ECE440_Carney_L8

Zaonvolumegrowsthethekspacedosgrows

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Unformatted text preview: of
states
 Note
we
diverge
from
the

 appendix
in
the
book
here
 states
per
volume
 differen?al
volume
in
k‐space
 keep
this
for
now
 Oops,
forgot
about
spin:
 dN k = 2Vk−1d 3 k = Vr 3 dk 3 4π But
I
want
states
in
energy…
 p2 2 k 2 E= = * 2m 2 m* k= ⎛ 1 m* ⎞ 1 dk = ⎜ dE ⎟ ⎝ 2 ⎠ E 2 m*E 2 d 3 k = d 2Ω k 2 dk Vr 3 Vr 2 Vr 2 Em *3 2 2 d k= d Ω k dk = d ΩdE 3 3 3 3 4π 4π 4π Vr 2 Em *3 2 Vr 2 Em *3 ∫ dnk = ∫ nE ( E ) dE ⇒ n ( E ) = 4∫π 3 4π 3 d Ω = 3π 2 total
number
of...
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This note was uploaded on 06/29/2013 for the course ECE 3420 taught by Professor Kent during the Fall '12 term at Lake Forest.

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