port of the Alexander-von-Humboldt. Foundation. ... P. V. Evans, G. Devaud, T. F. Kelly and Y. W. Kim, ... W. J. Boettinger, S. R. Coriell and R. Trivedi. in Rapid.
Pergamon 0956-7151(95)00334-7
Acia mater. Vol. 44, No. 6, pp. 2437-2443, 1996 Elsevier Science Ltd Copyright 0 1996 Acta Metallurgica Inc. Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00
UNDERCOOLING, CRYSTAL GROWTH STRUCTURE OF LEVITATION MELTED Ge-Sn ALLOYS D. Lit, Institut
K. ECKLER
AND PURE
GRAIN Ge AND
and D. M. HERLACH
fiir Raumsimulation,
DLR,
D-5 1140 K61n, Germany
(Received 10 May 1995; in revised form 4 August 1995) Abstract-Using containerless electromagnetic (EM) levitation, pure Ge, G&.39 at% Sn and Gee10 at% Sn alloys were undercooled by up to 426, 404 and 334 K, respectively. The crystal growth velocities in undercooled melts were measured with a photodiode technique. Crystal growth behavior was found to fall into three categories of lateral growth (LG) at low, continuous growth (CG) at moderate, and rapid growth (RG) at high undercoolings, leading to various microstructures. The measured growth velocities were analyzed in terms of slightly modified, current dendrite growth theory. The presence of solute, Sn, was found to have a strong influence not only on the magnitude of the growth velocity, but also on the growth kinetics. The latter effect indicates that the critical undercoolings corresponding to the transitions between solidification mechanisms monotonically decrease as the Sn content increases.
Zusammenfassung-Mit Hilfe elektromagnetischer
Levitation wurden die Schmelzen von reinem Ge sowie at% Sn und Gee10 at% Sn Legierungen urn jeweils bis zu 426, 404 und 334 K unterkiihlt. Die Geschwindigkeit des in die unterkiihlte Schmelze wachsenden Kristalls wurde mittels Photodioden gemessen. Es wurden drei Bereiche unterschiedlichen Wachstumsverhaltens gefunden: laterales Wachstum bei niedrigen, kontinuierliches Wachstum bei mittleren, und rasches Wachstum bei hohen Unterkiihlungen, die jeweils zu verschiedenen Mikrostrukturen fiihrten. Die gemessenen Wachstumsgeschwindigkeiten wurden analysiert im Rahmen einer geringfiigig modifizierten, modernen Theorie dendritischen Wachsturns. Es zeigte sich, daB das Zulegieren von Sn nicht nur die GriiDe der Wachstumsgeschwindigkeit stark beeinflu& sondern such die Wachstumskinetik. Letzteres deutet an, daI3 die kritischen Unterkiihlungen, die den UbergCngen zwischen den verschiedenen Erstarrungsweisen entsprechen, monoton mit zunehmendem Sn-Gehalt abnehmen. von Gea.39
1. INTRODUCTION
High undercooling has been a subject of extensive research interest, since solidification pathway and microstructural development are dependent on the bulk undercooling, AT. Over the years, the evident advances in this area not only mean that the degree of undercooling produced with various denucleation techniques has been greatly increased, but also involve a new understanding of microstructural evolution with increasing AT: (1) from faceted to nonfaceted, (2) from equilibrium to metastable phases, (3) from regular lamellar to irregular anomalous eutectic, and (4) from coarse dendrites to a fine-grained equiaxed structure. Except for the first transition, the morphological developments have been extensively studied for metallic systems. In contrast to metals, the work on undercooling and growth is still in the embryonic stage for semiconducting materials, especially high melting point semiconductors. One of the major problems remaining to
ton
leave from: Northwestern Xian. P. R. China.
Polytechnical
University,
be resolved is crystal growth at large undercoolings. Devaud and Turnbull [l] applied a fluxing technique to elemental Ge, and found that molten droplets of 0.34.5 mm diameter could be undercooled by 415 K below T,,, (T,,, stands for the melting temperature for pure Ge, or the liquidus temperature for Ge-Sn alloys in this paper). For the first time, (100) twin-free dendrites were revealed for Ge at AT 2 300 K. However, with regard to the solidified microstructures they presented, there would appear to be no reason why lamellar twins, the typical microstructure of Ge, could not be observed at small undercoolings. Repeatedly, B,03 flux was used to undercool bulk Ge samples by a range of l&342 K [2]. A new twin system (111) (110) was identified in the least undercooled regime, in addition to the ( 111) (2 11) lamellar twin system [3]. By comparison, the results of Refs [l] and [2] show some discrepancies not only in the maximum undercooling attainable, but also in the critical undercooling corresponding to the microstructural transformation. A 6.5 m drop-tube [4] was also utilized to investigate the solidification of Ge droplets in free fall, as a useful complement to the fluxing method. It was expected that more infor-
2431
2438
LI r/ c/i.: UNDERCOOLING
mation about solidification modes and microstructure effects could be provided according to the statistics on large populations of droplets of widely varying size. A simple Newtonian heat flow calculation yielded a value of AT z 450 K prior to nucleation. Unfortunately, the microstructure evidently consisted of faceted structure and twins in the largest undercooled splat [4]. The transformation from faceted to nonfaceted microstructure should proceed completely under this condition. unless the actual undercooling was much less than the estimated value of 450 K. Evans et al. [5,6] briefly summarized microstructures of Ge solidified at high undercooling using four techniques: fluxing, drop-tube, laser surface quenching and electrohydrodynamic atomization, and numerically analyzed the stability of the spherical growth form in undercooled Ge. In addition, the crystal growth velocity was calculated as a function of undercooling according to current dendrite growth theories. This computation needs to be verified by experimental results. On the other hand, only relying on the correlation between the as-solidified structure and undercooling would be insufficient to portray the crystal growth behavior and growth transition. Therefore, it is indispensable that the interrelationship “undercooling-growth velocityPsolidified structure” should be established in a wide range of undercoolings in order to gain further insight into the growth mechanisms from lateral to continuous, and eventually to rapid crystal growth. The present investigation was undertaken to study overall crystal growth characters and morphological developments of pure Ge and G&n alloys from small to very large undercoolings using electromagnetic levitation. 2. EXPERIMENTAL
PROCEDURE
In order to undercool liquids to the maximum extent, various techniques have been developed to eliminate heterogeneous nucleants from the melt and to remove container-wall induced nucleation. Among them, containerless EM levitation processing particularly catches the attention. Besides giving access to comparably large undercoolings, it opens a new window on directly measuring dendrite growth velocities in undercooled melts. Therefore containerless EM levitation processing would also be one of the best methods of acquiring high undercooling for semiconducting materials, because some of them, such as Si-based systems, are so reactive that an appropriate fluxing agent can be hardly found. Owing to the low electrical conductivity of Ge at ambient temperature, the direct induction heating and EM levitation of this material seems impossible. However, as is well known, there are two ways of enhancing the electrical conductivity of semiconductors: raising the temperature or doping with electrical active impurities. According to the former, EM levitation
CRYSTAI
GROW’lH
melting of a Q-based system becomes feasible through a so-called two-step heating process. First” a Ge or GeeSn (Ge 99.999%. and Sn 99.9999”ja pure from Heraeus) sample was preheated to about 500 C with a high purity graphite substrate which was itself heated by eddy currents induced by the alternating EM field of the levitation coil. The substrate is required not to react with the sample. After the Ge sample was stably levitated. the graphite substrate was withdrawn from the coil. The experiment chamber was initially evacuated to lower than 2 x IO-‘mbar. then back-filled with 80% He20% HI (better than 99.999% pure). An infrared pyrometer monitored and recorded the temperature of the sample. The crystal-growth velocity of the undercooled melts was measured with a silicon photodiode and a high speed data acquisition system. Detailed descriptions of the facility and the measurement principle are given in Ref. [7]. The composition of the etchents for metallographic analysis was HNO,:CH,COOH:HF: 5% aq. soln. AgNO, = 5 : 3 : 3 : 1 for the internal microstructure, and HF:HNOI:5% aq. soln. AgNO, = 2:1:2 fat external surface morphology.
3. MAXIMUM
UNDERCOOLING
To measure the maximum undercooling attainable, AT,,,, and the growth velocity in the levitated state, the following successive heating cycles were made about 10 times: melting-superheating by -300 K for - 5 min+ooling at a rate of about 5-30 K/s by gas flow-nucleation and crystal growth. The highest undercooling reproducibly observed was 426 K for bulk pure Ge melts (spheres of SlOmm diameter). This result slightly surpassed the maximum undercooling of 415 K obtained in small Ge droplets with fluxing [l]. This is due in the present work to the elimination of container-wall induced nucleation and to the creation of very clean environmental conditions. For the alloys the measured maximum undercooling was 404 K (Gee0.39 at% Sn) and 334 K (Gee10 at% Sn), respectively. The maximum undercooling strongly depends on the material composition, and the undercoolability shows an obvious tendency to decrease as the Sn content increases. The maximum undercooling for Gee0.39 at% Sn was 52 K less than that of Ref [I]. Simply explaining, this difference arises out of the fact that the volume of the samples in the present work is larger by a factor of IO4 than that of Ref. [ 11. On the other hand, the result on AT,,, of bulk Ge samples slightly larger than that of small Ge droplets, indicates that the sample size would not be a decisive factor to the undercooling level if the samples are presently in a range of about IO mm in diameter. This undercoohng essentially results from highly removing and deactivating nucleants within melts, instead of from quick cooling rate.
LI et al.: 4. GROWTH
UNDERCOOLING
VELOCITIES
Figure 1 shows the measured and calculated dendrite growth velocities, V, at different undercoolings, AT for pure Ge, the dilute alloy Gee0.39 at% Sn and the concentrated alloy Ge-10 at% Sn. First, regarding the measured data of pure Ge, the growth velocity was rather slow, as seen in Fig. 1, approaching 1 m/s at AT = 0.35T,,,, in contrast to undercooled metals (e.g. the dendrite growth velocity of pure Ni is V = 25 m/s at AT = 0.1 T, [7]). Especially below 200 K, the motion of the solidification interface appears to be quite sluggish, giving rise to recalescence times longer than looms. On the basis of the measured V-AT relation, two basic features are exhibited: (1) the existence of a threshold undercooling, AT = 200 K, necessary for the velocity to be measurable with the photodiode method, and (2) a change in growth behavior occurring at AT,, = 300 K, which implies the transition from LG to CG. For Gee0.39 at% Sn, the growth velocity climbs up to 5.5 m/s at the largest undercooling, AT, = 404 K, whereas compared with the dilute alloy, the velocity of Ge-10.0 at% Sn very markedly decreases approximately to the level of pure Ge. It is directly seen from Fig. 1 that the critical undercooling AT,, for LG+CG transition drops continuously as the Sn content increases. A current dendrite growth theory, usually called the LKT/BCT model [8,9] has been increasingly used for the free crystal growth in undercooled melts. This model’s validity has been recently confirmed by the experimental data from various metallic systems possessing nonfaceted S/L interfaces. In order to get a better interpretation of the V-AT correlation measured, it is worth studying if the model could be applied to Ge-based systems which initially belong to the LG region and then transfer into the CG region as the driving force of crystallization surmounts a threshold. We feel that two points merit consider-
100 150 200 250 300 350 400 450 Ge-0.39at%Sn
"100
150 200 250 300 350 Undercooling AT (K)
400
Fig. 1. Crystal growth velocity, V, as a function of cooling, AT, for pure Ge, a dilute alloy Gee0.39 at% a concentrated alloy Gee10 at% Sn. The points and correspond to measured values and predictions based modified dendrite growth model, respectively.
450
underSn and curves on the
CRYSTAL
GROWTH
2439
ation before calculating the growth velocity using the model. One is the transition from LG to CG. Below the critical undercooling AT,,, the crystal growth is governed by the significant interface kinetics which could be qualitatively described by the classic growth theories. Since the LKT/BCT model is thought to be good for the CG region, i.e. above ATc2, it should be modified somewhat for Ge-based systems: we should deduct a critical interface undercooling, AT:, below which Ge-based systems grow laterally, from the total undercooling AT. Although there have been several attempts [lo] to directly measure the actual interface undercooling, AT,, for a few low melting point materials, for many materials, the determination of AT, is rather difficult, if not impossible. Evans et al. [5] gave a plot of the interface temperature at the onset radius for instability, as a function of bulk undercooling for Ge according to their simulation on stability of spherical crystal growth. Because the critical interface undercooling, AT,*, is unknown ab initio, only from the critical bulk undercooling, ATc2 = 300 K determined experimentally, AT: of about 153 K can be figured out based on their computed curves. Therefore, the undercooling equation can be expressed as AT - AT: = AT, + AT, + ATk + AT,
(1)
with ATt = Iu(P,)AH/C, the thermal undercooling, AT, = 2r/R the curvature undercooling, ATk = V/p the kinetic undercooling. AH is the heat of fusion, C, the specific heat of the undercooled melt, gex;p
t) I;anztov& :;;;;z”&,
t~(;he;ale~$;;
number, R the radius of the curvature at the dendrite tip, a the thermal diffusivity, I = a/AS the GibbsThomson coefficient, 0 the S/L interface energy, AS the entropy of fusion, and p the interfacial kinetic coefficient. For pure materials, AT, = 0, but for alloys, the constitutional undercooling, AT,, should be taken into account [S, 91. Another equation needed for a unique calculation of the tip velocity V as a function of undercooling is the marginal stability criterion [8,9, 111. The predicted V-AT curves can be obtained using the undercooling and stability equations if the kinetic coefficient p, k = fAHV,/(R,Ti) is determined, where V, is the speed of sound and R, the gas constant. Here the factor ,f is the second point we should pay attention to. The factor f (5 1) accounts for the fact that not all available sites at the interface are growth sites. Based on the collision-limited growth assumption [12], it would be expected that fx 1 for a closed-packed metal growing from its own liquid, but crystalline Ge is a covalently bonded semiconductor and is isomorphous with Si. For pure Si, fx 0.02 can be inferred from the experimental results of Ref. [ 131. So we assume that f is of the order of lo-* for Ge, too. For pure Ge and for the Ge-Sn alloys, if the factor f is chosen as 1, the calculation apparently
144u
LI 400 K) for AT 2 325 K [Fig. 4(c)].
In brief, two coalesce regions for Ge and Sn phases separately were observed in the concentrated alloy Ge-10 at% Sn, when AT is below 150 K. For 150 K < AT < 300 K, this serious macrosegregation vanished, but the boundaries of the Ge dendrites were heavily aggregated by Sn. It is found that the refined equiaxed grain size of Ge-10 at% Sn at AT 2 300 K is much smaller than that of pure Ge and the dilute alloy Gee0.39 at% Sn within the undercooling regime for grain refinement. This is consistent with the prediction that the tip radius of the concentrated alloy Gee10 at% Sn is smaller than that of Ge and Gee0.39 at% Sn.
6. INTERRELATIONSHIP: UNDERCOOLING GROWTHSTRUCTURE
As the driving force for crystallization, or undercooling prior to nucleation, is going continuously up, a series of changes in solidification modes will take place. Within the undercoolings attained in the present work on pure Ge, there are four regions of
LI e/ al.:
Fig. 4. Microstructural
different
growth
behavior
UNDERCOOLING
transformation
GROWTH
of the Gee0.39 at% Sn with increasing (b) AT = 277 and (c) AT = 386 K.
undercooling:
(a) AT = 220
and grain structure: Table
Undercoohng (K)
< 100
C‘RYSTAL
(A?,,) 100-300 (AT,,) 300400 (AT,,) > 400
I.
Growth velocity (mm/s)
Growth mode
Not measurable
LG LG CG RG
Not measurable 100-800 800-1000
In the first two regions, solidification is controlled by significant lateral growth kinetics, resulting in the faceted structure. If the undercooling is larger than ATc2, there is a smooth but rapid increase in V which would be proof of CG. A randomly oriented equiaxed structure [Fig. 3(c)] in a Ge sample undercooled by 316 K (in the vicinity of ATc2), further affirms the LG+CG transition. The physical meaning of this LGXG transition is thought to be that the critical nucleation radius becomes comparable to the step size at the S/L interface when AT exceeds the critical value. It is suggested under this condition that the lateral step at S/L interface will loose its “identity”. It was at a critical growth velocity of about l’,, z 0.1 m/s that the kinetic transition from LG to CG came into being regardless of pure Ge or the G&n alloys. This could be interpreted as a similar physical mechanism of the break-down of the lateral growth in operation for the Ge-based materials. The last microstructural transformation, grain refinement, comes to pass at deeper undercoolings: AT 2 400 K for pure Ge; AT 2325K for Ge&X39at% Sn; and AT 2 300K for Gel0 at% Sn. For pure Ge and Gee0.39 at% Sn, the critical undercoolings of the LG-+CG transition and the grain refinement are on the whole in accord-
Grain
structure
Twin dendrites (I 1I)( I IO) Lamellar twins (I 1I)(21 I) Coarse equiaxed (100) Refined equiaxed (SO pm)
ante with the results of Devaud et al. [l], respectively. In the presence of solute, the critical undercooling for grain refinement, AT,,, was shifted from 400 to 300 K, but the transition was found to occur at approximately the same value of the crystal growth velocity, Vcz = 0.8 m/s. The link between V and grain refinement has been set forth by a few researchers [7]. The critical velocity Vcz is of the same order of magnitude as the limiting diffusive speed in the liquid. This has led to the suggestion that the grain refinement is linked with the onset of complete solute trapping during rapid growth. Aziz [ 151 has determined the diffusive speed limit VI, of Ge in Si from the CG model to be 1 m/s. In the light of the data, the maximum diffusive speed of Ge-Sn alloys, was assumed to be of the order of 1 m/s, which is in accordance with the measured critical velocity, Vc*, for grain refinement. This means that beyond Vc2= 0.8 m/s, the crystal growth is purely thermally controlled and partitionless. What the critical velocity, Vc2 means for pure Ge is still ambiguous. Combined with current dendrite growth theories, a dendrite break-up model [16] has been established to explain the physical mechanism of grain refinement for pure materials as well as alloys. It is expected that the specific mechanism of grain refinement in highly
LI er al.:
undercooled pure Ge will be brought help of the break-up model.
UNDERCOOLING
to light with the
CRYSTAL
GROWTH
2443
particular H. Miihlmeyer, T. Volkmann, R. Kouba, M. Barth, D. Holland-Moritz, J. Alkemper, M. Schwarz, J. Schroers and J. Schilz. Helpful discussions with Professor B. Feuerbacher are gratefully acknowledged.
7. CONCLUSIONS (1) Three basic modes of crystal growth in undercooled pure Ge and Ge-Sn alloys are revealed. (a) Appreciable interface kinetic effects are present during lateral growth at low undercoolings, leading to the twin structure. (b) Beyond a threshold undercooling, the growth mode changes from lateral to continuous. In this region, coarse equiaxed grains were found for pure Ge and dendrites for Ge-Sn alloys, respectively. (c) At deeper undercoolings, solidification enters a rapid growth region (V 2 0.8 m/s) which is merely thermally controlled, resulting in grain refinement. (2) The addition of Sn to pure Ge has two main effects on crystal growth: changing interface kinetics and constitutional undercooling. The first brings about the monotone reduction of various critical undercoolings for the growth mode transition with increasing Sn content, and the enhancement of growth velocity for the dilute alloy Ge-0.39 at% Sn. Considerable decrease in growth velocity for the concentrated alloy Gee10 at% Sn is due to the second effect. (3) The measured growth velocities are quantitatively analyzed on the basis of slightly modified current dendrite growth theory. Acknowledgements-D. Li acknowledges the financial support of the Alexander-von-Humboldt Foundation. He also thanks the assistance of his colleagues at the DLR, in
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