A typical intrinsic semiconductor has a nearly full valence band ending at and a nearly empty conduction band starting at , separated by
(1)
At finite temperature, the equilibrium Fermi level lies near the middle of the gap. In the nondegenerate parabolic-band approximation,
(2)
where are the two effective density of states values. Equal densities of states put it exactly at midgap; unequal masses or valley multiplicities shift it slightly. The left panel gives the requested energy-level sketch, with doped cases for comparison.
Figure 1.
Original schematic energy levels of intrinsic, donor-doped and acceptor-doped semiconductors, including the intrinsic Fermi level and band gap
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