The dependence on hydrostatic pressure and alloy composition of the Schottky-barrier height at ideal, defect-free, $\mathrm{Al}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}\mathrm{}\left(100\right)\mathrm{}$ junctions is investigated by means of an ab initio pseudopotential approach. The results reproduce closely the experimental data and, in contrast to recent proposals, demonstrate that the barrier heights can be explained without invoking interface defects. The alloy-composition dependence is understood by extending to metal/semiconductor contacts the linear-response-theory approach currently used for semiconductor heterojunctions. The pressure variation of the barriers can be obtained from the ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ band-edge deformation potentials.

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