Analytic Formulae for the Impact Ionization Rate for use in Compact Models of Ultra-Short Semiconductor Devices
H.C. Morris, M.M. DePass and H. Abebe
San Jose State University, US
Keywords: impact ionization, Boltzmann equation, hot electrons
Quade, Schöll and Rudan have showed that in the limit of large screening length the impact ionization rate per unit time can be expressed as an integral involving the electron density function. The assumption of a heated Maxwellian then leads to a closed form expression for the impact ionization rate. From Monte-Carlo simulations it is known that a single heated Maxwellian is not an adequate in short channel devices due to the existence of a high energy tail in the electron distribution. To remedy this other models have been proposed that incorporate a hot electron tail. In this paper we determine the analog of the Schöll-Quade formula for these more complicated distribution function models. The integrals involved can still be evaluated in terms of special functions but the resulting formulae are difficult to use. To obtain practical approximations a new integral approximation technique is introduced. The resulting approximate formulae involve only elementary functions and provide a practical and accurate formulae for the impact ionization rate.
Nanotech 2004 Conference Technical Program Abstract