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Dislocation-free InP and GaAs crystals have been grown by liquid encapsulation by means of an ’’impurity doping’’ procedure. It was found that grown-in dislocations were diminished when the crystals were pulled from melts to which certain kinds of impurities were added. The impurity effect on grown-in dislocation density was examined for Zn, S, and Te in InP, and Zn, S, Te, Al, and N in GaAs. It was found that these impurities were effective for reducing the grown-in dislocation density, except for Zn in GaAs. The effectiveness of impurities for reducing the dislocation density of the crystals was ascribed to the strength of the bonds formed between the substitutional impurity atoms and host crystal atoms surrounding the impurity atoms. The anomaly of Zn in GaAs was presumed to originate from the interstitial Zn.

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Abstract.Existence and uniqueness theorems for parabolic stochastic partial differential equations with space~time white noise are proved. The method is a combination of the characterization theorem for Hida distributions with the Feynman-Kac and Girsanov formulae.