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Sample_Final

# Sample_Final - School of Electrical and Computer...

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Unformatted text preview: School of Electrical and Computer Engineering EE 3040B: Migroelectronics Final Exam Georgia Institute of Technology NOTE: Please show all your work to obtain partial credit. The exam is closed boo You may use four handwritten sheets of formulas. NAB/[E Grade: / notes. mum...“ , “WW—W , ,WF. . maze «a “(Mm «.VxNMw-mmmw «aw—“van w Part I (30 points): In problems 1-10 circle the best answer to each problem. Each problem has 3 points. There is no penalty for incorrect answers. No partial credit is given. 1. What are the miller indices of the plane shown below? Assume that the lattice is cubic. Z a. (121) b. (212) c. (221) d. (211) 2. Al and Ga are both group HI elements, and As and Sb are both group V elements. Which one of the following represents a quaternary III-V semiconductor material? 21. A1025 Gaoso A5030 Pbms 13. A1025 Gao.75 A5035 Pbms 0. A1 Gaz AS sz d- a, b, and C 3. The energy band diagram of a semiconductor material is shown below. Using this ﬁgure, which one of the following statements is correct? a. Total current is zero everywhere (at all x). b. An externally applied electric ﬁeld exists. E F c. The material is uniformly doped with donors. , ’ ’ ' ' ' " ~ \ E . d. All of the above " A W 4. The excess hole concentration at the junction boundary on the n-side of a pn junction is 1/10 times the equilibrium hole concentration in the n—side (Apn(x=0) = 0.1 pno in the ﬁgure below). Assuming the junction to be at room temperature (T = 300 K), what is the bias voltage, VA? a. 0.025 V b. 0.6 V c. 0.0025 d. —0.6 V 5. Which one of the following statements about Fermi level (EF) is correct? a. The probability of ﬁnding an electron at energy E: is always 50%. b. The probability of a state at energy E1= EF— 2 AE being full is twice the probability of a state at E2 = E}: - AE c. The probability of a state at energy E1 = EF— AE being full is equal to the probability of a state at E2 = E: + AE being empty. d. The location of EF in a semiconductor material is approximately the middle of the bandgap. 6. In designing a two-stage BJT ampliﬁer shown below, we want to have a relatively large voltage gain, a moderate input resistance and a small output resistance. What combination of the stages is the appropriate choice? a. CE for stage 1 and CC for stage 2 \j: ~ ' + b. CE for both stages a - 9'43: \/,o 0. CE for stage 1 and CB for stage 2 ' ’ d. CC for stage 1 and CB for stage 2 - '3- 7. Which scattering mechanism :is the dominant source for mobility limitations in a MOSFET at room temperature? a. Impurity scattering b. Lattice scattering 0. Surface scattering d. All three mechanisms have comparable strengths 8. An ID-VD characteristic derived from an idea] MOSFET is pictured in the ﬁgure below. Given a turn-on voltage of VT = 1 V, what is the gate voltage one must apply to the MOSFET gate to obtain the pictured characteristics: a.VG=4V b.VG=9V c.VG=6V d.VG=llV vmssv IOV 9. What is the input resistance (R) of the ampliﬁer shown below? a. 1K9 b.2KQ c.4KS2 d. 00 10. What is the nominal output voltage at the low state (VOL) in the following MOS inverter? Assume that R = 100 KQ, Kn = 5 uA/Vz, and vTn = 1. L1 a. VOL = 0.25 V b. VOL = 0.5 V c. VG = 1 V d. none of the above V09 .1; V R Part H (70 points): Solve the following problems. Show all your work to obtain partial credit. Problem 1 (10 points) The resistance of a 1 cm long bar of n-type Si with cross sectional area of 2000 (pm)2 at equilibrium at room temperature (T = 300 K) is R = 100 K52. Assuming that for Si at room temperature, ni = 1010 cm'3, un= 1350 cmZ/(Vsec), and up=460 cmZ/(Vsec): (3) a. Find the concentration of donors (ND). (2) b. Find the location of Fermi level 03F) relative to E and draw the energy band diagram. (3) c. The sample is then uniformly illuminated with light. As a result, the resistance of the bar at steady state is reduced to R = 10 KS2. Find the excess hole concentrations (Apn) due to the light illumination. (2) d. Does low-level injection apply to this problem? Why? Problem 2 (13 points) A dimensioned energy band diagram for an ideal MOS-C operated at T = 300 K (ni = 1010 cm‘3 ) with VG at 0 is shown below. Using this ﬁgure: (4) (2) (2) (2) (3) EC \$0.661 2" :IO-Jev Ev a. Determine (pp and (pg. b. Is the semiconductor n-type or p-type? Also, ﬁnd the doping (donor or acceptor) concentration. 0. Determine V3. (1. Determine the oxide thickness x0. Use Ks = 11.8 and KO = 3.9. e. Sketch the block charge diagram corresponding to the state pictured in the energy band diagram. What is the state of the MOS-C (accumulation, depletion, or inversion)? L2 Problem 3 (10 points) Find and plot the transfer characteristics (v0 versus vi) for the following circuit. Assume both diodes are ideal. 61:9 Problem 4 (7 points) U Using Ebers-Moll model, derive the I-VA relationship for the device shown below. Problem 5 (14 points) For the MOSFET ampliﬁer circuits shown below, ﬁnd: (5) a. DC equivalent circuit and Q point (195 and VDS). (3) b. AC equivalent circuit, ampliﬁer conﬁguration (CS, CG or CD), and small signal model parameters. (2) 0. Voltage gain (vo/vs). (2) d. Input resistance Ri as speciﬁed in the circuit. (2) e. Output resistance R0 as speciﬁed in the circuit For the MOSFET, assume that VTn = 1 V, and K1] = 0.5 mA/VZ, and A. = 0. Problem 5 (14 points) For the MOSFET ampliﬁer circuits shown below, ﬁnd: (5) (3) (2) (2) (2) a. DC equivalent circuit and Q point (193 and VDS). b. AC equivalent circuit, ampliﬁer conﬁguration (CS, CG or CD), and small signal model parameters. c. Voltage gain (vo/vs). d. Input resistance R as speciﬁed in the circuit. e. Output resistance R0 as speciﬁed in the circuit For the MOSFET, assume that VTp = -1 V, and Kp = 0.4 mA/Vz, and A = 0. Other parameters are R1=2.2MQ,R2=2.2KQ,R4=22KQ,RD= l8KQ,andVDD= 18V. Extra work on Problem 5 Problem 6 (10 points) For the BJ T differential ampliﬁer circuits shown below, ﬁnd: (4) a. The Q point of the transistors (1c and VCE). Assume that the transistors are identical (3) b. Draw the differential-mode half-circuit and ﬁnd the differential-mode gain (Adm). (3) 0. Draw the common-mode half-circuit and ﬁnd the common-mode gain (Am). For both transistor, assume that VBE = 0.7 in the active region, and BF = [30 = 150, and VA = 00. Other parameters are REE = 200 KQ, R1 = 2 K9, RC = 200 K9, and VEE = Vcc = 22 V. I +VCC bl Problem 7 (6 points) Find the logic function (Y) implemented by the following NMOS logic circuit. ...
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