An Improved Analytic Method Based on Airy Functions Approach to Calculate Electron Direct Transmittance in Anisotropic Heterostructure with Bias Voltage

Abstract

An analytic expression of transmittance based on the Airy wavefunctions approach has been derived for an electron through an anisotropic heterostructure with an applied voltage to the barrier of the heterostructure. The Si(110)|Si0.5Ge0.5|Si(110) heterostructure was used to examine the analytic expression. In order to evaluate the Airy wavefunctions approach, the transfer matrix method, which is a method widely applied for various applications, was employed as a reference. It was found that the transmittance calculated by the Airy wavefunctions approach fits perfectly that obtained by the transfer matrix method. The exponential wavefunctions approach in obtaining the transmittance was also evaluated. The transmittance obtained by the exponential wavefunctions is always lower than the transfer matrix method-based transmittance. As the electron total energy or applied voltage increases, the difference between the exponential wavefunctions- and transfer matrix method-based transmittances increases. Thus, the Airy wavefunctions approach improves the exponential wavefunctions approach to calculate the electron direct transmittance.