Universal Formula for Secondary Electron Yield of Metals at High Electron Energy and Incident Angle θ

On the basis of the main physical processes of secondary electron emission, the relationships among the incident energy (W_p0) of primary electrons, the number of secondary electrons (δ_PEθ) released per primary electron entering the metal at high electron energy and incident angle θ and incident angle (θ) are deduced. In addition, the relationship between the number of secondary electrons (δ_PE0) released per primary electron entering the metal at θ= 0° and W_p0 is determined. From the experimental results, the relationships among the ratio β_θ (the subscript θ means the primary electron is incident at θ in this paper), the ratio at θ= 0° (β₀) and θ are obtained. On the basis of relationships among δ_PEθ, δ_PE0, β_θ, β₀, backscattered coefficient η_θ, backscattered coefficient at θ= 0° (η₀), secondary electron yield δ_θ, and secondary electron yield at θ= 0° (δ₀), the universal formula for expressing δ_θ using δ₀, η_θ, η₀, and θ is deduced. The secondary electron yield calculated from this universal formula and the yields measured experimentally from aluminum and copper are compared. The results suggest that the proposed formula is universal for the estimation of secondary electron yields in the angle range of 0–80° and the energy range of 10–102 keV.