An analysis of dislocation reduction by impurity hardening in the liquid-encapsulated Czochralski growth of 〈111〉 InP

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Abstract
Excessive impurity additions have been widely used to suppress dislocation generation in the liquid-encapsulated Czochralski (LEC) growth of InP. We have analyzed this approach by means of the quasi-steady-state heat transfer/thermal stress model. A strong motivation for the investigation was provided by the recent measurement of the critical resolved shear stress σCRS of InP as a function of temperature in the range 748–948 °K for several Ge and S concentrations. The experimental data were analyzed by the method of least squares via the usually accepted logarithmic dependence of σCRS on reciprocal temperature. The extrapolated values of σCRS exhibit a monotonic increase with impurity addition at temperatures near the melting point. Introducing the σCRS and realistic estimates of other physical properties (thermal diffusivity, thermal expansion coefficient, elastic constants, etc.) in the thermal stress model, the dislocation distribution pattern in a {111} substrate cut from a 〈111〉 boule was constructed. This necessitated a suitable recasting of the formalism that was previously applicable only to the {100} orientation. The computed dislocation contour maps on {111} wafers display sixfold symmetry resembling the ‘‘Star of David,’’ in overall agreement with etch-pit patterns. InP crystals 2.5 cm in diameter grown in a standard high ambient temperature gradient but containing a large amount of Ge (≂1019 cm−3) are predicted and observed to be dislocation-free. On the other hand, in nominally undoped material a large density of defects is forecast, especially at the periphery, in line with the etchpit configuration. Intermediate doping levels (∼1017 cm−3 Ge, ∼1018 cm−3 S) reduce the density in the core but leave the outer edge essentially unaltered.