, è stolta; se ci crede, scellerata. In tanta gente, in mezzo a cotesto bailamme, Filippo e Curio si confusero con gli altri, senza che veruno se ne addasse, e ciò tanto più potè farsi, che due barocciai, i quali erano d'intesa, entrarono nel fienile, e dati i debiti segni, si convertirono in facchini, ammonendo sommesso i due fuggitivi che pigliassero posto ai loro barocci. Parte dei barocci caricò strame, parte legna, di questi i barocci di Curio e di Filippo: poi si misero in moto per andare: alla prima svolta il guidaiolo capo del traino a voce alta ordinò: — Chi ha strame in casa Berretta; chi ha legna alla prefettura. Alla prefettura! pensarono d'accordo Curio e Filippo, di cui i barocci portavano legna, ma curvarono le spalle e proseguirono senza fiatare. Di vero fermaronsi davanti alla parte postica del palazzo della prefettura, e tosto diedero mano al discarico: indi in breve fu un brulichio, uno andare e un venire da disgradarne le formiche. Qui ad un tratto si presentava a Curio ed a Filippo l'uomo del fienile, il quale, mentre finge dare loro ordini pel trasporto, aggiunge sommesso: — Ora smettete il mestiere di barocciaio per pigliare quello di facchini; caricatevi un fascio di legna sopra le spalle e salite su franchi; troverete qualcheduno per le scale che vi guiderà. I nostri eroi, carichi come muli, seguitarono i compagni che osservarono avviarsi su per le scale, però che altri scendevano per recarsi alle cantine, ovvero alle cucine; ma pei nostri eroi, rifiniti dai patimenti, non fu piccola fatica portare quel tocco di fascio di legna in soffitta; venuta loro meno la balìa, si buttarono a sedere sopra gli scalini a riprendere fiato, mentre i compagni scendevano vociferando, e taluno motteggiandoli; riconfortati alquanto, scesero anch'essi pensosi se ad un secondo viaggio sarieno loro bastate le forze, quando ecco, mentre meno se lo aspettavano, apparve loro
- 66. sopra la porta del secondo piano un vecchio vestito civilmente che li salutò col saluto convenuto: Buon giorno e buon anno. Quelli avendo chiesto il santo, udirono rispondersi: Santo Ambrogio da Milano. Invitati entrarono in casa al vecchio; quivi per tutto cotesto giorno rimasero, alternando insieme molti e bei ragionamenti che non importa riferire; basti sapere ch'egli era un patriotta della stampa antica; la fortuna lo aveva fatto padre di un giovane che un dì, ardente garibaldino, per vanità infelice aveva fatto voltafaccia, e, Saulo alla rovescia, perseguitava ora i repubblicani coll'impeto col quale un dì aveva parteggiato per loro; infatti di presente si trovava a Lugano per tenerli di occhio; ma il vecchio si era mantenuto per genio proprio e per pericoli comuni durati per la libertà legato ai vecchi amici, onde questi non avevano saputo escogitare asilo più sicuro ai fuggitivi della casa del delegato capo di polizia, occhio diritto del prefetto e mignone dello stesso ministro dello interno, il quale aveva aperto con questo oggetto della sua tenerezza un conto corrente d'infamie e di croci; circa a quattrini adagio; ma al delegato di questi importava poco, perchè se li pigliava da sè. — È mio figliuolo, diceva il vecchio con un sospiro, l'ho unico sopra la terra, e odiare non lo posso: il mio dovere m'impone di stargli a canto, tentare di ricondurlo nel diritto sentiero; e in ogni caso, quanto più posso, emendare il male ch'egli fa: prima che finisca la settimana io non lo avrei ad aspettare, ma vado sicuro che lo richiameranno prima per isguinzagliarvelo dietro, chè senza di lui non sanno a quanti dì viene san Biagio. Ora lasciatemi andare a chiudere il cancello di mezze scale, e prima che si faccia più buio bisogna che vi accomodi nella soffitta, dove ho ammannito quanto ho potuto, stante l'angustia del tempo e la necessità di non destare sospetto: adattatevi e compatite; non fumate, non accendete lume, procurate non fare rumore, camminate scalzi; avvertite che qui in casa molta gente ci bazzica, e la serva fino a sera, chè allora va a dormire a casa sua; quando potrò verrò a vedervi, e se vi manca qualche cosa ve la provvederò; per la strada si assettano i basti. Passata la prima sfuriata, ci riuscirà facilissimo più che altri non pensa cavarvi da Milano e dal regno. Noi siamo potenti e molti; di
- 67. vero, chi mai potrebbe capacitarsi che vi abbiamo trovato asilo proprio su la testa del prefetto, anzi nel giaciglio del segugio che vi avrebbe a scovare? I successi si svolsero giusto nel modo presagito dal vecchio; il suo figliuolo, richiamato, tornò due giorni dopo dalla Svizzera, il quale ridottosi a parlamento col prefetto, col generale di divisione, col procuratore del re e col questore, si condusse a casa in fretta e in furia per rinnovare la biancheria della valigia, desinare e partire. Mangiò appena, le mani gli tremavano per la commozione; narrò, il governo sottosopra per la fuga del soldato condannato a morte e del carceriere; non sapeva distinguere chi più procedeva smaniosa in questa faccenda, o l'autorità civile o la militare; entrambe parergli frenetiche: se non giungeva a dare uno esempio solenne, addio disciplina; il regolamento urlava carne peggio di un lupo affamato: egli aveva rimesso il cuore in corpo a tutti: essere corso fra loro un patto: se a lui fosse riuscito in capo ad una settimana reintegrare i contumaci in Castello, gli avrieno impetrato dal governo una questura e la croce dei santi Maurizio e Lazzaro. Bel colpo, babbo mio! bel colpo! — Bada, gli notava il padre, bada, figlio mio; ho paura tu abbi preso una gatta a pelare; i repubblicani sono potenti; almeno se ne vantano. — Eh! dove sono adesso i repubblicani? Repubblicani erano i giovani, ma il governo li pesca alla mazzacchera delle preture, degli assessorati, delle delegazioni, delle questure; qualcheduno, che va per la maggiore, si abbarbaglia con lo specchietto delle prefetture; due l'hanno, quaranta l'aspettano; un flagello allunga il collo e pigola da mattina a sera; per me, vedete, con metà meno di brumeggio mi farei forte di chiapparvi una retata di deputati. Nè alcuno voglia osservarmi che sembra strano un tale linguaggio in bocca a costui, colpevole anch'egli, però che tale lebbra invada appunto l'anima venduta, la quale negli altri disprezza o aborre quello che in sè o non vede o non sente.
- 68. — Ci sono i vecchi, soggiunse il padre; ed essi non hanno speranze, ed anche meno timori. — Vecchi! una manata di sgangherati, conti della sputacchiera, duchi del cristere; cenere, cenere, soffiaci su, e andranno dispersi: afflavit Deus et dissipati sunt. — Ma hai pensato che se li agguanti, tu li meni al macello... — Babbo, mors tua vita mea; due più, due meno, non saranno la rovina nel mondo, e poi siamo troppi; non so e non credo che ci siamo condotti a vivere insieme per aiutarci, certo egli è che adesso stiamo insieme per divorarci. — Come così è, riprese il padre visibilmente commosso, io vo' tentare se mi riuscisse buscarmi un cento di lire a man salva: al caffè dove vado la sera ci è un gran chiacchierio su questo proposito; chi dice che li ripescheranno, chi no; tanto si sono incaloriti su tale contrasto, che ci sono già corse scommesse, ed altre ce ne correranno. — Scommettete pure che saranno presi, e figuratevi di avere i quattrini in tasca. — Dunque scrivimi quanto più spesso puoi, e tienmi bene informato, perchè, secondo gli avvisi, scommetta pel sì, o alla peggio anche pel no, onde non fare all'ultimo la figura dei pifferi di montagna. E ti tratterrai molto fuori? — Di una settimana mi avrebbe a bastare, perchè per quanto mi è riuscito conoscere spillando dintorno, fuori del confino non dovranno essere andati; staranno nascosti nel contado. Al vecchio veramente qualche scrupolo aveva trottato per la testa, ma le parole del figlio gli serenarono l'anima: egli non tradiva costui, bensì avrebbe tradito i miseri che aveva accolto nelle braccia; al figlio non noceva, all'opposto, seminandogli di triboli l'atroce cammino, sperava disgustarlo, e dato il caso riscattarlo; in ogni modo quelle due vite innocentissime, salvate e offerte a Dio, avrebbero giovato a impetrare la sua misericordia sul figlio perduto,
- 69. imperciocchè il vecchio repubblicano era, ma poneva ogni sua fidanza in Dio, e nel ben fare lo confermava la fede ch'ei lo vedesse e lo approvasse. Le lettere del figliuolo gli giungevano quasi ogni giorno, e per esse veniva a conoscere quanto stupida e volgare cosa sieno le reti che la polizia presume intrecciare con arguto magistero: nei prati ov'ella mena la falce non crescono altr'erbe che femmine da partito, pollastriere, lenoni, osti, barbieri, e soprattutto preti; senza di questi non raccoglierebbe una boccata di fieno. Il presuntuoso bargello scorrazzava a destra e a mancina come il cane con la polpetta in corpo; ogni momento stava lì per lì per acchiappare la preda, e poi stringeva mosche; certa volta corse con la lingua fuori fino a Domodossola; adesso non gli sguizzavano più; certi i segnali; sicuro il covo; stende la mano e piglia un cappellano e la moglie dell'organista scappati insieme; scattò di un pelo che il bargello scorrubbiato non tirasse il collo a tutti e due: molto più ch'entrambi con le mani su i fianchi urlavano: — O lei come ci entra nei fatti nostri? Chi le dà noia? Facciamo col nostro e non diamo fastidio a nessuno. Il peggio fu, quando ricondusse la moglie al marito (chè il prete lasciò ire per non entrare in disgrazia al ministro), dacchè questi gli si avventò come un basilisco gridando: — O chi le ha detto di pigliarsi questi pensieri del Rosso? Chi l'ha incumbenzato di andarmela a cercare? Chi di riportarmela? Lei se la infarini e lei se la frigga. E qui gli sbatacchiò la porta sul muso. Allora la donna si mise a guaire: — Ohimè! chi mi farà le spese? Chi mi vestirà, chi mi albergherà, chi mi nudrirà? Ora il marito mi scaccia, il cappellano non mi vorrà più a cagione dello scandalo; io verrò a stare con lei; lei è obbligato per coscienza a mantenermi, e per legge.
- 70. Il delegato scappò via per non darsi del capo nel muro: infellonito, frusta, rifrusta, da per tutto fruga, ci adopra l'estremo della sua malizia; invano; coloro ch'ei cercava stavano tranquilli a dormire in casa sua: scornato, ebbe a tornare con le pive nel sacco. Mentr'egli entrava in Milano, i nostri eroi ne uscivano. Molte le cautele, gli accorgimenti infiniti adoperati per trarli fuori di pericolo, e soprattutto non laudata quanto merita la fede inconcussa degli amici; io mi passo dal descriverli; basti al lettore che Filippo e Curio, travestiti da calderari istriani, passarono per Rocca di Anfo; rividero fremendo di pietà e di rabbia tutti i luoghi consacrati dall'altrui sangue italiano e dal proprio: appena giunti a Trento trovarono modo di avvisare Foldo, il quale non mancò di mandare subito alla signora Isabella il filo di pane co' due franchi dentro; di che se si facesse festa grande in casa di lei lascio che il lettore immagini: avresti giudicato che nel cuore della madre di Curio dovesse essere ben morta ogni litizia, e non fu così, perchè il cuore materno si accende tanto per una, quanto per cinque fiaccole: ed ella godè uno dei più bei giorni che avesse rallegrato la primavera della sua vita, sentendo a prova come la coppa della gioia e del dolore non si vuota mai tanto, che qualche gocciola in fondo non ne rimanga sempre. Da Trento scesero a Trieste, dove in grazia delle cure amorose del signor Giamari, greco, della libertà di tutti i popoli amante come fratello, di quella della Grecia e dell'Italia come figlio, ebbero comodità imbarcarsi per Londra; di questo ricevè lettere nunziatrici Isabella, le quali la confortavano a starsi di buono animo, confidare in Dio, che li avrebbe sovvenuti anche in avvenire. Ormai non potersi revocare più i mattini sereni; tuttavia dopo un giorno procelloso gli occhi si consolano a vedere il tramonto del sole circondato da mesti raggi, e l'anima ne gode. Io, scrittore, non conosco cosa nel mondo della quale sia stato detto tanto bene, ovvero tanto male, a seconda degli appassionati interessi, come delle sètte segrete: i governi lungamente mi perseguitarono, e ferocemente, pel sospetto che io fossi capo o parte principale di taluna di quelle: la verità è che io mi tenni fuori di
- 71. tutte; privato cittadino, sovvenni coll'opera e col consiglio, impiegandoci non pure le mie facoltà, ma altresì quelle di parecchi amici, quanto ci parve magnanimo, libero e onesto. Di questi amici alcuni morendo portarono seco nell'altra vita l'anima dirittamente intera, ed io li piango; altri durano tuttora nella vita, ma hanno fatto getto dell'anima intemerata, — e di questi piango troppo più. Ora che io e voi siamo giunti dinanzi la porta della morte e teniamo in mano il battente per picchiarci che ci apra: dite, vecchi compagni della mia gioventù, valeva il pregio avvilirvi? Il retaggio che lasciate ai vostri figli, unico inalienabile, è la fama contaminata. Ma tornando a parlare delle sètte segrete, è giusto che si affermi come, nonostante gli errori molti e qualche colpa commessa, elle fossero per la libertà ciò che furono le catacombe per la religione cristiana; loro mercè si mantennero accesi sopra il medesimo altare con fiamma congiunta l'amore della patria e l'odio contro lo straniero; colla parola li confessarono, col martirio li suggellarono; ed anche questo altro so, e veruno me lo potrebbe negare, che molti italiani vanno debitori all'opera delle sètte segrete della loro vita. — Com'essi l'abbiano spesa non considero, non voglio considerare; noi compimmo il nostro dovere; — non ora, ma più tardi, per quelli che mal vivendo perderono le cause del vivere, non può mancare chi in loro potendo più di loro li interrogherà: e voi come adempiste il vostro?
- 72. Capitolo XXIII. . . . . . . . . . . . . . . . . Più brevi sì, ma non però men gravi di quelli di Ulisse furono gli errori pei quali si avvolsero Curio e Filippo. Tutto essi provarono; l'ira immane dell'oceano, in mezzo a cui essi si conobbero troppo meno di atomi travolti nella immensità dello spazio: anzi più che ad altro andarono debitori della propria salvezza alla loro nullità: le ruote del carro non giungono a stritolare il granello di arena sul quale trapassano; videro la tremenda rabbia della natura quando si agita a rompere le leggi le quali tengonla infrenata come schiavo che tenti spezzare la sua catena, e i furibondi spasimi di lei allorchè intende ribellarsi alla tirannide di Dio che la flagella; — videro spaccarsi montagne, e dai fianchi lacerati avventare fiamme; — sentirono traballarsi sotto le gambe la terra, a mo' di creatura che ferita nel cuore baleni per cadere; — sparire a un tratto fiumi, e ad un tratto irrompere moltitudine di acque schierate come guerrieri in battaglia; — li atterrirono serpenti a sonagli lunghi ben diciotto piedi, e torme di alligatori andare a processione a guisa di formiche; i vermi stessi e i bruchi mezzo braccio e più: natura piuttosto immane che grande; paurosa, non bella. Alberi due volte tanto i nostri altissimi campanili. Conghi, tigri, leopardi, pantere, orsi, copracappelli, insomma una sterminata famiglia di enti maligni mettere in comunella la ferocia e il veleno. E gli uomini? Gli uomini trovarono tali da fare diventar rossa per vergogna la faccia ai coccodrilli se non l'avessero corazzata di scorza. Peggiori degli antichi lestrigoni i comanchi, i quali se divorassero interi i prigionieri è ignoto, tuttavia sappiamo che li scalpellavano di certo, ovvero svellevano dal cranio la pelle co'
- 73. capelli, e se ne ornavano la persona, a imitazione delle nostre croci; e si narra di un giovane ventenne, il quale portava penzoloni da un anello saldato intorno al braccio manco ben dodici di queste capelliere svelte di propria mano dal capo dei suoi nemici; — giovanetto di belle speranze senza dubbio costui. La umanità da per tutto è la medesima stoffa, gli uomini fogge tagliate dal costume diverso. Fra i popoli che in America si dicono civili, o almeno non selvaggi affatto, si praticava allora e tuttavia si pratica la legge del Lynch; e i nostri personaggi, approssimandosi a Brownsville, terra sul Rio Grande, la quale dopo il trattato Guadalupa-Hidalgo segna il confino tra il Messico e il Texas, si trovarono presenti ad un fatto che vale il pregio ricordare. In mezzo di una macchia folta videro tempestare un branco di bestie, uomini e cani frugando bramosamente per cespugli e per greppi; su quel subito giudicarono dessero la caccia alla pantera, ma in breve furon tolti d'inganno, imperciocchè si udissero disperate grida uscire dal prunaio, dove slanciavasi di corsa una maniera di colosso umano, ricomparendo di corto con una mano alla strozza di un uomo e con l'altra a quella di un cane di ferocissima razza, costà noti col nome di blood-hound: venuto allo aperto costui arrandellò il cane lungi da sè; il cane rotolando ringhiava minaccioso, e aveva ragione da vendere, perciocchè essendo stato educato con parecchi altri colleghi dagli uomini a lanciarsi addosso agli uomini, e lacerarli, ora dell'opera meritoria si trovava a ricevere quella razza di ben servito; e ciò, sebbene bracco, gli pareva ostico. Per senso di carità ci sarebbe da mettere l'esempio davanti gli occhi dei questori, assessori, apparitori, e di altri siffatti tutori e curatori della pubblica sicurezza, ma è tempo perso, mastini e questori non imparano mai nulla. Ai polli soprasta la stella della strozzatura; ai tordi l'altra dello spiedo; agli sbirri, finchè mondo è mondo, predomina l'astro della sassata e del bastone: così vuole il destino! Intanto il colosso si era vôlto alla terra traendo seco attanagliato il prigioniero, mentre la turba gli moveva dietro con schiamazzi e fischi. Curio e Filippo imbrancaronsi con gli altri, e curiosi di sapere la cosa, interrogati quanti più poterono spillarono: il colosso venuto in
- 74. lite col mastino essere il capitale magistrato della terra, cioè lo sceriffo; il prigione un indio bravo, il quale aveva allora allora fesso il ventre a un povero giovane del Kentuky, che spazzando davanti la porta del caffè dove stava per garzone, aveva per disgrazia buttato un po' di spazzatura su le scarpe di lui; il popolo infellonito volere mettere in pezzi l'omicida, che si era dato alla fuga per campare la pelle, ma lo sceriffo, e più il cane, gli avevano tronco il disegno. Lo sceriffo condusse (che senza offesa del vero non si potrebbe dire strascinasse, dacchè l'indio andava così di buon grado che non pareva fatto suo) il prigioniero dinanzi al cadavere del garzone, che giaceva supino in mezzo della strada dentro una pozzanghera di sangue, e di subito mise mano allo interrogatorio. — Conosci questo uomo? — Sì. — Chi lo ha ammazzato? — Io. — Come puoi provare di averlo ammazzato? — Hanno visto tutti. — Si, si, abbiamo visto tutti, urlava la turba, benchè pochi fossero quelli che si trovarono presenti al caso. — Perchè? — Perchè mi è parso di ammazzarlo; — perchè stamani ho bevuto acqua di fuoco più del consueto; — perchè col buttarmi la spazzatura addosso ha inteso insultarmi. — Dunque tu convieni che devi essere punito? — Siccome per conchiudere l'affare non è necessario il mio consenso, così chiedo astenermi da rispondere. — Come ti piace; ed ora, riprese a dire lo sceriffo volgendosi alla turba, tutti quelli che giudicano doversi impiccare... come ti chiami? — Che fa il nome alla cosa?
- 75. — Nulla; per la formalità, capisci! — A Lampasas mi chiamavano Lumediluna. — Sei cristiano? — Si; mi battezzarono a Georgetown. — E allora come t'imposero il nome? — Dianoro Bermudez. — Bene, prosegue lo sceriffo, tutti quelli che giudicano aversi a impiccare Dianoro Bermudez, del paese di Lampasas, passino dal mio lato sinistro. Non uno rimase dal lato destro del degno sceriffo, perfino i fanciulli, i quali per via della età quello che facessero ignoravano. — Tu lo vedi da te, o Dianoro, che adesso ti tocca a pensare sul serio di morire, disse lo sceriffo. — È cosa vecchia; ci pensai da quando nacqui. — L'uomo prudente è come la tavola degli osti, sta sempre apparecchiato: possiamo andare. Lo sceriffo s'incamminò verso la campagna; dietro lui Dianoro, e dietro Dianoro le turbe; venuti allo aperto occorse loro un bello, grande e forte cedro rosso, del quale si servono per fare le bacchette ai lapis; lo sceriffo, dopo averlo ben bene squadrato, domandò: — Dianoro, di' su, questo cedro non ti parrebbe al caso? — Per me, me ne lavo le mani; io non ci entro. — Ma... mi pareva che per qualche cosa ci entrassi anco tu. Tacque il dabbene sceriffo, e presa senz'altro indugio la corda si mise ad armeggiare per foggiarla a nodo scorsoio. Dianoro stava a guardarlo tranquillamente, ma vedendo poi che non veniva a capo di nulla, gli levò la corda di mano dicendo: — Si conosce chiaro che voi non siete del mestiere; lasciate fare a me.
- 76. E in un attimo annodò un cappio ch'era una delizia, e senza spavalderia se lo adattava al collo da sè. Lo sceriffo, incantato, a questo punto non si potè reggere, lo abbracciò forte forte e disse: — Dianoro! Ti giuro sul mio onore che se non ti avessi a impiccare ti piglierei per segretario; e ora, figlio mio, desideri nulla da me? — Intendo dare un avvertimento al popolo e fare una preghiera a voi; te, popolo, ammonisco che tu ti astenga dall'acqua arzente, o almeno bevine con discrezione, massime la mattina a digiuno, se ti preme non essere impiccato; se poi non te ne preme, è un'altra cosa. A voi, signore sceriffo, mi raccomando che non mettiate il mio nome pagano nè cristiano su i giornali della Contea, perchè non vorrei lo risapesse mia madre e ne sentisse dispiacere: siccome io non le ho dato veruna contentezza nel mondo, così vorrei che per cagione mia non patisse dolore. — Molto bene... benissimo... ti avanza nulla a desiderare da me? — Nulla; potete lanciarmi nella eternità. — Amen! Dopo un minuto Dianoro ciondolava come un pendolo dal cedro rosso, cullato soavemente dalla brezza vespertina. Di facoltà per sostentare la vita Curio e Filippo non soffrirono mancamento; all'opposto n'ebbero copia, ma ogni giorno più veniva meno per loro la speranza di raccogliere in breve quanto bastasse per tornare in Italia a ripigliarsi le dilette creature e condursele in parte dove poter vivere e chiudere gli occhi in pace; la quale persuasione, oltre ogni credere amara, li rendeva irrequieti, scontenti, non fermi mai in un luogo, e sempre in traccia di fortune di cui spiavano invano l'orma dinanzi a loro: arti e professioni esercitarono tutte, sonatori, maestri di musica, di armi, di lingue, di matematiche, massime medici, e veramente non ci era mestieri fior di scienza per salire in fama di clinici solenni in coteste parti. Lascio giudicarlo a voi; essi trovarono medici che ministravano ai tisici acido solforico, per bruciare (così dicevano) i tubercoli polmonari; per l'enteriti ordinavano cristei di cera lacca liquefatta, e cerusici che
- 77. senza tante giammengole segavano le braccia e le gambe con le seghe dei falegnami. Da San Patricio ebbero a venirsene via nottetempo a modo di fuggiaschi, fidati nelle gambe di cavalli mezzo salvatichi chiamati mustanghi, e ciò perchè la gente del paese intendeva ritenerli a forza, reputandoli santi, o almeno capaci di operare miracoli: causa di questo convincimento fa che, essendo scoppiato in coteste contrade il cholera, essi guarirono quanti ne capitò loro sotto mano. Se il rimedio che adoperarono possa giovare in Europa ignoro, in America faceva la mano di Dio: possano i miei lettori andare sempre immuni dal tetro morbo, tamen per amore di umanità io lo pongo qui; badiamo però, io non lo raccomando, chi vuole lo sperimenti; suo cuore, suo consiglio: me ne rimetto in lui. — Recipe un bicchiere da tavola di spirito canforato, e mescolavi dentro venti gocce di laudano, pepe del buono quanto vuoi, e acqua di Colonia; filtra per tela, e mandane giù; se ti riesce, almeno un terzo, e ti dirò: bravo! Per completare la informazione, mi corre l'obbligo di aggiungere che gl'infermi, conci a quel modo, spiccavano salti da sfondare il soffitto, e poi giravano sopra sè stessi più veloci dei fusi delle macchine da filare: non importa; guarivano, ed oltre alla salute del corpo, nel dì del giudizio potevano sostenere di avere avuto un acconto delle pene dello inferno. — Ahimè! ahimè! come mi sento stracco, sospira Curio gittandosi giù su l'erba in riva a un fiume; a cui Filippo: — Abbiamo camminato tanto oggi! Riposati, figliuolo mio. — O a me caro più del padre; non parlo del corpo io, bensì della vita; il cervello mi sta inerte dentro il cranio come morto nella bara; mi tocco il petto invano per sapere da qual parte io mi abbia il cuore: — egli non mi palpita più; sono sazio di giorni. — Ecco, questo ti avviene perchè ti lasci arrugginire dalla malinconia. Dimmi, che fai tu perchè la ruggine non ti roda la carabina? Ogni giorno che Dio mette in terra tu la strofini con la sua brava pomice e col suo bravo olio. Ora, il coraggio è l'olio e la speranza la pomice per la malinconia; e voi giovani sprecate questo olio col boccale, come se aveste a condire la insalata per ventiquattro, sicchè non ve
- 78. ne avanza una goccia per la estrema unzione. Bada, Curio, molti giovani, che con le armi in mano vinsero virtuosamente gli austriaci, si lasciarono vincere dallo sbadiglio. — Filippo, ricordo avere letto certa sentenza in un libro, credo nella prefazione del Pellegrinaggio del giovane Aroldo, una sentenza la quale diceva così: «L'universo è una maniera di libro, del quale ha letto una pagina sola chi ha visto unicamente il suo paese. Io ne ho voltate di molte, e mi sono apparse tutte cattive; però questo esame mi è riuscito fruttuoso, imperciocchè, odiatore prima della mia patria, quando ebbi considerato le ribalderie dei popoli in mezzo ai quali sono vissuto, tornai ad amarla; e se dalle mie pellegrinazioni non avessi ricavato benefizio, eccetto questo uno, non mi lagnerei delle spese fatte, nè delle fatiche sofferte.» Veramente se il pellegrino venne sincero a tale conchiusione, beato lui! Per me, sia che mi pigli gli uomini nel vecchio o me li abbia a pigliare nel nuovo mondo, mi paiono tutti fichi degni di penzolare dall'albero di Timone; e ormai diffido trovarne quaggiù meglio nè peggio, sicchè vorrei insalutato hospite uscirmene da questo mondo, dove non mi trattiene più nulla. [15] — Nulla! Nè anche la vista di quel superbo alligatore, che steso supino costà su i giunchi del fiume si gode la benedizione dei raggi del sole? — Non gode, bensì si travaglia inebetito di ripienezza a cagione della strage menata stamani di chi sa quante creature viventi. Ma sta' tranquillo, o coccodrillo, a te non può mancare il regno dei cieli, perchè ti scusano la fame, lo istinto della tua conservazione e la mancanza d'intelletto, mentre noi abbiamo visto l'uomo mosso a malfare per vanità, per ferocia, per avarizia, insomma per colpa di spirito viziato, non già per bisogno del corpo: noi viviamo in società con gli uomini come i cuochi in cucina presso la stia, per avere i polli sottomano onde arrostirli; meglio coccodrilli, che uomini. — Ecco, vedi, Curio mio, io giudico che un divario ci corra, e grande, perchè io piglio a cottimo, con una brava palla nel cranio ovvero nello stomaco, di mettere a partito anche un Francesco di Modena o
- 79. un Ferdinando di Napoli, mentre con tutte le sei palle della mia rivoltella nel grugno a quel mostro la sarebbe come se gli dicessi sei volte: ben levato a vostra signoria; quindi io reputerei atto prudenziale svignarsela di qua prima ch'ei si accorga della nostra presenza. — Tu me lo calunni, linguaccia; ed io pure conosco averlo offeso; però me ne pento e dico mea culpa; mira, Filippo, quanti vaghi uccelletti gli fanno festa aliandogli intorno al muso, ed egli sembra partecipare per loro la tenerezza che ne sentiva quell'anima candida di madama Sand. — Misericordia! Se tu non mandi a rimpedulare il cervello, un giorno o l'altro t'innamori di un coccodrillo; o lo sai perchè l'alligatore sta fermo? O lo sai perchè gli uccelli gli volano intorno ai denti? Perchè gli vanno a beccare i frusti della carne rimastigli nelle gengive, ed egli sentendosele rinettare se la gode più di canonico dopo pranzo. Interesse, Curio mio, interesse nato e sputato da una parte e dall'altra. — Lo vedi se ti ho colto in flagranti, Filippo; e le creature tutte pensi tu che le sieno mosse da altro che dal proprio interesse? — Accidenti alla disdetta, che ci rende tristi e villani, saltò su a gridare Filippo tutto acceso nel volto, ed io... io ti amo per interesse? — Oh! no... tu no. — E tua madre ti ama per interesse?... E...? — Taci per l'amor di Dio, esclama Curio rizzandosi in un attimo e chiudendo con la mano la bocca a Filippo, — non la rammentare nè manco. Pur troppo tu dici santamente; compagna iniqua alla coscienza dell'uomo è la sventura; se mi capitasse tra i piedi la piglierei pel collo e la strozzerei... ma tu, mio Filippo, senti quanto me lo schianto del cuore di amare come noi amiamo, e di essere amati come sanno amare quegli angioli, e non potere corrispondere con essi, non dare loro e non riceverne nuove? Nulla conoscere di quanto fanno, dicono, patiscono o sperano...
- 80. — E chi ti dice che noi non possiamo sapere questo di loro? O che i cuori amanti non conoscono altra corrispondenza eccetto quella del telegrafo sottomarino? Il sospiro delle anime appassionate va con ali più celeri della favilla elettrica, e in men che non balena si trasporta da un polo all'altro. — Ti sieno grazie della tua ottima mente, o padre mio; tu, a patto di darmi un po' di refrigerio, non ti tireresti indietro da sostenermi che le tavole girano e gli spiriti dei morti vengono a raccontarci a veglia le novelle dell'altro mondo. — Ascolta, figlio mio, a filo di ragione io ti confesso non avere mai saputo giusto quello che doveva credere, ovvero discredere: per me detesto gli empirici della scienza quanto gli empirici della fede: empirici tutti. Ma che vuoi tu? Io sento... o piuttosto parmi sentire che non morrò intero; questo parmi sicuro, che tra il cielo e la terra esistano creature in troppo maggior copia di quella che sappiamo immaginare noi; ed invero, infiniti oggetti sfuggono ai nostri occhi, comecchè armati di potentissimi arnesi, o perchè del pari infinite idee non isfuggiranno alla nostra miope intelligenza? Dunque, se dopo avere picchiato ad una porta, veruno mi risponde, dirò il vero affermando che la casa è disabitata? E senza attendere risposta Filippo si prostese sopra l'erba verde celandovi il viso, e alquanto ce lo tenne fermo in onta a Curio, il quale mentre ostentava irriderlo in cuore tremava; quando si rialzò egli aveva nella voce e negli occhi il pianto; per la quale cosa lo amico suo lo interrogava dicendo: — E ora, che novità è codesta? Parla, che hai? — In questo punto Arria, la tua sorella, è passata a miglior vita. La madre tua ed Eufrosina mia, inginocchiate intorno al letto, pregano pace all'anima di lei e piangono. — E come hai fatto a saperlo? — Il come ignoro: piglia ricordo del giorno e dell'ora, ed a suo tempo lo riscontrerai.
- 81. Se Filippo quello che disse credesse, o piuttosto il facesse per purgare l'animo dello amico dalla tetraggine che gli si era cacciata addosso, non saprei, fatto sta che Curio prese nota del caso, e gli si ravvivò lo spirito come lume per nuovo olio versato nella lucerna, — e insieme con lo spirito i sensi da lungo tempo inerti ripresero la consueta alacrità. — Raccattiamo dunque il bordone, disse Curio, e proseguiamo il pellegrinaggio: intanto seguirò il tuo consiglio, allontaniamoci dallo alligatore, che se ci vedesse non ci concederebbe andare un tratto per la via. — Giusto, era quello che pensava ancora io, perchè tanto, dinne quante vuoi, gli uomini meglio dei coccodrilli saranno sempre. — Quod est videndum, Filippo; — conchiuse Curio, ed entrambi mossero di conserva lungo la ripa del fiume, sperando imbattersi in barca o in chiatta che dall'altra sponda li traghettasse. — Poichè ebbero camminato per buono spazio, notarono con maraviglia la ripa torcersi a gomito e spingersi traverso al fiume, in guisa di penisola, mentre le acque, invece di arricciarsi a cagione di simile ostacolo, tentando passare di sopra, avvallansi gorgogliando scorrono per di sotto; allora sostarono dubbiosi di avventurarci il piede; notandovi poi segnato un calle assai trito, ci si commisero sopra. Considerando essi sottilmente, come avviene quando ci occorrano cose inopinate e strane, cotesta superficie osservarono che l'andava composta da una congerie di tronchi e di rami di alberi o rotti o sradicati; la superficie in parte compariva sottilissima, in parte più profonda e contenuta come in gabbionate di vimini; qua e là incontravi certa maniera di pozzi di cui le pareti erano formate di tronchi di albero l'uno incastrato dentro l'altro, donde si udivano le acque del fiume scorrere fragorose verso il mare. — Tutto qui mi fa perdere la tramontana, cominciò Curio a favellare; fiumi che invece di scavarsi l'alveo sopra terra, come usa fra noi, ci passano di sotto; foreste che si staccano dalla sponda e si mettono a viaggiare per trasferire altrove il proprio domicilio; acque colore
- 82. vermiglio, quasi che dopo tanti secoli non siano anche giunte a lavare la terra dal sangue di cui i ladroni spagnuoli la inzupparono... — Ecco che ti ribollono le solite fisime: se invece di erpicarti su pei peri tu porgessi attenzione a quello che si favella intorno a te, tu avresti udito e adesso rammenteresti due fiumi in America pigliare nome di Coloradi, uno dei quali scorre nel Texas, l'altro in California; qui, oltre il Colorado, vi ha un altro fiume chiamato Riviera Rossa, e ciò a cagione del mescolarsi che fanno le acque con certe terre ferruginose. — Lo sapeva, Filippo, e la fantasia mi ha posto le mani sugli occhi dell'intelletto, perchè se le acque dei fiumi avessero ad andare tinte di rosso per via del sangue umano mescolato fra loro, qual fiume al mondo potrebbe mostrarle limpide? Mario, dopo la strage dei teutoni, quando assetato e stanco scese in riva al fiume, non più bevve acqua che sangue; ma i teutoni a suo tempo ci barattarono un Mario in dieci Radetski. Basta; tiriamo innanzi e Deus providebit, come disse Abramo quando s'incamminava a scannare il figliuolo... a proposito, Filippo, sei tu amico della Provvidenza? — Certo; non però di quella a cui i preti appioppano per babbo san Gaetano e per mamma l'Accidia; io ho fede nella provvidenza che si lascia sempre trovare dall'uomo quando la cerca con virtuosa solerzia. — Bene vertant Dii! borbottò Curio, e non aggiunse verbo; molto più che gli oggetti circostanti pigliassero a legare i sensi suoi con parvenza mirabile: infinite gli si pararono dinanzi gli occhi le varietà delle piante e degli alberi, parecchi dei quali noti anche in Europa; i più domestici del luogo, come i cipressi calvi, i cedri rossi, i ginepri da lapis, alberi da arco, alberi ferro, aceri da zucchero, ebani, palme, in copia magnolie grandiflore, le quali così intensamente impregnavano l'aria di profumi, da dare il capogiro ai nostri viaggiatori; l'aria spirava ebbrezza; gli occhi dal tremolio della luce e dello azzurro restavano affascinati. Non ci era mestieri fantasia per popolare la foresta di uccelli diversi nella forma e nel volume, bellissimi di penne dai colori smaglianti; — però la natura matrigna
- 83. aveva negato loro la dolcezza del canto: uccello senza canto fa riscontro alla camelia senza odore; qualcheduno imitando la voce umana irrideva, donde il nome di uccello beffardo. Non era cotesta natura ravviata dall'arte, non aveva uccello predicatore arguto dei riti di Venere, e nondimanco dall'aura, dai rami, dalle piante e dagli animali usciva urgentissimo lo invito: . . . . . amiamo or quando Esser si puote riamati amando. A questo modo, studiando il passo per non ismarrire il sentiero, i nostri amici arrivarono all'estremo lembo di quella penisola, donde appuntando lo sguardo videro spingersi dalla parte opposta del fiume una lingua di terra pari a quella dove allora si trovavano, sia nella grandezza come nella forma, la quale si prolungava traverso della corrente. In quel punto il tratto che correva fra l'una e l'altra riva avrà misurato dalle cinquecento alle seicento braccia, nè per valicarlo appariva altro mezzo, eccetto una barca, la quale avrebbe cavato la voglia di entrarci anche alle ombre dei clienti di Caronte. Per giunta traccia di navalestri non si vedeva: cerca e ricerca, alfine venne lor fatto di scorgere accoccolate dentro il cavo di un albero smisurato due creature, che essi su quel subito non seppero a quale famiglia di bestie assegnare: avevano la pelle di una tinta, che colore onestamente non si sarebbe potuto dire, non castagno, nero neppure, piuttosto un miscuglio di molte maniere di sudiciumi: i capelli cenerini; ignudi erano, se togli una fascia traverso il corpo pendente giù fino a mezzo le cosce; grimi, pieni di schianze, orribili a vedersi. Stettero in forse di volgere loro la favella, ma pel gran bisogno che ne avevano ci si arrischiarono interrogandoli chi fossero: — uno di quelli, e propriamente colui che poteva supporsi uomo, rispose: — Siamo gente libera come vostra signoria, nel caso che siate uomo libero, cittadini della Unione Americana e barcaioli di mestiere al servizio di vostra signoria. — E dove abitano le loro eccellenze?
- 84. — Il nostro domicilio è qui. — In questo buco? — In questo buco. — Dove siete nati? — Chi lo sa! — Vi ci menarono di fuori? — Chi se ne rammenta! — Che sapete fare? — A frustate c'insegnarono la schiavitù i reverendi padri delle missioni. — La schiavitù non è mestiere; v'insegnarono altro? — Sicuro eh! C'insegnarono anche il rosario. — A frustate? — A frustate. — Siete cristiani? — Comandi? — Chiedo se credete in Gesù Cristo? — Crediamo nello inferno, dove bruceremo eternamente se non reciteremo il rosario, e se quando vivevamo in servitù rubavamo anche una pannocchia di maiz al padrone; ma ora siamo liberi e potremmo rubare senza paura della casa del diavolo, ma padrone noi non abbiamo più. — Ma mi sapreste dire come siete liberi? — Chi lo sa! Prima i padroni si scannavano per tenerci a catena, e poi si sono scannati per mandarci liberi. — Ma la differenza che trovate fra la libertà e la schiavitù me la sapreste dire?
- 85. — O non l'ho detta? Quando eravamo schiavi avevamo modo di rubare in questa vita ai padroni, e andavamo all'inferno nell'altra; ora che siamo liberi non possiamo più rubare ai padroni, e la fame ci ha aperto le porte del paradiso; e, se vuole, io ci ho notato un'altra differenza: con la schiavitù frusta quotidiana e pane tre volte la settimana, con la libertà, nè frusta nè pane. — E figliuoli ne generaste? Allora si rizzò su l'altra creatura, che Curio suppose essere femmina, la quale per abbaiare non ebbe mestieri come Ecuba essere trasformata in cagna, e prese a urlare: — Dodici! dodici! dodici! — La figliolanza d'Isdrael; e che ne avete fatto? — Questo è il conto dei miei figliuoli: cinque morirono pel morso avvelenato dei serpenti a sonagli; due ne sbranarono le pantere; tre se li inghiottì la febbre gialla; uno lo impiccarono le facce pallide perchè ruppe il cranio al figliuolo del padrone, che lo frustava senza discrezione; l'ultimo ebbe il cranio spaccato dal padrone; e così finì la chiocciata. — Era tanto bello il mio Candido! finito di parlare la femmina prese a guaire il negro; il padrone pianse tanto la morte di quel giglio di amore! Si sbatacchiava per terra, si mordeva le mani; credo che se io non lo avessi retto si sarebbe buttato via. Filippo, intento a guarire Curio dalle sue fantasticaggini di misantropia, osservò: — Tanto, è inutile che tu vada come i medici a cercare il male col fuscellino; anco dalle anime più buie trapela sempre qualche raggio di amore. E Curio senza badargli continuò ad interrogare il nero: — Dunque il padrone amava questo figliuolo assai? — Oh quanto! Il mio bel giglio, pel colore e per la forza, vinceva il re dei bufali; era alto un metro e ottantacinque centimetri; alla fiera di
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