= Dimensional interband threshold shapes
{title2=$\rho_{eh}(E)\propto(E-E_{\rm th})^{d/2-1}$}
Parabolic electron-hole continua with $d$ unconfined directions have cumulative state count proportional to $(E-E_{\rm th})^{d/2}$. Differentiating gives the threshold joint density proportional to $(E-E_{\rm th})^{d/2-1}$: a square root for bulk, a step for a well, and an inverse square root for a wire. A fully confined dot instead has discrete lines. Optical matrix elements, occupations, <excitons> and broadening determine the actual absorption beyond this counting argument.
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