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

Question

A silicon MOSFET has channel with length 0.2 mum and width 4mum. 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 + 3 V c) Find saturation current of this transistor for gate voltage + 6 V. d) Find mobility of the charge earners in the channel at a gate voltage of + 5 V. e) Find capacitance of the depletion area at voltages + 7 V and - 2V.

Explanation / Answer

a) The gate oxide capacitance is given by,

Cox = (e x eox) / tox = 3.9 x 8.85 x 10-14 / 3 x 10-7 = 1.15 x 10-6 F/cm2

c) Saturation current

I = u cox (W/L) (Vgs - Vt)2

and transconductance, gm = 2I / (Vgs - Vt)

from the transconductance equation we get current,

I = [ gm  (Vgs - Vt) ] / 2

I = [ 3 x 10-3 x ( 6 - 3 ) ] /2 = 4.5 mA

d) The saturation current equation of n-channel MOSFET is

I = u Cox (W/L)  (Vgs - Vt)2   ......... where u is the mobility

u = I / [ Cox (W/L)  (Vgs - Vt)2 ]

u = 4.5 x 10-3 / [ 1.15 x 10-6 x (4 /0.2) x ( 6 - 3)2] = 21.7 cm2 / V-s

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