A phenomenological parameter characterizing the relaxation of stresses caused by the lattice mismatch at a heteroboundary

An analytical formula is derived describing an increase in the bandgap width for a quantum cluster considered as an inclusion of the simplest shape (spherical or flat) featuring an arbitrary lattice mismatch with the surrounding matrix. A phenomenological relationship is introduced between this quantity and the stressed boundary relaxation parameter considered as the fitting parameter. The relaxation is small (or even absent) in a system with quantum wells and is completely manifested in a system with quantum dots.