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 (ε) is obtained. On the basis of the energy band of an insulator and the formula for ε, the formula for the average energy required to produce a secondary electron in an insulator (ε_i) is deduced as a function of the width of the forbidden band (E_g) and electron affinity χ. Experimental values and the ε_i values calculated with the formula are compared, and the results validate the theory that explains the relationships among E_g, χ, and ε_i and suggest that the formula for ε_i is universal on the condition that the primary electrons at any energy hit the insulator.