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Experimental investigation of dewetting models
Journal of Crystal Growth 324 (2011) 53–62
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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Experimental investigation of dewetting models Lamine Sylla a, Thierry Duffar b,n a b
Cyberstar, Echirolles, France SIMaP-EPM, Saint Martin d’He res, France
a r t i c l e i n f o
abstract
Article history: Received 30 January 2011 Received in revised form 25 March 2011 Accepted 26 March 2011 Communicated by P. Rudolph Available online 2 April 2011
A series of experiments was performed in order to look at the solid–liquid interface and meniscus region in dewetted Bridgman growth of GaSb and InSb in silica crucibles. In agreement with theoretical models, they show that a very stable dewetting was obtained for GaSb only if an oxidising atmosphere is present in the ampoule, and that it increased the wetting and growth angles. Stable dewetting of InSb was never obtained, which can be explained by wetting and thermodynamic considerations. Experiments with an easily dissolved gas (H2) have shown that a model of dissolution–rejection of ampoule gas cannot explain dewetting. Also the formation of hillocks has been observed. Finally, the selfstabilisation of the gas pressure difference is confirmed but remains largely unexplained. & 2011 Elsevier B.V. All rights reserved.
Keywords: A1. Oxidation A1. Wetting A2. Dewetted Bridgman B2. Semiconducting III-V materials
1. Introduction The so-called ‘‘dewetting’’ is a phenomenon occurring during Bridgman crystal growth of semiconductors, characterised by the absence of contact between the grown crystal and the crucible. Consequently, the quality of the crystal is improved, with smaller interface curvature, lower stresses and dislocation densities and less spurious grain and twin nucleation. Almost always spontaneous when crystals are grown under microgravity conditions, it rarely occurs spontaneously on the earth, only at the very end of the solidification when the hydrostatic pressure of the remaining liquid vanishes. ‘‘Dewetting’’ is also the name of a process by which the phenomenon is obtained artificially, by applying a gas pressure opposite to the hydrostatic pressure. The experimental observations of spontaneous occurrence of dewetting under microgravity conditions have been reviewed in [1,2] and the literature on the process achievement on the earth is analysed in [3]. Several explanations of the phenomenon have been proposed. The case of rough crucibles is studied in [4] and has been validated by experiments in space and on the earth; it is not considered in the present paper. The explanation of dewetting in the case of smooth crucibles is based on the assumption that a small liquid–vapour meniscus exists between the solid–liquid interface and the crucible wall and slides smoothly along the wall when solidification proceeds. The key parameters in this approach are: – The contact angle, y, of the melt on the crucible wall. It can be the thermodynamic Young angle, in case of a very pure
n
Corresponding author. E-mail address: [email protected] (T. Duffar).
0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2011.03.048
semiconductor and atmosphere and very clean and smooth crucible wall, values for semiconductors in crucibles are given in Table 1. It can also be an apparent contact angle, in case of pollution or crucible roughness: values higher than 1701 have been reported in the case of GaSb on sapphire [5] or Ge on graphite [6]. – The growth angle, a, of the semiconductor, see Table 1. It is also likely to be affected by pollution, but nothing is known about this effect. – The pressure of the gas, when gas is present, or more precisely the pressure difference, DP¼PH PC, between the hot and cold sides of the melt.
This general model gave birth to three variants, each generating specific theoretical developments (Fig. 1): a) Spontaneous occurrence without, or with very low hydrostatic pressure, Fig. 1a. In this model, which is essentially valid under microgravity conditions, the gas pressure is the same at the cold side and at the hot side of the crucible. In practise this applies if the crucible is under vacuum or, in case of gas filling, if both sides communicate, for instance in case of an open crucible [7]. A look on Fig. 1a shows that this configuration is possible only if y is higher than 901 and furthermore if:
y þ a 4 1801
ð1Þ
Values given in Table 1 reveal that this is impossible when the Young thermodynamic angle is considered. Hence this model is only valid in case of abnormal increase of y, for example with pollution of the system [7]. Simple geometry allows
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computing the thickness of the gap between the crystal and the crucible. It is proportional to the crucible radius and, for typical microgravity experiments, is of the order of tens of micrometres, depending on the value taken for y. b) Forced gas pressure acting on the meniscus and opposed to the hydrostatic pressure of the liquid, Fig. 1b. As shown on the figure, it is possible to control the shape of the meniscus through the gas pressure difference DP. This idea triggered the use of dewetting on the earth because the meniscus can be controlled for values of DP close to the hydrostatic pressure,
Phyd, of the remaining liquid [7,8,9]. Convex, concave and convexo-concave menisci can be obtained and the condition y þ a 41801 does not hold anymore for concave menisci (as can be seen on Fig. 1b-III). In this paper, concavity and convexity are defined as seen from the gas, see Fig. 2b. Calculation of gap thickness also predicts values of the order of tens of micrometres. An important result of this model is that the meniscus shape, and then the gap thickness, does not change with time t during solidification if ([10]):
Table 1 Growth angle of semiconductors and contact angle values on various crucible materials, at the melting point (selected from [30]).
c) Similar to above, but the gas pressure is appearing spontaneously by degassing of the liquid. This model, known in the literature as ‘‘detachment’’ or ‘‘detached solidification’’, supposes that gas is dissolved at the hot side of the liquid (Fig. 1c-A), rejected at the solid–liquid interface (Fig. 1c-B) and degassed through the meniscus in order to feed the gap (Fig. 1c-C) [11]. Numerical and analytical calculations predict gap thicknesses of the order of respectively 1 mm or hundreds of micrometres, and that dewetting cannot occur for too high growth rates [12–16].
Semiconductor
a (deg.)
Substrate
y (deg.)
Ge
13 71
SiO2 AlN Si3N4 C BN
115 122–153 136 135–166 139
Si
11 71.5
SiO2 AlN Si3N4 C BN
85 481 49 15–35 95–110
GaSb
31 72
SiO2 AlN C BN
119 103 128 129
InSb
25 71
SiO2 C BN
110 124 134
InP
7.07 0.5
SiO2 C BN
140–150 144 140–150
GaAs
16
SiO2 C BN
115 120 155
CdTe
Unknown
SiO2 C BN
83 116 132
DPðtÞPhyd ðtÞ ¼ Constant
Because solidification is a dynamic process and the gap thickness depends on capillary forces, there is no special reason to suppose that the process is stable: it might be very difficult to control the crystal radius. Stability analyses, generally based on Lyapunov’s approach [17], have been performed for the three models. Simple approaches considering only the capillary effect [9,10] as well as more thorough analyses taking into account coupling between capillarity, heat transfer and pressure fluctuations [18–23] give the same result: dewetting is stable only when the meniscus is convex at the liquid–crystal–gas triple line, which means that abnormally high values of y should be considered in order to fulfil relation (1). In the case of model 3, stability also depends on the transport of gas dissolved in the liquid [21]. Experimental verifications of these models have been almost only indirect but are generally positive (see reviews in [1,2,3]). Dewetting is always easiest on the earth, as well as in space, for crucible materials presenting high y values. It happens in case of open crucibles (equality of gas pressures) as well as closed
PH
θ
PH
I
θ
θ
Liquid
ð2Þ
Liquid
Liquid II
α
θ
Solid
α
θ
PC
Solid
III
Solid
Fig. 1. The three configurations used as models of dewetting. (a) Negligible hydrostatic pressure, (b) gas pressure difference, (c) dissolution A, rejection B and transport C of gases. For the cases (b) and (c), various meniscus shapes as controlled by the pressure difference [7]: (I) DPo Phyd, (II) DPEPhyd, (III) DP4Phyd.
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55
Gas PH Dark
Mobile furnace
Halogen bulbs
Bright
Liquid
Window
Bright
Camera Solid
Silica ampoule
Dark
Silica stand
Gas PC
Holder + Furnace
Fig. 2. (a) Sketch of the experimental set-up. (b) Observation of meniscus curvature, as observed from the gas; top: concave, bottom: convex.
crucibles. As facets are observed at the surface of the dewetted samples, it is clear that the gap exists at the level of the solid–liquid interface. Thicknesses, taking into account differential dilatation, have been measured in the range 10–70 mm; they are remarkably constant along several centimetres, clearly showing intrinsic stability of dewetting. On the earth, dewetting always needed experiments in presence of significant amounts of gas (some tenths of atm). Careful experiments have shown that the relationship between the applied DP and the gap thickness follows the predictions of the model (b). Also, experiments with InSb or Ge have shown that pollution by oxygen enhances the dewetting occurrence. However ridges or hillocks of partial contact with the crucible are often observed, that are not predicted by the models. Some experimental facts do not agree with predictions of model (c): growth rate is not a limiting parameter and experimental gap thicknesses are much lower than those predicted by the model. It should be noted that this model uses physical parameters, such as Henry, diffusion or segregation coefficients, which values are practically unknown for gases in liquid semiconductors. Few experiments have been performed in order to directly look at the solid–liquid interface region. Static photographs, presented in [10], have shown that it is possible to obtain a meniscus, all around a cylindrical crystal of InSb, by controlling the pressure of the gas at the cold side of the crucible. It is only in [24] that the authors presented the results of video recording of the dewetting process that clearly demonstrated the existence of the meniscus. They also noted that gaseous pollution enhanced dewetting. The objective of this paper is to present further experiments in order to answer the following questions: – For models (a) and (b), investigate the effect of pollution, more precisely oxidation, on the phenomenon. It is a very important point, because models can only explain the spontaneous
–
– – –
occurrence and stability of dewetting in space, and its remarkable stability on the earth, by using abnormally high values of the contact angle y. For model (b), investigate the pressure conditions necessary in order to get a stable dewetting, especially the shape, concave or convex, of the meniscus. Use a gas with high dissolution coefficient in order to investigate the occurrence of model (c). Compare the behaviour of InSb and GaSb under the same conditions. Investigate how ridges and hillocks are produced.
2. Experiments 2.1. Experimental procedure Observation of the meniscus imposes the use of transparent, i.e. fused SiO2, crucibles. InSb and GaSb were chosen as model materials because they have a low melting point (resp. 798 and 983 K), show high values for a and are less toxic. The experimental procedure has already been published [24]; in between the oil diffusion secondary vacuum pump has been replaced with a turbomolecular pump, for cleaner experiments. All the details concerning the design, optimisation and calibration of the set-up and experimental protocol can be found in [25]. In summary: – Undoped InSb and GaSb cylinders are synthetised in an electromagnetic furnace from stoichiometric amounts of electronic grade metals. – The electronic grade fused silica crucible has a diameter of 11 mm. Before the experiment, its internal diameter is measured precisely along the part where the growth will take place. Antimonide cylinder 74 mm long, manually fitted to the
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Industrial Argon and two experiments under Air. Under neutral or reducing atmospheres, it is possible to force a meniscus under stationary conditions, after melting and before solidification, but it never slid along the crucible wall and the growth was always attached. These observations confirm the results presented in [24]: at least a few ppm of oxygen are mandatory in order to obtain dewetting of GaSb in silica crucibles. In spite of the efforts made in order to form and stabilise a meniscus, stable dewetting of InSb has never been obtained, whatever the atmosphere used. Only one experiment, under Industrial Argon, has shown 5 mm of partial dewetting (gap thickness 10 mm) toward the top of the ingot. In general, some dewetting is obtained over a few mm at the beginning of pulling, but with huge efforts to maintain a meniscus, clearly showing that dewetting is not stable in this case. Fig. 3 shows extracts of a video taken during an attempt to get a useful meniscus in the case of InSb under Industrial Argon. The two triple lines can easily be seen, photo A. By increasing the temperature of the crucible holder by 10 K, the triple lines are distorted, photo B, the bubbling pressure is reached, a bubble is released (it carried up the already existing bubble on the left) and a less distorted meniscus is obtained, photo C. However this meniscus – which is concave, see Fig. 2 and previous paragraph – did not lead to dewetting. The pressure increase needed to reach the bubbling pressure is 840 Pa, as computed from the surface tension of InSb, slv(Insb) (0.420 J m 2) and the estimated radius of the bubble rbubble (1 mm):
crucible diameter, is introduced and the crucible is connected to a vacuum system and evacuated. Then it is filled with the appropriate gas and sealed. The initial pressure was chosen as P0 ¼200 mbar because it was recommended in [26] as the optimal value for dewetting of InSb. It should be noted that no experiment was performed with single crystal. – A sketch of the furnace is shown on the Fig. 2. The sealed crucible is introduced in a mobile mirror furnace. Its fixed stand consists in a small resistance furnace used to heat the lower part of the crucible and then control the gas pressure at the cold side of the sample. A window in the crucible wall allows observation and video record of the solid–liquid interface. The temperature gradient in the sample, at the solid– liquid interface, is 120 K cm 1. – The sample is melted to only 5 or 6 cm in order to leave a solid part and control easily the beginning of solidification. After adjusting the gas pressure at the cold side, by visual observation of the meniscus, pulling and video recording are started. For all experiments, the pulling rate was 5 mm h 1. The analysis of an experiment includes the video and temperature recording, estimation of the gap thickness by calliper measurement of the sample and crucible diameters, profilometry, optical and SEM observation and analysis of the sample surface. The video images presented in the next figures show the edge of the viewing window (which is 9 mm wide, this gives the scale of the pictures) and in the centre, a vertical thick dark bar which is an optical artifact due to the reflexion of the window aperture on the silica wall. The solid–liquid interface is easily seen because the emissivity of the liquid is higher than the emissivity of the solid. The curvature of the meniscus can be deduced from the fact that a concave meniscus (seen from the gas) is brighter at the bottom, which reflects hotter surfaces, and darker at the top, which reflects colder surfaces, and vice-versa for a convex interface, see Fig. 2b.
DPbubbling ¼ 2slvðInSbÞ =rbubble
ð3Þ
This corresponds to a 1.4% increase of the pressure at the cold part of the ampoule, estimated as 58,000 Pa. The corresponding DT, through the perfect gas law, is 11 K, in good agreement with the experimental value. The behaviour difference between GaSb and InSb is surprising at first sight, because they show comparable wetting and chemical properties. However, the sum y þ a is significantly lower for InSb (1351) compared to GaSb (1501) so that it is reasonable to expect a difference in dewetting ability. Furthermore, a thermodynamical analysis of the In–Sb–O–Si and Ga–Sb–O–Si systems has shown that liquid GaSb is covered by an oxide layer for temperatures exceeding the melting point by 60 K, while InSb oxides are not stable for temperatures exceeding the melting point by 15 K [25]. It is therefore concluded that an oxide layer which is stable at the surface of the meniscus is responsible of the occurrence of dewetting for GaSb in silica under oxidising conditions, while such a layer is not stable enough, or only marginally, for promoting complete dewetting in the case of InSb. This is in agreement with the fact that some dewetting of InSb in silica has been obtained for experiments in space [2], observed once in the experiments described here and has been previously reported on the ground: only on 10 mm, with suspicion of O2 contamination and with some difficulties [10].
3. Results and discussion 3.1. Effect of oxidation Several atmospheres were used in order to study the effect of oxygen on dewetting occurrence. The ‘‘Neutral’’ atmosphere was obtained by filling the ampoule with high purity argon from Air Products, with certified impurity levels, and introducing Zr-based getters in the lower part of the ampoule; they were thermally activated under vacuum just before sealing the ampoule and in front of the mirror lamps after sealing. The ‘‘Reducing’’ atmosphere was a 90%N2–10%H2 mixture provided by Air Products, with certified impurity levels. Two oxidising atmospheres were used: ‘‘Industrial Argon’’ containing some ppm of oxygen, and ‘‘Air’’. Table 2 gives analyses of these various atmospheres. Dewetting of GaSb has been observed only during the experiments under oxidising atmosphere: one experiment under
Table 2 Impurity composition of the various atmospheres used in the experiments (ppm or %). Atmosphere
Ar (%)
H20
O2
CH4
CO þ CO2
H2
Neutrala Reducing Industrial Argonb Airc
100 90 99.999 0.93
0.02 1 o3 r 2%
0.01 0.5 o2 20.95%
0.1 0.2 o 0.1 1.8
0.1 0.6 o 0.1 300
1 10% Unknown 0.5
a b c
Before getter activation. Typical values from provider data sheet. Standard values, contains 78% N2.
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57
bubble liquid
crucible-liquid-gas triple line
solid Solid-liquid interface
liquid 2 mm
solid
liquid
meniscus solid
Fig. 3. Video snapshots showing an attempt to force a meniscus in the case of InSb (see comments in the text).
3.2. Observation of stable menisci Fig. 4 shows a video sequence recorded during dewetting of GaSb in air. The meniscus has been easily established during the steady state before pulling, photo A. Beginning of solidification always shows a transient state where the gap is rather thick; after about 1 mm, the meniscus and gap thickness are stabilized, at the moment where photo A was taken. Pictures B and C, taken 15 mm ahead, i.e. 3 h after beginning of pulling, show that the meniscus and more generally the dewetting process, are very stable. The film shows that the process occurs smoothly, with the meniscus sliding gently on the crucible wall. From the pictures, the height of the meniscus is measured as 100720 mm, which is in agreement with predictions of model (b). The experimental set-up does not allow measuring gas pressure in the ampoule, so that the initial pressures of the hot and cold
gases are unknown: from perfect gas law, it comes that the pressure of the gas at the cold side should be of the order of 58,000 Pa. Therefore, only rough estimation of the pressure difference can be obtained. The temperature increase of the resistor furnace, in order to get the meniscus before pulling, ranged from 30 to 60 K for the three experiments where dewetting has been obtained. Applying the perfect gas law, this corresponds to gas pressure increases of 2200–4400 Pa, to be compared to the 3350 Pa of hydrostatic pressure exerted by the molten GaSb at the beginning of the solidification (specific mass of molten GaSb is 6.06 103 kg m 3). It can be observed that the upper side of the meniscus is brighter than the lower side. As drawn on Fig. 2b, this means that the meniscus is convex so that its lower part reflects colder places from the bottom furnace. It follows necessarily that inequality (1) is satisfied and then that the contact and growth angles are
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L. Sylla, T. Duffar / Journal of Crystal Growth 324 (2011) 53–62
LIQUID LIQUID Meniscus
SOLID
SOLID
LIQUID LIQUID
Fig. 4. Video sequence of the dewetting of GaSb under air. A Steady state before solidification, the meniscus has been created through pressure control. B Toroidal shape of the crystal at the beginning of solidification. Meniscus shape after 15 mm of growth, C and D, and hillock formation. Thin white arrows show dewetted surface.
c
B
hillocks
b
50 μm
5 μm contact with crucible
A
Dewetted surface
hillock 500 μm
a
hillock
A seed Seed
Seed
500 μm
Fig. 5. Optical and SEM pictures of the surface of the ingot grown under air.
increased by the presence of oxygen. On the contrary, as seen in Fig. 3, the shape of the forced meniscus obtained in the cases where dewetting could not be achieved is concave. These conclusions are in remarkable agreement with the stability analyses of the process, predicting that only convex menisci can provide stable dewetting. Experiments demonstrate furthermore that the process is particularly difficult to control when the meniscus is concave. Another occurrence of dewetting, under Industrial Argon, has been presented in [24] and gave exactly the same conclusions. Fig. 5 shows the external surface of the ingot of Fig. 4. The proportion of dewetted area is estimated to 60% in this ingot.
Fig. 6 shows profiles of the external surface of the sample. Four zones have been identified: – The unmolten solid, called ‘‘seed’’. – Zone A which shows stable dewetting along 18 mm. It is smooth and shiny. At the beginning, it has hillocks, the tops of which were in contact with the crucible wall, as shown by SEM. The gap thickness, measured relatively to hillock tops, is stable: 3475 mm (Fig. 6ii). – Zone B where dewetting is only partial. It is rougher than part A (Fig. 6iii–v) and had numerous contact zones with the crucible. SEM analysis and EDS spectroscopy have revealed
L. Sylla, T. Duffar / Journal of Crystal Growth 324 (2011) 53–62
μm
59
i
50 0 -50 -100 -150 -200 -250 -300
hilloc ks
Full dewetting zone A
Partial dewetting zone B
Seed 0
μm
2
4
8
6
10
12
14
16
18
20
22
24
26 mm
ii
70 60 50 40 30 20 10 0 -10 -20
Hillocks (in contact with crucible wall) e=34 μm
0 μm
0.5
1
2
1.5
2.5
3
3.5
4
4.5
5 mm
iii
20 15 10 5 0 -5 -10 -15
End of A
0
0.5
1
Beginning of B
1.5
2
2.5
3
3.5
4 mm
iv
μm 10 5 0 -5 -10 -15
Zone A 0
μm 8 6 4 2 0 -2 -4 -6 -8 -10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5 mm
v Contacts with crucible
Zone B 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3 mm
Fig. 6. Surface profiles of the ingot shown on Figs. 4 and 5. Vertical axis gives the radius deviation from an arbitrary origin and horizontal axis gives the length scale along the ingot. (i) First 26 mm above the seed. (ii) Profile of the hillock region. (iii) Profile at transition between zones A and B. (iv) Zoom on the profile in zone A. (v) Zoom on the profile in zone B.
oxygen at these places and it has already been mentioned in [24] that EDS analysis of these contact zones presents Si contamination. – Zone C does not show dewetting. Another dewetted zone, smooth and shiny, 10 mm long, appears between B and C. No change of the experimental conditions has been recorded at the transitions between zones A, B and C so that the reasons of these transitions remain unclear. It may be related to changes of the crucible wall surface, either before the experiment
(heterogeneous cleaning process) or during heating, for example due to the high temperature gradient, and longer liquid contact for the last to freeze part. However the strangest behaviour, also reported for other experiments [27,28], is that dewetting, when it occurs, is more stable than expected, because it shows pressure self-equilibration. According to the theoretical model (b), the gap thickness remains constant only if the condition (2) is satisfied all along the solidification. This means that the pressure difference DP should be decreased in order to follow the decrease of liquid length and
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LIQUID
LIQUID meniscus
meniscus
SOLID SEED
Fig. 7. Dewetted growth of GaSb under Industrial Argon, two snapshots showing occurrence of hillocks.
bubbles LIQUID LIQUID S/L interface
S/L interface
Fig. 8. Pictures taken during the growth of GaSb under reducing atmosphere. Numerous bubbles appear on the wall, close to the S/L interface and left marks on the solidified surface (white dashed circles).
hydrostatic pressure. However the temperature of the ampoule holder was kept perfectly constant, while stable dewetting occurred. During solidification, the whole ampoule is cooled down, but its hot side, close to the lamp bulbs, might possibly be cooled at a somewhat slower rate than the cold side. An increase of 10 K between both temperatures would lead to the compensation of 1.3 cm of hydrostatic pressure, but this cannot explain the constant gap thickness obtained along several centimetres (Fig. 6i). And this cannot be invoked in order to explain the stable gap obtained in Ref. [28] in a Stockbarger furnace, where a temperature difference shift was prohibited. It is rather expected that, while solidification proceeds, the hydrostatic pressure decreases and the difference of pressure acting on the meniscus increases. At some moment bubbling should occur. Indeed, there is some suspicion that the pressure difference self-equilibrates by exchange of gas between the cold side, where the hydrostatic pressure decreases, and the hot side. Only two or three times during this experimental work, layers of gas have been seen, quickly flowing between the wall and the liquid, from the meniscus toward the top of the ampoule. They did not look like bubbles, rather like a layer of air flowing between two paper sheets. Unfortunately this phenomenon is so subtle and rare that it was not possible to catch it on the video sequences. Clearly this behaviour needs further investigation.
crucible – or of the initial feed material – can interact with the dewetting process and creates hillocks, possibly ridges and maybe enhance or cancel the dewetting itself.
3.3. Ridges and hillocks
4. Conclusion
Fig. 7 shows again pictures already published in [24]. In this sequence GaSb is grown dewetted under Industrial Argon. On the left image, the black circle shows patterns on the surface of the crucible wall. After solidification of this part of the sample, the black circle on the right picture show that the patterns gave birth to hillocks on the dewetted surface of the sample. This indicates that defects, either chemical or geometrical, on the surface of the
The objectives of the paper were to check experimentally the hypotheses assumed by the various models of the dewetting phenomenon, and to carefully study the freezing process in order to obtain new information. The results confirm the observation, already reported in [24], that a meniscus exists and slides smoothly on the crucible wall, when stable dewetting occurs. As the external aspect of the samples is very comparable to what is
3.4. Gas dissolution Experiments with GaSb were performed under reducing atmosphere. No stable dewetting occurred, because no oxidation was possible, only a small zone, half a square centimetre, was detached. However the high solubility of hydrogen in liquid metals allowed studying the mechanism involved in model (c). The striking fact in the recording is the great number of bubbles that are observed on the crucible wall, and close to the solidification interface only Fig. 8. Accelerated reading of the video sequences allowed the observation of the nucleation, growth and disappearance of numerous bubbles, which are supposed to contain hydrogen, as it is the only parameter differing from experiments under neutral atmosphere. Bubbles nucleate about 1 cm above the S/L interface and their size increases with the approach of the interface. This validates the dissolution of gases in the liquid and their rejection at the solid–liquid interface. In spite of the initial presence of a meniscus that had been forced after melting, the rejected gas generated bubbles on the wall and did not feed the meniscus.
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observed at the surface of dewetted samples obtained in space and on the earth, this hypothesis is now totally confirmed. Results also allow establishing conclusions concerning the three main models found in the literature. – Model (a) is based on the hypothesis of an increase, possibly by pollution, of the growth and wetting angles in order to allow spontaneous dewetting in space. The experiments have shown unambiguously that in the case of GaSb, oxygen contamination is mandatory to obtain stable dewetting. Furthermore it was observed that the meniscus is convex in these experiments, which proves that the angles have been effectively increased. In the case of InSb, experiments show that dewetting is very difficult to control and is never stable, two reasons can be invoked: a smaller sum y þ a compared to GaSb and a less stable oxide at the melting point. However observation of a meniscus under microgravity conditions is needed in order to fully validate this model. – Model (b) is based on the assumption that a gap pressure difference between hot and cold sides of the crucible, of the order of the hydrostatic pressure, can control the shape of the meniscus and promote dewetting on the earth. This is in full agreement with the experimental results, and estimations of the gap height (100 mm), gap thickness (some tens of mm) and gas pressure increase (some thousands of Pa) are in the order of magnitude of the theoretical predictions. On the contrary, an experiment without any gas in the ampoule did not allow establishing a meniscus. – Model (c) is based on dissolution at the hot side of the liquid, segregation at the S/L interface and rejection at the meniscus, of gas present in the ampoule. Experiments with gas mixture containing H2 have validated the dissolution and segregation mechanisms; however the segregated gas formed bubbles on the crucible wall and never filled the gap through the meniscus. Also, this model predicts too large gap thickness (1 mm) and a critical velocity, above which detached growth is unstable. Experiments have shown that dewetting occurs also for very high growth rates [24,29]. Therefore it can be concluded that this model, while it could act in some specific cases, cannot be invoked in the general case of dewetting. – All stability analyses published so far claim that a convex meniscus, i.e. condition (1), is mandatory in order to get stable dewetting. The experiments fully confirm this prediction: a convex meniscus was observed in all cases of stable growth. Stability was impressive: a constant gap thickness has been obtained during 4 h of pulling. On the contrary, when the meniscus is concave, the process is extremely difficult to control, and invariably led to the disappearance of dewetting after a few millimetres of pulling. It can be expected that thorough control techniques should be used if dewetting is wanted in cases where condition (1) does not apply. – An experiment has shown that hillocks are caused by early contamination of the liquid sample–crucible wall surface.
In summary, it can be concluded that the theoretical models, except model (c), give a good understanding of the dewetting process. They can safely be used for prospective calculations concerning the phenomenon as well as the process, provided that a new parameter is taken into account: the effect of impurities on the wetting and growth angles. However the effect of self-stabilisation of the pressure difference, which apparently follows the decrease of hydrostatic pressure, is not understood yet. It will deserve further investigations in the future.
61
Acknowledgements This experimental work has been supported by the MAP-CdTe project of the European Space Agency and by funding of the CNES. The authors are grateful to C. Garnier, J.P. Paulin and G. Vian for their technical help. The SIMaP-EPM laboratory is under the cotutella of Grenoble institute of Technology, University Joseph Fourier and CNRS. References [1] L.L. Regel, W.R. Wilcox, Detached solidification in microgravity—a review, Microgravity Sci. Technol. XI/4 (1998) 152. [2] T. Duffar, in: P Capper (Ed.), Bulk Crystal Growth of Electronic, Optical and Optoelectronics Materials, John Wiley & Sons, 2005, pp. 477–524 (Chap. 17). [3] T. Duffar, L. Sylla, Vertical Bridgman and dewetting, in: T Duffar (Ed.), Crystal Growth Processes based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques, John Wiley & Sons Ltd., New York, ISBN 978-0-47071244-32010, pp. 355–411 (Chapter 6). [4] T. Duffar, I. Paret-Harter, P. Dusserre, Crucible de-wetting during Bridgman growth of semiconductors in microgravity, J. Cryst. Growth 100 (1990) 171–184. [5] I. Harter, P. Dusserre, T. Duffar, J.-Ph. Nabot, N. Eustathopoulos, Wetting of III–V melts on crucible materials, J. Cryst. Growth 131 (1993) 157–164. [6] W. Palosz, M.P. Volz, S. Cobb, S. Motakef, F.R. Szofran, Detached growth of germanium by directional solidification, J. Cryst. Growth 277 (2005) 124–132. [7] T. Duffar, P. Boiton, P. Dusserre, J. Abadie, Crucible de-wetting during Bridgman growth in microgravity II. Smooth crucibles, J. Cryst. Growth 179 (1997) 397–409. [8] S. Balint, L. Braescu, L. Sylla, S. Epure, T. Duffar, Dependence of the meniscus shape on the pressure difference in the dewetted Bridgman process, J. Cryst. Growth 310 (2008) 1564–1570. [9] S. Epure, T. Duffar, L. Braescu, On the capillary stability of the crystal-crucible gap during dewetted Bridgman process, J. Cryst. Growth 312 (2010) 1416–1420. [10] T. Duffar, P. Dusserre, F. Picca, S. Lacroix, N. Giacometti, Bridgman growth without crucible contact using the dewetting phenomenon, J. Cryst. Growth 211 (2000) 434–440. [11] W.R. Wilcox, L.L. Regel, Detached solidification, Microgravity Sci. Technol. VIII/1 (1995) 56–61. [12] D.I. Popov, L.L. Regel, W.R. Wilcox, Detached solidification. 1. Steady-state results at zero gravity, J. Mater. Synth. Process. 5 (1997) 283–297. [13] D.I. Popov, L.L. Regel, W.R. Wilcox, Detached solidification. 3. Influence of acceleration and heat transfer, J. Mater. Synth. Process. 5 (1997) 313–335. [14] Y. Wang, L.L. Regel, W.R Wilcox, Influence of contact angle, growth angle and melt surface tension on detached solidification of InSb, J. Cryst. Growth 209 (2000) 175–180. [15] Y. Wang, L.L. Regel, W.R. Wilcox, Steady-state detached solidification of water at zero gravity, J. Cryst. Growth 226 (2001) 430–435. [16] Y. Wang, L.L. Regel, W.R. Wilcox, Approximate material-balance solution to the moving meniscus model of detached solidification, J. Cryst. Growth 243 (2002) 546–550. [17] V.A. Tatarchenko, Shaped Crystal Growth, Fluid Mechanics and its Application, Kluwer, Dordrecht, 1993 (vol. 20). [18] L. Bizet, T. Duffar, Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions, Cryst. Res. Technol. 39 (2004) 491–500. [19] T. Duffar, S. Epure, Comment on the paper ‘‘Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions’’, Cryst. Res. Technol. 45 (2010) 1209–1210. [20] S. Balint, S. Epure, L. Braescu, T. Duffar, Dewetted Bridgman crystal growth in terrestrial conditions: practical stability over a bounded time period in a forced regime, J. Eng. Math., in press. [21] D.I. Popov, L.L. Regel, W.R. Wilcox, Detached solidification. 2. Stability, J. Mater. Synth. Process. 5 (1997) 299–311. [22] L. Braescu, On the pressure difference ranges which assure a specified gap size for semiconductor crystals grown in terrestrial dewetted Bridgman, J. Cryst. Growth 312 (2010) 1421–1424. [23] A. Yeckel, J.J. Derby, Existence, stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity, J. Cryst. Growth 314 (2011) 310–323. [24] L. Sylla, J.P. Paulin, G. Vian, C. Garnier, T. Duffar, Effect of residual gaseous impurities on the dewetting of antimonide melts in fused silica crucibles in the case of bulk crystal growth, Mat. Sci. Eng. A 495 (2008) 208–214. [25] L. Sylla, Etude expe´rimentale et thermodynamique du poce´de´ de de´mouillage applique´ aux semiconducteurs, Ph.D. thesis, 20th June 2008, Grenoble Insitute of Technology, in French. [26] J. Wang, L.L. Regel, W.R. Wilcox, Detached solidification of InSb on earth, J. Cryst. Growth 260 (2004) 590–599. [27] N. Chevalier, P. Dusserre, J.-P. Garandet, T. Duffar, Dewetting application to CdTe single crystal growth on earth, J. Cryst. Growth 261 (2004) 590–594.
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[28] T. Duffar, P. Dusserre, N. Giacometti, Growth of GaSb single crystals by an improved dewetting process, J. Cryst. Growth 223 (2001) 69–72. [29] M. Fiederle, T. Duffar, V. Babentsov, K.W. Benz, P. Dusserre, V. Corregidor, E. Dieguez, P. Delaye, G. Roosen, V. Chevrier, J.C. Launay, Dewetted growth of CdTe in microgravity (STS-95), Cryst. Res. Technol. 39 (2004) 481–490.
[30] N. Eustathopoulos, B. Drevet, S. Brandon, A. Virozub, Basic principles of capillarity in relation with crystal growth, in: T Duffar (Ed.), Crystal Growth Processes based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques, John Wiley & Sons Ltd., New York, ISBN 978-0-47071244-32010, pp. 1–49 (Chapter 1).
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Experimental investigation of dewetting models Lamine Sylla a, Thierry Duffar b,n a b
Cyberstar, Echirolles, France SIMaP-EPM, Saint Martin d’He res, France
a r t i c l e i n f o
abstract
Article history: Received 30 January 2011 Received in revised form 25 March 2011 Accepted 26 March 2011 Communicated by P. Rudolph Available online 2 April 2011
A series of experiments was performed in order to look at the solid–liquid interface and meniscus region in dewetted Bridgman growth of GaSb and InSb in silica crucibles. In agreement with theoretical models, they show that a very stable dewetting was obtained for GaSb only if an oxidising atmosphere is present in the ampoule, and that it increased the wetting and growth angles. Stable dewetting of InSb was never obtained, which can be explained by wetting and thermodynamic considerations. Experiments with an easily dissolved gas (H2) have shown that a model of dissolution–rejection of ampoule gas cannot explain dewetting. Also the formation of hillocks has been observed. Finally, the selfstabilisation of the gas pressure difference is confirmed but remains largely unexplained. & 2011 Elsevier B.V. All rights reserved.
Keywords: A1. Oxidation A1. Wetting A2. Dewetted Bridgman B2. Semiconducting III-V materials
1. Introduction The so-called ‘‘dewetting’’ is a phenomenon occurring during Bridgman crystal growth of semiconductors, characterised by the absence of contact between the grown crystal and the crucible. Consequently, the quality of the crystal is improved, with smaller interface curvature, lower stresses and dislocation densities and less spurious grain and twin nucleation. Almost always spontaneous when crystals are grown under microgravity conditions, it rarely occurs spontaneously on the earth, only at the very end of the solidification when the hydrostatic pressure of the remaining liquid vanishes. ‘‘Dewetting’’ is also the name of a process by which the phenomenon is obtained artificially, by applying a gas pressure opposite to the hydrostatic pressure. The experimental observations of spontaneous occurrence of dewetting under microgravity conditions have been reviewed in [1,2] and the literature on the process achievement on the earth is analysed in [3]. Several explanations of the phenomenon have been proposed. The case of rough crucibles is studied in [4] and has been validated by experiments in space and on the earth; it is not considered in the present paper. The explanation of dewetting in the case of smooth crucibles is based on the assumption that a small liquid–vapour meniscus exists between the solid–liquid interface and the crucible wall and slides smoothly along the wall when solidification proceeds. The key parameters in this approach are: – The contact angle, y, of the melt on the crucible wall. It can be the thermodynamic Young angle, in case of a very pure
n
Corresponding author. E-mail address: [email protected] (T. Duffar).
0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2011.03.048
semiconductor and atmosphere and very clean and smooth crucible wall, values for semiconductors in crucibles are given in Table 1. It can also be an apparent contact angle, in case of pollution or crucible roughness: values higher than 1701 have been reported in the case of GaSb on sapphire [5] or Ge on graphite [6]. – The growth angle, a, of the semiconductor, see Table 1. It is also likely to be affected by pollution, but nothing is known about this effect. – The pressure of the gas, when gas is present, or more precisely the pressure difference, DP¼PH PC, between the hot and cold sides of the melt.
This general model gave birth to three variants, each generating specific theoretical developments (Fig. 1): a) Spontaneous occurrence without, or with very low hydrostatic pressure, Fig. 1a. In this model, which is essentially valid under microgravity conditions, the gas pressure is the same at the cold side and at the hot side of the crucible. In practise this applies if the crucible is under vacuum or, in case of gas filling, if both sides communicate, for instance in case of an open crucible [7]. A look on Fig. 1a shows that this configuration is possible only if y is higher than 901 and furthermore if:
y þ a 4 1801
ð1Þ
Values given in Table 1 reveal that this is impossible when the Young thermodynamic angle is considered. Hence this model is only valid in case of abnormal increase of y, for example with pollution of the system [7]. Simple geometry allows
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computing the thickness of the gap between the crystal and the crucible. It is proportional to the crucible radius and, for typical microgravity experiments, is of the order of tens of micrometres, depending on the value taken for y. b) Forced gas pressure acting on the meniscus and opposed to the hydrostatic pressure of the liquid, Fig. 1b. As shown on the figure, it is possible to control the shape of the meniscus through the gas pressure difference DP. This idea triggered the use of dewetting on the earth because the meniscus can be controlled for values of DP close to the hydrostatic pressure,
Phyd, of the remaining liquid [7,8,9]. Convex, concave and convexo-concave menisci can be obtained and the condition y þ a 41801 does not hold anymore for concave menisci (as can be seen on Fig. 1b-III). In this paper, concavity and convexity are defined as seen from the gas, see Fig. 2b. Calculation of gap thickness also predicts values of the order of tens of micrometres. An important result of this model is that the meniscus shape, and then the gap thickness, does not change with time t during solidification if ([10]):
Table 1 Growth angle of semiconductors and contact angle values on various crucible materials, at the melting point (selected from [30]).
c) Similar to above, but the gas pressure is appearing spontaneously by degassing of the liquid. This model, known in the literature as ‘‘detachment’’ or ‘‘detached solidification’’, supposes that gas is dissolved at the hot side of the liquid (Fig. 1c-A), rejected at the solid–liquid interface (Fig. 1c-B) and degassed through the meniscus in order to feed the gap (Fig. 1c-C) [11]. Numerical and analytical calculations predict gap thicknesses of the order of respectively 1 mm or hundreds of micrometres, and that dewetting cannot occur for too high growth rates [12–16].
Semiconductor
a (deg.)
Substrate
y (deg.)
Ge
13 71
SiO2 AlN Si3N4 C BN
115 122–153 136 135–166 139
Si
11 71.5
SiO2 AlN Si3N4 C BN
85 481 49 15–35 95–110
GaSb
31 72
SiO2 AlN C BN
119 103 128 129
InSb
25 71
SiO2 C BN
110 124 134
InP
7.07 0.5
SiO2 C BN
140–150 144 140–150
GaAs
16
SiO2 C BN
115 120 155
CdTe
Unknown
SiO2 C BN
83 116 132
DPðtÞPhyd ðtÞ ¼ Constant
Because solidification is a dynamic process and the gap thickness depends on capillary forces, there is no special reason to suppose that the process is stable: it might be very difficult to control the crystal radius. Stability analyses, generally based on Lyapunov’s approach [17], have been performed for the three models. Simple approaches considering only the capillary effect [9,10] as well as more thorough analyses taking into account coupling between capillarity, heat transfer and pressure fluctuations [18–23] give the same result: dewetting is stable only when the meniscus is convex at the liquid–crystal–gas triple line, which means that abnormally high values of y should be considered in order to fulfil relation (1). In the case of model 3, stability also depends on the transport of gas dissolved in the liquid [21]. Experimental verifications of these models have been almost only indirect but are generally positive (see reviews in [1,2,3]). Dewetting is always easiest on the earth, as well as in space, for crucible materials presenting high y values. It happens in case of open crucibles (equality of gas pressures) as well as closed
PH
θ
PH
I
θ
θ
Liquid
ð2Þ
Liquid
Liquid II
α
θ
Solid
α
θ
PC
Solid
III
Solid
Fig. 1. The three configurations used as models of dewetting. (a) Negligible hydrostatic pressure, (b) gas pressure difference, (c) dissolution A, rejection B and transport C of gases. For the cases (b) and (c), various meniscus shapes as controlled by the pressure difference [7]: (I) DPo Phyd, (II) DPEPhyd, (III) DP4Phyd.
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55
Gas PH Dark
Mobile furnace
Halogen bulbs
Bright
Liquid
Window
Bright
Camera Solid
Silica ampoule
Dark
Silica stand
Gas PC
Holder + Furnace
Fig. 2. (a) Sketch of the experimental set-up. (b) Observation of meniscus curvature, as observed from the gas; top: concave, bottom: convex.
crucibles. As facets are observed at the surface of the dewetted samples, it is clear that the gap exists at the level of the solid–liquid interface. Thicknesses, taking into account differential dilatation, have been measured in the range 10–70 mm; they are remarkably constant along several centimetres, clearly showing intrinsic stability of dewetting. On the earth, dewetting always needed experiments in presence of significant amounts of gas (some tenths of atm). Careful experiments have shown that the relationship between the applied DP and the gap thickness follows the predictions of the model (b). Also, experiments with InSb or Ge have shown that pollution by oxygen enhances the dewetting occurrence. However ridges or hillocks of partial contact with the crucible are often observed, that are not predicted by the models. Some experimental facts do not agree with predictions of model (c): growth rate is not a limiting parameter and experimental gap thicknesses are much lower than those predicted by the model. It should be noted that this model uses physical parameters, such as Henry, diffusion or segregation coefficients, which values are practically unknown for gases in liquid semiconductors. Few experiments have been performed in order to directly look at the solid–liquid interface region. Static photographs, presented in [10], have shown that it is possible to obtain a meniscus, all around a cylindrical crystal of InSb, by controlling the pressure of the gas at the cold side of the crucible. It is only in [24] that the authors presented the results of video recording of the dewetting process that clearly demonstrated the existence of the meniscus. They also noted that gaseous pollution enhanced dewetting. The objective of this paper is to present further experiments in order to answer the following questions: – For models (a) and (b), investigate the effect of pollution, more precisely oxidation, on the phenomenon. It is a very important point, because models can only explain the spontaneous
–
– – –
occurrence and stability of dewetting in space, and its remarkable stability on the earth, by using abnormally high values of the contact angle y. For model (b), investigate the pressure conditions necessary in order to get a stable dewetting, especially the shape, concave or convex, of the meniscus. Use a gas with high dissolution coefficient in order to investigate the occurrence of model (c). Compare the behaviour of InSb and GaSb under the same conditions. Investigate how ridges and hillocks are produced.
2. Experiments 2.1. Experimental procedure Observation of the meniscus imposes the use of transparent, i.e. fused SiO2, crucibles. InSb and GaSb were chosen as model materials because they have a low melting point (resp. 798 and 983 K), show high values for a and are less toxic. The experimental procedure has already been published [24]; in between the oil diffusion secondary vacuum pump has been replaced with a turbomolecular pump, for cleaner experiments. All the details concerning the design, optimisation and calibration of the set-up and experimental protocol can be found in [25]. In summary: – Undoped InSb and GaSb cylinders are synthetised in an electromagnetic furnace from stoichiometric amounts of electronic grade metals. – The electronic grade fused silica crucible has a diameter of 11 mm. Before the experiment, its internal diameter is measured precisely along the part where the growth will take place. Antimonide cylinder 74 mm long, manually fitted to the
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Industrial Argon and two experiments under Air. Under neutral or reducing atmospheres, it is possible to force a meniscus under stationary conditions, after melting and before solidification, but it never slid along the crucible wall and the growth was always attached. These observations confirm the results presented in [24]: at least a few ppm of oxygen are mandatory in order to obtain dewetting of GaSb in silica crucibles. In spite of the efforts made in order to form and stabilise a meniscus, stable dewetting of InSb has never been obtained, whatever the atmosphere used. Only one experiment, under Industrial Argon, has shown 5 mm of partial dewetting (gap thickness 10 mm) toward the top of the ingot. In general, some dewetting is obtained over a few mm at the beginning of pulling, but with huge efforts to maintain a meniscus, clearly showing that dewetting is not stable in this case. Fig. 3 shows extracts of a video taken during an attempt to get a useful meniscus in the case of InSb under Industrial Argon. The two triple lines can easily be seen, photo A. By increasing the temperature of the crucible holder by 10 K, the triple lines are distorted, photo B, the bubbling pressure is reached, a bubble is released (it carried up the already existing bubble on the left) and a less distorted meniscus is obtained, photo C. However this meniscus – which is concave, see Fig. 2 and previous paragraph – did not lead to dewetting. The pressure increase needed to reach the bubbling pressure is 840 Pa, as computed from the surface tension of InSb, slv(Insb) (0.420 J m 2) and the estimated radius of the bubble rbubble (1 mm):
crucible diameter, is introduced and the crucible is connected to a vacuum system and evacuated. Then it is filled with the appropriate gas and sealed. The initial pressure was chosen as P0 ¼200 mbar because it was recommended in [26] as the optimal value for dewetting of InSb. It should be noted that no experiment was performed with single crystal. – A sketch of the furnace is shown on the Fig. 2. The sealed crucible is introduced in a mobile mirror furnace. Its fixed stand consists in a small resistance furnace used to heat the lower part of the crucible and then control the gas pressure at the cold side of the sample. A window in the crucible wall allows observation and video record of the solid–liquid interface. The temperature gradient in the sample, at the solid– liquid interface, is 120 K cm 1. – The sample is melted to only 5 or 6 cm in order to leave a solid part and control easily the beginning of solidification. After adjusting the gas pressure at the cold side, by visual observation of the meniscus, pulling and video recording are started. For all experiments, the pulling rate was 5 mm h 1. The analysis of an experiment includes the video and temperature recording, estimation of the gap thickness by calliper measurement of the sample and crucible diameters, profilometry, optical and SEM observation and analysis of the sample surface. The video images presented in the next figures show the edge of the viewing window (which is 9 mm wide, this gives the scale of the pictures) and in the centre, a vertical thick dark bar which is an optical artifact due to the reflexion of the window aperture on the silica wall. The solid–liquid interface is easily seen because the emissivity of the liquid is higher than the emissivity of the solid. The curvature of the meniscus can be deduced from the fact that a concave meniscus (seen from the gas) is brighter at the bottom, which reflects hotter surfaces, and darker at the top, which reflects colder surfaces, and vice-versa for a convex interface, see Fig. 2b.
DPbubbling ¼ 2slvðInSbÞ =rbubble
ð3Þ
This corresponds to a 1.4% increase of the pressure at the cold part of the ampoule, estimated as 58,000 Pa. The corresponding DT, through the perfect gas law, is 11 K, in good agreement with the experimental value. The behaviour difference between GaSb and InSb is surprising at first sight, because they show comparable wetting and chemical properties. However, the sum y þ a is significantly lower for InSb (1351) compared to GaSb (1501) so that it is reasonable to expect a difference in dewetting ability. Furthermore, a thermodynamical analysis of the In–Sb–O–Si and Ga–Sb–O–Si systems has shown that liquid GaSb is covered by an oxide layer for temperatures exceeding the melting point by 60 K, while InSb oxides are not stable for temperatures exceeding the melting point by 15 K [25]. It is therefore concluded that an oxide layer which is stable at the surface of the meniscus is responsible of the occurrence of dewetting for GaSb in silica under oxidising conditions, while such a layer is not stable enough, or only marginally, for promoting complete dewetting in the case of InSb. This is in agreement with the fact that some dewetting of InSb in silica has been obtained for experiments in space [2], observed once in the experiments described here and has been previously reported on the ground: only on 10 mm, with suspicion of O2 contamination and with some difficulties [10].
3. Results and discussion 3.1. Effect of oxidation Several atmospheres were used in order to study the effect of oxygen on dewetting occurrence. The ‘‘Neutral’’ atmosphere was obtained by filling the ampoule with high purity argon from Air Products, with certified impurity levels, and introducing Zr-based getters in the lower part of the ampoule; they were thermally activated under vacuum just before sealing the ampoule and in front of the mirror lamps after sealing. The ‘‘Reducing’’ atmosphere was a 90%N2–10%H2 mixture provided by Air Products, with certified impurity levels. Two oxidising atmospheres were used: ‘‘Industrial Argon’’ containing some ppm of oxygen, and ‘‘Air’’. Table 2 gives analyses of these various atmospheres. Dewetting of GaSb has been observed only during the experiments under oxidising atmosphere: one experiment under
Table 2 Impurity composition of the various atmospheres used in the experiments (ppm or %). Atmosphere
Ar (%)
H20
O2
CH4
CO þ CO2
H2
Neutrala Reducing Industrial Argonb Airc
100 90 99.999 0.93
0.02 1 o3 r 2%
0.01 0.5 o2 20.95%
0.1 0.2 o 0.1 1.8
0.1 0.6 o 0.1 300
1 10% Unknown 0.5
a b c
Before getter activation. Typical values from provider data sheet. Standard values, contains 78% N2.
L. Sylla, T. Duffar / Journal of Crystal Growth 324 (2011) 53–62
57
bubble liquid
crucible-liquid-gas triple line
solid Solid-liquid interface
liquid 2 mm
solid
liquid
meniscus solid
Fig. 3. Video snapshots showing an attempt to force a meniscus in the case of InSb (see comments in the text).
3.2. Observation of stable menisci Fig. 4 shows a video sequence recorded during dewetting of GaSb in air. The meniscus has been easily established during the steady state before pulling, photo A. Beginning of solidification always shows a transient state where the gap is rather thick; after about 1 mm, the meniscus and gap thickness are stabilized, at the moment where photo A was taken. Pictures B and C, taken 15 mm ahead, i.e. 3 h after beginning of pulling, show that the meniscus and more generally the dewetting process, are very stable. The film shows that the process occurs smoothly, with the meniscus sliding gently on the crucible wall. From the pictures, the height of the meniscus is measured as 100720 mm, which is in agreement with predictions of model (b). The experimental set-up does not allow measuring gas pressure in the ampoule, so that the initial pressures of the hot and cold
gases are unknown: from perfect gas law, it comes that the pressure of the gas at the cold side should be of the order of 58,000 Pa. Therefore, only rough estimation of the pressure difference can be obtained. The temperature increase of the resistor furnace, in order to get the meniscus before pulling, ranged from 30 to 60 K for the three experiments where dewetting has been obtained. Applying the perfect gas law, this corresponds to gas pressure increases of 2200–4400 Pa, to be compared to the 3350 Pa of hydrostatic pressure exerted by the molten GaSb at the beginning of the solidification (specific mass of molten GaSb is 6.06 103 kg m 3). It can be observed that the upper side of the meniscus is brighter than the lower side. As drawn on Fig. 2b, this means that the meniscus is convex so that its lower part reflects colder places from the bottom furnace. It follows necessarily that inequality (1) is satisfied and then that the contact and growth angles are
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L. Sylla, T. Duffar / Journal of Crystal Growth 324 (2011) 53–62
LIQUID LIQUID Meniscus
SOLID
SOLID
LIQUID LIQUID
Fig. 4. Video sequence of the dewetting of GaSb under air. A Steady state before solidification, the meniscus has been created through pressure control. B Toroidal shape of the crystal at the beginning of solidification. Meniscus shape after 15 mm of growth, C and D, and hillock formation. Thin white arrows show dewetted surface.
c
B
hillocks
b
50 μm
5 μm contact with crucible
A
Dewetted surface
hillock 500 μm
a
hillock
A seed Seed
Seed
500 μm
Fig. 5. Optical and SEM pictures of the surface of the ingot grown under air.
increased by the presence of oxygen. On the contrary, as seen in Fig. 3, the shape of the forced meniscus obtained in the cases where dewetting could not be achieved is concave. These conclusions are in remarkable agreement with the stability analyses of the process, predicting that only convex menisci can provide stable dewetting. Experiments demonstrate furthermore that the process is particularly difficult to control when the meniscus is concave. Another occurrence of dewetting, under Industrial Argon, has been presented in [24] and gave exactly the same conclusions. Fig. 5 shows the external surface of the ingot of Fig. 4. The proportion of dewetted area is estimated to 60% in this ingot.
Fig. 6 shows profiles of the external surface of the sample. Four zones have been identified: – The unmolten solid, called ‘‘seed’’. – Zone A which shows stable dewetting along 18 mm. It is smooth and shiny. At the beginning, it has hillocks, the tops of which were in contact with the crucible wall, as shown by SEM. The gap thickness, measured relatively to hillock tops, is stable: 3475 mm (Fig. 6ii). – Zone B where dewetting is only partial. It is rougher than part A (Fig. 6iii–v) and had numerous contact zones with the crucible. SEM analysis and EDS spectroscopy have revealed
L. Sylla, T. Duffar / Journal of Crystal Growth 324 (2011) 53–62
μm
59
i
50 0 -50 -100 -150 -200 -250 -300
hilloc ks
Full dewetting zone A
Partial dewetting zone B
Seed 0
μm
2
4
8
6
10
12
14
16
18
20
22
24
26 mm
ii
70 60 50 40 30 20 10 0 -10 -20
Hillocks (in contact with crucible wall) e=34 μm
0 μm
0.5
1
2
1.5
2.5
3
3.5
4
4.5
5 mm
iii
20 15 10 5 0 -5 -10 -15
End of A
0
0.5
1
Beginning of B
1.5
2
2.5
3
3.5
4 mm
iv
μm 10 5 0 -5 -10 -15
Zone A 0
μm 8 6 4 2 0 -2 -4 -6 -8 -10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5 mm
v Contacts with crucible
Zone B 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3 mm
Fig. 6. Surface profiles of the ingot shown on Figs. 4 and 5. Vertical axis gives the radius deviation from an arbitrary origin and horizontal axis gives the length scale along the ingot. (i) First 26 mm above the seed. (ii) Profile of the hillock region. (iii) Profile at transition between zones A and B. (iv) Zoom on the profile in zone A. (v) Zoom on the profile in zone B.
oxygen at these places and it has already been mentioned in [24] that EDS analysis of these contact zones presents Si contamination. – Zone C does not show dewetting. Another dewetted zone, smooth and shiny, 10 mm long, appears between B and C. No change of the experimental conditions has been recorded at the transitions between zones A, B and C so that the reasons of these transitions remain unclear. It may be related to changes of the crucible wall surface, either before the experiment
(heterogeneous cleaning process) or during heating, for example due to the high temperature gradient, and longer liquid contact for the last to freeze part. However the strangest behaviour, also reported for other experiments [27,28], is that dewetting, when it occurs, is more stable than expected, because it shows pressure self-equilibration. According to the theoretical model (b), the gap thickness remains constant only if the condition (2) is satisfied all along the solidification. This means that the pressure difference DP should be decreased in order to follow the decrease of liquid length and
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LIQUID
LIQUID meniscus
meniscus
SOLID SEED
Fig. 7. Dewetted growth of GaSb under Industrial Argon, two snapshots showing occurrence of hillocks.
bubbles LIQUID LIQUID S/L interface
S/L interface
Fig. 8. Pictures taken during the growth of GaSb under reducing atmosphere. Numerous bubbles appear on the wall, close to the S/L interface and left marks on the solidified surface (white dashed circles).
hydrostatic pressure. However the temperature of the ampoule holder was kept perfectly constant, while stable dewetting occurred. During solidification, the whole ampoule is cooled down, but its hot side, close to the lamp bulbs, might possibly be cooled at a somewhat slower rate than the cold side. An increase of 10 K between both temperatures would lead to the compensation of 1.3 cm of hydrostatic pressure, but this cannot explain the constant gap thickness obtained along several centimetres (Fig. 6i). And this cannot be invoked in order to explain the stable gap obtained in Ref. [28] in a Stockbarger furnace, where a temperature difference shift was prohibited. It is rather expected that, while solidification proceeds, the hydrostatic pressure decreases and the difference of pressure acting on the meniscus increases. At some moment bubbling should occur. Indeed, there is some suspicion that the pressure difference self-equilibrates by exchange of gas between the cold side, where the hydrostatic pressure decreases, and the hot side. Only two or three times during this experimental work, layers of gas have been seen, quickly flowing between the wall and the liquid, from the meniscus toward the top of the ampoule. They did not look like bubbles, rather like a layer of air flowing between two paper sheets. Unfortunately this phenomenon is so subtle and rare that it was not possible to catch it on the video sequences. Clearly this behaviour needs further investigation.
crucible – or of the initial feed material – can interact with the dewetting process and creates hillocks, possibly ridges and maybe enhance or cancel the dewetting itself.
3.3. Ridges and hillocks
4. Conclusion
Fig. 7 shows again pictures already published in [24]. In this sequence GaSb is grown dewetted under Industrial Argon. On the left image, the black circle shows patterns on the surface of the crucible wall. After solidification of this part of the sample, the black circle on the right picture show that the patterns gave birth to hillocks on the dewetted surface of the sample. This indicates that defects, either chemical or geometrical, on the surface of the
The objectives of the paper were to check experimentally the hypotheses assumed by the various models of the dewetting phenomenon, and to carefully study the freezing process in order to obtain new information. The results confirm the observation, already reported in [24], that a meniscus exists and slides smoothly on the crucible wall, when stable dewetting occurs. As the external aspect of the samples is very comparable to what is
3.4. Gas dissolution Experiments with GaSb were performed under reducing atmosphere. No stable dewetting occurred, because no oxidation was possible, only a small zone, half a square centimetre, was detached. However the high solubility of hydrogen in liquid metals allowed studying the mechanism involved in model (c). The striking fact in the recording is the great number of bubbles that are observed on the crucible wall, and close to the solidification interface only Fig. 8. Accelerated reading of the video sequences allowed the observation of the nucleation, growth and disappearance of numerous bubbles, which are supposed to contain hydrogen, as it is the only parameter differing from experiments under neutral atmosphere. Bubbles nucleate about 1 cm above the S/L interface and their size increases with the approach of the interface. This validates the dissolution of gases in the liquid and their rejection at the solid–liquid interface. In spite of the initial presence of a meniscus that had been forced after melting, the rejected gas generated bubbles on the wall and did not feed the meniscus.
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observed at the surface of dewetted samples obtained in space and on the earth, this hypothesis is now totally confirmed. Results also allow establishing conclusions concerning the three main models found in the literature. – Model (a) is based on the hypothesis of an increase, possibly by pollution, of the growth and wetting angles in order to allow spontaneous dewetting in space. The experiments have shown unambiguously that in the case of GaSb, oxygen contamination is mandatory to obtain stable dewetting. Furthermore it was observed that the meniscus is convex in these experiments, which proves that the angles have been effectively increased. In the case of InSb, experiments show that dewetting is very difficult to control and is never stable, two reasons can be invoked: a smaller sum y þ a compared to GaSb and a less stable oxide at the melting point. However observation of a meniscus under microgravity conditions is needed in order to fully validate this model. – Model (b) is based on the assumption that a gap pressure difference between hot and cold sides of the crucible, of the order of the hydrostatic pressure, can control the shape of the meniscus and promote dewetting on the earth. This is in full agreement with the experimental results, and estimations of the gap height (100 mm), gap thickness (some tens of mm) and gas pressure increase (some thousands of Pa) are in the order of magnitude of the theoretical predictions. On the contrary, an experiment without any gas in the ampoule did not allow establishing a meniscus. – Model (c) is based on dissolution at the hot side of the liquid, segregation at the S/L interface and rejection at the meniscus, of gas present in the ampoule. Experiments with gas mixture containing H2 have validated the dissolution and segregation mechanisms; however the segregated gas formed bubbles on the crucible wall and never filled the gap through the meniscus. Also, this model predicts too large gap thickness (1 mm) and a critical velocity, above which detached growth is unstable. Experiments have shown that dewetting occurs also for very high growth rates [24,29]. Therefore it can be concluded that this model, while it could act in some specific cases, cannot be invoked in the general case of dewetting. – All stability analyses published so far claim that a convex meniscus, i.e. condition (1), is mandatory in order to get stable dewetting. The experiments fully confirm this prediction: a convex meniscus was observed in all cases of stable growth. Stability was impressive: a constant gap thickness has been obtained during 4 h of pulling. On the contrary, when the meniscus is concave, the process is extremely difficult to control, and invariably led to the disappearance of dewetting after a few millimetres of pulling. It can be expected that thorough control techniques should be used if dewetting is wanted in cases where condition (1) does not apply. – An experiment has shown that hillocks are caused by early contamination of the liquid sample–crucible wall surface.
In summary, it can be concluded that the theoretical models, except model (c), give a good understanding of the dewetting process. They can safely be used for prospective calculations concerning the phenomenon as well as the process, provided that a new parameter is taken into account: the effect of impurities on the wetting and growth angles. However the effect of self-stabilisation of the pressure difference, which apparently follows the decrease of hydrostatic pressure, is not understood yet. It will deserve further investigations in the future.
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Acknowledgements This experimental work has been supported by the MAP-CdTe project of the European Space Agency and by funding of the CNES. The authors are grateful to C. Garnier, J.P. Paulin and G. Vian for their technical help. The SIMaP-EPM laboratory is under the cotutella of Grenoble institute of Technology, University Joseph Fourier and CNRS. References [1] L.L. Regel, W.R. Wilcox, Detached solidification in microgravity—a review, Microgravity Sci. Technol. XI/4 (1998) 152. [2] T. Duffar, in: P Capper (Ed.), Bulk Crystal Growth of Electronic, Optical and Optoelectronics Materials, John Wiley & Sons, 2005, pp. 477–524 (Chap. 17). [3] T. Duffar, L. Sylla, Vertical Bridgman and dewetting, in: T Duffar (Ed.), Crystal Growth Processes based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques, John Wiley & Sons Ltd., New York, ISBN 978-0-47071244-32010, pp. 355–411 (Chapter 6). [4] T. Duffar, I. Paret-Harter, P. Dusserre, Crucible de-wetting during Bridgman growth of semiconductors in microgravity, J. Cryst. Growth 100 (1990) 171–184. [5] I. Harter, P. Dusserre, T. Duffar, J.-Ph. Nabot, N. Eustathopoulos, Wetting of III–V melts on crucible materials, J. Cryst. Growth 131 (1993) 157–164. [6] W. Palosz, M.P. Volz, S. Cobb, S. Motakef, F.R. Szofran, Detached growth of germanium by directional solidification, J. Cryst. Growth 277 (2005) 124–132. [7] T. Duffar, P. Boiton, P. Dusserre, J. Abadie, Crucible de-wetting during Bridgman growth in microgravity II. Smooth crucibles, J. Cryst. Growth 179 (1997) 397–409. [8] S. Balint, L. Braescu, L. Sylla, S. Epure, T. Duffar, Dependence of the meniscus shape on the pressure difference in the dewetted Bridgman process, J. Cryst. Growth 310 (2008) 1564–1570. [9] S. Epure, T. Duffar, L. Braescu, On the capillary stability of the crystal-crucible gap during dewetted Bridgman process, J. Cryst. Growth 312 (2010) 1416–1420. [10] T. Duffar, P. Dusserre, F. Picca, S. Lacroix, N. Giacometti, Bridgman growth without crucible contact using the dewetting phenomenon, J. Cryst. Growth 211 (2000) 434–440. [11] W.R. Wilcox, L.L. Regel, Detached solidification, Microgravity Sci. Technol. VIII/1 (1995) 56–61. [12] D.I. Popov, L.L. Regel, W.R. Wilcox, Detached solidification. 1. Steady-state results at zero gravity, J. Mater. Synth. Process. 5 (1997) 283–297. [13] D.I. Popov, L.L. Regel, W.R. Wilcox, Detached solidification. 3. Influence of acceleration and heat transfer, J. Mater. Synth. Process. 5 (1997) 313–335. [14] Y. Wang, L.L. Regel, W.R Wilcox, Influence of contact angle, growth angle and melt surface tension on detached solidification of InSb, J. Cryst. Growth 209 (2000) 175–180. [15] Y. Wang, L.L. Regel, W.R. Wilcox, Steady-state detached solidification of water at zero gravity, J. Cryst. Growth 226 (2001) 430–435. [16] Y. Wang, L.L. Regel, W.R. Wilcox, Approximate material-balance solution to the moving meniscus model of detached solidification, J. Cryst. Growth 243 (2002) 546–550. [17] V.A. Tatarchenko, Shaped Crystal Growth, Fluid Mechanics and its Application, Kluwer, Dordrecht, 1993 (vol. 20). [18] L. Bizet, T. Duffar, Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions, Cryst. Res. Technol. 39 (2004) 491–500. [19] T. Duffar, S. Epure, Comment on the paper ‘‘Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions’’, Cryst. Res. Technol. 45 (2010) 1209–1210. [20] S. Balint, S. Epure, L. Braescu, T. Duffar, Dewetted Bridgman crystal growth in terrestrial conditions: practical stability over a bounded time period in a forced regime, J. Eng. Math., in press. [21] D.I. Popov, L.L. Regel, W.R. Wilcox, Detached solidification. 2. Stability, J. Mater. Synth. Process. 5 (1997) 299–311. [22] L. Braescu, On the pressure difference ranges which assure a specified gap size for semiconductor crystals grown in terrestrial dewetted Bridgman, J. Cryst. Growth 312 (2010) 1421–1424. [23] A. Yeckel, J.J. Derby, Existence, stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity, J. Cryst. Growth 314 (2011) 310–323. [24] L. Sylla, J.P. Paulin, G. Vian, C. Garnier, T. Duffar, Effect of residual gaseous impurities on the dewetting of antimonide melts in fused silica crucibles in the case of bulk crystal growth, Mat. Sci. Eng. A 495 (2008) 208–214. [25] L. Sylla, Etude expe´rimentale et thermodynamique du poce´de´ de de´mouillage applique´ aux semiconducteurs, Ph.D. thesis, 20th June 2008, Grenoble Insitute of Technology, in French. [26] J. Wang, L.L. Regel, W.R. Wilcox, Detached solidification of InSb on earth, J. Cryst. Growth 260 (2004) 590–599. [27] N. Chevalier, P. Dusserre, J.-P. Garandet, T. Duffar, Dewetting application to CdTe single crystal growth on earth, J. Cryst. Growth 261 (2004) 590–594.
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L. Sylla, T. Duffar / Journal of Crystal Growth 324 (2011) 53–62
[28] T. Duffar, P. Dusserre, N. Giacometti, Growth of GaSb single crystals by an improved dewetting process, J. Cryst. Growth 223 (2001) 69–72. [29] M. Fiederle, T. Duffar, V. Babentsov, K.W. Benz, P. Dusserre, V. Corregidor, E. Dieguez, P. Delaye, G. Roosen, V. Chevrier, J.C. Launay, Dewetted growth of CdTe in microgravity (STS-95), Cryst. Res. Technol. 39 (2004) 481–490.
[30] N. Eustathopoulos, B. Drevet, S. Brandon, A. Virozub, Basic principles of capillarity in relation with crystal growth, in: T Duffar (Ed.), Crystal Growth Processes based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques, John Wiley & Sons Ltd., New York, ISBN 978-0-47071244-32010, pp. 1–49 (Chapter 1).