________________________________________________________________________________ MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.012 Microelectronic Devices and Circuits Homework #6 Problem 1 You are given an npn bipolar transistor which has uniform doping concentrations NdE = 1019 cm -3 NaB = 1017 cm -3 NdC = 1016 cm -3 . Assume the base width is 1 µm from the B-E junction to the B-C junction. The area of the emitter and collector is 10-6 cm2, µn = 1000 cm2/V-sec, µp = 500 cm2/V-sec. Ignore the depletion region width of forward biased junctions. a) Given VBE = 0.66V and VBC = -3V sketch the minority carrier concentration vs. x in all three regions of the device. b) Calculate xn and xp at the base-collector junction. c) Find the emitter width WE such that βF = 200. d) Find the collector width WC such that βR = 5. e) Calculate IS2 Problem 2 You are given the npn transistor with the parameters and operating point from Problem 1 above, with the additional information that Van = 20V. a) Find the transconductance, gm b) Find the input resistance, rπ c) Find the output resistance ro d) What is the minority electron storage QNB? e) Find Cπ f) At what frequency does 1 / j!C" = r" ? Problem 3 Silicon-Germanium bipolar transistors were developed in the late 1980’s to improve the current gain βF over that of conventional silicon transistors. When the emitter is made of this material we can assume that the intrinsic carrier concentration in the emitter is reduced to109 cm-3. This transistor is biased in the forward active region and has a collector current IC = 100µA. Use the same dimensions and doping concentrations as Problem 1 for this problem. a) Calculate the new VBE such that IC = 10µA b) Find the forward active current gain, βF. c) Determine the base doping level that will yield the same value of βF as the transistor would have if its emitter were silicon instead of SiGe? Problem 4 Howe and Sodini P7.6MIT 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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