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. β 0 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. δ 0 ), the backscattering coefficient at 0 (i.e. η θ ), the coefficient at θ = 0° (i.e. η 0 ), δ PEθ and δ PE0 we deduce the universal formula for δ θ , δ 0 , η θ , η 0 , 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°.