= Solution
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
$$
\boxed{E_g=E_c-E_v>0.}
$$
At finite <temperature>, the equilibrium <Fermi level> lies near the middle of the gap. In the nondegenerate parabolic-band approximation,
$$
\boxed{E_F=\frac{E_c+E_v}{2}+\frac{k_{\rm B}T}{2}\ln\frac{N_v}{N_c},}
$$
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.
\Image[/past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2022/paper-2-semiconductor-levels.png]
{title=Original schematic energy levels of intrinsic, donor-doped and acceptor-doped semiconductors, including the intrinsic Fermi level and band gap}
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