Page 1 of 15

EE 330 Name_ _ _ _ _ _ _ _ _ _ _ _ _ _

Final Exam

Fall 2013

Instructions: Students may bring 4 pages of notes (4 front + 4 back) to this exam. There

are 10 questions and 8 problems. There are two points allocated to each question. All

problems are worth 10 points. Please solve problems in the space provided on this exam.

Attach extra sheets only if you run out of space in solving a specific problem.

If references to semiconductor processes are needed beyond what is given in a

specific problem or question, assume a CMOS process is available with the following key

process parameters; nCOX=100A/V2 pCOX=nCOX/3 ,VTNO=0.5V, VTPO= - 0.5V,

COX=4fF/2, = 0, and If reference to a bipolar process is made, assume this

process has key process parameters for an npn transistor of JS=10-15

A/2, βn=100 and

VAFn = ∞ and those for a pnp transistor are JS=10-15

A/2, βp=20 and VAFp = ∞. If any

other process parameters are needed, use the process parameters associated with the

process described in the attachments to this exam. Specify clearly what process

parameters you are using in any solution requiring process parameters. Several tables

that may be of use are appended at the end of the exam.

1. (2 pts) When sizing devices in static CMOS gates, one strategy is “equal worst-case

rise and fall times”. Why is the adjective “worst-case” added rather than simply

stating “equal rise and fall times”?

2. We have used the terms n-, n, and n

+ to denote relative doping levels of silicon. In the

context of the CMOS processes we have discussed, what is the approximate ratio of

doping levels between regions designated with n and those designated with n+ ?

3. (2 pts) In static CMOS circuits, NAND gates offer some benefits over NOR gates

when the number of inputs is large. Give one of the major benefits of the NAND

gates.

4. (2 pts) What company is the largest semiconductor manufacturer in the world?

Page 2 of 15

5. (2 pts) In the 90nm process node, the thickness of the SiO2 gate is about 1.2nm.

How many SiO2 molecules stacked vertically on top of each other is required to make

the 1.2nm gate oxide?

6. (2pts) There are many tradeoffs in performance between minimum-sized static

CMOS logic gates and equal worst-case rise/fall time static CMOS gates. One of the

advantages of minimum-sized static CMOS logic gates is the reduced area though

that benefit is often small because overhead for layout and interconnects is still

dominant. But one benefit of minimum-sized gates is substantial. What is that?

7. (2pts) What is the major limitation of NMOS logic compared to CMOS logic?

8. (2 pts) Of the basic MOS amplifier structures, which is noted for having a large

noninverting voltage gain?

9. (2 pts) What is the major contributor to defects in semiconductor process?

10. (2pts) Why is COX for the n-channel transistors and the p-channel transistors nearly

identical for the 0.5µm CMOS process?

Page 3 of 15

Problem 1 A polysilicon interconnect that is 1mm long and 1µm wide is driving an

equal rise/fall inverter with an OD of 20 as shown in the figure. Assume this interconnect

is in the process characterized by the description in the attachment at the end of this

exam. A reference inverter in this process is shown below.

a) Using a three-segment Elmore delay model, calculate the delay of a Boolean low-

to-high signal transition that propagates from point A to point B in this interconnect bus.

b) Calculate the propagation delay (tHL+tLH) from A to C. Assume VDD=3.5V.

1μ

50fF

A B

20

C

Page 4 of 15

Problem 2 The standard static CMOS inverter is shown below. The trip point for

this inverter is given by the expression

Mathematically derive this expression.

M1

M2

VDD

VINVOUT

p1 2

Tn DD Tp

1 n 2

TRIP

p1 2

1 n 2

μW WV V +V

L μ LV

μW W

L μ L

Page 5 of 15

Problem 3 An amplifier circuit is shown below. Assume C1 is large.

a) Determine the quiescent output voltage

b) Determine the small-signal voltage gain in terms of the small-signal model

parameters and the resistors in the circuit

c) Numerically determine the small-signal voltage gain.

VIN

VOUT

VDD=5V

C1

W=20µ

L=4µ

10K

300µA

2.5K

RB

RD

Page 6 of 15

Problem 4 A section of a logic block is shown below. Assume all devices are sized

for equal worst-case rise and fall times and that the overdrives, if different than 1, are as

indicated. If the input A is a 10MHz square wave, determine the dynamic power

dissipation in the inverter with OD=2. Assume VDD=3.5V. The characteristics of a

reference inverter in the process used for the design of the logic block are shown below.

A F

6

2

Page 7 of 15

Problem 5 A segment of a logic block is shown below. Assume the lengths of all

devices are LMIN. Assume all gates are sized for equal worst-case rise and fall times.

Gates with an overdrive factor that is different than 1 are as indicated by a number on the

gate. Assume that the process in which these gates are fabricated is characterized by a

minimum length reference inverter with

tREF=20ps, CREF=4fF, RPDREF=2.5K

a) Determine the worst-case propagation delay from B to F

4

4

8

A

B

F

4

2

10fF 12fF

24fF

H

Page 8 of 15

b) Repeat part a) if all gates are minimum sized.

Page 9 of 15

Problem 6 A nonlinear two-port network is shown below along with the relationship

between the electrical port variables for this network.

V2V1

I1 I2

Nonlinear Two-Port

3

I 1

2

2 1 2

I = 0.25 V -2

I = V V

a) Determine I1Q and I2Q if V1Q=4V and V2Q=2V

b) Obtain the small-signal equivalent circuit at the Q-point defined in part a)

c) Obtain the small-signal two-port amplifier model (RIN, ROUT, AV, AVR) at the Q-

point defined in part a)

Page 10 of 15

Problem 7 Consider the amplifier block shown below. Assume all MOS transistors

are operating in the saturation region and the BJT is operating in the forward active

region. Assume the capacitors are all large.

a) Draw the small-signal equivalent circuit of this amplifier

b) Determine the small-signal voltage gain in terms of the model parameters of the

transistors and the components in the circuit

c) Determine the input impedance in terms of the model parameters of the transistors

and the components in the circuit

Q2

M4

M3M1

R1R3

R2

R5

R4

VOUT

VIN

VXX=10V

W=10µ

L=1µ

W=20µ

L=1µ

W=9µ

L=8µ

AE=100µ2

R6

C1

C2

Page 11 of 15

Problem 8 The ID-VDS characteristics for a MOSFET with different values of VGS are

shown below. The dimensions of the device are W=15µm and L=3µm.

a) Determine VTH for this transistor

b) Determine µCOX for this transistor

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10

ID(m

A)

VDS

VGS=2.5V

VGS=3V

VGS=3.5V

VGS=4V

VDS

I D(m

A)

Page 12 of 15

TRANSISTOR PARAMETERS W/L N-CHANNEL P-CHANNEL UNITS

MINIMUM 3.0/0.6

Vth 0.78 -0.93 volts

SHORT 20.0/0.6

Idss 439 -238 uA/um

Vth 0.69 -0.90 volts

Vpt 10.0 -10.0 volts

WIDE 20.0/0.6

Ids0 < 2.5 < 2.5 pA/um

LARGE 50/50

Vth 0.70 -0.95 volts

Vjbkd 11.4 -11.7 volts

Ijlk <50.0 <50.0 pA

Gamma 0.50 0.58 V^0.5

K' (Uo*Cox/2) 56.9 -18.4 uA/V^2

Low-field Mobility 474.57 153.46 cm^2/V*s

COMMENTS: XL_AMI_C5F

FOX TRANSISTORS GATE N+ACTIVE P+ACTIVE UNITS

Vth Poly >15.0 <-15.0 volts

PROCESS PARAMETERS N+ACTV P+ACTV POLY PLY2_HR POLY2 MTL1 MTL2 UNITS

Sheet Resistance 82.7 103.2 21.7 984 39.7 0.09 0.09 ohms/sq

Contact Resistance 56.2 118.4 14.6 24.0 0.78 ohms

Gate Oxide Thickness 144 angstrom

PROCESS PARAMETERS MTL3 N\PLY N_WELL UNITS

Sheet Resistance 0.05 824 815 ohms/sq

Contact Resistance 0.78 ohms

COMMENTS: N\POLY is N-well under polysilicon.

CAPACITANCE PARAMETERS N+ACTV P+ACTV POLY POLY2 M1 M2 M3 N_WELL UNITS

Area (substrate) 429 721 82 32 17 10 40 aF/um^2

Area (N+active) 2401 36 16 12 aF/um^2

Area (P+active) 2308 aF/um^2

Area (poly) 864 61 17 9 aF/um^2

Area (poly2) 53 aF/um^2

Area (metal1) 34 13 aF/um^2

Area (metal2) 32 aF/um^2

Fringe (substrate) 311 256 74 58 39 aF/um

Fringe (poly) 53 40 28 aF/um

Fringe (metal1) 55 32 aF/um

Fringe (metal2) 48 aF/um

Overlap (N+active) 206 aF/um

Overlap (P+active) 278 aF/um

Page 13 of 15

Page 14 of 15

CIN/CREF

Equal Rise/Fall

Inverter

NAND

NOR

1

3k+1

4

3+k

4

Minimum Sized

Overdrive

HL

LH

1

1

1/2

1/2

1/2

1

1/3NOR

NAND

Inverter

HL

LH

HL

LH

1

1

1

1

1

1/(3k)

1/k

1/3

Equal Rise/Fall(with OD)

OD

3k+1OD

4

3+kOD

4

Asymmetric OD (ODHL, ODLH)

HL LHOD +3 OD

4

OD

OD

OD

OD

OD

OD

HL LHOD +3k OD

4

HL LHk OD +3 OD

4

ODHL

ODLH

ODHL

ODLH

ODHL

ODLH

n

I(k+1)

k=1 k

F

OD

n

I(k+1)

k=1

F 1

n

I(k+1)

k=1 HLk LHk

1 1F

2 OD ODtPROP/tREF

1

n

I(k+1)

k=1 HLk LHk

1 1F

2 OD OD

MOD

HL

LH

OD

OD

Propagation Delay in Logic Circuits with OD and Asymetry

Page 15 of 15