EC6201D- Digital Integrated Circuit Design

Dhanaraj K. J.
Assistant Professor
ECED, NIT Calicut

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The value of gate-to-source voltage VGS needed to cause surface
inversion (to create the conducting channel) is called the threshold
voltage VT.
Increasing the VGS (gate to source voltage) above and beyond VT will
not affect the surface potential and the depletion region width. They
will remain approximately constant and equal to their values attained
at the onset of surface inversion.

The main four physical components of the threshold voltage are

1) The work function difference between the gate and the channel
2) The gate voltage component to change the surface potential
3) The gate voltage component to offset the depletion charge
4) The gate voltage component to offset the fixed charges in the
gate-oxide and in the silicon-oxide interface.
 Voltage drop across oxide
due to depletion charge
Voltage drop across Surface Charge : due to imperfection in
Depletion region the oxide/substrate interface & doping
At inversion Implants: to adjust VT by
introducing a small doped
region at oxide/substrate surface
QB QOX
VT = MS - 2F - -
Cox Cox

Work-function
difference between
Gate-Oxide Capacitance per unit area
gate material and Si
Oxide permittivity
Depletion Layer Charge
OX = 3.5 x 10 -13 F/cm
COX =
tOX Oxide thickness
~ a few nm
 The threshold voltage of a MOSFET is affected by the voltage which
is applied to the back contact, which is called Body Effect (Substrate
bias effect). The voltage difference between the source and the
bulk, VBS changes the width of the depletion layer and therefore also
the voltage across the oxide due to the change of the charge in the
depletion region.
 Substrate can be thought of as a second gate, and is sometimes
referred to as the back gate, and accordingly the body effect is
sometimes called the back-gate effect.

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 QB Qox
VT  MS  2F  
Cox Cox
QB 0 Qox QB  QB 0
 MS  2F   
Cox Cox Cox
QB  QB 0   2F  VSB   2F 
 VT 0   VT 0  2qN A Si 
Cox  Cox 
 

VT  VT 0    2F  VSB   2F 
 ox
2qN A Si Cox 
 , substrate - bias (or body - effect) coefficient. tox
Cox
For nMOS F is negative,  is positive and VSB is positive.
For pMOS F is positive,  is negative and VSB is negative.
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Q. Find Vx for the following circuit if =0.4, kn=200A/V2. VT0=1V, |-2F|=0.6

 Vx2 
T2 linear; I D 2  k n  5  1Vx  
 2 

T1 saturation; I D1 
kn
5  Vx  VT 1 2
2
Vx2
1
5  Vx  VT 1   4Vx 
2

2 2

VT1 Vx
5  Vx  VT 1 2  8Vx  Vx2 ……..(1)

1 1.17 VT 1  VT 10     2F  VSB   2F 

 
1.064 1.21
1.069 1.21 VT 1  1  0.4 0.6  Vx  0.6 ……..(2)
 Vx  1.21V
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An n-channel MOSFET in saturation region will have the drain
current equal to
 nCox W  nCox
ID  . VGS  VT 
2
 .
W
VGS  VT 2
2 L 2 L  L
C
 n ox .
W
VGS  VT 2
2  L 
L1  
 L 
1
 nCox W 2 L 
 . VGS  VT  1  
2 L  L 
 nCox W
ID  . VGS  VT 2 1  L   L  L
2 L  L 

 nCox W L L
ID  . VGS  VT  1  VDS 
2   VDS or  VDS
2 L L L
  is called channel length modulation coefficient (V-1), an empirical
parameter.
 The above mentioned model is a simplified one and hence not very
accaurate.
 The channel length shortening L actually depends on the square
root of VDS-VDsat.
 In general  is proportional to the inverse of channel-length.
 Channel length modulation is more pronounced in short channel
MOSFETs.
 In applications where constant current is required, long channel
MOSFETs are preferred.

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 With an increase in source potential, threshold voltage of n-channel
MOSFET will
◦ A. Increase
◦ B. decrease
◦ C. remains the same

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1. Streetman, B.G. and Banerjee, S., 2001. Solid state electronic
devices. Prentice-Hall of India.
2. Kang, S.M. and Leblebici, Y., 2003. CMOS digital integrated
circuits. Tata McGraw-Hill Education.
3. https://inst.eecs.berkeley.edu/~ee40/su06/lectures/lecture13.pdf

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