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...
View
Full
Document
This document was uploaded on 01/15/2014.
 Fall '14

Click to edit the document details