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# hw3 - 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 #3 - September 23, 2005 Due: September 30, 2005 at recitation 2 PM latest) (late homework will not be accepted) Please write your recitation session time on your problem set solution. 1. [30 points] In a certain region of an n-type semiconductor in thermal equilibrium at room temperature, there is an electric ±eld distribution in space as sketched below. E (V/cm) x ( μ m) 0 0 1 0.5 1200 for 0 <x< 1 μm : E = 600 { 1 + cos[10 4 π (2 x - 10 - 4 )] } V/cm with x in cm everywhere else: E =0 a) [10 points] Derive an analytical expression and sketch the electrostatic potential distri- bution in this region. b) [10 points] Derive an analytical expression and sketch the net volume charge density in this region. c) [10 points] If you are told that the equilibrium electron concentration at x =0is n o = 10 17 cm - 3 , compute the equilibrium electron concentration at x =1 μm ? 2. [20 points] A device design engineer in a group incharged of developing a very aggressive Si npn bipolar process becomes concerned with the suitability of the company’s device simulation tools to do the job. She argues that in an eﬀort to push the frequency response of the transistor, the base might become so thin, that perhaps carriers could cross it without (

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signifcant scattering. In this case, a device CAD tool that incorporates “ballistic” transport
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hw3 - Fall 2005 6.012 Microelectronic Devices and Circuits...

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