Kesterite thin films solar cells have been studied in recent years as a potential earth abundant alternative to other thin film technologies such as the ones based on the chalcopyrite Cu(In,Ga)Se2 (CIGS). However, the efficiency of the kesterite devices is still low and needs further development. In order to increase the performance of the kesterite solar cells, a better understanding of the influence of variations of compositions on the crystal lattice of the absorber layer is needed. This paper presents a study of how variations in the Cu content in the Cu2ZnSnSe4 (CZTSe) absorber layer affects the crystal structure and therefore changes the optoelectronic properties of the solar cell. Three sets of CZTSe absorbers with different Cu content were synthesised by sputtering of metallic targets followed by a rapid thermal selenisation process. An accurate characterisation of the lattice parameters of the unit cell is presented, showing that a decrease of the Cu content in the CZTSe absorber layer diminishes the unit cell volume. This decrease in volume is related to an increase in the concentration of [VCu+ZnCu] and the ordering of the Cu/Zn atoms in the (001) plane. The variations in the lattice of CZTSe induced by decreasing the Cu content cause an increase of the bandgap of absorber layer, which leads to an increase of the open circuit voltage (VOC) in the devices. The best solar cell was based on the absorber layer with the lowest Cu content and yielded an efficiency of 8.1% with a fill factor of 59.8%, Jsc=31.1 mA/cm2 and Voc=434 mV.