# hw4 - Fall 2005 6.012 Microelectronic Devices and Circuits...

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Fall 2005 6.012 Microelectronic Devices and Circuits Prof. J. A. del Alamo Homework #4 ­ September 30, 2005 Due: October 7, 2005 at recitation ( 2 PM latest) (late homework will not be accepted) Relative capacitance Please write your recitation session time on your problem set solution. 1. [30 points] In a paper on Si p­n junction varactors, you see the following graph with the capacitance­voltage characteristics of the diode at room temperature: 1 0.8 0.6 0.4 0.2 0 C(V=0)=8 pF A=16,000 µ m 2 -5 -4 -3 -2 -1 0 Voltage (V) Assuming that the diode is highly asymmetrically doped, reverse engineer the diode. a) [10 points] Estimate the built­in potential of the junction. b) [10 points] Estimate the depletion region thickness at V = 5 V . c) [5 points] Estimate the doping level of the lowly­doped side, N L . d) [5 points] Estimate the doping level of the highly­doped side, N H .

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2. [40 points] Consider the following MOS structure: n + polySi oxide p-Si � (N A =10 17 cm -3 ) contact contact V GB x -t ox 0 a) [10 points] Calculate the ﬂatband voltage.± b) [10 points] Calculate the extent of the depletion region in the
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