# hw4 - obtain the intrinsic carrier concentration at 500 K...

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ECE 440 Homework IV 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. 2. A silicon sample is doped with 1x10 14 As atoms/cm 3 . (a) What are the electron and hole concentrations, respectively, at 500 K under equilibrium conditions? (b) Where is E F positioned relative to E i ? (c) Draw the energy band diagram for the material assuming that E i coincides with the center of the band gap. Refer to Fig. 3-17 or the attached graph to
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Unformatted text preview: obtain the intrinsic carrier concentration at 500 K. Also, the band gap energy is reduced to 1.08 eV at 500 K. 3. A compensated germanium sample is doped with 4x10 13 /cm 3 acceptors and 4x10 15 /cm 3 donors. (a) What are the electron and hole concentrations, respectively, at room temperature under equilibrium conditions? Repeat for (b) 4x10 13 /cm 3 acceptors and 4x10 14 /cm 3 donors (c) 4x10 13 /cm 3 acceptors and 6x10 13 /cm 3 donors and (d) 4x10 13 /cm 3 acceptors and 4.1x10 13 /cm 3 donors. Determine the percentage of error in each case for the majority carrier concentration if one simply assumes that the majority carrier concentration approximately equals the difference between the densities of donors and acceptors....
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