We present a general theory of stress effects on the solid solubility of impurities in crystalline materials, including the effects of ionization and the Fermi level in semiconductors. Critical errors and limitations in previously proposed theory are discussed, and a rigorous accurate treatment incorporating charge-carrierinduced lattice strain and correct statistics is presented. Considering all contributing effects, we find that the strain compensation energy is the primary contribution to solubility enhancement in essentially all material systems of interest. An exception is the case of low-solubility charged impurities in semiconductors, where a Fermi-level contribution is also found. We present explicit calculations for a range of dopant impurities in Si, utilizing this system as a model example and vehicle for comparison with experiment. Our results agree closely with experimental solubilities for dopants with widely different ionic sizes.The effect of stress on impurity solubility is one of the simplest examples of a mechanical effect on the phase diagram of a material system. It influences mechanical properties such as ductility 1 and crack evolution 2 electronic properties such as carrier density in semiconductors 3 and other phenomena, such as superconductivity. 4 Consequently it has a role to play in research topics ranging from materials science, geophysics, and superconductivity to semiconductor technology.Despite this very broad significance, our basic understanding of impurity solubility under stress is incomplete and no general physical model has yet emerged. In the case of dopant solubility in silicon, where the phenomenon has been closely studied, previously reported theoretical works have shown either inconsistencies 5,6 or important differences in formulation. 7-9 Until we understand the origin of these weaknesses it is uncertain whether solubility theory can be reliably applied to key technology problems, for example, dopant activation in nanoelectronic devices where high stress levels are introduced for band gap and mobility engineering, or stress-driven fracture 2 during the lifetime of critical engineering components. Moreover, since a small set of accurate experimental measurements has recently been reported for the case of impurities in Si, 3,10,11 it is especially worthwhile to develop an accurate comprehensive model to compare with these data and test theoretical understanding.Early theoretical work investigated stress-dependent B solubility in Si ͑Refs. 5 and 6͒ and suggested that the main contributing effect is a stress-induced change in the Fermi level. It was concluded that Fermi-level change produces a strong enhancement of B solubility in compressively strained silicon, while a relatively small additional enhancement occurs as a result of strain compensation arising from the size mismatch between B and Si. Adey et al. 6 later predicted that Fermi level and strain compensation contributions are both important in the case of As in Si but are of nearly equal magnitude and opposite i...