Lattice-relaxation effects at point imperfections in semiconductors

We discuss some of the fundamentally inherent limitations involved in calculations of lattice-relaxation effects at point imperfections. We show that differences of tetrahedral covalent radii between impurity and host atoms cannot reliably determine whether the nearest-neighbor atoms move inward or outward. A massive minimization-of-total-energy calculation may yield reliable information for deep levels but for shallow levels the problem is inherently intractable; even if one knew which way the neighboring atoms move, neither the sign nor the size of the change in binding energy could be determined reliably, either by a full calculation or, even more so, by qualitative arguments.