We have studied the effect of introducing an insulating ultrathin Al₂O₃ with a very wide band gap (~ 7 eV) into a CBTS/CdS heterojunction to analyze the tunnelling effect in a Mo/MoS₂/CBTS/Al₂O₃/CdS/ZnO/AZO/Al solar cell using experimentally calibrated numerical simulation. We first investigated the intra-band tunnelling of electrons from the p-CBTS absorber to the n-CdS emitter through the insulator layer (Al₂O₃). In the second analysis set, we found that the thickness of Al₂O₃ must be sufficient (~ 3 nm) to allow the minority carrier penetration. It is shown that the CBTS/Al₂O₃/CdS structure enhances the collection efficiency in the short- and long-wavelength regions, resulting in higher performance. Indeed, with an Al₂O₃ layer between CBTS and CdS, the device exhibits efficiency of 11.89% with V_OC, J_SC, and FF of 1.08 V, 15.45 mA/cm² and 71.41%, respectively, compared to the device without Al₂O₃, which presents an efficiency of 6.75%, V_OC = 0.69 V, J_SC = 15.09 mA/cm² and FF = 64.84%. This study provides a guide to further optimise the performance of kesterite solar cells.