Cu2ZnSnSe4 (CZTSe) is a semiconductor used as the absorber layer in highly promising sustainable thin film solar cells. The authors study the effect of Ar+ etching of copper deficient and zinc excess CZTSe thin films deposited on Mo/glass substrates on the surface elemental composition, measured by x-ray photoelectron spectroscopy, and photoluminescence (PL) spectra. Low temperature PL spectra reveal a broad asymmetrical band at 0.95 eV. The temperature and excitation intensity dependencies of this band suggest that it is a free-to-bound (FB) recombination of electrons from the conduction band with holes localized at an acceptor affected by potential fluctuations. The surface composition of the as grown films demonstrates a strong copper deficiency: [Cu]/[Zn + Sn] = 0.33. The etching of the film surface using Ar+ beam increases [Cu]/[Zn + Sn] to 0.51, which is significantly smaller than that of 0.78 in the bulk, measured by wavelength dispersive x-ray analysis, demonstrating the presence on the surface of a copper-depleted layer. The Ar+ etching drastically reduces the FB band intensity by a factor of 4.5, broadens it and develops a low energy tail. Ar ions displace atoms in CZTSe lattice creating primary radiation defects, vacancies, and interstitials, which recombine at room temperature forming antisite defects with deep energy levels. Some of them generate the observed low energy tail and increase the mean depth of potential fluctuation γ, determined from the shape of the low energy side of FB band, from 24 meV before Ar+ etching to 35 meV after. Other deep defects work as nonradiative recombination centers reducing the intensity of the FB band.