Effect of Phonon Energy Loss on Photoemissive Yield near Threshold

Abstract

A phenomenological band-theoretic model for photoelectric emission which includes the effects of energy loss due to phonon scattering is developed. The model is applicable near threshold when the optical absorption depth is large compared to the phonon scattering length of hot electrons, and is particularly useful for cesiated surfaces with positive electron affinity. It is shown that in the low-photon-energy range one must include the dispersion of the optical constants in the yield expression. Formulas are given for photoelectric yield and for energy distribution curves in the cases of direct, indirect, and nondirect volume transitions; direct transitions give the commonly observed cube law for yield near threshold, changing to linear and square laws at higher energy. The theory is illustrated on experimental data for the following cesiated single crystals: Si (indirect transitions), GaAs, GaSb, ${\mathrm{Ga}}_{0.6}$ ${\mathrm{In}}_{0.4}$As, and Ge (all direct transitions), and is shown to provide in each case an excellent fit over a range of at least ${10}^3$ in the yield (1 eV in photon energy). Its applicability to amorphous materials is discussed and illustrated on Ge. Information on hot-electron scattering lengths in the above materials is also extracted and the voltage dependence (due to barrier lowering) of the yield predicted by this model is given.