_____________________________________________________________ 6.012 Microelectronic Devices and Circuits Spring 2007 April 25, 2007 Quiz #2 Problem #points NAME___________________________________ 1___________ RECITATION TIME___________________________ 2___________ 3___________ Total______________ General guidelines (please read carefully before starting): • Make sure to write your name on the space provided above. • Open book: you can use any material you wish. But no computers. • All answers should be given in the space provided. Please do not turn in any extra material. • You have 120 minutes to complete the quiz. • Make reasonable approximations and state them, i.e. low-level injection, extrinsic semiconductor, quasi-neutrality, etc. • Partial credit will be given for setting up problems without calculations. NO credit will be given for answers without reasons. • Use the symbols utilized in class for the various physical parameters, i.e. Na, τ, ε, etc. • Pay attention to problems in which numerical answers are expected. An algebraic answer will not accrue full points. Every numerical answer must have the proper units next to it. Points will be subtracted for answers without units or with wrong units. In situations with a defined axis, the sign of the result is also part of the answer. Unless otherwise stated, use: q = 1.6 X 10-19 C kT/q = 25 mV at room temperature ni = 1010 cm-3 for silicon at room temperature εsi = 10-12 F/cm εox = 3.45X10-13 F/cm 11. (30 points) You are given a CMOS inverter with a step input voltage from 0 to VDD at t = 0 , resulting in an output voltage VOUT vs. t shown below. The load capacitance CL = 0.1pF accounts for all load capacitance components. VIN VDD VIN VOUT VDD CL = 0.1pF t0 ΔVOUT Δt =1 V nS VDD VDD 2 VOUT t0 (a) Given VDD = 1.5V and that the devices are sized such that VM = VDD ,2 calculate tpHL . 2(b) Calculate the current IDn at 0 < t < tpHL . 50µAW(c) Given VTn = 0.5V and µnCox = , find of the NMOS transistor. V 2 L 3For parts (d) and (e) assume VDD = 2.5V . ΔVOUT (d) Calculate the new slope of the output voltage , at 0 < t < tpHL .Δt (e) Calculate the new tpHL . 42. (35 points) You are given a p-n junction diode that is conducting a current ID equal to 2µA when a voltage, VD , is applied. Assume no generation or recombination inside the diode, and ignore the space charge region width in your calculations for this problem. VD →IDND = 1016 cm−3 + − NA = 1016 cm−3 Diode parameters Dn = 20cm2 / sec Dp = 10cm2 / sec Area 2x10−6 cm2 −5µm 05µm (a) Calculate the minority carrier concentrations np (0), pn (0) . 5(b) Calculate VD . (c) What is the total majority carrier current on the n-side of the diode? 6(d) Calculate the majority carrier diffusion current on the n-side of the diode. Hint: Quasi neutrality implies nn (x) = pn (x) . (e) Calculate the electric field in the quasi-neutral region on the n-side of the diode. 73. (35 points) An npn bipolar transistor has Dn = 25cm2/ s and Dp = 12.5cm2/ s . The common emitter output characteristics are as follows: IC (A) IC = 300µA IC = 318µA ↓↓ IB = 3µA VCE VCE (V )54321 IB → (a) Find the transconductance, gm , at VCE = 2V, IB = 3µA . (b) Find the input resistance, rπ , at VCE = 2V, IB = 3µA . 8(c) Find the output resistance, ro , at VCE = 2V, IB = 3µA. (d) Given the input capacitance, Cπ= 0.2 pF at VCE = 2V, IB = 3µA , estimate the width of the quasi-neutral base region. Neglect the capacitance due to the emitter-base space charge region. 9(e) Estimate the number of excess minority electrons in the base under the same bias conditions as in (d) above. (f) If the quasi-neutral base width is reduced by a factor of two, calculate the number of excess electrons in the base under the same bias conditions as in (e) above. 10MIT OpenCourseWare http://ocw.mit.edu 6.012 Microelectronic Devices and CircuitsSpring 2009 For information about citing these materials or our Terms of Use, visit:
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