MOSFET: Device structure, Operation with I-V Characteristics.pdf

UNIT-II
MOSFETs
Ref: Adel S.Sedra, Kenneth C.Smith Microelectronic circuits, Oxford University press, USA, sixth edition, 2009
Anil Neerukonda Institute of Technology & Sciences (Autonomous)
(Affiliated to AU, Approved by AICTE & Accredited by NBA (ECE, EEE, CSE, IT & Mech.) & NAAC)
Sangivalasa-531 162, Bheemunipatnam Mandal, Visakhapatnam District
Phone: 08933-225083/84/87 Fax: 226395
Website: www.anits.edu.in email: principal@anits.edu.in

Objectives of Module
• The physical structure of the MOS transistor and how it works.
• Current–Voltage characteristics.
• To analyze and design circuits that contain MOS transistors, resistors, and DC sources.
• How the transistor can be used as amplifier and switch
• Basic MOSFET amplifier configurations
ANIL PRASAD DADI/Dept. of ECE 2

Introduction
• Three-terminal devices are used in a multitude of applications, ranging from signal amplification
to digital logic and memory.
• The basic principle is voltage between two terminals controls the current flowing in the third
terminal.
• The three-terminal device can be used to realize a controlled source which is the basis for
amplifier design and act as a switch which is the basis for the realization of the logic inverter, the
basic element of digital circuits.
• e.g MOSFET , BJT

Device structure and physical operation: NMOS
• Device structure

Device structure and physical operation
• Source: Source is the terminal throughwhich majority charge
carriers enter into the semiconductor bar.

• Drain: Drain is the terminal throughwhich majority charge carriers leave the
semiconductor bar

semiconductor bar
• Channel: Channel is the path between source(S) and drain(D) through which majority
charge carriers travel from S to D

semiconductor bar
• Channel: Channel is the path between source(S) and drain(D) through which majority
charge carriers travel from S to D
• Gate: Gate is the terminal to control the flow of charge carriers from S to D.

Test your understanding
• Why the name MOSFET/insulated-gate FET or IGFET?
• How many terminals does MOSFET have?
• Why do MOSFET is considered as three terminal device?
• Is MOSFET is a symmetrical device?

Operation with Zero Gate Voltage
• With vGS=0V, two back-to-back diodes exist in series
between drain and source. These back-to-back
diodes prevent current conduction from drain to
source when a voltage vDS is applied. In fact, the path
between drain and source has a very high resistance
(of the order of 1012 Ω).

Creating a Channel for Current Flow

• The induced n region thus forms a channel
for current flow from drain to source.
Induced channel is also called as an inversion
layer.
• Threshold Voltage: The value of vGS at which
a sufficient number of mobile electrons
accumulate in the channel region to form a
conducting channel is called the threshold
voltage and is denoted Vt typically lies in the
range of 0.3 V to 1.0 V.

MOS capacitor
• The gate and the channel region of the
MOSFET form a parallel-plate capacitor, with
the oxide layer acting as the capacitor
dielectric.
• The positive gate voltage causes positive
charge to accumulate on the top plate of the
capacitor (the gate electrode). The
corresponding negative charge on the
bottom plate is formed by the electrons in
the induced channel. An electric field thus
develops in the vertical direction.
• Origin of the name “FET”

MOS capacitor
• The voltage across this parallel-plate capacitor,
that is, the voltage across the oxide, must
exceed Vt for a channel to form.
• When vDS = 0, the voltage at every point along
the channel is zero, and the voltage across the
oxide (i.e., between the gate and the points
along the channel) is uniform and equal to vGS
• We can express the magnitude of the electron
charge in the channel by |Q|=Cox(WL)vOV
where W is the width of the channel, and L is
the length of the channel. The oxide
capacitance is given by

Applying a small vDS
• We first consider the case where VDS is small (i.e., 50 mV or so). The
voltage VDS causes a current iD to flow through the induced n channel.
Current is carried by free electrons traveling from source to drain
(hence the names source and drain).

(hence the names source and drain).(Let’s calculate value of iD)
• The channel charge Q is given by |Q|=Cox(WL)vOV

• The current iD is given by iD =
|𝑄|
𝑢𝑛𝑖𝑡 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
= CoxWvOV

• The current iD is given by iD =
|𝑄|
= CoxWvOV
• The voltage establishes an electric field E across the length of the channel, |E|=
𝑣𝐷𝑆
𝐿

•
|𝑄|
= CoxWvOV
• The voltage establishes an electric field E across the length of the channel, |E|=
𝑣𝐷𝑆
𝐿
• This electric field in turn causes the channel electrons to drift toward the drain with a velocity given by
Electron drift velocity = µn|E|= µn
𝑣𝐷𝑆
𝐿

• The value of iD can now be found by multiplying the charge per unit
channel length by the electron drift velocity
iD = |Q|× vd = Cox(W)vOV × µn
𝑣𝐷𝑆
𝐿
iD = [µn Cox
𝑊
𝐿
vOV ] 𝑣𝐷𝑆
• Thus, for small vDS, the channel behaves as a linear resistance whose
value is controlled by the overdrive voltage , which in turn is
determined by vGS : iD = [µn Cox
𝑊
𝐿
(vGS-Vt) ] 𝑣𝐷𝑆
• The conductance of the channel is given by
gDS = [µn Cox
𝑊
𝐿
(vGS-Vt) ]

Different terms in channel conductance
• µn Cox: It is determined by process technology used to fabricate MOSFET. Its unit is A/V2. Process
transconductance parameter. K’n = µn Cox (m2/V-s)(F/m2) or A/V2, n denotes channel

•
𝑾
𝑳
: It is dimensionless quantity determined by device designer to give I-V characteristics as
desired. It is transistor aspect ratio

•
𝑾
𝑳
• µn Cox
𝑾
𝑳
: MOSFET transconductance parameter Kn= K’n
𝑾
𝑳
= µn Cox
𝑾
𝑳

•
𝑾
𝑳
• µn Cox
𝑾
𝑳
: MOSFET transconductance parameter Kn= K’n
𝑾
𝑳
= µn Cox
𝑾
𝑳
• vOV=vGS-Vt : It is very important circuit design parameter

• We conclude that with vDS kept small, the MOSFET behaves as a linear
resistance whose value is controlled by the gate voltage vGS. It finds
application as an electronic switch.
rDS=
𝟏
𝒈𝑫𝑺
=
𝑣𝐷𝑆
iD
=
𝟏
µn Cox
𝑊
𝐿
(vGS−Vt)
iD = µn Cox
𝑊
𝐿
(vGS-Vt) 𝑣𝐷𝑆

• We conclude that with vDS kept small, the MOSFET behaves as a linear
resistance whose value is controlled by the gate voltage vGS. It finds
application as an electronic switch.
rDS=
𝟏
𝒈𝑫𝑺
=
𝑣𝐷𝑆
iD
=
𝟏
µn Cox
𝑊
𝐿
(vGS−Vt)
iD = µn Cox
𝑊
𝐿
(vGS-Vt) 𝑣𝐷𝑆
• Deep triode region: 𝒗𝑫𝑺 << 2(vGS-Vt)
• For the MOSFET to conduct, a channel has to be induced. Then, increasing
vGS>Vt enhances the channel, hence the names enhancement-mode
operation and enhancement-type MOSFET. Finally, we note that the
current that leaves the source terminal (iS ) is equal to the current that
enters the drain terminal (iD ), and the gate current iG = 0.

Operation as vDS is increased
• Let vGS>Vt be constant i.e MOSFET is operated at constant vOV
• vDS appears as voltage drop across length of channel
• As we travel along the channel from source to drain, the voltage
(measured relative to the source) increases from zero to vDS. Thus the
voltage between the gate and points along the channel decreases
from vGS=Vt+vOV at the source end to vGD=vGS-vDS =Vt+VOV-vDS at the
drain end.
• Since the channel depth depends on this voltage, and specifically on
the amount by which this voltage exceeds Vt, we find that the
channel is no longer of uniform depth. (deepest at source end and
shallowest at the drain end)

Operation as vDS is increased
➢ At any applied VDS channel potential decreases from drain to source.
Hence drain end side PN junction between channel and body is at
more RB compared to source end side PN junction between channel
and body.
➢ Thus penetration of depletion region in channel is more at drain end
side compared to source end side.
➢ As vDS is increased, the channel becomes more tapered and its
resistance increases correspondingly. Thus, the curve does not
continue as a straight line but bends
0V 1V 2V 3V 4V 5V
At low RB
depletion
region
At high RB
depletion
region

Derivation of Drain current of a MOSFET
• Channel Charge Density, |Q|=CoxW(vGS-Vt)

• Let x be a point along the channel from source to drain, and v(x)
its potential, |Q|=CoxW[vGS-v(x)-Vt]

• Let x be a point along the channel from source to drain, and v(x)
its potential, |Q|=CoxW[vGS-v(x)-Vt]
• iD = |Q|× vd = CoxW[vGS-v(x)-Vt] × µn
𝑑𝑣
𝑑𝑥
iD = µn Cox w [vGS-v(x)-Vt]
𝑑𝑣
𝑑𝑥

• iD = µn Cox w [vGS-v(x)-Vt]
𝑑𝑣
𝑑𝑥

𝑑𝑣
𝑑𝑥
• ‫׬‬
0
𝐿
𝑖𝐷 𝑑𝑥= µn Cox w ‫׬‬
0
𝑣𝐷𝑆
[vGS−v(x)−Vt] dv

𝑑𝑣
𝑑𝑥
• ‫׬‬
0
𝐿
0
𝑣𝐷𝑆
• iDL= µn Cox w ‫׬‬
0
𝑣𝐷𝑆
[vGS−Vt]dv − ‫׬‬
0
𝑣𝐷𝑆
v(x)dv

𝑑𝑣
𝑑𝑥
• ‫׬‬
0
𝐿
0
𝑣𝐷𝑆
0
𝑣𝐷𝑆
0
𝑣𝐷𝑆
v(x)dv
• iDL= µn Cox w| (vGS−Vt)𝑣−
𝑣2
2
|𝑣𝐷𝑆
0

𝑑𝑣
𝑑𝑥
• ‫׬‬
0
𝐿
0
𝑣𝐷𝑆
0
𝑣𝐷𝑆
0
𝑣𝐷𝑆
v(x)dv
𝑣2
2
|𝑣𝐷𝑆
0
• iDL= µn Cox w[(vGS−Vt)𝑣𝐷𝑆−
𝑣𝐷𝑆
2
2
]

𝑑𝑣
𝑑𝑥
• ‫׬‬
0
𝐿
0
𝑣𝐷𝑆
0
𝑣𝐷𝑆
0
𝑣𝐷𝑆
v(x)dv
𝑣2
2
|𝑣𝐷𝑆
0
• iDL= µn Cox w[(vGS−Vt)𝑣𝐷𝑆−
𝑣𝐷𝑆
2
2
]
• iD= µn Cox
𝑊
𝐿
[(vGS−Vt)𝑣𝐷𝑆−
𝑣𝐷𝑆
2
2
]

Operation for vDS ≥vOV
• The channel have finite (nonzero) depth at the drain end when vDS
should be sufficiently small such that vGD exceeds Vt
• vDS must not exceed vOV
• When vDS=vOV=vGS-Vt; vGD=Vt the channel depth at the drain end
reduces to zero gives rise to the term channel pinch-off.

• Increasing vDS beyond this value (i.e., vOV) has no effect on the
channel shape and charge, and the current through the channel
remains constant at the value reached for vDS=vOV=vGS-Vt and
saturates and drain to source voltage is called VDSsat= vOV=vGS-Vt
• It should be noted that channel pinch-off does not mean channel
blockage: Current continues to flow through the pinched-off
channel, and the electrons that reach the drain end of the channel
are accelerated through the depletion region that exists there and
into the drain terminal.

• Any increase in vDS above vDSsat appears as a voltage drop across
the depletion region. Thus, both the current through the channel
and the voltage drop across it remain constant in saturation.
• iD=
1
2
µn Cox
𝑊
𝐿
(vGS−Vt)2

Current Voltage Characteristics
• The applied vDS establishes an Electric field, E
across length of channel from drain to
source. This Electric field causes the channel
electrons to drift towards drain with a drift
velocity.
• With increase in vDS the current iDS increases
linearly for small electric field established by
vDS ( because vd is proportional to E)
• With further increase in vDS the channel
resistance increases with vDS. Hence curve
bends indicating decrease in current.

• With further increase in vDS, complete
channel is depleted at drain end side only at
which value of vDS is called vDS(Sat), where
vDS(sat)=vGS-Vt

vDS(sat)=vGS-Vt
• With further increase in vDS above vDS(Sat)
depletion region further increases, Electric
field further increases and drift velocity with
which channel electrons drift towards drain
becomes saturated and therefore the current
remains constant or saturated

Regions of Operation
• Linear region: vDS< vGS-Vt
iD= µn Cox
𝑾
𝑳
[(vGS−Vt)𝒗𝑫𝑺−
𝒗𝑫𝑺
𝟐
𝟐
]
• Deep triode region: vDS<<2( vGS-Vt)
iD = µn Cox
𝑾
𝑳
(vGS-Vt) 𝒗𝑫𝑺
• Saturation region: vDS≥( vGS-Vt)
iD=
𝟏
𝟐
µn Cox
𝑾
𝑳
(vGS−Vt)𝟐

Circuit symbols of NMOS

How to determine region of Operation
• Linear region: vDS< vGS-Vt
• Deep triode region: vDS<<2( vGS-Vt)
• Saturation region: vDS≥( vGS-Vt)
➢ When vGD > Vt, the MOSFET is in triode region.
➢ When vGD≤ Vt, the MOSFET enters saturation region.

The iD–vGS Characteristic
When the MOSFET is used to design an amplifier, it is operated in the
saturation region. In saturation the drain current is constant
determined by vGS(or VOV) and is independent of vDS. That is, the
MOSFET operates as a constant-current source where the value of
the current is determined by vGS. In effect, then, the MOSFET
operates as a voltage-controlled current source with the control
relationship described by
iD=
𝟏
𝟐
µn Cox
𝑾
𝑳
(vGS−Vt)𝟐

Finite output resistance in Saturation
• In saturation, iD is independent of vDS . Thus, a change
ΔvDS in the drain-to-source voltage causes a zero change
in iD , which implies that the incremental resistance
looking into the drain of a saturated MOSFET is infinite.
• But, in practice, increasing vDS beyond vOV does affect
the channel somewhat. Specifically, as vDS is increased,
the channel pinch-off point is moved slightly away from
the drain, toward the source.

• voltage across the channel remains constant at vOV , and the
additional voltage applied to the drain appears as a voltage
drop across the narrow depletion region between the end
of the channel and the drain region.
• This voltage accelerates the electrons that reach the drain
end of the channel and sweeps them across the depletion
region into the drain. However, with depletion-layer
widening, the channel length is in effect reduced, from L to
L-∆L, a phenomenon known as channel-length modulation.
Now, since iD is inversely proportional to the channel length
iD increases with vDS .

• iD=
𝟏
𝟐
µn Cox
𝑾
𝑳
(vGS−Vt)𝟐(1+λ𝒗𝑫𝑺 )
• vDS=-VA iD=0
• VA=
𝟏
λ
• r0=
VA
iD
• r0=
1
λiD

Device structure and physical operation: PMOS
• In P-channel MOSFET, substrate is n-type.
• This device is symmetric, so either of the p+ regions can
be source or drain.
• The gate is formed by polysilicon, and the insulator by
Silicon dioxide.
• Channel is created by inverting the substrate surface
from n-type to p-type. Hence induced channel is also
called inversion layer.
• When vDS is applied between drain and source, current
flows through this induced p-region carried by mobile holes

• The value of vGS at which sufficient number of mobile
holes accumulate in the channel region to form a
conducting channel is called threshold voltage.
OR
• Vt is also called as vGS required to turn ON the device
• In PMOS, all polarities are reversed.
vGS<0 or vSG>0
vDS<0 or vSD>0
iDS<0 or iSD>0

holes to drift towards drain with a drift
velocity.

velocity.

velocity.
• With further increase in vDS the channel
resistance increases with vDS. Hence curve
bends indicating decrease in current.

vDS(sat)=vSG-|Vtp |

vDS(sat)=vSG-|Vtp |
• With further increase in vDS above vDS(Sat)
depletion region further increases, Electric
field further increases and drift velocity with
which channel holes drift towards drain
becomes saturated and therefore the current
remains constant or saturated

Regions of Operation
• Linear region: vSD< vSG-|Vtp |
iD= µp Cox
𝑾
𝑳
[(vSG−Vtp)𝒗𝑺𝑫−
𝒗𝑺𝑫
𝟐
𝟐
]
• Deep triode region: vSD<<2(vSG-|Vtp|)
iD = µp Cox
𝑾
𝑳
(vSG-Vtp) 𝒗𝑺D
• Saturation region: vSD≥(vSG-|Vtp|)
iD=
𝟏
𝟐
µpCox
𝑾
𝑳
(vSG−Vtp)𝟐

How to determine region of Operation
• Linear region: vSD< vSG-|Vtp |
• Deep triode region: vSD<<2(vSG-|Vtp |)
• Saturation region: vSD≥(vSG-|Vtp |)
➢ When vDG > Vtp, the MOSFET is in triode region.
➢ When vDG≤ Vtp, the MOSFET enters saturation region.

Thank you
for listening

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