Formula for average energy required to produce a secondary electron in an insulator

Based on a simple classical model specifying that the primary electrons interact with the electrons of a lattice through the Coulomb force and a conclusion that the lattice scattering can be ignored, the formula for the average energy required to produce a secondary electron (epsilon) is obtained. On the basis of the energy band of an insulator and the formula for epsilon, the formula for the average energy required to produce a secondary electron in an insulator (epsilon(i)) is deduced as a function of the width of the forbidden band (E-g) and electron affinity chi. Experimental values and the epsilon(i) values calculated with the formula are compared, and the results validate the theory that explains the relationships among Eg, chi, and epsilon(i) and suggest that the formula for epsilon(i) is universal on the condition that the primary electrons at any energy hit the insulator.