To
be practical, semiconductors need to be doped. Sometimes, they
need to be doped 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 a 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 material properties. Our approach, which builds
upon the semiconductor defect theory applied to a suitably devised
(tight-binding) model system, reveals analytic relationships between
intrinsic material 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.