ISSN 10637745, Crystallography Reports, 2011, Vol. 56, No. 3, pp. 531–534. © Pleiades Publishing, Inc., 2011. Original Russian Text © G.Kh. Azhdarov, Z.M. Zeynalov, Z.A. Agamaliyev, S.O. Mamedova, 2011, published in Kristallografiya, 2011, Vol. 56, No. 3, pp. 570–574. 531 INTRODUCTION Certain progress has been made in the growth of single crystals of silicon–germanium solid solutions over the two last decades. Along with the conventional Czochralski, Bridgman, and floating zone methods, as well as their different modifications [1–16], a promis ing new method [4] has been used to grow these crys tals. The essence of this method is that a crystal grows from a melt with a silicon feeding rod through contin uous constitutional supercooling of the melt at the crystal–melt interface. Later this method was used to grow Ge 1– x Si x crystals with a linearly increasing sili con concentration along the crystallization axis [17, 18]. Note that the name of this method has not been established in the literature. In [4] and [17] it was called, respectively, multicomponent zone melting and diffusion through liquid phase. In this study we will refer to it as directional constitutional supercool ing of the melt. The necessary condition for growing single crystals of semiconductor solid solutions is a low crystalliza tion rate. For example, for concentrated solid solu tions of the Ge 1– x Si x system, the singlecrystal growth rate is more than two orders of magnitude lower than the growth rates of their components [2, 6, 9]. This is caused by the constitutional supercooling of the melt near the crystal–melt interface. The critical rate above which the growing Ge 1– x Si x crystal becomes polycrys talline can be estimated from the relation [2] (1) Here, К is the silicon segregation coefficient, х is the fraction of silicon atoms in the crystal, is the tem ∇θ = > ∇ −  , ( 1). ( 1) c D K K TxK v ∇θ perature gradient in the melt, is the liquidus slope, and D = (30 – 24х) × 10 –5 cm/s [2] is the diffu sion coefficient of silicon in the melt. In this paper we report a solution to the problem of the growth dynamics of Ge 1– x Si x crystals with a lin early changing composition along the crystallization axis during growth by directional constitutional super cooling of the melt with a silicon feeding rod. Our pur pose was to determine the process parameters and optimal regimes of melt crystallization for growing germanium–silicon single crystals with a specified axial gradient of component concentrations. CONCEPT AND THEORETICAL ANALYSIS Figure 1 schematically shows the growth of Ge 1– x Si x single crystals by directional constitutional supercooling of the melt. A germanium charge is mol ten above a singlecrystal germanium seed in a heater, which provides axial linear heating in the working vol ume (Fig. 1b). After a stabilizing period, a silicon rod is inserted (with a specified velocity) into the melt from above. The crystal grows statically, i.e., without displacing the crucible with respect to the heater. At the initial instant, the temperature at the crystal–melt interface is equal to the germanium melting tempera ture. After some time, part of silicon that dissolved at the upper boundary of the melt reaches (due to the dif fusion) the interface. This leads to the formation of the supercooled melt at the crystal–melt interface and the growth of a Ge–Si crystal. The continuous increase in the silicon concentration at the interface leads to an increase in the melt liquidus temperature. If, at t 1 the ∇  T CRYSTAL GROWTH Growth Dynamics of Ge 1–x Si x Single Crystals Obtained by Directional Constitutional Supercooling of the Melt G. Kh. Azhdarov a , Z. M. Zeynalov b , Z. A. Agamaliyev a , and S. O. Mamedova b a Institute of Physics, Azerbaijan National Academy of Sciences, pr. Dzhavida 33, Baku, AZ1143 Azerbaijan email: zangi@physics.ab.az b Ganja State University, pr. Shakh Ismail Khatai 187, Ganja, Azerbaijan Received October 4, 2010 Abstract—The problem of growth dynamics for crystals of binary solid solutions, obtained by the constitu tional supercooling of the melt with a silicon feeding rod, has been solved within the Pfann approximation. The dependences of the change in the axial growth rate of Ge 1– x Si x crystals (0 ≤ x ≤ 0.3) are calculated. It is shown that the Ge 1– x Si x crystallization rate significantly changes during growth. The results make it possible to determine the optimal conditions and technological parameters for growing Ge 1– x Si x single crystals (0 ≤ x ≤ 0.3) with a specified concentration gradient along the crystallization axis. DOI: 10.1134/S1063774511030023