 Effective density of states

ID: effective-density-of-states

The effective density of states of a parabolic semiconductor band is its density of states integrated against a thermal Boltzmann factor measured from its edge. For one spin-degenerate valley,

N_{c} = 2 (\frac{m _{e}^{*} k _{B} T}{2 π ℏ ^{2}})^{3/2}, N_{v} = 2 (\frac{m _{h}^{*} k _{B} T}{2 π ℏ ^{2}})^{3/2} .

These quantities have units of number per volume, unlike the energy-resolved density of states. In a nondegenerate semiconductor,

n = N_{c} e^{- (E_{c} - μ) / (k_{B} T)}

and

p = N_{v} e^{- (μ - E_{v}) / (k_{B} T)}

; multiple equivalent valleys add their contributions.

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