Week7HWSolutionsV2

Finally use v in iv dn j nx nq ne x qdn dn

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Unformatted text preview: ⎪ F (η ) k T 1 dn ⎪ = σ n ⎨ 1/ 2 F B +E x ⎬ dx ⎪F −1/ 2 (η F ) q n dx ⎪ ⎩ ⎭ J nx = σ nE x + σ n F 1/ 2 (η F ) k BT 1 dn F −1/ 2 (η F ) q n dx Now write σ n = nqµn and use in (iii) to find: ECE- 656 2 Fall 2013 Mark Lundstrom J nx = nqµ nE x + F 1/ 2 (η F ) F −1/ 2 (η F ) k BT µ n dn dx Define the diffusion coefficient as F (η ) k T Dn = 1/ 2 F × B µ n q F −1/ 2 (η F ) 10/5/13 (iv) (v) For a nondegenerate semiconductor, η F = Fn − EC ( ) k BT << 0 and we find k BT µ , qn which is the familiar Einstein relation. Finally, use (v) in (iv) Dn = J nx = nqµ nE x + qDn Dn F 1/ 2 (η F ) k BT = µ n F −1/ 2 (η F ) q dn dx 3) In 1D, we write R1D = 1 σ 1D L , in 2D R2 D = 1 σ 2 D L W , and in 3D R3 D = 1 σ 3 D L A . ( ) ( ) ( ) 2q 2 M ( E F ) and develop h expressions for the 1D, 2D, and 3D “ballistic conductivities.” Assuming a degenerate conductor, begin with Gball = Solution: 1D Gball = 2q...
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