Impurity stability based upon stress-corrected strain representation

Using strain to control the formation energy or concentration of impurities, defects, and alloy components in semiconductors is crucial to improving their device functions. However, under small strains, existing studies on predicting impurity formation energy have three problems: incorrect strain representation due to inconsistency in the equilibrium state of the system before and after doping, incorrect stress sampling, and problems in the classification and analysis of stress introduced by impurities. To solve the above problems, we first define the volume ratio before and after doping in the equilibrium lattice. To obtain this volume ratio, we proposed a method to use the linear fitting of stress in a small strain range. Furthermore, we obtained the correct representation of strain before and after doping, and under this representation, we corrected the formula of impurity induced stress and formation energy under strains. Based on this theory, taking doped GaN and silicon as examples, we quantitatively studied impurity induced stress and formation energy under applied strain and found that the prediction accuracy was improved by about six times and four times, respectively, which confirmed the effectiveness of the strain correction formula. Based on the representation, we proposed a new method to estimate the size of dopants using fully compensated doping, thereby further classifying and analyzing the response mechanism of dopant induced stress to external strains. For substitutional impurities, this mechanism consists of the electron gas effect and the size effect; for nitrogen vacancy, there is a local coupling effect of dangling bonds of gallium atoms.