problemset3 - Massachusetts Institute of Technology...

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_____________________________________________________________ Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.012 Microelectronic Devices and Circuits Homework #3 Problem 1 (10 points) The device drawn below is biased as shown, and a capacitance-voltage (C-V) measurement is taken. The area of the device is 10 -6 cm 2 . Assume the electrostatic potential in the n+ silicon region, φ n+ =550mV. A plot of (1/C) 2 as a function of the DC voltage, V, where C is the capacitance is shown below. The device is in reverse bias. The slope, S, is -5 * 10 26 F -2 V -1 . NOTE: The polarity of the DC source is shown correctly.
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a) Derive an expression for the doping, N a , in the p-type region in terms of the slope S, shown in the plot, and other known parameters (e.g. constants like q, ε Si , the device area). b) Assume now that N a is 10 17 cm -3 . Estimate the DC voltage V’ where the slope of the plot of (1/C) 2 vs. voltage changes, as seen in the graph. Problem 2 (35 points) A metal-oxide-semiconductor (MOS) device is pictured below. T ox is 15nm. Assume φ n+ =0.55V, and that N a in the p region is 10 16 cm -3 .
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