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ece340Spring04HW4Sol

# ece340Spring04HW4Sol - ECE 340 Homework IV Spring 2004 Due...

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ECE 340 Homework IV Spring 2004 Due: Monday, February 09, 2004 (30 points) 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 c F E E kT c n N e = , for intrinsic material, n 0 = n i , E F = E i , ( )/ c i E E kT i c n N e = Equation (3-23): /2 g E kT i c v n N N e = Therefore, / 2 ( )/ g c i E kT E E kT c v c N N e N e = , after simplification, we have: ln 2 g v i c c E N E E kT N = + The energy level at the center of band gap 2 g center c E E E = The displacement ln v i center c N E E kT N = Equation (3-16), (3-20), 3 2 * 2 2 2 n c m kT N h π = , 3 2 * 2 2 2 p v m kT N h π

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