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A Fully 2-dimensional Poisson-Schrodinger modeling of the HEMT: Effects of short gate lengths

The need for a quantum mechanical analysis of III-V semiconductor based HEMTs has been recognized from the very early work of Delagebaudef and Linh [1] where a simple infinite barrier of triangular crossection was used for the channel potential. Under this assumption for the form of the channel potential an analytical but indirect expression for the channel carrier concentration ns (Cb/cm) in terms of the device characteristics and the gate bias VG was obtained. If one neglects the Fermi level height Ef from the bottom of the channel well then one obtains the well-known linear expression ens = ( 1/d1) · (VG-VT), where VT is the threshold potential and 1, d1 are the dielectric constant and the depth of the AlGaAs layer (see Fig. 1). Further work in [2] and [3] took into account the variation of Ef with ns resulting in improved but nonlinear models. The next step in the modeling of the HEMT came from the work of Snowden et al [4] where the approximation of the triangular infinite barrier was lifted and the channel potential was obtained by a self-consistent solution of the Poisson and Schrödinger equations. However Schrödinger’s equation was solved in one dimensional (1D) cuts perpendicular to the channel direction thereby leaving out information on the top structure of source – gap – gate – gap – drain. We wish to emphasize from the start that if the gate is long enough (Lg >200 nm) such matters are not important. But for nanometric scale gate lengths they become very important. It is the purpose of this paper to investigate such effects by a fully 2D self-consistent solution of the Poisson and Schrödinger equation. Although state of the art HEMTs don’t have pure GaAs channels, we have performed our calculations on a conventional AlGaAs/ GaAs HEMT, for which the material parameters are well established. Note however that our results are determined by the geometry of the device and that our model is immediately extendable to other materials. II. METHOD