QUANTUM-MECHANICAL MODELING OF ACCUMULATION LAYERS IN MOS STRUCTURE

An original method is used for the quantum-mechanical modeling of n-type silicon accumulation layers. Contrarily to previous methods, which were only valid near 4.2 K, our approach is valid up to room temperature and beyond. The obtained self-consistent results are compared with those of the standard classical model for the accumulation layer, and the differences between them are found to be relevant for the modeling of important device applications. In particular, it is shown that the semiconductor voltage drop and the oxide barrier height for Fowler-Nordheim (F-N) tunnel injection are largely modified by the quantization of the accumulation layer. The dependences of these two magnitudes (accumulation voltage drop and effective F-N barrier height) on oxide electric field and substrate doping are reported. Experimental F-N current-voltage characteristics of production-quality <100>-Si(n)/SiO2/poly-Si(n+) MOS capacitors are used to validate the presented quantum results and to show that the standard classical model is not adequate even if the barrier height is considered as a fitting parameter. Finally, approximate analytical expressions giving the semiconductor voltage drop and the effective F-N barrier height as a function of oxide field and substrate doping are derived for <100> and <111> n-type silicon at 77 and 300 K. These analytical expressions allow to introduce the effects of the quantization of accumulation layers into even very simple device simulators.