hw4_solutions - ECE 440 Homework IV Solutions Spring 2006...

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ECE 440 Homework IV Solutions Spring 2006 Due: Wednesday, February 08, 2006 1. In practice we assume that the intrinsic Fermi level, E i , coincides with the center of the band gap. In reality it is not true. Derive an expression relating the intrinsic level E i to the center of the band gap. Find the displacement of E i from the center of the band gap for both silicon and germanium at room temperature. The effective mass values are m n * = 0.55 m o for Ge and 1.1 m o for Si, m p * = 0.37 m o for Ge and 0.56m o for Si where m o is the free electron mass. We know that at thermal equilibrium, the intrinsic carrier concentrations for electrons and holes are equal. By setting equations 3-15 & 3-19 equal to one another, a relationship between the intrinsic Fermi Level and temperature can be found. At this stage, it is a good idea to draw an energy band diagram to visualize what these quantities physically mean. What we are saying here is that our intrinsic Fermi Level is simply half the energy band gap plus some offset term. You could have also defined the intrinsic Fermi Level as half the band
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hw4_solutions - ECE 440 Homework IV Solutions Spring 2006...

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