Crystals with a very open lattice, such as silicon, germanium, etc., having the cubic (
A
4 or
B
3) structure, all tend to increase their interatomic distance by fairly large amounts on solidification from the melt, and severe stresses can be set up if conditions are such that the crystal cannot expand freely on solidification in the crucible. The uneven distribution of temperature in the crystal, and its uneven decrease during the cooling-down period, can cause plastic deformation even in freely ‘pulled’ crystals. The density of dislocations produced by plastic flow under conditions of a radial temperature gradient and external constraint is given by
n
= (
α
/
b
)
δT
/
δr
, where
α
= thermal expansion coefficient and
b
= Burgers’s vector. The temperature distribution in a cylindrical ingot being pulled from the melt has been calculated, and the corresponding density of dislocations has been estimated. Monocrystals of germanium and silicon have been pulled from the melt under extreme conditions of temperature gradient and thermal stress. Etching techniques have been developed to show up dislocations on various crystal faces, and the distribution of etch pits has been studied throughout the volume of an ingot. Pits are found to be concentrated near the cylindrical surface— the ‘skin’—of most ingots, and especially near their top and bottom ends, whilst the central part is relatively free of pits. It is shown that the regions of high etch-pit concentration are related to a curved interface—concave or convex—of the growing ingot with the melt. In the central part of the ingot, where its diameter is nearly constant, the interface remains nearly flat and the etch-pit concentration is largely reduced, but sudden changes in temperature, recognizable by slight changes in the ingot diameter, cause the formation of pronounced slip bands starting from the edge of the interface. They are propagated back into the hot ingot as far as it is still in the plastic temperature range. It is suggested that the tangential or ‘hoop’ stress set up by differential contraction as the ingot cools down from the melting-point is relieved by slip, and, especially in crystals grown along a [100] direction, possibly also by polygonization. Effects in silicon are similar to those in germanium, but pit densities are several times as high, presumably owing to the higher temperature during crystal growth. Reasonable correlation has been obtained between etch-pit density and certain electrical characteristics of the ingot, such as the lifetime of minority carriers, transistor action and the highest inverse voltage that can be sustained by a rectifying point contact. For solid-state devices requiring material of highest perfection, the portion near the centre of the grown ingot is probably most suited.
Comparison of thermal stresses for exponential and actual temperature gradient along the depth of E-FG plate
