# hw2 - 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 #2 ­ September 16, 2005 Due: September 23, 2005 at recitation ( 2 PM latest) (late homework will not be accepted) Please write your recitation session time on your problem set solution. 1. [20 points] Consider a p­type Si sample with a resistivity of 2 Ω .cm at 300 K. At 300K, estimate the magnitude of: 1a. [5 points] Hole concentration, p o . 1b. [5 points] Electron concentration, n o . 1c. [5 points] What is an appropriate value for the hole mobility, µ p ? 1d. [5 points] What is an appropriate value for the electron mobility, µ n ? State whatever assumptions you need to make. 2. [20 points] Consider a sample prepared from the same material as in problem 1. This sample is at 300K. The geometry of the sample is such that it can be considered a one­ dimensional situation. At a certain location in this sample, we measure a drift current density of 10 4 A/cm 2 . J=10 4 A/cm 2 2a. [5 points] Estimate the magnitude of the electric ±eld at this location.² 2b. [5 points] Estimate the relative contribution of electron and hole drift to the total² current. 2c. [5 points] Estimate the hole drift velocity. 2d. [5 points] Estimate the electron drift velocity.

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3. [20 points] Consider a piece of n­type Si in thermal equilibrium at 300 K. In a region deFned by 0 x ( µm ) 10, there is a spatially varying electron concentration as sketched below. n o (cm -3 ) 10 17 n o ( x )= 10 17 0 . 2 x cm 3 with x in µm 10 16 10 15 10 14 0 5 1 0 x ( µ m) 3a) [5 points] Derive an analytical equation for the minority carrier concentration in space.
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## hw2 - Fall 2005 6.012 Microelectronic Devices and Circuits...

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