Week6HWSolutions

Week6HWSolutions - Mark Lundstrom SOLUTIONS ECE 656...

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Mark Lundstrom 9/27/13 ECE-656 Fall 2013 1 SOLUTIONS: ECE 656 Homework (Week 6) Mark Lundstrom Purdue University 1) In Lecture 14, we discussed M(E) for a 3D semiconductor with parabolic energy bands. Answer the following two questions about a 3D semiconductor with non-parabolic energy bands. a) Assume that the non-parabolicity can be described by E 1 + ! E ( ) = ! 2 k 2 2 m * 0 ( ) . Derive an expression for the corresponding M E ( ) . b) Using the following numbers for GaAs m * 0 ( ) = 0.067 m 0 = 0.64 , plot M E ( ) from the bottom of the ! valley to E = 0.3 eV comparing results from the non-parabolic expression derived in part a) to the parabolic expression quoted in the lecture. Solutions: a) Begin with the definition: M 3 D E ( ) = h 4 x + D 3 D E ( ) (1) x + = 1 2 ( ) E ( ) (2) Step 1: compute D 3 D E ( ) for non-parabolic bands Step 2: compute E ( ) for non-parabolic bands Step 3: multiply the two to get the answer
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Mark Lundstrom 9/27/13 ECE-656 Fall 2013 2 Step 1: D 3 D ( E ) dE = N 3 D k ( ) ! 4 " k 2 dk = 1 4 3 4 k 2 dk = 1 2 k 2 dk (3) E 1 + !
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Week6HWSolutions - Mark Lundstrom SOLUTIONS ECE 656...

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