Theoretical investigation of thermionic electron emission from semiconductors and insulators and mean escape probability of internal secondary electrons

Abstract

From the definitions of parameters of thermionic electron emission, theories of insulators and semiconductors (IS) and field emission, and those of the escape of electron-induced internal secondary electrons (EIISE), the formulas for j, G, EAve, and B of IS and semiconductors with high-density surface energy states (SHS) were deduced, respectively. Here, j, G, and EAve denote the current density, spectrum, and average energy of hot electrons, respectively; B is the average probability that a hot electron escapes into vacuum upon reaching the surface. The deduced formulas were analyzed and compared with existing results. It is concluded that the deduced formulas for j of IS and SHS are theoretically correct, and that the formulas for G, EAve, and B derived here can express those quantities for IS and SHS, respectively. From the definition of Bs and the fact that, when the absolute temperature in the formula for G is taken as a given value, the deduced G of IS can express the spectra of secondary electrons from IS, the formula for Bs and a more accurate method for calculating Bs were deduced and presented, respectively. Here, Bs denotes the mean escape probability of EIISE reaching the emission surface of IS. The method for calculating ΔQ using the formula for j of SHS derived here was presented, where ΔQ is the quantity of band bending due to high-density surface energy states of semiconductors. The two presented methods were analyzed, and it is concluded that they are correct.