ece340Fall03HW3sol - ECE 340 Homework III Fall 2003 Due:...

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ECE 340 Homework III Fall 2003 Due: Monday, September 15, 2003 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. Solutions: Equation (3-15): () / 0 cF EE k T c nN e −− = , for intrinsic material, n 0 = n i , E F = E i , / ci EEk T ic e = Equation (3-23): /2 g Ek T v N e = Therefore, / g T T cv c NNe Ne = , after simplification, we have: ln 2 g v c E N EE k T N =− + The energy level at the center of band gap 2 g center c E The displacement ln v i center c N k T N −= Equation (3-16), (3-20), 32 * 2 2 2 n c mk T N h π ⎛⎞ = ⎜⎟ ⎝⎠ , * 2 2 2 p v T N h = So we have * * 3 ln 4 p i center n m k T m (**) At T = 300K, 23 21 1.38 10 300 4.14 10 0.0259 kT J eV ×=× = For silicon, *
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ece340Fall03HW3sol - ECE 340 Homework III Fall 2003 Due:...

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