Dependence of the Peak Energy of the Pair-Photoluminescence Band on Excitation Intensity

An analytical expression is derived for the dependence of the peak energy of the broad-band pair-recombination emission on the excitation intensity. Experimental values given in the literature were fitted by a nonlinear-least-square computer program to the theoretical expression. The fit gave values for the limiting photon energy for distant pairs ($h{\nu }_{\infty }$) and for the Bohr radius ($R_B$) for the shallow hydrogenic impurity in the crystal. Values obtained for GaP were $h{\nu }_{\infty }=2.189\mathrm{}$ eV and $R_B=24.2\mathrm{}$ Å (averages from two sets of experimental results). For ZnSe we obtained $h{\nu }_{\infty }=2.691\mathrm{}$ eV and $R_B=28.1\mathrm{}$ Å. The present method is specifically useful in crystals in which the discrete-line pair emission is not observable. It can, however, also help as a guide and a check in the classification of the discrete lines according to their shell number.