Chapter 4b

pn junction open circuit
• Consider a sample of Si is doped n-type and the
other p-type.
– Assume there is an abrupt discontinuity between
the p and n regions, called metallurgical junction,
M.
– the fixed ionized donors and free electrons in the
n-region
– fixed ionized acceptors and holes in the p region.

Depletion region
• Due to the hole concentration gradient from the p-
side (p= ppo) to then n-side (p= pno)
– Holes diffuse towards n-region and recombine with the
electrons in this region.
– The n-side near the junction becomes depleted of majority
carriers and therefore has exposed positive donor ions (As+)
of concentration Nd.
• Similarly, the electron concentration gradient drives
the electrons by diffusion towards the p-side, which
exposes acceptor ions (B–) of concentration Nd in the
region.

Depletion Region
Depletion region

Space charge layer (SCL)
Figs (a) & (b): The regions on both sides of the junction M
consequently becomes depleted of free carriers in
comparison with the bulk p and n regions far away from the
junction.
– There is therefore a space charge layer around M.
– Also known as the depletion region around M.
Fig (c): the hole & electron concentration profiles
Fig (d): the net space charge density across the semiconductor
Fig (e): the variation of the electric field across the pn-junction
Fig (f): taking the potential on the p-side far away form M as
zero, then V(x) increases in the depletion region towards the
n-side.

nno
x
x = 0
pno
ppo
npo
log(n), log(p)
-eNa
eNd
M
x
E ( x)
B-
h+
p n
M
As+
e–
Wp Wn
Neutral n-regionNeutral p-region
Space charge region
Vo
V(x)
x
PE(x)
Electron PE(x)
Metallurgical Junction
( a)
( b )
( c)
( e)
( f )
x
–Wp
Wn
( d )
0
eVo
x ( g )
–eVo
Hole PE(x)
–Eo
Eo
M
rnet
M
Wn–Wp
ni

Ec
Ev
Ec
EFp
M
EFn
eVo
p n
Eo
Evnp
(a)
V
I
np
Eo
–E
e(Vo
–V)
eV
Ec
EFn
Ev
Ev
Ec
EFp
(b)
Energy band diagrams for a pn junction under (a) open circuit, (b) forward
bias
SCL

Energy band diagrams for a pn junction under
(c) reverse bias conditions. (d) Thermal generation of electron hole
pairs in the depletion region results in a small reverse current.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
(c)
Vr
np
e(Vo+Vr)
Ec
EFn
Ev
Ev
Ec
EFp
Eo
+E (d)
I = Very Small
Vr
np
Thermal
generation
Ec
EFn
Ev
Ec
EFp
Ev
e(Vo
+Vr)
Eo
+E

Open Circuit
• Given EFp and EFn are the Fermi levels in the p and n
sides, then in equilibrium and in the dark, the energy
band diagram for open circuit is shown Fig (a):
– The Fermi level must be uniform through the two
materials
– Far from the metallurgical junction M, we should still have
an n-type semiconductor and (Ec– EFn) should be the same
as in the isolated n-type material
– Similarly, (EFn– Ev) far away from M inside the p-type
material should also be same as in the isolated p-type
material
– Keeping EFp and EFn the same & the band gap Ec– Ev the
same.
– To draw the band diagram, we have to bend the bands Ec
and Ev near the junction at M

Forward Bias
• When the pn-junction is forward biased, majority of the
applied voltage drops across the depletion region, Fig (b)
shows the effect of forward bias:
– The applied voltage is in opposition to the built-in potential to
reduce the PE barrier from eVo to e(Vo – V)
– The electrons at Ec in the n-side can now readily overcome the
PE barrier and diffuse to the p-side
– The diffusing electron from the n-side can be replenished easily
by the negative terminal of the battery and the positive
terminal of the battery can replenish those holes diffusing
away from the p-side.
– There is therefore a current flow through the junction and
around the circuit.

Reverse Bias
• When a reverse bias, V= -Vr, is applied to the pn-
junction the voltage again drops across the SCL.
– Vr adds to the built-in potential Vo so that the PE barrier
becomes e(Vo+Vr) as shown in Fig (c).
– The field in the SCL at M increases to Eo+E where E is the
applied field
– There is hardly any reverse current because if an electron
were to leave the n-side to travel the positive terminal, it
cannot be replenished from the p-side.
• Virtually no electrons on the p-side
– However, there is a small reverse current arising from
thermal generation of Electron-Hole Pairs (EHP) in the SCL
as shown in Fig (d).
• The generated electron falls down the PE hill to the n-side to be
collected by the battery.
• Similarly the generated hole makes it to the p-side.

Introduction
• One of the most popular optoelectronics sources
– Inexpensive, consumes very little power & easily
adaptable to electronics circuitry
• In an LED, the semiconductor has a high energy
gap and the junction is constructed so that
radiation from the junction can escape
– In a normal Si diode, the radiated wavelength is long
(infrared range), the radiation is absorbed by the
surrounding semiconductor materials

Electrical characteristic
• LED is a semiconductor diode.
– Its characteristics and limitation are similar
to a normal p-n junction diode
• The breaking voltage is about 1.2 to 2V
depending on the semiconductor
material.
– Dynamic resistance ranges from a few ohms
to tens of ohms.

I–V characteristic of a p-n junction.

LED types
Infrared - 1.6V
Red - 1.8 to 2.1V
Orange - 2.2V
Yellow - 2.4V
Green - 2.6V
Blue - 3.0 to 3.5V (White same as blue)
UltraViolet - 3.5V

Principles of LED
• A LED is typically made from a direct band gap
semiconductor e.g. GaAs
– in which the Electron-Hole Pairs (EHP) recombination
results in the emission of a photon
– The emitted photon energy is approximately equal to
the band gap energy, h Eg.

Energy band diagram of unbiased pn+-junction
device in Fig.1(1)
• n side is more heavily doped than p side
• The band diagram is drawn to keep the Fermi level uniform
through the device,
– which is a requirement of equilibrium without bias.
• The depletion region extends mainly into the p-side
• There is a Potential Energy (PE) barrier eVo from EC on the n -side
to EC on the p-side, Vo is the built-in voltage
• The higher concentration of conduction electrons in the n-side
encourages the diffusion from the n to the p side.
• The net electron diffusion is prevented by the electron PE barrier,
eVo.

h Eg
Eg ( 2)
V
( 1)
p n+
Eg
eVo
EF
p n+
Electron in CB
Hole in VB
Ec
Ev
Ec
Ev
EF
eVo
Electron energy
Distance into device
(1) The energy band diagram of p-n+
(heavily n-type doped) junction without any bias.
Built-in potentialVo prevents electrons from diffusing fromn+
to p side. (2) The applied
bias reduces Vo and thereby allows electrons to diffuse, be injected, into thep-side.
Recombination around the junction and within the diffusion length of the electrons in the
p-side leads to photon emission.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Fig.1: Principles of LED

Energy band diagram of pn+-junction device
with a forward bias V in Fig.1(2)
• As soon as a forward bias V is applied, this voltage drops
across the depletion region
– since this is the most resistive part of the device.
• The built-in potential Vo is reduced to Vo – V
• Allows the electrons from the n+side to be injected into the p-
side
– The hole injection component from p into n+ side is much smaller than
electron injection component from n+to p side
• The recombination of injected electrons in the depletion
region & p-side results in the spontaneous emission of
photons

Injection Electroluminescence
• Recombination primarily occurs within the depletion region
and within a volume extending over the diffusion length of the
electron in the p-side
– This recombination zone is frequently called the active region
• The phenomenon of light emission from EHP recombination as
a result of minority carrier injection is called injection
electroluminescence
• Because of the statistical nature of the recombination process
between electrons and holes, the emitted photons are in
random direction
– They result from spontaneous processes in contrast to stimulated
emission

Light output
Insulator (oxide)
p
n+ Epitaxial layer
A schematic illustration of typical planar surface emitting LED devices. (a) p-layer
grown epitaxially on an n+ substrate. (b) First n+ is epitaxially grown and then p region
is formed by dopant diffusion into the epitaxial layer.
Light output
p
Epitaxial layers
(a) (b)
n+
Substrate Substrate
n+
n+
Metal electrode
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig 2: Device structures

Device structures of LED
• In its simplest technological form, LEDs are typically
fabricated by epitaxially growing doped semiconductor
layers on a suitable substrate (e.g. GaAs or GaP) as shown in
Fig.2(a).
– It is formed by the epitaxial growth of first the n-layer and then the
p-layer
• The substrate is essentially a mechanical support for the pn-
junction device and can be of different material
• The p-side is on the surface
– from which light is emitted
– it is also made narrow (a few microns) so that photons is allowed to
escape without reabsorbed
GaP: Gallium Phosphide
GaAs: Gallium Arsenide

Low pressure chemical vapor deposition
(LPCVD) reactor for Epitaxially Growing Doped
Not only a film is deposited, but single crystal
growth must also be maintained

Device structures, cont
• To ensure that most of the recombination takes place
in the p-side, the n-side is heavily doped
– Those photons that are emitted towards the n-side become
either absorbed or reflected back.
– In Fig 2(a), the use of a segmented back electrode will
encourage reflections from the semiconductor-air interface.
• It is also possible to form the p-side by diffusing
dopants into the epitaxial n+-layer, which is diffused
junction planar LED as shown in Fig 2(b).

Defect of Device structures
• If the epitaxial layer and the substrate crystals have different
crystal lattice parameters
– Mismatch between the two crystal structures will exist
– This causes lattice strain in the layer and leads to crystal defects.
– Such defects encourage radiationless EHP recombination acting as
recombination center
• Such defects are reduced by lattice matching the LED epitaxial
layer to the substrate crystal
– AlGaAs alloys is a direct bandgap semiconductor in the red emission
region.
– It can be grown on GaAs substrate with excellent lattice match to produce
high efficiency LED devices.

Light output
p
Electrodes
Light
Plastic dome
Electrodes
Domed
semiconductor
pn Junction
(a) (b) (c)
n
+
n
+
(a) Some light suffers total internal reflection and cannot escape. (b) Internal reflections
can be reduced and hence more light can be collected by shaping the semiconductor into a
dome so that the angles of incidence at the semiconductor-air surface are smaller than the
critical angle. (c) An economic method of allowing more light to escape from the LED is
to encapsulate it in a transparent plastic dome.
Substrate
Fig. 3: Optical design

Optical Design of LED
• Figs. 2(a) & 2(b) show the planar pn-junction based
simple LED structures.
– Not all light rays reaching the semiconductor-air interface can
escape because of Total Internal Reflection (TIR)
– Those rays with incidence angle > critical angle (c) will be
reflected back as shown in Fig.3(a)
– For GaAs-air interface, c is only 16
• It is possible to shape the surface of the semiconductor
into a dome/hemisphere
– So that light strikes the surface at angles less than c and
therefore do not experience TIR as shown in Fig.3(b).

Encapsulation of LED
• The main drawback is
– the additional difficult process in fabricating such domed LEDs
and
– the associated increase in expense
• An inexpensive and common procedure that reduces
TIR is the encapsulation of the semiconductor junction
within a transparent plastic medium (epoxy)
– has higher reflective index than air
– has a domed surface on one side of pn-junction as shown in
Fig.3(c)

LED materials
• There are various direct bandgap semiconductor
materials that can be readily doped to make
commercial pn-junction LEDs that emit radiation
in the red & infrared range of wavelength
– In visible spectrum is III-V ternary alloys based on
alloying GaAs & GaP donated as GaAs1–yPy.
– In this compound, As & P atoms (Group V) are
distributed randomly at normal As sites in the GaAs
crystal structure.

Band gaps of some common semiconductors
relative to the optical spectrum.

Direct & Indirect bandgap
semiconductor
• When y <0.45, the alloy GaAs1–yPy is a direct bandgap
semiconductor and hence the EHP recombination
process is direct.
– The rate of recombination  the product of electron and hole
concentration
– The emitted wavelength range from 630nm (red) for y=0.45
(GaAs0.55P0.45) to 870nm (Infrared) for y = 0 (GaAs)
• When y >0.45, the alloy GaAs1–yPy is a indirect bandgap
semiconductor.
– The EHP recombination processes occur through recombination
centers
– It involves lattice vibrations rather than photon emission

Isoelectronic Impurites
• If isoelectronic impurites, N atoms (Group V), is added
into semiconductor crystal, some of N atoms substitute
for P atoms to form the same number of bonds.
• The positive nucleus of N is less shielded by electrons
compared with that of the P atom.
– A conduction electron in the neighborhood will be attracted
and trapped at this site
– Therefore N atoms introduce localized energy level (electron
traps), EN near the conduction band.

Isoelectronic Impurites, cont
• When the electron is captured at EN, it can attract a
hole in its vicinity by Coulombic attraction
– Eventually recombine with it directly and emit a photon.
– The emitted photon energy is slightly less than Eg.
• The recombination process depends on N doping, it is
not as efficient as direct recombination
– Thus the efficiency of LEDs from N doped indirect band gap
GaAs1–yPy semiconductors is less than those from direct band
gap semiconductor
• N doped with indirect band gap alloys are widely used
in inexpensive green, yellow and orange LEDs.

Two types of blue LED materials
1. GaN is a direct bandgap semiconductor with Eg of 3.4eV
– The blue GaN LEDs actually use the GaN alloy
– InGaAs has a bandgap of about 2.7eV, which corresponds to blue
emission.
2. The less efficient type is the Al doped SiC, which is an indirect
bandgap semiconductor
– The acceptor type localized energy level captures a hole from the
valence band
– A conduction electron then recombines with this hole to emit a photon
– As the recombination process is not direct and therefore not as efficient,
the brightness of blue SiC LEDs is limited.
GaN: Gallium Nitride
SiC: Silicon Carbide

Commercially important direct bandgap
semiconductor materials
• Ternary (3 elements) and Quarternary (4 elements) alloys based
on III & V elements (III-V alloys)
• Ternary alloy, Al1–xGaxAs, in which x <0.43 are direct bandgap
semiconductors
– The composition can be varied to adjust the bandgap and hence the
emitted radiation from 640nm-870nm (deep red-infrared light)
• InGaAlP is a quarternary III-V alloy that has a direct bandgap
variation with composition over the visible range
– It can be lattice-matched to GaAs substrate when in the composition
range In0.49Al0.17Ga0.34P to In0.49Al0.058Ga0.452P
• This LED material is likely to dominate high intensity visible
range.

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Blue
Green
Orange
Yellow
Red

1.7
Infrared
Violet
GaAs
GaAs0.55P0.45
GaAs1-yPy InP
In0.14Ga0.86As
In1-xGaxAs1-yPy
AlxGa1-xAs
x = 0.43
GaP(N)
GaSb
Indirect
bandgap
InGaN
SiC(Al)
In0.7Ga0.3As0.66P0.34
In0.57Ga0.43As0.95P0.05
Free space wavelength coverage by different LED materials from the visible spectrum to the
infrared including wavelengths used in optical communications. Hatched region and dashed
lines are indirect Eg materials.
In0.49AlxGa0.51-xP
Fig.5: Spectrum range

External efficiency
• External efficiency ext of an LED quantifies the efficiency of
conversion of electrical energy into an emitted external optical
energy
– The input of electrical power into an LED is simply the diode current
and diode voltage product (IV).
– Pout is the optical power emitted by the device.
• For indirect bandgap semiconductor ext are generally less than
1%, but for direct band gap semiconductor with the right
device structure, ext can be larger.
  %100
optical
ext 
IV
Pout


Heterojunction high intensity LEDs
• A junction between 2 differently doped
semiconductor that are of the same material (same
band gap) is called a homojunction.
• A junction between 2 different band gap
semiconductors is called a heterojunction
• A semiconductor device structure that has junctions
between different band gap materials is called a
heterostructure device (HD)

Refractive index and band gap
• The refractive index of a semiconductor materials
depends on its band gap.
– Wider band gap semiconductor has a lower refractive
index
• This means that by constructing LEDs from
heterostructures, we can engineer a dielectric
waveguide within the device
– Thereby channel photons out from the recombination
region.

The homojunction LED has two
drawbacks.
1. The p-region must be narrow to allow the photons to escape
without much re-absorption
– When p side is narrow, some of the injected electrons in the p side
reach the surface by diffusion and recombine through crystal defects
near the surface
– The radiationless recombination process decreases the light output
2. If the recombination occurs over a relatively large volume
(distance), due to long electron diffusion length, then the
chances of re-absorption of emitted photons becomes higher.
– The amount of re-absorption increases with the material volume

Double Heterostructure
• LED constructions for increasing the intensity of the output light
make use of the Double Heterostructure (DH) structure.
– Two junctions between different semiconductor materials with different
band gaps
• In Fig 6(a), DH consists of AlGaAs with Eg2eV and GaAs with
Eg1.4eV.
– DH has an n+p heterojunction between n+-AlGaAs and p-GaAs
– Another heterojucntion between p-GaAs and p-AlGaAs.
– The p-GaAs region is a thin layer (a fraction of micron) and is lightly doped

Fig. 6: Double Heterostructure
2eV
2eVeVo
Holes in VB
Electrons in CB
1.4eV
No bias
Ec
Ev
Ec
Ev
EF
EF
(a)
(b)
pn+ p
DEc
~ 0.2 mm
AlGaAsAlGaAs
(a) A double
heterostructure diode has
two junctions which are
between two different
bandgap semiconductors
(GaAs and AlGaAs)
(b) A simplified energy
band diagram with
exaggerated features. EF
must be uniform.
GaAs

With
forward
bias
(c)
(d)
GaAs AlGaAsAlGaAs
ppn+
(c) Forward biased
simplified energy band
diagram.
(d) Forward biased LED.
Schematic illustration of
photons escaping
reabsorption in the
AlGaAs layer and being
emitted from the device.
Fig. 6: Double Heterostructure

Band Diagram of Double
Heterostructure
• The simplifies energy band diagram for the whole device
in the absence of an applied voltage is shown in Fig.6(b)
– The Fermi level EF is continuous through the whole structure
– There is potential energy barrier eVo for electrons in the CB of
n+-AlGaAs against diffusion into p-GaAs.
– There is a band gap change at the junction between p-GaAs
and p-AlGaAs that results in a step change, DEc.
– DEc is effectively a potential energy barrier that prevents any
electrons in the CB in p-GaAs passing to the CB of p-AlGaAs

When a forward bias is applied, majority of this
voltage drops between n+-AlGaAs and p-GaAs
• Reduces the potential barrier eVo
• This allows electrons in the CB of n+-AlGaAs to be injected into p-
GaAs as shown in Fig.6(c)
• These electrons are confined to the CB of p-GaAs since there is a
barrier between p-GaAs and p-AlGaAs.
• The wide bandgap AlGaAs layers act as confining layers that
restrict injection electron to the p-GaAs layer
• The recombination of injected electrons and the holes already
present in this p-GaAs layer results in spontaneous photon
emission.
• Since the bandgap Eg of AlGaAs is greater than GaAs, the emitted
photon do not get reabsorbed as they escape the active region
and can reach the surface of the device as shown in Fig.6(d)

Defect of Double Heterostructure
• Since light is also not absorbed in p-AlGaAs, it can be
reflected to increase the light output
• There is no lattice mismatch between the two crystal
structure in AlGaAs/GaAs heterojunction.
• Negligible strain induced interfacial defects (e.g.
dislocation) in the device compared with the defects at
the surface of the semiconductor in conventional
homojunction LED structure.
• The DH LED is much more efficient than the
homojunction LED.

LED characteristics
• The energy of an emitted photon from LED is not
simply equal to band gap energy Eg
– because electrons in the CB are distributed in energy and so
are holes in the valence band.
• Fig.7(a) and 7(b) illustrate the energy band diagram
and the energy distribution of electrons and holes in
the CB and VB respectively
• The energy concentration per unit energy in CB is
given by g(E)f(E)
– g(E) is the density of states
– f(E) is the Fermi Dirac function

LED characteristics, 1
• In Fig 7(b), the electron concentration in the CB
as a function of energy is asymmetrical
– has a peak at ½kBT above Ec.
– The energy spread of these electrons is typically
about 2kBT from Ec.
– Similarly, hole concentration spread from Ev in the
VB

Fig.7: LED characteristics
(a) Energy band
diagram with possible
recombination paths.
(b) Energy
distribution of
electrons in the CB
and holes in the VB.
The highest electron
concentration is
(1/2)kBT above Ec
E
Ec
Ev
Carrier concentration
per unit energy
Electrons in CB
Holes in VB
CB
VB
(a) (b)
1/2kBT
Eg
1 2 3
2kBT

h
1
0
Eg
h1 h2 h3

Relative intensity
1
0
1
2
3
DDh
Relative intensity
(c) (d)
Eg + kBT
(2.5-3)kBT
(c) The relative light intensity as a function of photon energy
based on (b). (d) Relative intensity as a function of wavelength in
the output spectrum based on (b) and (c).

The rate of direct recombination is proportional to
both electron and hole concentrations
1. The transition, which is identified as 1 in Fig 7(a), has
the relative small intensity of light with photon energy
hv1.
– The carrier concentrations near the band edges are very
small and hence does not occur frequently
2. The relative intensity of light corresponding to
transition hv2 is maximum
– The transitions that involve the largest electron and hole
concentration occur most frequently.
3. The light intensity at the relative high photon energies
hv3 occurred through transition 3 is small.
– The energetic electron and hole concentrations are small

Output Spectrum
• The relative light intensity vs photon energy
characteristic of the output spectrum is shown in Fig
7(c).
– It represents an important LED characteristic
• Given the spectrum in Fig 7(c), we can also obtain the
relative light intensity vs wavelength characteristic as
shown in Fig (d) because =c/
– The linewidth of the output spectrum, D or D, is defined
as width between half-intensity points.

V
2
1
(g)
0 2 0 4 0
I (mA)0
(e)
6 0 0 6 5 0 7 0 0
0
0 .5
1 .0

Relative
intensity
2 4 nm
D
6 5 5 nm
(f )
0 2 0 4 0
I (mA)0
Relative light intensity
(e) A typical output spectrum (relative intensity vs wavelength) from a red GaAsP LED.
(f ) Typical output light power vs. forward current. (g) Typical I-V characteristics of a
red LED. The turn-on voltage is around 1 .5 V.

Output Spectrum, 2
• The wavelength for the peak intensity and the
linewidth of the spectrum are obviously related to
– Energy distributions of the electrons and holes in the CB
and VB
– Density of states in these bands (individual semiconductor
properties)
• The photon energy for the peak emission is roughly
Eg+kBT
– It corresponds to peak-to-peak transitions in the energy
distributions of the electrons and holes
– The linewidth D(h) is typically between 2.5kBT to 3kBT as
shown in Fig.7(c)

Output spectrum, 3
• The output spectrum (relative intensity vs
wavelength characteristics) from an LED
depends
– The semiconductor material
– The structure of the pn-junction diode including the
dopant concentration levels
• The spectrum in Fig 7(d) represents an idealized
spectrum without including the effects of heavy
doping on the energy bands

Red LED characteristics
• Typical characteristics of a red LED (655nm) are
shown in Fig 7(e) to 7(g).
– The output spectrum exhibits less asymmetry than
the idealized spectrum
– The width of the spectrum is about 24 nm, which
corresponds to a width of about 2.7kBT in the
energy distribution of the emitted photons

LED current
• As the LED current increases, so does the injected
minority carrier concentration,
– thus the rate of recombination and hence the output light
intensity
– However, the increase in the output power is not linear with
the LED current -> Fig.7(f)
• At high current levels, strong injection of minority
carriers leads to the recombination time depending on
the injected carrier concentration
– Hence on the current itself; this leads to a non-linear
recombination rate with current

Current-Voltage Characteristics
• Typical current-voltage characteristics are shown in Fig
7(g)
– It can be seen that the turn-on or cut-in voltage is about 1.5V
(current increases sharply with voltage)
• The turn-on voltage depends on the semiconductor and
generally increases with energy bandgap Eg
– For example, typically it is about 3.5-4.5V for a blue LED
– It is about 2V for a yellow LED
– It is around 1V for a GaAs infrared LED

Example LED output spectrum
• Given that the width of the relative light
intensity vs photon energy spectrum of an
LED is typically about ~3kBT, what is the
linewidth D½ in the output spectrum in
terms of wavelength ?
• Given = 870 nm, 1300 nm, 1550 nm
• T = 300 K

Solution
 
structureLEDon thedependesexact valutheandvaluestypicalarelinewidthsThese
149,1550
105,1300
47,870atThus,
3
find,weofin termsforngsubstitutiandlattertheusingThen,
.3spectrum,outputtheofthenergy widgiven theareWe
then//e.g.
atedifferentiby)(orintervalsorchangessmallrepresentcanWe
getweenergyphotonrespect towithatedifferentiweIf
byenergyphotonthetorelatedishwavelengtemittedthat thenoteWe
2
2
2
nmnm
nmnm
nmnm
hc
Tk
E
TkhE
E
E
hc
dEdE
E
hc
dE
d
E
E
hcc
E
B
ph
Bph
ph
ph
phph
phph
ph
ph
ph
D
D
D
D
DD
DD
DD
D
















Example: LED output wavelength
variations
• Consider a GaAs LED. The band gap of GaAs
at 300K is 1.42eV, which changes
(decreases) with temperature as dEg/dT= –
4.510–4 eVK–1. What is the change in the
emitted wavelength if the temperature
change is 10C?

Solution
  
 
 
  
books.data
inquotedLEDsGaAsforvaluestypicalof10%withinischangecalculatedThis
erature.with tempincreaseshwavelengttheerature,with tempdecreasesEgSince
8.2100.277nmK
isC10forhwavelengtin thechangeThe
0.277nmKor1077.2that,So
106.1105.4
106.142.1
10310626.6
,havewe/takingandtermtheNeglecting
1
1110
194
219
834
2
nmKT
dT
d
T
mK
dT
d
dT
dE
E
hc
dT
d
EhcTk
g
g
gB
D





D
DD


























Example: InGaAs on InP substrate
• The ternary alloy In1–xGaxAsyP1–y grown on an InP crystal
substrate is a suitable commercial semiconductor
material for infrared wavelength LED and laser diode
applications. The device requires that the InGaAsP layer
is lattice matched to the InP crystal substrate to avoid
crystal defects in the InGaAsP layer. This in turn requires
that y 2.2x. The bandgap Eg of the ternary alloy in eV is
then given by the empirical relationship,
• Eg  1.35 – 0.72y + 0.12y2; 0x0.47
• Calculate the compositions of InGaAsP ternary alloys for
peak emission at a wavelength of 1.3 mm

Solution
  
  
0.340.660.30.7
2
619
348
g
6
PAsGaInisalloyyquarternarThe
0.3.2.2/66.0Then.66.0givescalculatoraonequationquadraticthisSolving
12.072.035.1928.0
,satisfyinghavemustthenInGaAsPThe
928.00259.0
103.1106.1
10626.6103
,taking,103.1atand
olts,electron vinThen./isemissionpeakatenergyphotonThe
.interestofhwavelengtat thebandgaprequiredtheneedthat wenotefirstWe












xy
yy
y
eVeVE
Tm
e
Tk
e
hc
E
TkEhc
E
B
g
Bg
g
300K



Chapter 4b

More Related Content

What's hot (20)

Similar to Chapter 4b (20)

More from Gabriel O'Brien (20)

Recently uploaded (20)

Chapter 4b