Analytical evaluation of the thermionic emission probability for semiconductor-insulator interfaces using incomplete gamma functions

In this study, a new efficient method for calculation of the charge carrier emission probability over energy barriers in semiconductor devices is presented. As will be seen, the present formulation yields compact closed-form expressions which enable the ready calculation of electron emission function. The results are amenable for use in further theoretical studies of thermionic emission probability for semiconductor-insulator interfaces where analytical methods may be desirable. Finally, the numerical results are presented and compared with results using alternative evaluation schemes.