4H-SiC vertical double implanted metal-oxide-semiconductor drift region-energy aspects of its formation and analysis

Abstract

A conventional vertical double implanted metal-oxide-semiconductor structure contains two n+ regions beneath two symmetrically posed source biases. These n+ regions are surrounded by a p-doped layer, which itself has an abrupt transition to the vertical drift region. Owing to the existence of these p-layers, the 'drift' region has varying cross sections: it is reduced going upward from the bottom (drain bias) to the top. Such a drift region is usually described either by a three piecewise model, which begins with constant cross section that at some point starts narrowing until at some other point it becomes reduced to the region between two p-regions, or by a two piecewise model, whose narrowing region starts right above the drain bias and finishes in the manner described before. The crucial geometrical parameters of the flow profile in the drift region, such as the slope of the cross-section reducing region and the length of the narrowest (accumulation) region are widely used but never determined, or even estimated, in the available literature. In this paper, the least-action principle has been utilized successfully in order to determine the exact values of these parameters and so make the existing models closed. The proof has also been provided, which shows that the three piecewise model described the flow profile better than a two piecewise model more adequately as long as it was permitted by the length of the entire drift region (the energy necessary to restore the specific value of drain current is smaller than for the three piecewise model). The two piecewise model can be accepted in practical calculations only for higher values of drain current far from a triode regime.