Energy of arrays of nonperiodic interacting dislocations in semiconductor strained epilayers: Implications for strain relaxation

The interaction energy EirrI of arrays of dislocations with nonperiodic (or irregular) distribution is calculated. The calculations have been made for uniform-random and Gaussian distributions of dislocations. The method used is, however, general and can also be applied to any arbitrary or an observed distribution of dislocations. The results for several values of average spacing p̄ and standard deviation σ are given and are compared with the energy EI of periodic arrays with spacing p=p̄. The total energy EirrT of strained layers containing nonperiodic dislocation arrays is also calculated. The results for both 90° and 60° dislocations are given. For sufficiently large numbers of dislocations, EirrI is always larger than EI. The difference between the energies EirrI and EI increases rapidly as the standard deviation σ of the nonperiodic distribution increases. The equilibrium strain relaxation in thick layers and the strain relaxation on annealing the metastable layers are usually calculated by modeling the nonperiodic array as an equivalent periodic array with p=p̄. It is found that this procedure for the calculation of the strain relaxation is not valid.