practice final exam

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 1 Practice Final Exam, EE3040A (Fall 2005)

Family Name:____________________________ Given Name___________________________ Georgia Tech ID#: _________________________ Instructions: Leave these sheets stapled together during the exam. Do not look at any pages of the exam (except this one) until I tell you

to begin.

PRINT your name on the exam (above) now and sign it below when you are finished with the exam.

IF you have questions, stay in your seat and raise your hand. I will come to your seat to discuss the exam.

The END sheets have equations and constants for your use in solving the problems on the exam.

No programmable calculators with pre-programmed equations should be used in this exam.

Turn off all cell phones, pagers, PDAs, i-pods, etc. Write legibly it I cant read it, you will get no credit! The exam will end at 5:40 PM when I will ask you to stop. Please

stop immediately when I tell you to.

Read all the problems carefully and thoroughly before you begin working. You are not allowed to

use any other notes or data in any form, including electronic form, during this exam. You are allowed to use a calculator without programmed equations. There are 245 REGULAR POINTS, 25 BONUS POINTS, and TWO ALTERNATE PROBLEMS in this exam. Observe the point value of each problem and allocate your time accordingly. SHOW ALL WORK AND CIRCLE YOUR FINAL ANSWER WITH THE PROPER UNITS INDICATED WHERE APPROPRIATE. Write legibly. If I can not read it, it will be considered to be a wrong answer. Do all work on the paper provided. You must turn in all pages of this exam before you leave. Good luck!

Report any and all ethics violations to ME immediately by raising your hand. At the end of the exam, sign your name on ONE of the two following statements: I DID NOT observe any ethical violations during this exam. __________________________ I DID observe an ethical violation during this exam. _________________________________

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 2 Short Answer Questions. Please answer the questions below as briefly as possible. 1. (4 pts) The general name for the crystalline structure of GaAs is _________________________ 2. (5 pts) What is the definition of a nondegenerate

semiconductor?________________________

3. (4 pts) What are the two dominant scattering mechanisms that determine the carrier mobility in a semiconductor?

4. (2 pt) Which one will predominate at high temperature? ________________________________ 5. (4 pts) State the photon energy requirement that corresponds to direct band-to-band

photogeneration of electron-hole-pairs in a semiconductor. _______________________________

6. (7 pts) In addition to the temperature, what seven other specific primary experimental parameters or values are required in to extract the Hall mobility of the semiconductor?

7. (2 pts) A 12 in. diameter Si wafer is doped with arsenic (Column V) at an impurity concentration level of 1 10 17 cm-3. The measured 300K electron mobility is 801 cm2/V-s and the hole mobility is 331 cm2/V-s for this silicon wafer. What is the type of the minority carrier (e or h)?

8. (4 pts) What are the two major breakdown mechanisms that account for the increase in the reverse-bias current in a real p-n junction diode________________________________________

9. (4 pts) What biasing condition is required in order for a light emitting diode (LED) to emit light?

10. (4 pts) What interaction(s) between electrons and holes is (are) is responsible for the photon emission under forward bias?

11. 4 pts) Which region of the LED (i.e., QNR, DR, etc.) contributes to the most photon generation?

12. (6 pts) How many equivalent {111} planes are there for a diamond structure? What are the specific Miller indices of these planes?

13. (4 pts) How can you tell an enhancement mode MOSFET from a depletion-mode MOSFET with just an Ohm meter?

14. (4 pts) What carrier type controls the operation of all bipolar transistors?

15. (4 pts) What carrier type controls the operation of all MOSFETs? Explain your answer.

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 3

16. (4 pts) The I-V characteristic for a Schottky barrier on n-type material is fundamentally different from that of an Ohmic contact to n-type material. What specific characteristic(s) of the metal-semiconductor junction is (are) primarily responsible for this difference?

17. (4 pts) What current transport process inside a semiconductor p-n junction that is illuminated with above-bandgap light is primarily responsible for the generation of power?

18. (4 pts) Consider a photodiode operating in an optical communication system. (1) What quadrant do you want to operate this device in? (2) What carrier transport process controls the magnitude of the current flowing in the device under illumination?

(1) (2)

19. (5 pts) A piece of n-type silicon with ND = 1017cm-3 is heated to 1000K. Sketch the energy band diagram under equilibrium at this temperature using the axes below. Clearly specify the positions of the following parameters: EG, Ev, Ec, EF, and Ei .

0

E

x 20. (4 pts) Clearly label and identify the four operation modes of a BJT in the following plot that

shows a typical common-emitter characteristic of a npn-BJT. Sketch the boundaries of these modes on the plot.

IC

VCE (for npn)

21. (4 pts) In a normal portable electronic circuit, the chemical reactions in a battery supply the

energy for the flow of current and the generation of a voltage drop. What process inside the

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 4 semiconductor provides this energy for a solar power panel, e.g., on the solar panels on the Opportunity and Spirit Mars Rovers?

22. (4 pts) Is the carrier mobility in the inversion layer of a Si MOSFET is generally LOWER or HIGHER than the mobility in a BULK layer having the same net free carrier concentration? Briefly explain your answer._______________________________________________________

23. (3 pts) In a normal PNP bipolar transistor, what are the generally desired relative doping concentrations in the emitter, base, and collector? NAE ___ NDB ; NDB ___ NAC ; NAC ___ NAE

24. (6 pts) What and where are the most important current components which control the magnitude of the current flowing in a p-n junction? Be very specificindicate the carrier type and the current type!

What:

Where:

25. (2 pts) In an enhancement-mode MOSFET, the most important change in the total charge for gate bias voltages beyond inversion is due to what source? _______________________________

Longer Answer Questions. Please answer the questions below draw diagrams carefully and write neatly! 26. (6 pts) In our simple model, there are two distinct sources of capacitance in a p-n junction.

What are they? Be specific and describe them completely!! Draw the charge distributions for these sources of capacitance on the scales below and label them clearly.

(1)

(2)

xp xn0 0

P N DR

5Ln 5Lp

QQ

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 5 27. PMOS band diagrams a. (10 pts) On the energy vs. x scales (shown on the next page) labeled "equilibrium", draw the

schematic energy-band diagram at equilibrium (V = 0) for a "real PMOS" capacitor made of a metal, SiO2 and Si. Draw the "complete" diagram including the vacuum energy level, Eo. Assume that the metal has a work function, m, that is larger than the semiconductor work function, s. Also assume that there are no extra insulator or interface charges. Assume that approximately 60% of the applied voltage is across the oxide layer and 40% is across the semiconductor. Label your drawing clearly, showing each of the important energies and potentials:

m, s, Ecox, Ec, Ev, EFs, EFm, Ei, Eo (or Evac), s, F,and s. b. (10 pts) On the E vs. x scales (shown on the next page) labeled "accumulation", draw the

schematic energy-band diagram for the above capacitor under the accumulation condition. Label all of the above energies and potentials, and the appropriate applied voltage, VA. For full credit, you MUST label the drawing completely.

c. (10 pts) On the E vs. x scales (shown on the next page) labeled "strong inversion", draw the schematic energy-band diagram for the above capacitor under strong inversion conditions. Label all of the energies and potentials listed in Part 1a, and the appropriate applied voltage, VA. For full credit, you MUST label the drawing completely.

28. (12 pts) In the diagram below, draw the total minority carrier distribution on a LINEAR SCALE for a P+-N-P- BJT under NORMAL FORWARD-ACTIVE MODE OPERATION. Clearly specify the polarity of VEB and VCB, the minority carrier types, and the boundary values (equations) of minority carrier concentrations in each region (in list below the figure). To construct carrier distribution profiles, you can use the narrow base approximation to simplify your drawing. The sketch of each curve should also reflect relative magnitudes of the equilibrium and excess carrier concentrations for a P+-N-P- BJT. Random drawings will receive zero crediteven if they look like a Picassouse your best engineering artistic skills.

pB nE nC P- DR DR

N

x'

base emitter collectorP+

x" 0 0 0 W x nE (x"=0) =______________________________; pB (x=0) = ______________________________ pB (x=W) = ___________________________nC (x=0) = _________________________________

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 6 Diagram for above Problem 27: Show a PMOS Capacitor with m >s: Show m, s, Ecox, Ec, Ev, EFs, EFm, Ei, Eo (or Evac), s, F, and s as well as the applied bias voltage,VA for each case.

M O S

M O S

M O S

equilibrium accumulation

strong inversion

E

E

E

x

x

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 7 29. (6 pts) Sketch below an inverting amplifier circuit and a non-inverting amplifier circuit

using a single ideal op-amp and a few selected resistors. In each diagram, label the circuit elements and the source voltage, vs, the input source current, is, the output current, io, and the output voltage, vo.

inverting op amp amplifier circuit noninverting op amp amplifier circuit 30. (6 pts) What are the voltage gain (in dB), input resistance, and output resistance of the inverting

amplifier if your values are R1 = 4.7k and R2 = 220k? 31. (6 pts) What are the voltage gain (in dB), input resistance, and output resistance of the

noninverting amplifier if your values are R1 = 8.2k and R2 = 680k?

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 8 32. (10 pts) Find the Q-point (ID,VDS) for the MOSFET in the two-resistor bias circuit as shown in

the following graph.

VDD

RDRG

ID

IG

+VGS -

+VDS

-

=10 k= 2

= 3.3 VKn = 260 A/V

2

VTN = 1 V

33. (15 pts) Analysis of an instrumentation amplifier: Assume ideal op amps in the circuit below

and also given that V1 = 2.5 V, V2 = 2.25 V, R1 = 15 k, R2 = 150 k, R3 = 15 k, and R4 = 30 k. Find the following values: va, vb, and vo, as defined in the graph.

va___________________________________; vb __________________________________; vo __________________________________

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 9 34. (5 pts) List the assumptions of the characteristics of an ideal op amp in terms of: input resistance: input current: output resistance: voltage gain: voltage relationship between two input terminals: 35. a. (10 pts) The voltage transfer characteristic (VTC) of a symmetrical CMOS inverter is shown

in the following graph. The VTC can be divided into five different regions as shown in the graph as well. Assume VTN = |VTP| = 1 V. Fill out the following table for the transistors operation modes in each region.

Region Input Voltage

VI Output Voltage

NMOS Transistor PMOS Transistor

1 vI VTN VH = VDD 2 VTN

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 10 36. A common-emitter amplifier stage shown schematically in the following plot is biased by

symmetrical positive and negative 5-V power supplies. The use of the second supply permits elimination of on e of the bias resistors in the base circuit. The remaining 100 k resistor is required to isolate the base node from ground so that the input-signal voltage can be applied to the base. Assume that the BJT parameters are F = 65 and VA = 50 V.

a. (10pts) Find DC Q-point (IC, VCE) and IB. Also verify the operation mode of the transistor. b. (5 pts) Draw the ac equivalent circuit below with the incorporation of small-signal BJT model.

Use a dashed line to identify the BJT portion. c. (15 pts) Given gm=40IC, r=F(kT/q)/IC, and ro=(VA+VCE)/IC for BJT small signal model, find the

AC small-signal input resistance (Rin), output resistance (Rout), and voltage gain (AV=vout/vI), as specified in the plot.

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 11 Alternate problems: You may substitute these ENTIRE Alternate problems for any of the above pointsyou must select problems totaling in the range of points from the above problemsyou cannot give these problems any other point value and you cannot do just part of these problems. Do not do these problems in addition to all of the above problems. You will not get any credit for these problems if you attempt all of the above problems. Indicate which problem(s) you are substituting for each Alternate Problem: Alternate Problem Al. Problem(s) ______________________

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 12 Alternate Problem A2. (8-10 pts) Problem(s) ______________________ A2.


Constants: kT(300K) = 0.026 eV k = 1.38x10-23 J/K h = 4.14x10-15 eV-sec q = 1.6x10-19 C mo = 9.11x10-31 kg k = 8.62x10-5 eV/K 1eV = 1.9x10-19 J 1 township = 23,040 sq. yards 1 kilometer = 49.71 chains 1 link = 0.01 chains Eg(Si, 300K) = 1.11eV 1 m = 1.0936 yards Eg(GaP, 300K) = 2.26eV Eg(GaAs, 300K) = 1.43eV Eg(Ge, 300K) = 0.67eV Eg(InP, 300K) = 1.35eV ni(Si, 300K) = 1.5 x 1010 cm-3 ni(Ge, 300K) = 2.5 x 1013 cm-3 1 pipe = 2 hogsheads 1 township = 23,040 sq. yards 1 square pole = 30.25 sq. yards 1 puncheon = 70 gallon 1 gill = 0.03125 gallon 1 square link = 1/24.7 m2 1 square perch = 1/160 acre 1 hand = 10.16 cm 1 cubit = 45.72 cm acre = 4,840 sq. yards PN-Junction:

soKxE

=

soKxV

=

2

2

2/1

)(2

+= biDADAos

n VNNNN

qKx

2/1

)(2

+= biDAADos

p VNNNN

qKx

2/1)(2

+=+ bi

DA

DAospn VNN

NNq

KxxW nDpA xNxN = )ln( 2i

DAbi n

NNq

kTV =

022

=n

ppn

ndx

ndD dx

ndqADI pnn

=

)/Lx(/kT)(qV

A

i

N

Nn

)/Lx(/kT)(qV

D

i

P

Pp

NA

PA

)e-eNn

LqDxJ

)e-eNn

LqDxJ

''

'

1()"(

1()(

2

2'

=

= )-eNL

DNL

DqnJ /kT)(qVAN

N

DP

Pi

A 1)(11(2 +=

qkTD =


MOS Capacitor:

TG VV inversion, strong ofonset theat

torsemiconduc type-n afor

torsemiconduc type-p afor

==

=

FS

i

D

i

A

F

nN

qkT

nN

qkT

2

ln

ln

==

i

A

A

oSF

A

oST n

NNq

kTKqNKW ln22 2

( ) FSSoS

Athicknessoxide

ox

SSG K

qNxKK

V 22 += 0for

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 16 MOSFET: ( ) )()()( NMOSyVVCyQ TGSoxN TGS VVfor Square-law

( ) TGSDsatDSDSDSTGSoxnD VVandVVVVVVLCZ

I

= 0.............2

2

( )[ ] DSDsatTGSoxnDsatD VVVVLCZII == ..............2 2 DSV

gs

DSm V

Ig | 9.3, == ox

oxide

oxoox Kt

KC

( )[ ]( ) DSDsatDSTGSoxnDsatD VVVVVLCZII +== 12 2 Small-Signal Y-parameters: For MOSFET common-source configuration: ig = y11vgs + y12vds id = y21 vgs + y22 vds For BJT common-emitter configuration: ib = y11vbe + y12vce ic = y21 vbe + y22 vce

gm = y21=I

C

VT

40IC

r = 1y21

= oVTI

C

= og

m ro = 1y

22

= VA +VCEI

C

VAI

C

Avt = vcvb =vovbe

=gmRL

Av = vovi =vovbe

vbevi

= Avt vbevi

Av = gmRLR

Br

RI+ R

Br( )

For pnp BJT:

)]1)()/sinh()/cosh(()1(

)/sinh(1[ /00

/0 += kTqV

B

BB

B

BC

C

CkTqV

BB

B

BC

CBEB eLWLWp

LDn

LDe

LWp

LDqAI

)]1()/sinh(

1)1)()/sinh()/cosh([( /0

/00 += kTqV

BB

BB

kTqV

B

B

B

BBE

E

EE

CBEB eLWL

DpeLWLW

LDpn

LDqAI

11/23/2005 Practice Final Exam Copyright R. D. Dupuis 17 Ebers-Moll Model (for pnp BJT):

))/sinh()/cosh(( 000

B

B

B

BBE

E

EF LW

LWLDpn

LDqAI += )1( /0 = kTqVFF EBeII

))/sinh()/cosh(( 000

B

BB

B

BC

C

CR LW

LWpLDn

LDqAI += )1( /0 = kTqVRR CBeII

)1()1( /0

/0 = kTqVRRkTqVFE CBEB eIeII

)1()1( /0/

0 = kTqVRkTqVFFC CBEB eIeII ICBO = (1- aF aR)IR0 ICEO = [(1- aF aR)/(1- aF )]IR0 BJT Small-Signal Performance Parameters

y12 =i

b

vce vbe = 0

= iBvCE Q po int

= 0

y21 =i

c

vbe vce = 0

= iCvBE Q po int

= ICVT

y22 =i

c

vce vbe = 0

= iCvCE Q po int

= ICVA +VCE

y11 =i

b

vbe vce = 0

= iBvBE Q po int

= ICoV

T Op Amps

AA

vvA

s

ov +== 1 2

111RRAideal +== 21

1

RRR+=

practice final exam

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