Plasmon theory of electron-hole pair production: efficiency of cathode ray phosphors

Abstract

Fast electrons in solids lose energy primarily to plasmons which subsequently decay into an electron‐hole pair. The electron and hole may create additional electron‐hole pairs if they have sufficient energy. The average energy to create an electron‐hole pair, E_x, is thus given essentially by ℏ ω_p/n, where ℏ ω_p is the plasmon energy and n is the number of pairs which are created by the plasmon and its decay products. The values of n and hence E_x depend on the ratio ℏω_p/E_g, where E_g is the usual band gap in semiconductors and insulators. We have found that for a simple model of direct and indirect materials, sharp thresholds exist for various values of n. For direct‐gap materials, n=1 for 1< ℏω_p/E_gn=3 for 4< ℏω_p/E_gk conservation indicate that the changes in n vs ℏω_p/E_g should be smoothed for real materials. but not eliminated. Our theoretical values for E_x/E_g allow values lower than previous treatments and give good agreement with known experimental values. Some problems associated with determining the theoretical value of ω_p for materials with d electrons are discussed. Some experiments for testing the theory are suggested. The importance of E_x in determining the efficiency of phosphors is also discussed.