New Determinations of Diffusion Coefficients for Various Dopants in Liquid Silicon

The objective of this article is to propose new determinations of the diffusion coefficients of various dopants in liquid silicon. The approach of this work is based on an analysis of the effective segregation coefficients obtained by Kodera in Czochralski growth of silicon-based alloys. However, it will be shown that the solidification model used by Kodera presents some serious deficiencies as it does not account for (i) the dependence of the solute boundary layer thickness on the iInterface velocity and (ii) the effect of density change upon freezing. In addition, the values of the thermophysical parameters used by Kodera can be questioned in view of recently published data. The approach proposed in the present work can be used to provide a much sounder physical basis for the analysis of the data, but it should be stated that the uncertainty on the partition coefficients is such that a measurement technique based on solidification experiments cannot be expected to be very accurate. In this respect, the scatter of the data, hardly avoidable in Czochralski growth experiments, is also discussed. To put things on a quantitative basis, an error analysis is carried out to quantify the error bar attainable by such a measurement technique.