The present invention relates to a process for the production of III-V-, IV-IV- or II-VI-compound semiconductor crystals. The process starts with providing of a substrate with optionally one crystal layer (buffer layer). Subsequently, a gas phase is provided, which comprises at least two reactants of the elements of the compound semiconductor (II, III, IV, V, VI) which are gaseous at a reaction temperature in the crystal growth reactor and can react with each other at the selected reactor conditions. The ratio of the concentrations of two of the reactants is adjusted such that the compound semiconductor crystal can crystallize from the gas phase, wherein the concentration is selected that high, that crystal formation is possible, wherein by an adding or adjusting of reducing agent and of co-reactant, the activity of the III-, IV- or II-compound in the gas phase is decreased, so that the growth rate of the crystals is lower compared to a state without co-reactant. Therein, the compound semiconductor crystal is deposited at a surface of the substrate, while a liquid phase can form on the growing crystal. Further, auxiliary substances may be added, which can also be contained in the liquid phase, but is only incorporated in low amounts into the compound semiconductor crystal. Herein, 3D- and 2D- growth modes can be controlled in a targeted manner. The addition of auxiliary substances and the presence of a liquid phase favour these means. The product is a single crystal of the respective III-V-, IV-IV- or II-VI-compound semiconductor crystal, which, compared to respectively conventional compound semiconductor crystals has a lower concentration of inclusions or precipitates and nevertheless has no or only a very low curvature.