Within the scope of this present contribution, the impact of the hydrostatic pressure (HP) on the donor-impurity binding energy ( \(\:{\text{E}}_{\text{b}\text{i}\text{n}\text{d}}\) ) and the self-polarization (SP) is analyzed for a \(\:\text{G}\text{a}\text{A}\text{s}/{\text{G}\text{a}}_{1-{\upmu\:}}{\text{A}\text{l}}_{{\upmu\:}}\text{A}\text{s}\) pillbox quantum dot embedded in a \(\:{\text{G}\text{a}}_{1-{\upupsilon\:}}{\text{A}\text{l}}_{{\upupsilon\:}}\text{A}\text{s}\) matrix, using a variational approach within the framework of the effectivemass approximation (EMA). In addition to the structural parameters, namely the quantumdot width ( \(\:{\text{L}}_{\text{w}}^{\propto\:}\) ), the barrier thickness, and the impurity location inside the quantum dot, this work gives special emphasis to clarifying the role of externally applied hydrostatic pressure on the SP behavior. Our calculations reveal that both the \(\:{\text{E}}_{\text{b}\text{i}\text{n}\text{d}}\) and the SP are strongly affected by the applied pressure, the impurity site, and the quantumdot thickness. In particular, the binding energy decreases with the dot width, whereas it increases as the hydrostatic pressure increases. Moreover, the SP exhibits an opposite trend to that of the binding energy and shows a pronounced dependence on the barrier thickness. In this sense, our present work complements earlier theoretical studies by accounting for the barrier width, which has not been investigated so far in our system.
