The conversion efficiency of crystalline silicon solar cells depends on the solidification process of the silicon material. During solidification, several kinds of grain structures can build up and some of them induce a decrease of the solar cell efficiency. The objective of our model is to predict the transition from large grains to small detrimental grains as a function of solidification parameters. As an abnormally high number of SiC particles have been observed in the small grains regions, the first hypothesis of our model is that segregation of C occurs during growth and provokes the precipitation of SiC. In a further step, free Si grains nucleate on the SiC particles and lastly, a competition between the planar front and the free Si grains takes place. This phenomenon can be compared to the columnar to equiaxed transition. From a simple analytical model, in a thermal gradient - growth rate diagram, we were able to draw transition maps between the different domains: equiaxed, planar+equiaxed and planar. This model allowed giving efficient recommendations to avoid the occurrence of the small detrimental grains during the industrial process.