Evidence for Transitions from Lateral to Continuous ...

EUROPHYSICS LETTERS

20 October 1995

Europhys. Lett., 32 (3), pp. 223-227 (1995)

Evidence for Transitions from Lateral to Continuous and to Rapid Growth in Ge-lat%Si Solid Solution. D. LI(*), K. ECKLERand D. M. HERLACH Institut f i r Raumsimulution, DLR, 0-51140 Kiiln, Germany (received 18 May 1995; accepted 1 September 1995)

PACS. 68.35Rh - Phase transitions and critical phenomena. PACS. 64.70Dv - Solid-liquid transitions.

Abstract. - The interrelationship andercooling-growbh velocity-solidifed structure,, was studied for Ge-lat%Si solid solution. Three structural morphologies, faceted twins, coarse dendrites and refined equiaxed grains, were observed in a wide range of undercoolings from 80 to 394K achieved by a levitation technique. Corresponding to low, intermediate and high undercoolings, these types of microstructures originated from lateral, continuous and rapid crystal growth, respectively.

Introduction. - The Ge-Si system tends to strongly segregate which makes it sensitive to the change of undercooling, and forms a faceted morphology under normal growth conditions. It is also suspected that a transition from a faceted to a rough microstructure would happen when a critical driving force for crystallization is reached. Therefore, this system is excellent for studying solidification kinetics and structure transformation as a function of bulk undercooling. Secondly, at present crystal growth from the liquid phase mostly employs Czochralski, Bridgman, and xone-melting techniques. The diverse containerless processes now under development promise a new field of interest for wall-free crystal growth. The realization of containerless electromagnetic (EM) melting of semiconducting materials is an attempt in this respect. Moreover, containerless EM levitation processing offers an elegant approach to achieving high undercooling and to directly measuring dendrite growth velocity in undercooled melts, especially for semiconducting materials, since some of them, e.g. molten Si, are so reactive that it is dficult to search for an appropriate fluxing reagent. Thirdly, the possibility is worth being explored that single crystals of semiconducting materials could be produced through high-undercooling-induced ADS (autonomous directional solidification), a technique recently initiated by Ludwig et al. [l].Thus, deep undercooling and crystal growth of the semiconductor by containerless EM levitation processing is of interest to scientists and engineers. Investigations on undercooling and microstructure of pure Ge and pure Si were conducted using a variety of techniques, e.g. Bz03 fluxing [2,31, drop tube 141, pulsed-laser surface quenching 151 and electrohydrodynamic atomization 161. However, they are restricted to (*)

On leave from Northwestern Polytechnical University, PRC.

0 Les Editions de Physique

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analyses of the already solidified products, which would be insufficient to probe into growth processes. In this work, by realizing the E M levitation of Ge-lat%Si alloy, we were able to obtain a substantial degree of undercooling of up to 394 K for bulk spheres and to measure the growth velocities in the undercooled melts. The interrelationship andercooling-growth velocity-solidified structure. in a wide range of undercoolings was explored, which is of fundamental importance to the understanding of the transitions on solidification modes. Moreover, the V-AT correlation measured for Ge-lat%Si was analysed within a slightly modified dendrite growth theory. Experiments. - Direct electromagnetic levitation of semiconducting materials looks improbable, because of its low electrical conductivity at room temperature. However, there are two ways of enhancing the electrical conductivity of semiconductors: raising the temperature or doping with electrically active impurities. According to the former method, E M levitation melting of a Ge-based system becomes feasible through a so-called two-step heating process. Since pure Ge does not wet carbon, a Ge (99.999% pure from Heraeus) sample was preheated to about 500 "Cwith a high-purity graphite substrate which was itself heated by the eddy currents induced by the alternating E M field of the levitation coil. After the Ge sample had been stably levitated, the graphite substrate was removed from the coil. Subsequently, a certain amount of Si pellet (99.9995%pure, Ventron) was fed to the levitated Ge melt with a sample holder, and a Ge-lat%Si alloy was thus prepared. The experiment chamber was initially evacuated to lower than 2 x 1OP6mbar, then back-filed with 80% He/20% H2 (better than 99.999% in purity). An infrared pyrometer recorded the temperature of the sample. The growth velocity of the undercooled melts was measured with a silicon photodiode and a high-speed data acquisition system. To measure the maximum undercooling attainable and the growth velocities in the levitated state, the following 300 K successive heating cycles were made about ten times: melting + superheating by for 5 min + cooling at a rate of about 20 K / s by gas flow + nucleation and growth. Further details are given elsewhere [7].

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Results and analyses. - The highest undercooling reproducibly observed was 394 K (0.32T,, TL is the liquidus temperature) for bulk Ge-lat%Si melts (spheres of 8-10" diameter). As shown in fig. 1, three microstructure categories were found. Below a lower undercooling limit of about AT,, = 250 K, faceted and lamellar twins were the unique structure (fig. la)). When an upper critical undercooling, AT, = 330 K was exceeded, segregation-free and fine equiaxed grains completely replaced the faceted structure. In the

Fig. 1. - Microstructure morphologies of differently undercooled Ge-lat%Si solution: a) a faceted structure at AT = 180 K ( < ATcl ); b ) coarse grains of dendrite segregation at AT = 316 K and c) a refined equiaxed structure of a sample undercooled by 373 K ( > ATc2).

D. LI

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undercooling AT (K) Fig. 2. - Growth velocity, V, as a function of undercooling, AT, for Ge-lat%Si solid solution. experimental, -calculated.

U

moderate range of undercoolings, the grains contained cross dendrites, evidencing the microsegregation. The dendrite trunks are enriched by Si (dark region in fig. lb)) since, according to the phase diagram, the equilibrium distribution coefficient of Si is much larger than 1. As is well known, two different solidification modes exist in terms of the solid/liquid (S/L) interface structure: lateral growth (LG) related to strongly faceting materials, and continuous growth (CG) associated with most metals. But according to Cahn's model [8],for all systems there should appear LG at sufficiently small undercoolings, and the transition from LG to CG should take place at a critical interface undercooling AT:. The Ge-lat%Si solution initially belongs to a faceted material, so the faceted structure was observed under normal conditions, ie. at AT < 250 K. With increasing AT, the instability of LG sets in and a transition from LG to CG emerges, which is indicated by the dendrite structure solidified in the intermediate undercooling range. As the driving force for crystallization, or undercooling prior to nucleation, is further enhanced, the second transition or morphology appears, resulting in a grain-refined equiaxed microstructure. The physical mechanism of the grain refinement in undercooled semiconductors as well as metallic alloys can be elucidated by a dendrite break-up model [91. The two transitions are also clearly visible in the measured V-AT relation (fig. 2): first, when the undercooling is smaller than 250 K, the velocities rise slightly and crystal growth is dominated by interface kinetics. At AT,, = 250 K, V has a rapid and smooth increase which is an evidence for continuous growth. Secondly, the upper undercooling threshold, AT, for grain refinement corresponds to a critical growth velocity of V, = 1 m/s at which the region of rapid crystal growth is entered. Beyond V, = 1 m/s, the crystal growth is purely thermally controlled and partitionless. The evidence for this conclusion can also be provided from the microstructural aspect in fig. IC)in which no segregation patterns of cross dendrites can be discerned. The interpretation of the measured K A T ) function is based on the dendrite growth theory, usually called the LKT/BCT model, developed by a number of researchers [lo, 111. But two points need to be considered before calculating the growth velocity using the model. The frst concerns the transition from LG to CG. Below the critical undercooling AT,,, crystal growth is significantly dominated by interface kinetics. Since the LKT/BCT model has been proved valid for the CG regime, i.e. above AT,,, it should be slightly modified for Ge-based systems: the effective undercooling for CG is thought to be the total undercooling minus a critical interface undercooling, AT? for the LG-CG transition. It is rather difficult to directly measure the interface temperature, however Evans et aL[12] gave a plot of the

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interface temperature a t the onset radius for instability as a function of the bulk undercooling for Ge according to their computation on stability of spherical crystal growth. From the computed curve, one can read AT? = 153 K at the critical bulk undercooling AT,, = 300 K for pure Ge. This computation has not been carried out for the Ge-lat%Si solution yet, the value of AT: is assumed to be 153 K for Ge-lat%Si too, because of similar physical mechanism for the LG + CG transition. The undercooling equation consists of different contributions,

with AT, = Iv(P,) AH/C, the thermal undercooling, ATr = 2 r / R the curvature undercooling, AT, = V / p the kinetic undercooling, and AT, the constitutional undercooling, the formulae of

\ exp -tl t -'dt, ffi

which are given by [lo, 111. Iv is the Ivantsov function, Iv(x)= x.exp [XI

[

X

AH the heat of fusion, C, the specific heat of the undercooled melt, Pt = V R / (2a)the thermal Peclet number, R the radius of the curvature at the dendrite tip, a the thermal diffusivity, r = a/AS the Gibbs-Thomson coefficient, (T the S / L interface energy, AS the entropy of fusion, and p the interfacial kinetic coefficient. Another equation required for a unique calculation of the tip velocity V as a function of undercooling is provided by the marginal-stability criterion [10,111. According to the undercooling and stability equations, the growth velocities can be calculated if the kinetic coefficient p, p = fAHV8/(R,T:) is determined, where V , is the speed of sound and R, the gas constant. Here the prefactor f is the second point we should pay attention to. Based on the assumption of collision-limited growth [13], it would be expected that f = 1 for a metal growing from its own liquid. This has been confirmed by analysis of the velocities of rapidly growing dendrites into pure undercooled Ni melts [14], and by pulsed-laser melting experiments on Cu and Au [15]. But the semiconductor Ge-lat%Si has a structure distinct from that of melts. For pure Si,f- 0.02 can be inferred from the measurement of S / L interface temperature during pulsed excimer laser melting[16]. Thus, we can suppose thatfis of the order for Ge-lat%Si, too. If the prefactorfis set equal to 1 for Ge-lat%Si, the prediction apparently deviates from the values measured. When f = 0.015, a good agreement is achieved between the calculated curves by the slightly modified BCT/LKT model and the experimental data. Conclusion. - The microstructural observations and the measurements of growth velocities in a wide range of undercoolings indicate the transition of the solidification mechanism from lateral to continuous, and finally to rapid crystal growth in the system Ge-lat%Si. Two undercooling thresholds, ATcl and AT,, were experimentally determined. Below AT,,, crystal growth is governed by interface kinetics, bringing about the faceted structure; beyond AT,, solidification is purely thermally controlled, giving rise to refined equiaxed grains. When the undercooling varies between ATc1and AT,, coarse dendrites with obvious segregation patterns solidify. This suggests that growth is dominated by both redistribution of heat and solute. The measured V A T ) function is well described within the current theory of dendrite growth, provided the L G - + C G transition is taken into account.

*** The authors thank Prof. B. FEUERBACHER for continuous support. DL acknowledges the financial support of the Alexander-von-Humboldt Foundation and also thanks H. MUHLMEYER, T. VOLKMA",R. KOUBA,M. BARTH,D. HOLLAND-MORITZ, M. SCHWARZ, J. SCHROERS and W. SOELLNER for consistent help.

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