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

Abstract

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 ( PE ) released per primary electron entering the metal at high electron energy and incident angle and incident angle () are deduced. In addition, the relationship between the number of secondary electrons ( PE0 ) released per primary electron entering the metal at ¼ 0 and W p0 is determined. From the experimental results, the relationships among the ratio (the subscript means the primary electron is incident at in this paper), the ratio at ¼ 0 ( 0 ) and are obtained. On the basis of relationships among PE , PE0 , , 0 , backscattered coefficient , backscattered coefficient at ¼ 0 ( 0 ), secondary electron yield , and secondary electron yield at ¼ 0 ( 0 ), the universal formula for expressing using 0 , , 0 , and 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.

Formula for the Probability of Secondary Electrons Passing over the Surface Barrier into a Vacuum

“…For a secondary electron emitter, 𝐵 is a constant and is not a function of the incident energy of primary electrons. [1,2,[4][5][6]15,19] Therefore, Eq. ( 18) for 𝐵 deduced under the condition that primary electrons at a high electron energy hit on insulators is universal for the estimation of 𝐵 under the condition that primary electrons at any energy hit on insulators.…”

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

“…The secondary electron emission is an important research topic. [1][2][3][4][5][6][7][8][9][10] Computational approaches based on the Monte-Carlo method allow us to calculate the secondary electron emission. [11][12][13][14][15] Modern technologies such as secondary electron dopant mapping [16,17] and critical dimension scanning electron microscopy [14,18] allow us to research the secondary electron emission.…”