Line width and exciton-impurity scattering in Cu 2O

Abstract

The variation of the line width of the n = 1 line of the yellow series in Cu 2O as a function of the concentration N of substitutional Ag + ions (ref. 1) is interpreted on ground of a theory similar to the Lorentzian collision line broadening theory. It is shown that the line must acquire a Voīgt shape when the concentration of Ag + increases. This Voīgt shape line is obtained from the convolution of a Gaussian component of a constant line width Δ v G = 0.57 cm −1 (obtained from the experiment by extrapolation to N → 0) and a Lorentzian component of line width Δ v l variable with N. The shape of the experimental (ref. 1) lines for different concentrations N and the theoretical lines calculated is in surprinsingly good agreement. From this comparison a collision cross-section and mean free path of excitons can be calculated. The obtained values are σ ⋍ 10 14 cm 2 and XXX = 3.2 10 −5 cm for a concentration N = 10 18 cm −3. Further discussion of these results leads to useful information.