A Universal Formula for the Secondary Electron Yield of Metals at an Incident Angle of θ

Based on the main physical processes, we deduce the relationships among the incident energy W_p0 of the primary electron, the number of released secondary electrons (i.e. δ_PEθ) per primary electron entering the metal at incident angle θ and the angle θ itself. In addition, the relationship of δ _PEθ at θ = 0°, i.e. δ_PE0, with W_p0 is determined. From the experimental results, the relationship of the ratio at θ = 0°, i.e. β₀ which is the ratio of the average number of released secondary electrons generated by a single primary electron backscattered at the metal surface to that generated by a single primary electron entering the metal, with W_p0 is determined. Moreover, the relationships among the ratio β_θ , W_p0 and θ are obtained. Based on the relationships among the secondary electron yield at θ (i.e. δ_θ), the yield at θ = 0° (i.e. δ₀), the backscattering coefficient at θ (i.e. η_θ), the coefficient at θ = 0° (i.e. η₀), δ_PEθ and δ_PE0, we deduce the universal formula for δ_θ,δ₀, η_θ, η₀, and W_p0 for the primary electrons at an incident energy of 2–10 keV. The secondary electron yields calculated from the universal formula and the experimental yields of some metals are compared, and the results suggest that the proposed formula is universal for estimation of secondary electron yields at θ=0°−80°.