Problem of attaining constant impurity concentration over ingot height

The possibility of growing crystals with homogeneous impurity distribution over crystal height has been demonstrated in a study of segregation during silicon and germanium growth from thin melt layers using the submerged heater method. Numeric simulation of 200 mm diam. antimony-doped germanium crystallization has shown that, beginning from a 40 mm melt layer thickness, the exact problem solution with convection allowance is identical to the unidimensional heat exchange problem solution in the central ingot part. The conditions under which convection can be ignored in mass transport calculation are more rigorous: the melt layer height must be within 20 mm. In this case Tiller’s ratio can be used for calculating the longitudinal impurity distribution for predominantly diffusion-controlled mass transport pattern. Analysis of the existing attempts to describe the experimental crystal growth results using the simplified formulae shows that they only yield acceptable results if the actual growth rate or change in melt layer thickness during crystallization are taken into account, e.g. as in the formula suggested by Marchenko et al. One can therefore analytically describe the longitudinal impurity distribution in the ingot, e.g. B and P distribution in silicon, and recommend the degree of additional doping of the melt zone under the heater so that to provide a constant impurity concentration over the ingot height. Homogeneous material can be obtained after residual layer solidification in the end portion of the ingot if the growth rate is controlled through varying the cooling rate.