Kesterite materials are among the most promising emerging photovoltaic absorbers, despite the number of challenging issues this technology presents. The use of soft thermal post-deposition treatments (PDT) is key to improving the CdS/kesterite interface quality. Thermal treatments can result in a low-temperature phase transition which affects the optoelectronic properties. In this work, the effects of applied voltage during a full device thermal PDT above the critical temperature of the phase transition are explored. The applied voltage modifies the formation energy and drives in-depth migration of ionized defects, which can generate a shallow doping density gradient (SDDG). Supporting the experimental findings, the effects of an SDDG on the current-voltage curves and the external quantum efficiency are modelled using drift-diffusion calculations. The presence of bulk recombination centers in the modelling is a key aspect to precisely reproduce the experimental results. The SDDG in opposite directions precisely matches the experimental results for opposite voltage polarizations. The effects on the band structure of the device are presented proving this as a promising strategy for improving charge carrier selectivity. In this sense, the results and their thorough physical interpretation will potentially open new perspectives in the field of materials engineering.