Week2HWSolutions

Unprimed valleys m 2 n 2 2 d2 d gv t 2 gv

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Unformatted text preview: ierret (Advanced Semiconductor Fundamentals) on pp. 94- 95 helpful. Solution: In this case, we write E k x , k y as: ( ) 22 2 k x2 k y E= + * 2 mxx 2 m*y y * For the case shown, mxx is the longitudinal effective mass and m*y is the transverse y effective mass. 2 2 ⎡ ⎤ 22 2 k x2 k y 2 k x2 ⎢⎛ m0 ⎞ ⎛ m0 ⎞ ⎥ Re- write E = as E = k ⎟ +⎜ k ⎟ + ⎜ * * 2 m0 ⎢⎝ mxx x ⎠ ⎜ m*y y ⎟ ⎥ 2 mxx 2 m*y ⎝ ⎠⎥ y y ⎢ ⎣ ⎦ Now define a “stretched” k- space: kx = m0 k * mxx x ky = m0 k m*y y y ECE- 656 10 Fall 2013 Mark Lundstrom 8/24/2013 ECE 656 Homework 2 (Week 2) (continued) Now we can write the E(k) in the stretched k- space: 2 2 2 , k = k 2 + k 2 = k , (*) E kx y y * * 2 m0 x 2 m0 which looks like a simple, circular band in 2D. But we must realize that states are spaced ( 2π L ) in k , but they are spaced ( 2π L ) × m m in k . Accord...
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