Formula for the Probability of Secondary Electrons Passing over the Surface Barrier into a Vacuum

Based on a simple classical model that primary electrons at high electron energy interact with the electrons of lattice by the Coulomb force, we deduce the energy of secondary electrons. In addition, the number of secondary electrons in the direction of velocity of primary electrons per unit path length, n, is obtained. According to the energy band of the insulator, n, the definition of the probability B of secondary electrons passing over the surface barrier of insulator into the vacuum and the assumption that lattice scattering is ignored, we deduce the expression of B related to the width of the forbidden band (E_g) and the electron affinity χ. As a whole, the B values calculated with the formula agree well with the experimental data. The calculated B values lie between zero and unity and are discussed theoretically. Finally, we conclude that the deduced formula and the theory that explains the relationships among B, χ and E_g are correct.