Alloy broadening in photoluminescence spectra of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">As</mml:mi></mml:math>

The origins of line broadening in photoluminescence spectra of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ are analyzed. Thermal broadening, the influence of macroscopic inhomogeneity, and alloy broadening due to random cation distribution are investigated. Quantitative models for the linewidths of the bound exciton and the band-to-acceptor transition are developed, based on compositional fluctuations within the crystal volumes which are characteristic of the two transitions. The linewidths are calculated without any fitting parameter and agree with experimental results. Alloy clustering can be definitely excluded for samples grown (1) in (100) orientation and (2) under optimum conditions. The investigation of alloy broadening in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ leads to a quantitative understanding of low-temperature photoluminescence spectra of ternary and also of quaternary III-V semiconductors.