Kesterite solar cells show the highest efficiency when the absorber layers (Cu2 ZnSnS4 [CZTS], Cu2 ZnSnSe4 [CZTSe] and their alloys) are non-stoichiometric with Cu / (Zn + Sn) ≈ 0.8 and Zn / Sn ≈ 1.2. The fundamental cause is so far not understood. Using a first-principles theory, we show that passivated defect clusters such as Cu Zn+ SnZn and 2 CuZn+ SnZn have high concentrations even in stoichiometric samples with Cu/(ZnSn) and Zn/Sn ratios near 1. The partially passivated CuZn+ SnZn cluster produces a deep donor level in the band gap of CZTS, and the fully passivated 2CuZn+ SnZn cluster causes a significant band gap decrease. Both effects are detrimental to photovoltaic performance, so Zn-rich and Cu, Sn-poor conditions are required to prevent their formation and increase the efficiency. The donor level is relatively shallower in CZTSe than in CZTS, which gives an explanation to the higher efficiency obtained in Cu2 ZnSn (S, Se)4 (CZTSSe) cells with high Se content.