ECE230A
Homework #4
Homework due: December1, 2009
1.
In class, we derive the expression of mobility from the Boltzman transport equation
and find
ߤൌ
כ
ۃఛ௩
మ
ۄ
ۃ௩
మ
ۄ
where
τ
is the relaxation time.
Derive
(a) Derive the expression of diffusivity D from the Boltzman transport equation.
(b) Show that for nondegenerate semiconductors, the Einstein relation
ఓ
ൌ
்
is satisfied.
(c) Explain why the results of mobility and diffusivity only work under low field
condition.
2.
When we derived the continuity equation for the excess carriers, we strated from the
following continuity equations of total electron and hole populations:
డ
డ௧
ൌߤ
డሺா
ೣ
ሻ
డ௫
ܦ
డ
మ
డ௫
మ
െ
ି
ఛ
(1)
డ
డ௧
ൌെߤ
డሺா
ೣ
ሻ
డ௫
ܦ
డ
మ
డ௫
మ
െ
ି
ఛ
(2)
(a) Complete the derivation to achieve the final result:
డ
భ
డ௧
ൌܦ
ᇱ
డ
మ
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 '09
 minority carrier concentration, Boltzman

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