**Formulae for secondary electron yield and the ratio of the average number of secondary electrons generated by a single backscattered electron to that generated by a single primary electron**

#### Abstract

**On the basis of the characteristic of secondary electron emission, the number of secondary electrons (**

*δ*_{PEθ}) released per primary electron entering metals in the incident energy (*W*_{p0}) range 10-102 keV and the incident angle (*θ*) range 0-89° was deduced. In addition, the number of secondary electrons released per primary electron entering metals at*θ=*0 (*δ*_{PE0}) was obtained. Based on the deduced*δ*_{PEθ}, the characteristic of the emission angle distribution of the backscattered electrons and the definition of*β*_{θ}, the relationships among*β*_{θ}, cos*θ*and the parameter*x*were given, where*β*_{θ}is the ratio of the average number of secondary electrons generated by a single backscattered electron to that generated by a single primary electron entering the emitter at*θ*. Considering the relationship between*δ*_{PEθ}and*δ*_{PE0}and the relationship between the secondary electron yields at*W*_{p0}=10-102 keV and*θ=*0-89°*(**δ*_{θ}) and the secondary electron yields at*θ=*0(*δ*_{0}), a universal formula for expressing*δ*_{θ }through*δ*_{0}, the backscattered coefficient at*θ*(*η*_{θ}), the backscattered coefficient at*θ=*0(*η*_{0}), cos*θ*and the parameter*x*were deduced. Further, the parameters*x*related to beryllium, uranium, aluminium and copper were computed with the deduced formula and experimental results; then, the formulae for expressing*δ*_{θ}from the four metals through*δ*_{0},*η*_{θ},*η*_{0}*and cos**θ*were obtained; and the relationships between*β*_{θ}of the four metals and cos*θ*were found. The*δ*_{θ }calculated with the formulae and the yields measured experimentally were compared. Finally, it is concluded that the formulae for*δ*_{θ}and*β*_{θ}from the four metals at*W*_{p0}=10-102 keV and*θ=*0-89° have been established, respectively.#### Keyword(s)

Secondary electron yield; Emission angle distribution; Backscattered electron; Incident angle

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