Growth rate dependence of the interface distribution coefficient in the system Ge-Ga

144

Journal of Crystal Growth 60(1982) 144—146 North-Holland Publishing Company

LETTER TO THE EDITORS GROWTH RATE DEPENDENCE OF THE INTERFACE DISTRIBUTION COEFFICIENT IN THE SYSTEM Ce-Ga C.A. WANG, J.R. CARRUTHERS

*

and A.F. WITT

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Received 3 August 1982

Segregation analyses in the system Ge—Ga establish a growth rate dependence of the interface distribution coefficient for rates smaller than 1.5 gm/s.

For solidification of very dilute melts (doped semiconductor systems), it is generally assumed that the interface distribution coefficient of the dopant element, k~,is numerically identical with k0, the equilibrium distribution coefficient. The validity of this assumption has been disputed on theoretical grounds by Thurmond [11, Tiller [21, Chernov [3] and others [41.The issue, however, remains unresolved so far for lack of reliable experimental segregation data, Anomalous segregation effects observed during solidification of Ga-doped Ge in a reduced gravity environment [5] motivated an investigation of microsegregation in this system. This on-going study provides experimental evidence for the dependence of the interface distribution coefficient, k, of Ga on the rate of solidification at rates ranging from zero to about 1.5 rem/s. Ge crystals of ~111) orientation were grown (without central facet formation) in a vertical Bridgman configuration from electronic grade Ge, doped with Ga (99.9999% pure) at concentration 9/cm3 in the levels 4 X 1018 to 7cm X lO’ melt. ranging The seedfrom crystals (1.26 diameter) were Ga-doped at concentrations ranging from 8 X 1014 to 8 X 1018/cm3 the crucibles were made of high purity boron nitride and high purity graphite. For this investigation of the rate dependence of k,, growth conditions were selected under which

the build-up of concentration boundary layers was minimized, i.e. microsegregation was studied for very low, constant growth rates (0.2 to 1.0 ~t m/s) and for transient growth rates from zero to 4 p~m/s.Conditions of virtually constant growth rates were achieved for~desired growth lengths of several millimeters by lowering the crucible at fixed rates through a tube furnace; conditions of zero growth rate (equilibrium segregation) and transient growth rates were investigated (a) for seeding and initial growth after partial melt-back and thermal equilibration of up to 45 mm and (b) for lowering arrests, ranging from 5 mm to 12 h. All segregation analyses were performed on differentially etched, longitudinal crystal slices; microscopic composition and corresponding growth rate profiles were obtained from spreading resistance measurements and interface demarcation spacings [6] (time intervals of 10 s) respectively; the absence of interference with segregation by coded interface demarcation was ascertained. The segregation forofinitial transient growth, after partialbehavior melt-back a doped seed (Ga concentration C~ CL X 0.087 *) and equilibration for 30 mm is shown in fig. 1. Accordingly, the dopant concentration (top curve) is a maximum (7.3 >< 10’8/cm3 k 1 = 0.098) at the seed—crystal interface and decreases with increas*

*

Hewlett-Packard Laboratories, Palo Alto, California, USA.

0022-0248/82/0000—0000/$02.75

©

1982 North-Holland

0.087 is the generally accepted value of the equilibrium distribution coefficient (k0) of Ga in Ge.

CA. Wang et aL

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ing rate of solidification during the initial growth period; it assumes the level anticipated for growth in the absence of a significant concentration 18/cm3) only in =excess layerat solidification (C~ CL Xrates 0.087 6.5 xof l0 1.5 ~tm/s. The rate dependence of k 1 is unaffected

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by the Ga concentration level in the seed and in the melt and moreover is found to be the same whether equilibrium conditions prior to growth

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were approached by hot seeding (melt-back) or cold seeding (uncontrolled growth). The segregation behavior associated with

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lowering arrests of 5 and 30 mm is shown in fig. 2. During the arrest period of 5 mm (A), thermal

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equilibration led to a relocation of the growth interface in the upward direction, i.e. resulted in

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growth rate decreasing continuously to an ultimate value of about 0.2 ~sm/s before increasing again upon resumption of crucible lowering. The corresponding composition plot shows a concentration

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maximum for the growth rate minimum and rate dependence of k for both decreasing and increasing rates of solidification. This particular segrega-

Fig. 1. Dopant concentration and corresponding growth rate profiles for seeded Bndgman growth in which see melt-back was accomplished by raising the charge into the hot zone. The period of zero charge displacement (equilibration) prior to the initiation of growth by charge lowering was 30 mm. The circles in the growth rate diagram indicate omitted current pulses (time coded interface demarcation). C)

tion study is important insofar as any significant concentration boundary layer build-up which may

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Growth rate dependence of interface distribution coefficient

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146

C.A. Wang et al.

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have occurred prior to the lowering arrest is subject to decay during the period of equilibration, and thus cannot contribute to the observed rate dependence of k, which results in increasing dopant incorporation under a decreasing rate of growth. Moreover, since the rate dependence of k1 is found to be virtually the same for decreasing growth rates (boundary layer decay) and increasing growth rates (boundary layer build-up), it is concluded that boundary layer effects did not contribute to the observed segregation behavior. The experiment involving a 30 mm lowering arrest (B) in fig. 2 provides evidence for melt-back during equilibration. The related segregation behavior thus exhibits the same basic characteristics observed for seeding in fig. 1 since the crystal portion grown under decreasing rate of growth has been cornpletely eliminated by melt-back. The rate dependence of the interface distribution coefficient was also investigated at constant growth rates of 0.2, 0.3, 0.4 and 0.95 p.m/s. These experiments confirmed the results obtained under conditions of transient growth rate. It should be pointed out that the precision of the segregation analyses is controlled by the limited spatial resolution (about 10 p.m) of spreading resistance measurements. Thus, the accuracy of analyses for transient growth, with the growth rate approaching zero, decreases continuously and the -

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value of k0 can only be obtained by extrapolation. The experimentally determined growth rate dependence of k1 is summarized in fig. 3 where the distribution coefficient for rates larger than 2.0 ~.tm/s is taken to be constant at 0.087. The authors wish to express their appreciation to the National Aeronautics and Space Administration (Materials Processing in Space Division, Grant No. NSG 7645) for their financial support and cooperation in this study.

References [I] C. Thurmond, in: Semiconductors, Ed. N.B. Hannay (Reinhold, New York, 1959) ch. 4. [2] WA. Tiller and KS. Ahn, J. Crystal Growth 49(1980) 483. [3] E.g., A.A. Chernov, Soviet Phys.-Usp. 13 (1970) 101. [4] For example, see: R.N. Hall, J. Phys. Chem. 57 (1953) 836; A. Trainor and BE. Bartlett, Solid-State Electron. 2 (1961) 106; P.J. Holmes, J. Phys. Chem. Solids 24 (1963) 1239; JR. Carruthers, Can. Met. Quart. 5 (1966) 55. [51A.F. Witt, M. Lichtensteiger and H.C. Gatos, J. Electrochem. Soc. 120 (1973) 1119. [6] A.F. Witt, H.C. Gatos, M. Lichtensteiger and C.J. Herman, ~ Electrochem. Soc. 125 (1978) 1832.