= Solution
\b[Three routes are donor doping, acceptor doping and above-gap illumination.] All increase mobile carrier populations if the added states or excitations are effective rather than strongly trapped.
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{title=Original band diagrams for donor doping, acceptor doping and photogeneration in a gapped material}
An appropriate <donor impurity> provides an occupied level just below the <conduction band>. Thermal ionization requires the smaller donor binding energy rather than the full host gap, supplying mobile electrons and <n-type semiconductor> behaviour. An appropriate <acceptor impurity> creates an available level just above the <valence band>; accepting a valence electron leaves a mobile hole, giving <p-type semiconductor> behaviour. Doping concentrations and compensation must permit useful carriers; an arbitrary impurity need not be an effective dopant.
For <photoconductivity>, absorbed photons with $h\nu\gtrsim E_g$ can excite valence electrons into the conduction band, producing electron–hole pairs. For the stated $2.7\,\mathrm{eV}$ gap, the nominal threshold is about $1240/2.7\simeq459$ nm. Optical selection rules and absorption strength can shift the practical onset. The conductivity increase persists only while generation maintains carriers against recombination and trapping; it is not necessarily a permanent change to the material.
In each case, $\sigma=e(n\mu_n+p\mu_p)$ connects increased carrier density to conductivity. Defect-induced reductions in mobility can offset some of the gain, so the diagrams specify mechanisms rather than guarantee a numerical improvement for an unspecified preparation.
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