Metal-Semiconductor Contact
The metal-semiconductor interface is among the most challenging problems in the field of solid-state theory and device physics. A variety of physical phenomena, e.g. the influence of interface states on barrier height [4.20, 4.34], the effect of interfaci
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Metal-Semiconductor Contact
The metal-semiconductor interface is among the most challenging problems in the field of solid-state theory and device physics. A variety ofphysical phenomena, e.g. the influence of interface states on barrier height [4.20, 4.34}, the effect of interfacial layers (dipole, oxide, or contamination) [4.2, 4.6, 4.15, 4.18}, inelastic scattering events [4.16, 4.22}, recombination, trapping [4.5, 4.1O} and trap-assisted tunneling [4.9}, vertical and lateral potential fluctuations [4.8}, barrier height fluctuations [4.33}, interface roughness [4.30}, band-state mixing [4.12}, realistic image forces, hot carrier effects, and some other issues make the theoretical modeling a complicated task Simplified contact models, e.g. suitable for device simulation, have to neglect most of all these effects. A step towards a more physics-based model compared to the commonly used boundary conditions for ideal Ohmic contacts (neutrality, equilibrium) and ideal rectifying (Schottky) contacts (thermionic emission neglecting tunneling) has been made in Ref [4.27}, where an analytical model based on the well established formula of thermionic field emission (TFE) and a simplified WKB transmission probability of the parabolic potential barrier was derived. Separating the contact region, where the carriers move ballistically, from the rest of the device, where the current is governed by drift-diffusion (Crowell and Sze [4.16), Chang and Sze [4.8]) and adding a proper boundary condition for the Poisson equation, the model is able to describe the transition from Schottky to Ohmic contacts as the doping level increases. A shortage in this treatment is the use of the WKB approximation which breaks down, if the de Broglie wavelength becomes comparable to the barrier width (Ohmic contact or strong reverse bias) and/or if the current flows predominantly in the vicinity of the maximum of the barrier (Schottky contact). In this chapter we will substitute the WKB approximation by another approach, which preserves the accuracy of an "exact" reference model over the entire doping range. This reference model is chosen as follows: parabolic potential barrier (i.e. constant doping level in the barrier region for all applied voltages, Schottky approximation, no image-force effect, no interfacial layer, etc.), independence of the transmission probability on transverse momentum, and constant effective A. Schenk, Advanced Physical Models for Silicon Device Simulation © Springer-Verlag/Wien 1998
4.1 Emission Current Through a Parabolic Barrier
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mass for all energies above and below the band edge of majority carriers. For such a model the exact transmission coefficient (TC) is well known, and the corresponding results may be directly compared with those of our analytical approach.
4.1 Emission Current Through a Parabolic Barrier We assume an n-type semiconductor with a parabolic conduction band in this chapter. Fig. 4.1 defines the basic quantities: barrier height B, barrier width XB = XB(Uappl), the two quasi-Fermi levels, and
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