YOUR NAME Page 1 of 10 Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology 6.012 Electronic Devices and Circuits Exam No. 2 Wednesday, April 16, 2008 7:30 to 9:30 pm Notes: 1. An effort has been made to make the various parts of these problems independent ofeach other so if you have difficulty with one item go on, and come back later. 2. Some questions ask for an explanation of your answer. No credit will be given for answers lacking this explanation. 3. Unless otherwise indicated, you should assume room temperature and that kT/q is0.025 V. You should also approximate [(kT/q) ln 10] as 0.06 V. 4. Closed book; one sheet (2 pages) of notes permitted. Formula sheet provided. 5. All of your answers and any relevant work must appear on these pages. Any additional paper you hand in will not be graded. 6. Make reasonable approximations and assumptions. State and justify any such assumptions and approximations you do make. 7. Be careful to include the correct units with your answers when appropriate. 8. Be certain that you have all ten (10) pages of this exam booklet and the six (6) pageformula sheet, and make certain that you write your name at the top of this page inthe space provided. 6.012 Staff Use Only PROBLEM 1 (out of a possible 34) PROBLEM 2 (out of a possible 32) PROBLEM 3 (out of a possible 34) TOTALPage 2 of 10 Problem 1 - (34 points) A collection of independent short questions in two groupings. (a) You are in charge of a CMOS fabrication line and you have a problem because thethresholds of your n- and p-channel MOSFETs, which are supposed to be +1 V and -1 V, respectively, are turning out to be +3 V and +1 V, instead. You suspect thatthe interface between the silicon and the 20 nm thick oxide is contaminated with ions. (i) [4 pts] What type of device is each transistor, enhancement mode (no channel when vGS = 0) or depletion mode (strongly inverted when vGS = 0)? Explain your answers. n-channel MOSFET: because: Depletion mode ; Enhancement mode p-channel MOSFET: because: Depletion mode; Enhancement mode (ii) [4 pts] If you are right about the ions being the problem, what sign must theyhave, positive or negative. Explain your answer. Ion polarity: Positive; Negative because: (iii) [4 pts] You are able to reduce the ion problem sufficiently to have the thresholds now be 1.5 V for the n-channel device and - 0.5 V for the p-channel. What impact, if any, does this remaining threshold asymmetry have on aninverter with respect to the current charging the output node, changing it fromlow to high, when the input goes from high to low, compared to the ideal case?Assume VDD = 3 V. Explain. larger; smaller; it is similar because: Problem 1 continues on the next pageVGS: VBS: VDS: vgs: vds: vbs: Element: = Problem 1 continues on the next page Page 3 of 10 Problem 1 continued (iv) [4 pts] You are eventually able to solve the threshold asymmetry problem sothat the thresholds have the same magnitude, but to do so you had to double theoxide thickness of all MOSFETs (no other dimensions were changed). What impact, if any, does this thicker oxide have on the magnitudes of the thresholds,relative to the original design? Explain. larger; smaller; unchanged because (b) These questions concern the low frequency linear equivalent circuits of MOSFETs. (i) [6 pts] Consider the n-channel MOSFET circuit pictured to the right. The circuit is biased with VAC = 2 Volts. The MOSFET has following parameters: K = 2 mA/V2 VT = 1 V α = 1 λ = 0.01 V-1 η = 0.2 A small signal voltage, vac(t), is added to the 2 V bias so now vAC(t) = 2 V + vac(t). First find the bias and small signal values of vGS, vDS, and vBS, and then draw a single element small signal linear equivalent circuit for this connection and give an expression for this element in terms of gm and go. GSBDAC3V+!Linear equivalent circuit:Transconductance, gm = Output conductance, go = Page 4 of 10 Problem 1 continued (ii)[3 pts] Consider two MOSFETs, one an n-channel MOSFET and the other a p-channel MOSFET. They have identical dimensions, and both are biased in saturation at the same drain current, |ID|. Which of the devices, if either, would have the larger transconductance, gm, and why? n-channel; p-channel; they are similar because: (iii) [3 pts] Consider two MOSFETs, one an n-channel MOSFET and the other a p-channel MOSFET. They have identical dimensions, and both are biased in sub-threshold at the same drain current, |ID|. Which of the devices, if either, would have the larger transconductance, gm, and why? n-channel; p-channel; they are similar because: (iv) [6 pts] An n-channel MOSFET in a circuit was mistakenly biased in its linear region. Derive expressions in terms of VGS, VDS, and K for its transconductance, gm, and output conductance, go, in this situation. Assume vBS = 0 and α = 1, and ignore the Early effect, i.e., assume λ = 0. End of Problem 1Page 5 of 10 Problem 2 - (32 points) The ID-VDS plot for an ideal n-channel MOSFET (α=1) is shown below. The substrate bias, VBS, is 0 V, the saturation current, IDsat, is 10 mA, and the saturation voltage, VDS,sat,is 5 V. For this device tox=10 nm, εox= 3.5 x 10-13 F/cm, W= 50 µm, and L=10 µm. vDS [V]iD [mA]501.03.04.05.06.07.08.010ABC2.0(a) [4 pts] Given that VT = 1 V, what is the gate voltage VGS that must be applied to obtain the characteristic shown above? VGS = Volts (b) [5 pts] What is the slope, diD/dvDS of the characteristic at VDS = 0V? Make sure you provide a formula as well as a value so that your answer is independent of the correctness of your Part (a). diD/dvDS @ VDS = 0: Formula Value S Problem 2 continues on the next pagePage 6 of 10 Problem 2 continued (c) [8 pts] Since α =1 you can assume that VT is independent of position in the channel.With this assumption in mind calculate the inversion layer sheet charge density, qN*(y) corresponding to Bias Point A (i) adjacent to the source (the source end, y = 0)and (ii) adjacent to the drain (drain end, y = L). (i) qN*(0) at source end for Bias Point A: Coul/cm2 (ii) qN*(L) at drain end for Bias Point A: Coul/cm2 (d) [6 pts] Calculate the electron drift velocity, se-Drift, at the (i) source end and (ii) drain end of the channel at Bias Point A. If you could not solve
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