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. Unlike previous methods, which were only valid near 4.2 K, the approach is valid up to room temperature and beyond. The self-consistent results obtained 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. The dependences of the accumulation voltage drop and effective F-N (Fowler-Nordheim) barrier height on oxide electric field and substrate dopine are reported. Experimental F-N current-voltage characteristics of production-quality MOS capacitors are used to validate the quantum results and to show that the standard classical model is not adequate even if the barrier height is considered as a fitting parameter. 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