Numerical method for thermal donors formation simulation during silicon Czochralski growth

Various upgrades of the Czochralski (Cz) growth process are currently being investigated in order to increase throughput and reduce production cost of high efficiency silicon-based solar cells. However, as-grown thermal donors (TD) in Cz silicon can significantly reduce the conversion efficiency of such solar cells. An accurate simulation tool is therefore required to investigate and optimize TD formation during crystal growth. A nu-merical method combining thermo-hydraulic simulations and a kinetic TD formation model was improved by the implementation of a more appropriate TD formation model, identified through a benchmark of the different models available in the literature. Three different Cz growth processes were investigated both numerically and experimentally. Numerical results are in remarkable agreement with TD concentrations measured along the three ingots by the OxyMap technique developed at CEA. The simulations were then used to detect when TD were formed during Cz processes. The reliability of the method was also assessed through sensitivity analyses, highlighting the critical importance of the input interstitial oxygen concentration. These results show that accurate estimates of axial TD concentration profiles can be obtained and so for very different Cz processes, supporting the robustness of the developed method and its relevance to process optimization and furnace design to reduce TD concentrations.