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To be practical, semiconductors need to be doped. Sometimes, to nearly degenerate levels, e.g. in applications such as thermoelectric, transparent electronics or power electronics. However, many materials with finite band gaps are not dopable at all, while many others exhibit strong preference toward allowing either p- or n-type doping, but not both. In this work, we develop a model description of semiconductor dopability and formulate design principles in terms of governing materials properties. Our approach, which builds upon the semiconductor defect theory applied to a suitably devised (tight-binding) model system, reveals analytic relationships between intrinsic materials properties and the semiconductor dopability, and elucidates the role and the insufficiency of previously suggested descriptors such as the absolute band edge positions. We validate our model against a number of classic binary semiconductors and discuss its extension to more complex chemistries and the utility in large-scale material searches.