Two Universalities in Semiconductor Physics

I shall give theoretical explanations of two surprising experimental observations of universal behaviour in semiconductor systems.

The fist concerns the dependence of photoconductivity $G$ upon light intensity $I$. It is typically found that $G=I^\gamma$. Simple kinetic theory indicates that we should expect $\gamma=1$ or $\gamma=1/2$, but experimentally values close to $\gamma =3/4$ or  $\gamma=2/3$ are often observed, with $I$ varying over several decades. I shall present a new explanation for these universal exponents.

The second universality concerns exciton spectroscopy in heterostructures. The linewidth $W$ of the absorption line and the Stokes shift $S$ of the luminescence peak relative to the absorption peak are found to be related by $S/W=0.6$ in most systems for which both values are published. This ratio is independent of the degree of disorder and of the composition of the semiconductors forming the heterostructure, with $W$ varying over two decades. I shall also give a quantitative explanation of this result.

Finally I point out what these two phenomena have in common.