Module 1 : Unit 1

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MOSFET

1) Functioning/Working & types & Symbol.

2) Equations

3) Short channel effects

DIBL
Hot carrier effects
Subthreshold current
Velocity saturation
Mobility degradation

4) Impact of substrate bias

5) Channel length Modulation

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Types

1) Enhancement

NMOS
PMOS

2) Depletion

NMOS
PMOS

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Transfer Characterstics

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$V_{TO} = \phi_{GC} - 2\phi_F - \frac{Q_{BO}}{C_{OX}} - \frac{Q_{OX}}{C_{OX}}$

1. Channel Length Modulation

$I_D(sat) = \frac{U_nC_{OXW}}{2L}(V_{GS} - V_T)^2(1 + \lambda V_{DS})$

$\lambda$ = Channel length modulation coeff

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2. Substrate Bias effect

$V_T(VSB) = V_{TO} + \nu((|2\phi_F| + VSB)^{1/2} - (|2\phi F|)^{1/2})$

$I_D(lin) = \frac{U_nC_{OXW}}{2L}[2(V_{GS} - V_{T(VSB)})V_{DS} - V_{DS}^2]$

$I_D(sat) = \frac{U_nC_{OXW}}{2L}[V_{GS} - V_{T(VSB)}]^2$

$V_{SB}$ and $\nu$ = +ve for nmos

$V_{SB}$ and $\nu$ = -ve for pmos

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1) Constant field scaling

2) Constat Voltage scaling

-> Device dimensions

W, L, Xj, $T_{OX}$

-> Potentials and supply

$V_{DD}, V_{TO}$

-> Doping densities

NA, ND

3) Impact OnKey parameters - i) Cox

ii) Id

iii) Power Dissipation

iv) Power Densities

v) Current density

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S.no.	Device Dimensions	Const field scaling	Const voltage scaling
1.	Chanel Length (L)	$L^{'} = L/S$	$L^{'} = L/S$
2.	Channel width (W)	$W^{'} = W/S$	$W^{'} = W/S$
3.	Junction width (Xi)	$Xj^{'} = Xj/S$	$Xj^{'} = Xj/S$
4.	Oxide Thickness (Tox)	$T_{OX}^{'} = T_{OX}/S$	$T_{OX}^{'} = T_{OX}/S$
5.	Supply Voltage $V_{DD}$	$V_{DD}^{'} = V_{DD}/S$	Remain Unchanged
6.	Threshold Voltage $V_{To}$	$V_{To}^{'} = V_{To}/S$	Remain Unchanged
7.	Doping densities	$NA^{'} = SNA$	$NA^{'} = S^2NA$
8.	$C_{OX}$	$C_{OX}^{'} = S.C_{OX}$	$C_{OX}^{'} = S.C_{OX}$
9.	$I_D$	$I_D^{'} = I_D/S$	$I_D^{'} = I_D.S$
10.	Power dissipation	$P^{'} = P/S^2$	$P^{'} = P.S$
11.	Power density	$P^{'}/A = P/A$	$P^{'}/A = S^3P/A$
12.	Current density	$I_D^{'}/A = S.I_D/A$	$I_D^{'}/A = S^3.I_D/A$

1) $C_{OX} = \frac{E_{OX}}{T_{OX}} = \frac{E_{OX}}{T_{OX}}.S$

2) $I_D^{'}(lin) = \frac{I_D(lin)}{S}$

Similarly,

$I_D^{'}(sat) = \frac{I_D(sat)}{S}$

3) Power Dissipation

$P^{'} = P/S^2$

4) Power density

$\frac{P^{'}}{Area} =\frac{P}{Area}$

5) Current density

$\frac{I_D^{'}}{Area} = S\frac{I_D}{Area}$

Cross Sectional view and top view (mask view) of a typical n-channel MOSFET

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Total Capacitance	Cut-Off	Linear	Saturation
$C_gb(total)$	$C_{OX}.WL$	0	0
$C_gd(total)$	$C_{OX}.WL_D$	1/2$C_{OX}.WL$	$C_{OX}.WL_D$
$C_gs(total)$	$C_{OX}.WL_D$	1/2$C_{OX}.WL$	2/3$C_{OX}.WL$

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3D view of $n^{+}$ diffusion within the p-substarte.

$C_{Sb}$ = Volatage dependent juction cap $C_{db}$ = Volatage dependent juction cap

Dimensions = Y, Xj and UN

Abrupt PN junction profiles are assumed

(2), (3), (4) => surrounded by $p^{+}$ regions

(1) => Surrounded by p

(5) => Surrounded by p substrate

Channel stop implant = 16 NA

Type	Area	$Ju^n$	Depletion Cap
$n^{+}/P$	WXj	(1)
$n^{+}/P^{+}$	yXj	(2)	$C_{jo} = (\frac{E_{si}}{2}q(\frac{N_A + N_D}{N_A + N_D})\frac{1}{\phi_o})^{1/2}$
$n^{+}/P^{+}$	W.Xj	(3)
$n^{+}/P^{+}$	Y.Xj	(4)	$\phi_o = \frac{KT}{q}ln(\frac{N_AN_D}{n_i^2})$
$n^{+}/P$	Wy	(5)

During Dynamic process, Junction cap varies due to change in depletion layer as $V_{ds}$ changes.

Junction Capacitances :

Voltage dependent source substrate $E_1 C_{ab}$ junction to depletion capacitance.
It is due to depletion region surrounding the respective S & D diffusion regions embeded in the body.
Both junction are reversed biased under normal conditons
Junction cap is function of applied voltages.

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