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Middle East Technical University

Electrical and Electronics Engineering Department

EE 212-Semiconductor Devices and Modeling

Homework (not to be collected)

Due May 21, 2014

1. Fill in the boxes given in the figure.

2. Consider the following MOS capacitor Draw the energy band diagram (only on thesemiconductor side) and charge distribution (on the metal and semiconductor sides)

under the following conditions. Show Ei and EFon the energy band diagram and define

the sources of semiconductor side charge on the charge distribution diagram.

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3. Draw the energy band diagram of a MOS capacitor on n-typesubstrate at the onset of stronginversion under an applied bias of V. Include and label in your diagram the following:

Metal Fermi Level: EFM

Semiconductor (Bulk) Fermi Level: EFS

Intrinsic Level: Ei

ECand EV

Surface Potential: S

Provide all the other necessary labels.

The dashed lines below show the boundaries between metal-oxide and oxide-semiconductor.

Metal Oxide Semiconductor

4. The following figure shows the characteristics of an enhancement type MOSFET. Provide therequired information.

MOSFET Type (n or p-channel):

Threshold Voltage:

Transconductance Parameter:

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5. Consider the following MOSFET. Assume that VDis small enough to operate the devicein the linear region.

a) Write the expression for the resistance (R) of the elemental volume (with length x) interms of x, electron mobility in the inversion layer (i), inversion charge per unit area (Q (x))and the other necessary parameters.

b) Express the inversion layer charge per unit area at location x (Q(x)) in terms of oxide

permittivity(),oxide thickness(tox),channel potential (V(x)), VGS and other necessaryparameters.

c) Express the potential drop ( V) on the channel elemental volume (with length x) in termsof channel current (ID), tox, , V(x), VGS, i, xand the other necessary parameters.

d) Derive the expression for the drain current (ID) in terms of tox, , VDS=VD, VGS,i, xand theother necessary parameters. You must use your result in part (c).

R=

V=

V(x)=VD=VDSat x=L

V(x)=VS=0 at x=0Threshold voltage=VT

Channel thickness (depth) at x=h(x)

Q(x)=

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6. Draw the internal structure of a p-channel enhancement type MOSFET operating in linear region onthe figure given below. Determine the range of the biasing voltage values (VGSand VDS) to operate thetransistor in linear region and fill in the boxes accordingly.

VGS

VDS

DS

G

B

v(0)=

vox

(0)=

v(L)=

vox

(L)=

v(x)=Potential at

point x with respect

to source

vox

= Potential

across the oxide

layer

VTP

0

a)The parameters of the transistor are: length of the channel (L), width of the channel (W), and thecapacitance per unit area (Cox). Express the average charge stored per unit length in the channel in terms

of the transistor parameters and biasing voltages. Clearly show each step of your derivation. (Hint:Assume v(x) changes linearly across the channel and use its average value).

b)Express the average drift velocity of the holes in the channel in terms of p, transistor parameters andbiasing voltages. Clearly show each step of your derivation and use the hint given in part (a).

c)Express ISDin terms of transistor parameters and biasing voltages.