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Unformatted text preview: Page 1 of 12 YOUR NAME Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology 6.012 Electronic Devices and Circuits
Open book. Notes: 1. Unless otherwise indicated, assume room temperature and that kT/q is 0.025 V, kT/q ln 10 = 60 mV, and ni = 1010 cm-3 for Si. 2. This test is designed so that most parts can be worked independently of the others. 3. All of your answers and any relevant work must appear on these pages. Any additional paper you hand in will not be graded. 4. Make reasonable approximations and assumptions. State and justify any such assumptions and approximations. 5. Be certain that you have all twelve (12) pages of this exam booklet and make certain that you write your name at the top of this page as indicated. 6. You may see your final exam in Room 13-3058 beginning June 5, 2000. Grader Use Only PROBLEM 1 PROBLEM 2 PROBLEM 3 PROBLEM 4 TOTAL (out of 20 possible) (out of 25 possible) (out of 28 possible) (out of 27 possible) Problem 1 - (20 points) Warm-up questions: a) Page 2 of 12 A sample of silicon is known to contain 101 7 cm-3 arsenic atoms (column V) and 5 x 101 6 cm-3 boron atoms (column III). What are the thermal equilibrium hole and electron concentrations in this sample at room temperature where ni = 101 0 cm-3? no = po = b) cm-3 cm-3 A high quality long base silicon p-n diode is inadvertently irradiated in a nuclear reactor with the consequence that the minority carrier lifetimes on the n- and psides decrease from 10-4 s to 10-8 s (no other materials parameters change). How much, if at all, does the diode saturation current change? IES(after) IES(before) c) i) Rank order the common-emitter (CE), common-base (CB), emitter follower (EF) bipolar linear amplifier configurations in order of increasing input resistance, assuming comparable bias levels, IC: Lowest Explanations: Middle Highest ii) Rank order the common-source (CS), common-gate (CG), source follower (SF) MOSFET linear amplifier configurations in order of increasing output resistance, assuming comparable bias levels, ID: Lowest Explanations: Middle Highest Problem 1 continues on the next page. Problem 1 continued d) Answer in five words or less: Page 3 of 12 i) CMOS is one of the fastest MOSFET logic families and it is used in the highest speed microprocessors. At the same time, one of the most important applications for CMOS is in low speed circuitry. What is CMOS's advantage for low speed applications? ii) What major structural change was made to enable the 486 to run faster than the 386 (and again to make the Pentium faster than the 486)? iii) Why is CMOS attractive for linear amplifier applications? Give one reason (there are several). e) A certain common-emitter bipolar transistor amplifier is fabricated using resistors whose resistance is insensitive to temperature and with transistors whose forward current gain, b F, Early voltage, VA, and base-emitter knee voltage, VBE,ON, are essentially unchanged between room temperature (25C) and 100C. None the less, when this amplifier is heated to 100C its voltage gain, Av, drops noticably. Give an explanation as to why the voltage gain might change and use your explanation to estimate Av(100C)/Av(25C). Av(100C)/Av(25C) End of Problem 1 Problem 2 - (25 points) Page 4 of 12 The symmetric p-n diode shown below, with NAp = NNn = 101 6 cm-3, is illuminated by steady state light that generates M hole-electron pairs/cm2 -s uniformly over the plane at x = 2 wn/3. The p- and n- region widths, wn and wp, are both 6 m, and both minority carrier diffusion lengths are much larger than this, i.e., Le, Lh >> 6 m. The electron mobility, e, is 1600 cm2 /V-s, and the hole mobility, h, is 600 cm2 /Vs. Neglect the depletion region widths relative to 6 m. M
Ohmic Ohmic A V
AB + -w p
(-6m) p-type -3 1016cm n-type 1016cm-3 B wn
(6m) x a) On the axes below plot the excess minority carrier concentrations throughout the diode when VAB = 0.54 V and M = 0. n'(x), p'(x) -w p b) wn x If we take as the criterion for low level injection (LLI) that the excess minority carrier concentration must not exceed 10% of the equilibrium majority carrier concentration, how large can VAB be before LLI is violated when M = 0? VAB c) Now consider setting VAB = 0, i.e., short circuiting the diode, and applying illumination, M = 3.75 x 101 3 cm-2s-1. On the axes provided at the top of the next page plot the excess minority carrier concentrations throughout the diode now. Assume p' has the value indicated on the axes at x = 2wn/3. Problem 2 continues on the next page. Problem 2 continued n'(x), p'(x) p'(2wn/3) Page 5 of 12 d) x wn -w p On the axes below make labeled plots of the hole current density, jH; the electron current density, jE ; and the total current density, jTOTAL; throughout the shortcircuited, illuminated device. i) Hole current density: jH -w p wn x ii) Electron current density: jE -w p wn x iii) Total current density: j TOTAL -w p wn x Problem 2 continues on the next page. Problem 2 continued e) i) What is p'(2wn/3)? Page 6 of 12 p'(2wn/3) = ii) How large can M be before LLI is violated when VAB = 0? M End of Problem 2 Problem 3 - (28 points) Page 7 of 12 Consider the two silicon device structures shown in cross-section below: Device A: G
n+ Device B: G
n+ 15 m p-Si B 5 m 20 m p-Si B Both of these devices are made on p-type silicon with a net doping level of 1017 cm-3, and are 20 m wide normal to the page. The n+ regions are doped to 1018 cm-3, and the n+-p junction is 1 m from the top surface. The thin oxide is a high quality thermal oxide 16 nm thick, and covers an area 20 m wide by 15 m long. In Device A the n+ region is 20 m wide by 5 m long and extends just up to the edge of the thin oxide, while in Device B it is 20 m wide by 20 m long and extends all the way under the thin oxide, as shown in the figure. You may assume that throughout the silicon the electron mobility, e, is 1600 cm2/V-s and the hole mobility, h , is 600 cm2/V-s (except in an inversion layer in which case e = 600 cm2/V-s and h = 400 cm2/V-s); that the intrinsic carrier concentration, ni , is 1010 cm-3 at room temperature; and that the dielectric constant, eS i, is 10-12 F/cm. The dielectric constant of the oxide, eox, is 3 x 10-13 F/cm, and the electrostatic potential of the gate metal relative to intrinsic Si is 0.3 V. a) i) What is the electrostatic potential of the p-type silicon, relative to intrinisic silicon, in thermal equilibrium at room temperature? Electrostatic potential = ii) What is the built-in potential of the unbiased n+-p junction at room temperature? Built-in potential = Problem 3 contines on the next page. Problem 3 continued b) Page 8 of 12 What are the flat band voltages, VF B, of the MOS capacitor structures in Devices A and B, respectively? VF B (Device A) = VF B (Device B) = c ) The magnitude of the threshold voltage, |VT|, for the MOS structure is 1 V in one of these devices, and 4 V in the other. Use this information and your knowledge of MOS capacitors to deduce the magnitude and sign of VT for each of these MOS capacitors, i.e., the one made on p-Si and the made on n+-Si. VT (Device A) = VT (Device B) = d) What is the condition (accumulated, depleted, or inverted) of the semiconductor surface under the thin oxide in each of these devices with a gate voltage, VGB, of 2 Volts? Also give the identity and sheet density of any mobile holes or electrons induced at the oxide-silicon interface. Device A: Surface condition: Carrier type and sheet concentration: Device B: Surface condition: Carrier type and concentration: Problem 3 continues on the next page Problem 3 continued Page 9 of 12 Next consider using these devices as the storage capacitor in the dynamic memory cell illustrated below. The MOSFET is an n-channel device with a threshold voltage, VT, of 0.75 V (ignor any variation with vB S) and a drain current in saturation of 0.1 (vGS VT)2 mA.
A n-channel MOSFET +2V + vAB
G + vG - Device A or B B e) If VGB is initially 0 V and VA B is increased from 0 V to 2 V, what will the new value of VGB be? f) After having been 2 V for a long period of time, VA B is switched to 0 V at t = 0. How will VGB vary with time for t > 0? Give its initial value and describe how it changes with time, if at all. End of Problem 3 Problem 4 - (27 points) Consider the differential amplifier circuit illustrated below: +2V R4 = 6.4 kW Q4 Q3 + vIN2 CS IBias Q7 R5 Page 10 of 12 R2 R3 0V IQ4 = 2 mA R1 + vIN1 - Q1 Q2 + vOUT 100 W Q5 Q6 -2V In this circuit the three n-channel MOSFETs are identical; they have a threshold voltage, VT, of 1 V, a drain current in saturation of 2.5(vGS - VT)2 mA, and an Early voltage of 10 V. The MOSFETS do not operate properly if (vGS - VT) is less than 0.2 V. The npn bipolar junction transistors (BJTs) all have forward betas, b F , of 100, reverse betas, b R, of 5, and an Early voltage of 50 V. The BJT sizes have been adjusted to that to a good approximation you may use |VBE,ON| = 0.6 V; |VCE,SAT| = 0.2 V. Assume C S is a short at mid-band frequencies, and R2 and R3 are identical. Note that value of the resistor R4, the quiescent collector current on Q4, and minimum quiescent voltage on the gate of Q3 are indicated on the schematic, as are the supply voltages. a) What must the bias level (IBias) on Q3 be to have a quiescent output voltage of approximately 0 V? (Assume that the quiescent collector current of Q4 is 2 mA, as indicated, and do not forget its base current.) IBias = Problem 4 continues on the next page mA Problem 4 continued b) Page 11 of 12 Select R5 be to be consistent with a quiescent collector current in Q4 of 2 mA, and a quiescent output voltage of approximately 0 V. R5 = c) W Select R1 to give a bias current through Q5 of 1 mA. You may ignor the base currents of Q5, Q6, and Q7. R1 = d) W i) In the space below sketch a small signal linear equivalent half circuit one could use to calculate the signal voltage on the gate of Q3 due to the difference-mode input signal, vin1 - vin2. Find an expression for this voltage in terms of incremental linear equivalent circuit model parameters. ii) Write an expression for the differential-mode voltage gain of the differential stage (Q1, Q2) in terms of the resistors, the MOSFET K-factors, and the quiescent bias levels of Q1 and Q2. Select R2 (= R3) and the drain current of Q1 and Q2 to maximize this voltage gain (magnitude). ID = mA, R2 = (= R3) , |Avd,max| = Problem 4 continues on the next page Problem 4 continued e) Page 12 of 12 Suppose you can replace R2 and R3 with a current mirror made with p-channel MOSFETs with |VT| = 1 V and |VA| = 20 V. In the space below draw the schematic of such a current mirror, and discuss what inpact this would have on the voltage gain. f) Looking at the output stage, what are the most positive and negative values of vout possible? Explain your answers. < vout < End of Problem 4 and the Exam. ...
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This note was uploaded on 07/20/2009 for the course CSAIL 6.012 taught by Professor Prof.cliftonfonstadjr. during the Fall '03 term at MIT.
- Fall '03