We investigate the excitation behavior of a repulsive impurity doped quantum dot under the combined influence of dopant drift and associated time variation in its spatial spread. We have considered Gaussian impurity centers. In order to make the investigation rational, the time-dependence of the spatial spread has been connected with the instantaneous location of the dopant. Looking at the general applicability of the findings, we have considered linear and random propagation of the dopant. For a systematic analysis, we have proceeded in a stepwise manner during the investigation. Thus, at first we have not considered the time-dependence of spatial spread of dopant and concentrated only on the dopant drift. Subsequently, we have introduced time-dependence in the spatial spread and observed the outcome. Although the incorporation of time-dependence in spatial stretch makes the calculation much more tedious and involved, yet this adequately describes the role played by the time-varying impurity domain exclusively in modulating the excitation rate. The varied nature of dopant propagation interplays delicately with the time-dependent modulation of its spatial stretch giving some important insight into the physics underlying the excitation process.

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