  Enhancing the dopability of semiconductors via strain engineering is critical
to improving their functionalities, which is, however, largely hindered by the
lack of fundamental rules. In this Letter, for the first time, we develop a
unified theory to understand the total energy changes of defects (or dopants)
with different charge states under strains, which can exhibit either parabolic
or superlinear behaviors, determined by the size of defect-induced local volume
change ({\Delta}V). In general, {\Delta}V increases (decreases) when an
electron is added (removed) to (from) the defect site. Consequently, in terms
of this unified theory, three fundamental rules can be obtained to further
understand or predict the diverse strain-dependent doping behaviors, i.e.,
defect formation energies, charge-state transition levels, and Fermi pinning
levels, in semiconductors. These three fundamental rules could be generally
applied to improve the doping performance or overcome the doping bottlenecks in
various semiconductors.
