# hw5_solutions - ECE 440 Homework V Solutions Spring 2006...

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ECE 440 Homework V Solutions Spring 2006 Due: Friday, February 17, 2006 1. (a) A Si bar 0.1 cm long and 100 μm 2 in cross-sectional area is doped with 5x10 16 /cm 3 arsenic atoms. Find the current at 300 K with 10 V applied across the length. To find current, use Ohm’s law: Since we already know the bias, all we need to do is find is the resistance (R) in order to solve for the current. Equation (3-44) gives resistance in terms of area, charge carriers, and mobilities. If we substitute (3-44) into Ohm’s Law, we get the following expression for current. Notice that this is the formula for the drift current which was derived in the text. Keep in mind that this expression is only valid if the drift velocity of the carriers is smaller than the saturation velocity. The saturation velocity is fixed for a particular material system. For Silicon, the saturation velocity is approximately 10 7 cm/s. First, we need to check that we are not in the saturation condition. For an electron concentration of 5x10 16 cm -3 , we can find an electron mobility of 825 cm 2 /V- s. Plugging into the equation we find Since we are not in the saturation condition we can use (*) to solve for the current.

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(b) Repeat for a similar Si bar 1 μm long. Using the same procedure as in (a) we first check saturation: Since we are in the saturation condition, we have to calculate current using the saturaton velocity. (c) Back to part (a); assuming the silicon bar warms up considerably to 600 K due to poor heat conduction, do you expect the current readout stays the same as that at 300 K? Will the current increase or decrease? Will the carrier concentration remain about the same? Use the attached carrier-temperature chart in HW IV to estimate the carrier concentration. If we were to raise the temperature to 600K, several system parameters would change. Some
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## This note was uploaded on 12/01/2011 for the course ECE 340 taught by Professor Leburton during the Spring '11 term at University of Illinois, Urbana Champaign.

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hw5_solutions - ECE 440 Homework V Solutions Spring 2006...

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