Distribution of Al and in impurities along homogeneous Ge-Si crystals grown by the Czochralski method using Si feeding r
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ICAL PROPERTIES OF CRYSTALS
Distribution of Al and In Impurities along Homogeneous Ge–Si Crystals Grown by the Czochralski Method Using Si Feeding Rod V. K. Kyazimova, A. I. Alekperov, Z. M. Zakhrabekova, and G. Kh. Azhdarov Institute of Physics, Academy of Sciences of Azerbaijan, G. Javid av., Baku, Az1143 Azerbaijan email: [email protected] Received August 13, 2013
Abstract—A distribution of Al and In impurities in Ge1 – xSix crystals (0 ≤ x ≤ 0.3) grown by a modified Czo chralski method (with continuous feeding of melt using a Si rod) have been studied experimentally and the oretically. Experimental Al and In concentrations along homogeneous crystals have been determined from Hall measurements. The problem of Al and In impurity distribution in homogeneous Ge–Si single crystals grown in the same way is solved within the Pfann approximation. A set of dependences of Al and In concen trations on the crystal length obtained within this approximation demonstrates a good correspondence between the experimental and theoretical data. DOI: 10.1134/S1063774514020114
Al and In impurities are highly soluble (1019– 10 cm–3 [1]) in Si and Ge and thus determine the electronic properties of these semiconductors in a wide temperature range. The equilibrium impurity dis tribution coefficients KAl (KIn) are 2 × 10–3 (4 × 10–4 ) in Si and 7.3 × 10–2 (1 × 10–3) in Ge at the crystallization temperature of the corresponding semiconductor [2– 4]. Such small КAl and КIn values lead to a significant impurityconcentration gradient along the crystalliza tion axis in Si and Ge ingots grown by the conven tional Czochralski method. The study of the distribu tion of impurity centers in crystals is an urgent prob lem because of their key role in the formation of electronic properties of semiconductors. For simple semiconductors this problem has been solved rather completely within different approximations. In this paper we report the results of solving the problem of Al and In distribution in homogeneous Ge–Si crystals (grown by the Czochralski method using a Si feeding rod) within the Pfann approxima tion and the model of virtual crystal for solid solutions [5, 6]. A mathematical simulation of the impurity con centration distribution in a Ge–Si crystal grown by the technique providing the homogeneous distribution of matrix atoms in it is based on the scheme presented in Fig. 1. After melting a charge composed of Ge, Si, and impurity (Al or In) in a corresponding ratio in a cruci ble and setting the liquidus temperature of a specified Ge–Si melt, a Si feeding rod and a seed were brought into contact with the melt surface. After a certain sta bilization time, crystal pulling began simultaneously with immersing the feeding rod into the melt. A homogeneous crystal with Ge and Si atoms in a given ratio was grown by maintaining the achieved tempera 20
ture at the crystallization front; the melt composition was balanced by the corresponding ratio of the crystal lization and feeding rates [6]. The problem of Al and In impurity dist
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