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Approximation of the electron emission integral [semiconductor devices]

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Article

Approximation of the electron emission integral [semiconductor devices]

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Abstract

Recent research has focused on the mathematical formulation of charge-carrier emission over energy barriers in semiconductor devices. The description of this process includes an improper integral that cannot be evaluated explicitly. Approximate representations based on the Gauss-Laguerre quadrature are proposed for high accuracy over the physical range of interest. These approximations are formulated and their accuracy quantified

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In this study, a new efficient method for calculation of the charge carrier emission probability over energy barriers in semiconductor devices is presented. As will be seen, the present formulation yields compact closed-form expressions which enable the ready calculation of electron emission function. The results are amenable for use in further theoretical studies of thermionic emission probability for semiconductor–insulator interfaces where analytical methods may be desirable. Finally, the numerical results are presented and compared with results using alternative evaluation schemes.
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Handbook of Mathematical Functions
  • M Abramowitz
  • I Stegun