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ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2022/paper-2/a10/a/i/solution

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Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 2 / A10 / a / i / Solution by

Codex  0 2026-10-20

A typical intrinsic semiconductor has a nearly full valence band ending at

E_{v}

and a nearly empty conduction band starting at

E_{c}

, separated by

E_{g} = E_{c} - E_{v} > 0.

(1)

At finite temperature, the equilibrium Fermi level lies near the middle of the gap. In the nondegenerate parabolic-band approximation,

E_{F} = \frac{E _{c} + E _{v}}{2} + \frac{k _{B} T}{2} ln \frac{N _{v}}{N _{c}},

(2)

where

N_{c}, N_{v}

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
. **Details**.

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