Universal Formula for Secondary Electron Yield of Metals at High Electron Energy and Incident Angle $\theta$

Based on the characteristics of secondary electron emission and the relationships among parameters of secondary electron yield [Formula: see text] in the low-energy range of [Formula: see text] eV (low-energy [Formula: see text]), the universal formula for low-energy [Formula: see text] as a function of [Formula: see text], [Formula: see text] and maximum [Formula: see text] was deduced, where [Formula: see text] and [Formula: see text] are the incident energies of primary electron and of [Formula: see text], respectively. From the deduced universal formula and experimental low-energy [Formula: see text] from metals, semiconductors and insulators, special formula for low-energy [Formula: see text] from metals as a function of [Formula: see text], [Formula: see text] and [Formula: see text] and that for low-energy [Formula: see text] from semiconductors and insulators as a function of [Formula: see text], [Formula: see text] and [Formula: see text] were deduced, respectively. The results were analyzed, it can be concluded that the two deduced special formulae can be used to calculate low-energy [Formula: see text] from metals, semiconductors and insulators, respectively.

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THE FORMULAS FOR THE SECONDARY ELECTRON YIELD AT HIGH INCIDENT ELECTRON ENERGY FROM GOLD AND ALUMINUM

Modern Physics Letters B ◽

10.1142/s0217984909020503 ◽

2009 ◽

Vol 23 (19) ◽

pp. 2331-2338 ◽

Cited By ~ 14

Author(s):

AI-GEN XIE ◽

CHUAN-QI LI ◽

TIE-BANG WANG ◽

YUAN-JI PEI

Keyword(s):

Energy Range ◽

Electron Energy ◽

Incident Energy ◽

Secondary Electron ◽

Primary Electron ◽

Incident Electron ◽

Experimental Results ◽

Incident Electron Energy ◽

Secondary Electron Yield ◽

Electron Yield

Based on the main physical processes of secondary electron emission from metals, the relation that the product of the number of secondary electron released per primary electron at high incident electron energy and the (n-1)th power of incident energy of primary electron is equal to constant C was deduced, where n is the energy exponent, based on the relation between the number of secondary electron released per primary electron at high incident electron energy and secondary electron yield. The relation that the product of the secondary electron yield at high incident electron energy and the (n-1)th power of incident energy of primary electron is equal to constant D was deduced. The constant D and the energy exponent n of the primary electron in the energy range 10 to 100 keV hitting on gold and aluminum are computed with the ESTAR program and experimental results in scanning electron microscope (SEM), respectively, therefore, the formulas for the incident energy dependence of secondary electron yield in the energy range 10 to 100 keV from gold and aluminum were deduced. The formulas were proved to be true by experimental results in SEM. The results were discussed and a conclusion was drawn. The formulas from gold and aluminum were successfully deduced.

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Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180860 ◽

1990 ◽

Vol 48 (1) ◽

pp. 422-423

Author(s):

John C. Russ

Keyword(s):

Monte Carlo ◽

Energy Loss ◽

Secondary Electron ◽

Secondary Electron Emission ◽

Analytical Calculation ◽

Mean Free Path ◽

Single Scattering ◽

High Energy ◽

Secondary Electron Yield ◽

Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

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