1d Analytical Model of the Metal-semiconductor Contact beyond the Wkb Approximation
نویسنده
چکیده
-A ID analytical model of the metal-semiconductor contact is developed in the framework of emission theory which exploits an improved description of the transmission probability. The usual WKB approximation is substituted by an interpolation scheme where the eigensolutions of a given potential barrier are expressed by Airy functions and then mapped to Gaussians in order to enable analytical integration. The method is demonstrated for a parabolic barrier where the eigenfunctions are known and direct comparison between the model and an "exact" reference is possible. Contact currents are given in a fully analytical form and agree well with those from the reference model over the whole range of doping concentrations from Schottky to Ohmic. Boundary conditions for device simulation are derived by merging the calculated emission current to the drift-diffusion current at a certain distance from the metal-semiconductor interface. Experimental data of Ti on intermediately doped n-Si are used to compare with the model and to discuss the influence of the most important parameters.
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