A silicon MOSFET has channel with length 0.2 mum and width 4 mum. The gate oxide

Question

A silicon MOSFET has channel with length 0.2 mum and width 4 mum. The gate oxide layers is 3 nm thick. The transconductance of the transistor is 3 mS. For this transistor. a) Find capacitance of the gate oxide. b) Find doping concentration of the wafer if the threshold voltage of this transistor is + 3V. c) Find saturation current of this transistor for gate voltage + 6V. d) Find molality of the change carries in the channel at a agate voltage of + 5V. e) Find capacitance of the depletion area at voltages + 7 V and - 2 V.

Explanation / Answer

Solution:

A) Oxide capacitance is given by ,

Cox =( e x ex ) A / tox   ... A = area ,  tox = oxide thickness , e x ex = oxide permittivity

Cox = 3.9 x 8.85 x 10 -14 / 3 x 10-7 = 1.15 uF / cm2

B) The threshold voltage is given by,

Vt = sqrt( 2 x es x q x Na ) / Cox ... Approximately because we do not have given other quantities like Vto , Vsb, fi F etc

Vt = sqrt( 2 x es x q x Na ) / Cox = sqrt (2 x 11.9 x 8.85 x 10-14 x 1.6 x 10-19 x Na ) / 3.9 x 8.85 x 10-14 / 3 x 10-7

3 x 1.3 x 8.85 x 10-7= sqrt (2 x 11.9 x 8.85 x 10-14 x 1.6 x 10-19 x Na )

( 1191.28 x 10-7 )2 = 2 x 11.9 x 8.85 x 10-14 x 1.6 x 10-19 x Na

Na = 4.21 x 1017 cm-3

C) The transconductance is given by

gm = 2ID / (Vgs - Vt) .... for the MOSFET to be in saturation

ID = gm (Vgs - Vt) / 2 = 3 x 10-3 (6-3) / 2 = 4.5 mA

D) The saturation current in MOSFET is given by,   

ID = uCox (W/L) (Vgs - Vt)2

u =  ID / [ Cox (W/L) (Vgs - Vt)2 ] = 4.5 x 10-3 / [ 1.15 x 10-6 x (4/0.2) x (5-3)2 ] = 49 cm2/ V-s

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