  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.
