Semiconductors: DOF and number of electrons/holes

Physics Q&A
1

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I was studying the derivation of the semiconductor number of particles, but don’t understand how they solved this integral, because, even when using the defined integral below, it seems to me that they would still be left with an integral from 0 to Ev or Ec.

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You need to change the integration variables to x = (E + E_V) / kT (or a similar expression for electrons). Then the integral for x goes from 0 to \infty.