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Heat treatment studies on silver gallium diselenide (AgGaSe2) crystals
MATERIALS SCIENCE & ENGINEERING
g
ELSEVIER
Materials Science and Engineering B38 (1996) 229-235
Heat treatment studies on silver gallium diselenide (AgGaSe2) crystals Nam-Hun Kim a, Dong Hyuk Shin b, Roberts S. Feigelson ° ~Omega Division, Applied Materials, Santa Clara, CA 95054, USA bDepartment of Metallurgy and Materials Science, Hanyang University, Ansan, Kyunggi-Do, 425-791, South Korea °Department of Materials Science and Engineer#~g, Stanford University, Stanford, CA 94305, USA Received 13 April 1995
Abstract
Silver gallium diselenide (AgGaS%) is an important materiaI for nonIinear optical frequency generation in the infrared region. Crystals have been difficult to produce in high optical quality form because of the presence of precipitates in as-grown material. A post-growth heat treatment process has been developed to remove these precipitates and 'render the crystals usable for optical applications. However, the details of the chemical interdiffusion processes involved in this method have not been well understood. In this study, the heat treatment procedure was analyzed through mass transport measurements and phase identification by powder X-ray diffractometry. A chemical mass balance model, and how it relates to our current understanding of the phase equilibrium in the Ag2Se-GaaSe 3 pseudobinary system are presented. The estimated flux, based on Knudsen's equation, has enabled us to predict the optimum annealing time for a given temperature and crystal size. Keywords: Heat treatment; Silver gallium diselenides; Annealing
1. Introduction
AgGaSe2 crystallizes in the chalcopyrite structure with a space group I742d, and single crystals with high optical quality have important nonlinear infrared optical applications [1]. However, owing to an off-stoichiometric congruency, AgGaSe2 always grows slightly richer in Ga2Se3 than the stoichiometric composition, in accordance with the phase diagram shown in Fig. 1 [2,3]. This inevitably leads to the formation of Ga2Segrich precipitates upon cooling. These precipitates cause appreciable optical scattering in the near-infrared wavelength (0.73-2 /zm) region. The precipitates can be eliminated either by quenching or heat-treating the crystals in the presence of Ag2Se [4-6]. In the quenching technique, as-grown crystals are cooled rapidly from a temperature where they are within the single phase existence region, fi, to room temperature and metastable equilibrium. Although effective in eliminating the precipitates, quenching usually leads to cracking of the crystals. For this reason, the heat-treatment process [5,6], which causes less damage to the crystals, is preferred. In the heat treatment 0921-5107/96/$I5.00 © I 9 9 6 - Elsevier Science S.A. All rights reserved
process, AgzSe (approximately 0.5 tool.% ) serves as an annealing medium to compensate for the excess GazS% in as-grown material (Y-composition in Fig. 1). Typically, the AgzSe annealing medium is placed in direct contact with the crystals and heat treatment is carried out at 800 °C, well above the eutectic temperature (728 °C). In this temperature range, a liquid phase forms at the interface where the two materials touch as a result of chemical reaction. Owing to surface migration effects, a thin layer of Ag-rich material covers the entire surface of the as-grown crystals within a short time and excess Ga2Se3 is then eliminated from the bulk by solid-state diffusion [7]. The stoichiometric Y'-composition that is formed yields a clear material upon cooling because this composition is invariant with temperature. In the closely related compound, AgGaS2, the corresponding precipitate phase can be completely eliminated through a contactless heat treatment procedure in which the crystal does not make direct mechanical contact with the annealing medium. As in the heattreatment of AgCaS%, a thin layer of Ag-rich material resulting from a chemical reaction between the AgGaS2 crystal and the AgzS annealing medium also ends up
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N.-H. Kim et al. / Materials Science and Engineering B38 (1996) 229-235
covering the surface of the crystal, but in this case transport occurs through the vapor state. Excess GazS3 is then eliminated from the bulk by solid-state diffusion
[6-8]. In the case of igGaSe2, contactless heat-treatment reduces the density of precipitates but has not been found to eliminate them completely. Direct mechanical contact seems to be necessary to achieve their total elimination. However, the direct contact heat treatment also leads to fracturing of the crystals in the contact region if annealing is carried out above the eutectic temperature, where a liquid phase can form. This is owing to stresses caused by differential thermal expansion of the phases formed during cooling. (Annealing is not carried out at lower temperatures because the kinetics of the process are sluggish.) While the degree of cracking is usually less than that caused by quenching, it would be desirable to eliminate it completely. Several variations in the annealing technique have been reported, depending on whether or not there is contact between the crystal and annealing medium, or whether there is an annealing medium present at all [2-6,8-10]. Nonetheless, a systematic analysis of the heat treatment process has not yet been presented. Previously, analyses of the chemical reaction products and the condensed volatile species found on the ampoule walls for annealing temperatures in the temperature 500-800 °C range have revealed no significant differences between the contact and the contacttess cases [6,8]. Therefore, a chemical mass balance model has been developed to analyze the chemical reaction products and to quantify the chemical reaction kinetics between these two cases. This work complements a previous study on the kinetics of the heat treatment process that determined the chemical interdiffusion coefficients for the mobile species [7].
2. Experimental procedure AgGaS% single crystals were grown for use in the heat-treatment experiments using the bottom-seeded vertical Bridgman technique described elsewhere [6,8]. C-axis seeds, stoichiometric melts and growth rates of nominally 6 mm per day were used. Centimeter-size crystals, weighing in the region of 6-10 g were cut from the boules with a diamond saw and polished with alumina powder. Polycrystalline AgzSe used as the annealing medium was synthesized by melting silver and selenium shot (purity 6-9's and 5-9's) in a carboncoated, sealed quartz ampoule placed inside a rocking furnace at 950 °C for about 10 h. Prior to heat-treatment, all the crystals were cleaned and weighed with a microbalance to a precision of 10 - 4 g. Three different kinds of heat-treatment procedures were carried out using a resistance furnace and sealed
fused quartz ampoules that were vacuum sealed at 10 - 4 Torr or better. The first procedure was to anneal the AgGaS% test crystal in a vacuum without any annaling medium present. Vacuum annealing was carried out at 800 °C for 7 days. The second procedure involved annealing with the annealing medium not in contact with the test crystals. A neck in the quartz ampoules separated the test crystal from the AgzSe annealing media. Since only vapor transport was possible in this case, temperatures above 728 °C, the eutectic temperature, were used in some cases to maximize the rates of chemical reaction and vapor phase transport. Annealing was performed at 670 °C for 7 days, and at 800 °C for 2.5 days. The third type of annealing procedure involved direct contact between the test crystals and the annealing medium. The crystals were positioned vertically on top of the annealing media in order to ensure mechanical contact. The annealing temperature had to be maintained below the eutectic temperature (728 °C) to prevent the formation of a liquid phase, which would have complicated the problem of separating diffusive from vapor transport effects. After heat treatment, the ampoules were opened and the crystals carefully separated from the annealing media. The crystals were weighed using a microbalance, and analyzed using powder X-ray diffractometery. The chemical composition of the thin film which formed on the surfaces of many crystals heat-treated with an annealing medium present, was analyzed using a four circle X-ray diffractometer. /
90O
9O0
/
32 800,
8OO
.....
d
T(°C) .w'( 728
700
700
U
V =
AggGaSea + AgGaSea
10C z
0
Ag2Se
10
=
=
125
AgGaSea +
1
1
I
20
30
40
Z'
Z
50
Mole P e r c e n t
too
l
1
1
1
60
?0
80
90
Ga2Sea
101
GaaSea
Fig. 1. Ag2Se-GazS % pseudobinary phase diagram. Quenching follows a path ( Y - Z ) and annealing of the crystal with AgaSe follows a path (X- 1I). Since the liquid is involved in a path (Z- 10, contactless annealing can be done using that path, and contact annealing was done using a path (U-V) in this work.
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N,-H. Kim et al. / Materials Science and Engineer#zg B38 (i996) 229-235
Table 1 Low temperature annealing-weight changes and the resulting phases of the crystal and annealing medium for before and after annealing at 670 °C for 7 days Weight and species
Sample Annealing medium
Annealing condition
Weight(g) Species* Weight(g) Species*
Contactless case
Contact case
Before
After
Before
After
0.1751 I12+ 1711 2.9300 201
0.1740 112 2.9310 201 +916
0.175I 112+1711 2.9300 201
0.5443 112+916 2.5604 201 +916
* 112, 1711, 916 and 201 represent AgGaSe2, AgGa7Seli, AggGaSe6 and Ag2Se respectively.
3. Results and discussion
Table 1 and Table 2 summarize the weight changes and the phases found after low temperature (670 °C) heat-treatment with and without contact, and after high temperature heat-treatment (800 °C) without contact. All X-ray patterns corresponded to one or more of the phases found on the pseudobinary join, indicating that in the condensed phase, pseudobinary approximation is reasonably accurate. In some cases, a slight discrepancy existed between initial and final weights, owing, we concluded, to condensation of small amounts of material on the quartz ampoules. In no case did the condensed material on the quartz wall exceed 3% of the total mass transported during processing. The weight change of the AgGaSe2 crystals during vacuum annealing without the annealing media present was negligible as expected, since no condensed material was detected on the ampoule walls after processing. We analyzed the experimental results using a chemical mass balance procedure based upon the following assumptions: (a) The Ga2Ses-rich precipitates which form during the growth of AgGaSe2 have the composition AgGa7Sei1 in accordance with the phase equilibria first determined by Mikkelsen [3]. (b) When as-grown AgGaS% crystals containing precipitates are heated above the solvus, a solid solution Table 2 High temperature contactless annealing-weight changes and the resulting phases of the crystal and annealing medium for before and after annealing at 800°C for 2.5 days Weight and species
Annealing
Before
After
Sample
Weight(g) Species* Weight(g)
5.3427 112+1711 0.0710
5.3097 112 0.1029
Species*
201
I12+916
Annealing medium
* 112, 1711, 201 and 916 represent AgGaS%, AgGaTSeli, AggGaSe6 and Ag2Se respectively.
(fi) is formed, meaning that the precipitates dissolve in the crystal, in accordance with the modified phase equilibria shown in Fig. 1. The fl solid solution can be thought of as either AgGaSe2 with m tool.% of AgGa7Se11 in solution, or AgGaSe 2 with 3 m mol.% of Ga2Se3 in solution: AgGaSe2 + mAgGa7Sell = (1 + m)AgGaSe2 + 3 m Ga2Se 3
(1)
(c) During annealing, mass is transported through the vapor phase from the crystal to the annealing medium. However, it is not known what the species are. Several possibilities include Ga2Se3, Ga2Se, GaSe and G a + S e atoms [11]. After annealing, a small amount of reddish-black material was found deposited on the ampoule walls. X-ray analysis failed to identify its exact composition. From previous research and current annealing experiments, it is clear that the AgGa7Sezl precipitates in as-grown crystals are eliminated while the crystals lose weight, as the mass transport data in Table 1 and Table 2 show [8]. This means that the weight loss of the crystal is directly related to the combination of two Ga atoms and three Se atoms. Thus, even though the exact transporting species is not known, we can assume that the weight change of the crystal before and after annealing is owing to a unit with composition 2Ga:3Se which we refer to as Ga2S%. (d) The concentration of the precipitate phase in as-grown crystals is estimated from optical measurements to be 0.5 mol.%. (e) There is no solid solubility between Ag2Se and AggGaSe6, or between AggGaSe6 and AgGaSe2, consistent with the modified phase diagram, Fig. 1. (f) When diffusive transport occurs during contact annealing, the number of moles of Ga2Se3 vapor transported to the annealing medium is negligible as compared with the number of moles of Ag2Se3 transported by solid-state diffusion to the crystal. This has been demonstrated clearly in our diffusivity measurements cited previously [7].
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N.-H. Kim et al. / Materials Science and Engineering B38 (i996) 229-235
3.1. Low temperature studies Previous research on AgGaSe2 and AgGaS2 has shown that the contact annealing process is significantly faster in reducing precipitate densities than contactless annealing [6,8]. But, as mentioned before, a liquid phase forms at the junction between the crystal and the annealing medium, and this makes it difficult to separate the crystal from the annealing medium in order to measure the resulting weight change and decouple the vapor transport component from the diffusive transport component. Thus, in both the contact annealing case and the contactless case as well, a temperature lower than the eutectic temperature, 670 °C, was used to prevent the formation of a liquid phase. Early research studies [6,8], in which the relative quantities of annealing medium used were in the 0.51.5 mol.% range, resulted in the annealing medium being completely transformed into AgGaSea by the time the heat-treatment process was complete, similar to the experimental results for AgGaS2. This is not true in the general case. The final composition of the crystal and remaining annealing medium depend upon the annealing temperaure, the annealing time, the initial composition of the crystal and the composition and initial relative weight of the annealing medium. In order to determine the kinetics of the heat treatment process, an analysis was carried out for the case where the temperature is fixed at 670 °C and the weights of the crystal and the annealing medium are given in Table 1. Case L When the amount of the annealing medium is just sufficient to compensate for the excess (AgGaTSeix) precipitate phase. From the crystal (c), the excess GazSe3 out-diffuses and volatilizes as follows: AgGaSe2(c) + AgGa7Sei 1(c) = AgGaSe2(c) ÷ Ga2Se3~"
(2)
At the surface of the annealing medium (m), the vapor transported GazSe3 reacts with Ag2Se to form AgGaSe: as follows: Ag2Se(m) + GazSe3(m) = 2AgGaSez(m)
annealing medium
annealing medium
(3)
Case H. When the amount of the annealing medium is more than sufficient to compensate for the excess (AgGavSe11) precipitate phase. (In our experiments the weight of the crystal was made smaller than that of the annealing medium, which is opposite from the usual case during the heat-treatment. This modification was made to increase resolution by enhancing the mass transport effects as much as possible.) The contactless annealing case was analyzed first. For contactless annealing, four parameters (t, m, q and j) are required to analyze the transport processes
crystal
jc
(a)
(b) annealing medium c~'ystal
(j-27m)C +
6zE
(c) annealing medium
~
G
~mD
ann°altng medium
t
crystal
cry
(k+n)C
} (z+q)B
I 3q0*-l(s)
(d)
annealing medium (n-27m)C +
6mE
armealinffmedium crystal [[4(t*m)÷~laokll4l h +
[Ik4qlla] S
(f)
(¢)
Fig. 2. Schematic representation of low temperature heat ~reatment processing. (a), (b), and (c) show the initial stage, mass transfer, and the final stage, respectivelyfor contactless annealing, while (d), (e), (f') and (g) show the initial stage, mass transfer, and intermediate stage, and final equilibrium stage for contaetless annealing. The symbols used are as follows: t: number of moles of AgGaS%; m: number of moles of AgGavSe~ resulting in vapor transport; q: number of moles of AgGaTSe~ reacted with diffused Ag2Se;j: number of moles of initial AgaSe (=n + k); n: number of moles of Ag2Se reacted with vapor transported GazS%; k: number of moles of Ag2Se diffused through the crystal; A: molecular weight of AgGaS%; B: molecular weight of AgGa7Se~; C: molecular weight of Ag'2Se; D: molecular weight of Ga2Se3; E: molecular weight of AggGaSea. as illustrated in Figs. 2(a)-(c). Here, the elimination of the precipitate phase is not allowed to go to completion. Thus, in the crystal, q moles of the precipitate phase still remains after annealing. Since the concentration of the precipitate in as-grown crystals has been estimated to be 0.5 mol.%,
( m + q ) / ( t + m + q ) = 5 x 10 .3
(4)
Table 1 shows the actual weight loss of the annealed crystal after contactless annealing at 670 °C. The data clearly indicate that GazS% moved from the crystal to the annealing medium (which gained a corresponding amount of weight) via vapor transport. The concentration of the precipitate phase after contactless annealing, which is expressed as q/(t + re+q), was found to be 0.3 tool.%. This implies
N.-H. Kim et al. / Materials Science and Engineering B38 (1996) 229-235
that 40% of the precipitate phase in the as-grown crystal was eliminated. For the contact annealing case, three reaction mechanisms must be considered. The first involves vapor phase transport since Ga2S% vapor is transported toward the Ag2Se annealing medium, where compound formation through chemical reaction takes place. The second involves solid-state diffusive transport where Ag2Se diffuses into the crystal. The third involves solid-state diffusive transport where Ga2S% out-diffuses from the crystal and reacts with the Ag2Se annealing medium. However, we have assumed that the concentration of this third mechanism is negligible because of the low effective diffusivities for Ag + measured in a previous study [3,7]. The first two mechanisms have their own rate determining step, and which one predominates depends mainly on the temperature. Five parameters (t, m, q, k and n) are required to analyze the transport process in the contact annealing case, as illustrated in Figs. 2(d)-(f). Since under our experimental conditions, 3q moles of GazS% are much smaller than k moles of AgzSe, all the GazSe3 is transformed into the intermetallic compound Ag9GaSe 6 as the annealing time increases. The concentration of precipitates after contact annealing, expressed as q/(t + m + 4q + k), is found to be 0.08 mol.%. This implies that 84% of the precipitates in as-grown crystals were eliminated. Comparing this case with the previous contactless case, it can be seen clearly that contact annealing is a more efficient method than contactless annealing for eliminating precipitates. Our previously cited diffusivity measurements on chemical interdiffusion between AgGaSe2 and Ag2Se indicated that in this system, diffusion occurs as a cooperative phenomena in which the species move as units having molecular stoichiometry, such as AgzSe and Ga2Se3, in order to preserve electrical neutrality [7]. Furthermore, it was found that the effective diffusivity of Ag2Se into AgGaSe2 is far too low to account for the experimentally determined rate at which the precipitate phase is eliminated from asgrown crystals. The annealing process cannot, therefore, involve diffusion of the AggGaSe6 phase into the AgGaS% phase. We concluded instead that elimination of the precipitate phase most likely occurs by out-diffusion of excess GazSe3 from the crystal. The phases found in both the crystal and the annealing medium as a result of heat-treatment can be compared with what we would expect by applying the lever rule to the Ag2Se-GazS% phase diagram in Fig. 1. Analysis of the possible phases after contact annealing shows that the composition of the crystal after contact annealing for our particular experiment was approximately 40 tool.% AgGaSe2 and 60 tool.%
233
AggGaSe6, and that the final composition of the annealing medium was approximately 99.93 tool.% Ag2Se and 0.07 tool.% AggGaSe6. This particular experiment ended up with the "crystal" far to the left of the b phase boundary, in the middle of the twophase AggGaSe6 + AgGaSe2 system. This was owing to the unusual mass ratio between the test crystal and the annealing medium. Normally, it is desirable that the "crystal" equilibrate as close as possible to the left hand /7 phase boundary to minimize damage caused by formation of the AggGaSe6 phase. From these low temperature heat-treatment studies, we deduce the following: (a) The diffusive transport process can be decoupled from the vapor transport process. (b) The rate at which precipitates are eliminated during contact annealing is much faster than for contactless annealing because the former involves an additional diffusive transport component. Furthermore, the diffusive term becomes predominant as the annealing temperature increases because diffusive transport has an e x p ( - b / T ) dependence, while vapor transport has an e x p ( - a / T ) / T m dependence, where a and b are constants. (c) The annealing processes can be controlled by varying the annealing temperature, annealing time and the amount of the annealing medium. (d) It is, in principle, possible to modify the heattreatment processes by changing the annealing medium. For example, using AggGaSe6 as an annealing medium would prevent continued reaction between the annealing medium and the test crystal once the precipitate phase had been totally eliminated. It might also enhance the rate at which precipitates are eliminated. .3.2. High temperature studies As we indicated earlier, analysis of the transport phenomena occurring during contact annealing is not possible at temperatures higher than the eutectic temperature because a liquid phase forms, this complicates the problem of separating the annealing medium from the test crystal and obtaining accurate weight gain/loss data. It is relatively easy to analyze the transport phenomena at higher temperature in the contactless annealing case, however, since vapor transport is the only mass transport process occuring. Higher temperatures have the added benefit of enhancing the vapor transport process, as indicated. However, while the precipitate phase can, in principle, be eliminated using the contactless annealing process with Ag2Se as the annealing medium, the rate of elimination of the precipitat phase is known to be slow [8] and complete removal has never, to our knowledge, been demonstrated under controlled conditions.
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N.-H. Kim et al. / Materials Science and Engineering B38 (1996) 229-235
Four steps are involved in the.high temperature, contactless annealing case: (i) the dissolution of AgGa7Sex1 precipitates into the /? solid solution, (ii) out-diffusion of GazSe> (iii) transport of GaaSe3 through the vapor phase, and (iv) a chemical reaction between GazSe3 and AgzSe in the annealing medium. The overall reaction rate at high temperature depends on the slowest step. Fig. 3 shows a schematic diagram of the high temperature annealing process. Four parameters (t, m, q and j) are again required to determine the mass transport. This case bears closer resemblance to the commercially used process since the crystal mass is significantly larger than the annealing medium and the annealing temperature is well above the eutectic (800 °C). (There is no direct contact, however.) The chemical reaction between Ga2Se3 vapor and the Ag2Se annealing medium is considered to be spontaneous and irreversible. The rate at which the precipitate phase is eliminated depends, therefore, mainly on outdiffusion of Ga2Se3 and the flux through the vapor phase. The overall reaction between the annealing medium of the GaaSe3(v) follows the AgzSe-Ga2Se3 phase equilibria shown in Fig. 1, and depends on the relative magnitude of j and m. The concentration of the precipitate phase in the crystal after this particular experiment is estimated to have been 0.3 mol.%, and we conclude that 40% of the precipitates had been eliminated. This is consistent with experimental findings in which measurable amounts of the precipitate phase were found routinely in test crystals even after many weeks of heat-treatment. The expected reaction products, AgGaS% and AggGaSe6, were detected in the annealing medium after completion by powder X-ray diffraction analysis. The ratio of AgGaSe2 to AggGaSe6 in the annealing medium, apcrystal tA +
proximately 4:1, was different from that calculated using the lever rule and the phase diagram shown in Fig. 1. One possible reason for the discrepancy might be that this system was not yet in thermodynamic equilibrium. The temperature dependence of the flux owing to vapor transport can be also determined. The evaporation reaction can be expressed as follows: Ga2Se3ts) = Ga2Se3(v?
(5)
A G = A G O+ R T In Po,~2s~3(v~
(6)
At equilibrium, A G O= - R T In PG,2s~3(v)
The flux J tool cm -2 sec- l, based on the Knudsen's equation [12] can be expressed as follows:
1 dn~ .P,o: i J = -S d---[= x / 2 ~ M ~ R T '
where S is the surface area of a crystal, n; is the number of moles transported in the form of vapor, Pi is the partial vapor pressure of the ith species in the vapor, cq is the evaporation constant ( < 1), M t is the molecular weight of the ith species in grams, R is the gas constant in J m o l - a K, and T is the absolute temperature. Here i represents GazSe3 and ~i is a constant close to one. From Eqs. (7) and (8), the flux J can be expressed as follows: Kexp( J--
AH°~ RT/
,/T
where A H °, is the standard enthalpy of vaporization in kJ mol-1 and K is a constant. A H °, and K can be obtained from the data shown in Table 1 and Table 2:
(t+m)A
Thus the flux owing to vapor transport can be expressed as:
qB
(m+q)B
0.0226exp( (b)
(a) crystal medium [(27m-j)/4] A +
qB
(9)
A H ° = 143.6 kJ mol- t
+
+
(8)
crystal
medium
(t+m)A
(7)
[(j-3m)/41E
(c) Fig. 3. A schematic representation of the high temperature heat treatment process: (a), (b), and (c) show the initial stage, mass transfer, and final stage, respectively. The crystal is much larger than the medium and this situation is close to the actual heat treatment process.
J--
~T
and
K = 0.0226
(10)
143.6'~R__T] (11)
The following data support this calculation. Contactless annealing of 600 °C for 7 days with X s = 2.2301 g resulted in a weight change of 0.0015 g, and the experimentally obtained flux was 2.05 x 10-12 mol cm -2 s. (The surface area, 3.22 cm2, was estimated using the density of as-grown AgGaSez single crystal, 5.67 g c m - 3. The sample shape was assumed to be cubic). The estimated flux using Eq. (11) was 1.96 x 10 -lz mot cm -a sec, which is very close to the experimental value. The temperature dependence of the flux is shown in Fig. 4. This, in combination with the out-diffusion of
N.H. Kim et al. / Materials Science and Eng#wering B.38 (1996) 229-2.35 -10.0
t~] - 1 1 . 0
o
-12.0
0.9
1.0
.
.
.
.
.
1.1
.
.
.
1.2
1/T(K -1) x lo ~ Fig. 4. Temperature dependence of the flux due owing to vapor transport. Flux owing to vapor transport increases with annealing temperature.
Ga2Se 3 from the crystal, predicts the kinetics of the contactless heat-treatment process. In addition, it enables us to predict an optimum annealing time once information about the annealing temperature and the density of the precipitate phase in the as-grown crystal is known.
4. Summary and conclusions The kinetics involved in the heat treatment process for eliminating precipitates in as-grown AgGaSe2 crystals have been analyzed for the case where Ag2Se is used as the annealing medium by the development of a chemical mass balance model. Heat treatment at two temperatures was studied; the low temperature case involved both contactless and contact annealing, while the higher temperature case involved only the contactless technique. Quantitative mass transport measurements for three different cases (1) contact annealing, (2) contactless annealing and (3) vacuum annealing without an annealing medium present, permitted us to decouple the diffusive transport component from the vapor transport component, and determine the kinetic differences between the contact and contactless cases. Diffusive transport was found to be significantly faster than vapor phase transport, and this explains why
235
contact annealing appears to be more effective than contactless annealing in eliminating precipitates. The chemical mass balance model and identification of the phases formed during the heat-treatment process, suggest that the mobile species which plays the dominant role in the elimination of the precipitated from asgrown AgGaS% crystals is Ga2S%. The basic mechanism and fundamental constants that control the vapor transport process during contactless heat treatment at high temperature have been determined. These, together with a diffusion model making use of the diffusivity measurements studied previously, comprise a reasonably complete quantitative understanding of the heat treatment process.
Acknowledgements This work was supported in part by DARPA, ARO, ONR, NASA and the National Science Foundation's NSF-MRL program through the Center for Materials Research at Stanford University.
References [1] J.L. Shay and J.H. Wemick, Ternary Chalcopyrite Semiconductors-Growth, Electronic Properties and Applications, Pergamon Press, 1975, Ch. I. [2] R.K. Route, R.S. Feigelson and R.J. Raymakers, J. C~yst. Growth, 24/25 (1974) 390. [3] J.C. Mikkelsen Jr., Mater. Res. Bull., I2 (1977) 497. [4] R.K. Route, R.S. Feigelson, R.J. Raymakers and M.M. Choy, J. Cryst. Growth, .33 (1976) 239. [5] R.S. Feigelson and R.K. Route, Proc. SHE, 567 (I985) 2. [6] R.S. Feigelson and R.K. Route, Optical Eng., 26 (I987) I13. [7] N.H. Kim, R.S. Feigelson and R.K. Route, J. Mater. Res., submitted for publication. [8] R.S. Feigelson and R.K. Route, Mater Res. Bull., 25 (1990) 1503. [9] G.W. Iseler, H. Kildal and N. Menyuk, Inst. Phys. Conf. Ser. No..35, (1977) 73. [10] N.B. Singh, R.H. Hopkins, R. Mazelsky and H.H. Dorman, Mater. Lett., (1986) 357. [I1] David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 72nd edn., CRC Press, 1991. [12] M. Knudsen, Ann. Phys., 47 (I915) 687.
g
ELSEVIER
Materials Science and Engineering B38 (1996) 229-235
Heat treatment studies on silver gallium diselenide (AgGaSe2) crystals Nam-Hun Kim a, Dong Hyuk Shin b, Roberts S. Feigelson ° ~Omega Division, Applied Materials, Santa Clara, CA 95054, USA bDepartment of Metallurgy and Materials Science, Hanyang University, Ansan, Kyunggi-Do, 425-791, South Korea °Department of Materials Science and Engineer#~g, Stanford University, Stanford, CA 94305, USA Received 13 April 1995
Abstract
Silver gallium diselenide (AgGaS%) is an important materiaI for nonIinear optical frequency generation in the infrared region. Crystals have been difficult to produce in high optical quality form because of the presence of precipitates in as-grown material. A post-growth heat treatment process has been developed to remove these precipitates and 'render the crystals usable for optical applications. However, the details of the chemical interdiffusion processes involved in this method have not been well understood. In this study, the heat treatment procedure was analyzed through mass transport measurements and phase identification by powder X-ray diffractometry. A chemical mass balance model, and how it relates to our current understanding of the phase equilibrium in the Ag2Se-GaaSe 3 pseudobinary system are presented. The estimated flux, based on Knudsen's equation, has enabled us to predict the optimum annealing time for a given temperature and crystal size. Keywords: Heat treatment; Silver gallium diselenides; Annealing
1. Introduction
AgGaSe2 crystallizes in the chalcopyrite structure with a space group I742d, and single crystals with high optical quality have important nonlinear infrared optical applications [1]. However, owing to an off-stoichiometric congruency, AgGaSe2 always grows slightly richer in Ga2Se3 than the stoichiometric composition, in accordance with the phase diagram shown in Fig. 1 [2,3]. This inevitably leads to the formation of Ga2Segrich precipitates upon cooling. These precipitates cause appreciable optical scattering in the near-infrared wavelength (0.73-2 /zm) region. The precipitates can be eliminated either by quenching or heat-treating the crystals in the presence of Ag2Se [4-6]. In the quenching technique, as-grown crystals are cooled rapidly from a temperature where they are within the single phase existence region, fi, to room temperature and metastable equilibrium. Although effective in eliminating the precipitates, quenching usually leads to cracking of the crystals. For this reason, the heat-treatment process [5,6], which causes less damage to the crystals, is preferred. In the heat treatment 0921-5107/96/$I5.00 © I 9 9 6 - Elsevier Science S.A. All rights reserved
process, AgzSe (approximately 0.5 tool.% ) serves as an annealing medium to compensate for the excess GazS% in as-grown material (Y-composition in Fig. 1). Typically, the AgzSe annealing medium is placed in direct contact with the crystals and heat treatment is carried out at 800 °C, well above the eutectic temperature (728 °C). In this temperature range, a liquid phase forms at the interface where the two materials touch as a result of chemical reaction. Owing to surface migration effects, a thin layer of Ag-rich material covers the entire surface of the as-grown crystals within a short time and excess Ga2Se3 is then eliminated from the bulk by solid-state diffusion [7]. The stoichiometric Y'-composition that is formed yields a clear material upon cooling because this composition is invariant with temperature. In the closely related compound, AgGaS2, the corresponding precipitate phase can be completely eliminated through a contactless heat treatment procedure in which the crystal does not make direct mechanical contact with the annealing medium. As in the heattreatment of AgCaS%, a thin layer of Ag-rich material resulting from a chemical reaction between the AgGaS2 crystal and the AgzS annealing medium also ends up
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covering the surface of the crystal, but in this case transport occurs through the vapor state. Excess GazS3 is then eliminated from the bulk by solid-state diffusion
[6-8]. In the case of igGaSe2, contactless heat-treatment reduces the density of precipitates but has not been found to eliminate them completely. Direct mechanical contact seems to be necessary to achieve their total elimination. However, the direct contact heat treatment also leads to fracturing of the crystals in the contact region if annealing is carried out above the eutectic temperature, where a liquid phase can form. This is owing to stresses caused by differential thermal expansion of the phases formed during cooling. (Annealing is not carried out at lower temperatures because the kinetics of the process are sluggish.) While the degree of cracking is usually less than that caused by quenching, it would be desirable to eliminate it completely. Several variations in the annealing technique have been reported, depending on whether or not there is contact between the crystal and annealing medium, or whether there is an annealing medium present at all [2-6,8-10]. Nonetheless, a systematic analysis of the heat treatment process has not yet been presented. Previously, analyses of the chemical reaction products and the condensed volatile species found on the ampoule walls for annealing temperatures in the temperature 500-800 °C range have revealed no significant differences between the contact and the contacttess cases [6,8]. Therefore, a chemical mass balance model has been developed to analyze the chemical reaction products and to quantify the chemical reaction kinetics between these two cases. This work complements a previous study on the kinetics of the heat treatment process that determined the chemical interdiffusion coefficients for the mobile species [7].
2. Experimental procedure AgGaS% single crystals were grown for use in the heat-treatment experiments using the bottom-seeded vertical Bridgman technique described elsewhere [6,8]. C-axis seeds, stoichiometric melts and growth rates of nominally 6 mm per day were used. Centimeter-size crystals, weighing in the region of 6-10 g were cut from the boules with a diamond saw and polished with alumina powder. Polycrystalline AgzSe used as the annealing medium was synthesized by melting silver and selenium shot (purity 6-9's and 5-9's) in a carboncoated, sealed quartz ampoule placed inside a rocking furnace at 950 °C for about 10 h. Prior to heat-treatment, all the crystals were cleaned and weighed with a microbalance to a precision of 10 - 4 g. Three different kinds of heat-treatment procedures were carried out using a resistance furnace and sealed
fused quartz ampoules that were vacuum sealed at 10 - 4 Torr or better. The first procedure was to anneal the AgGaS% test crystal in a vacuum without any annaling medium present. Vacuum annealing was carried out at 800 °C for 7 days. The second procedure involved annealing with the annealing medium not in contact with the test crystals. A neck in the quartz ampoules separated the test crystal from the AgzSe annealing media. Since only vapor transport was possible in this case, temperatures above 728 °C, the eutectic temperature, were used in some cases to maximize the rates of chemical reaction and vapor phase transport. Annealing was performed at 670 °C for 7 days, and at 800 °C for 2.5 days. The third type of annealing procedure involved direct contact between the test crystals and the annealing medium. The crystals were positioned vertically on top of the annealing media in order to ensure mechanical contact. The annealing temperature had to be maintained below the eutectic temperature (728 °C) to prevent the formation of a liquid phase, which would have complicated the problem of separating diffusive from vapor transport effects. After heat treatment, the ampoules were opened and the crystals carefully separated from the annealing media. The crystals were weighed using a microbalance, and analyzed using powder X-ray diffractometery. The chemical composition of the thin film which formed on the surfaces of many crystals heat-treated with an annealing medium present, was analyzed using a four circle X-ray diffractometer. /
90O
9O0
/
32 800,
8OO
.....
d
T(°C) .w'( 728
700
700
U
V =
AggGaSea + AgGaSea
10C z
0
Ag2Se
10
=
=
125
AgGaSea +
1
1
I
20
30
40
Z'
Z
50
Mole P e r c e n t
too
l
1
1
1
60
?0
80
90
Ga2Sea
101
GaaSea
Fig. 1. Ag2Se-GazS % pseudobinary phase diagram. Quenching follows a path ( Y - Z ) and annealing of the crystal with AgaSe follows a path (X- 1I). Since the liquid is involved in a path (Z- 10, contactless annealing can be done using that path, and contact annealing was done using a path (U-V) in this work.
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N,-H. Kim et al. / Materials Science and Engineer#zg B38 (i996) 229-235
Table 1 Low temperature annealing-weight changes and the resulting phases of the crystal and annealing medium for before and after annealing at 670 °C for 7 days Weight and species
Sample Annealing medium
Annealing condition
Weight(g) Species* Weight(g) Species*
Contactless case
Contact case
Before
After
Before
After
0.1751 I12+ 1711 2.9300 201
0.1740 112 2.9310 201 +916
0.175I 112+1711 2.9300 201
0.5443 112+916 2.5604 201 +916
* 112, 1711, 916 and 201 represent AgGaSe2, AgGa7Seli, AggGaSe6 and Ag2Se respectively.
3. Results and discussion
Table 1 and Table 2 summarize the weight changes and the phases found after low temperature (670 °C) heat-treatment with and without contact, and after high temperature heat-treatment (800 °C) without contact. All X-ray patterns corresponded to one or more of the phases found on the pseudobinary join, indicating that in the condensed phase, pseudobinary approximation is reasonably accurate. In some cases, a slight discrepancy existed between initial and final weights, owing, we concluded, to condensation of small amounts of material on the quartz ampoules. In no case did the condensed material on the quartz wall exceed 3% of the total mass transported during processing. The weight change of the AgGaSe2 crystals during vacuum annealing without the annealing media present was negligible as expected, since no condensed material was detected on the ampoule walls after processing. We analyzed the experimental results using a chemical mass balance procedure based upon the following assumptions: (a) The Ga2Ses-rich precipitates which form during the growth of AgGaSe2 have the composition AgGa7Sei1 in accordance with the phase equilibria first determined by Mikkelsen [3]. (b) When as-grown AgGaS% crystals containing precipitates are heated above the solvus, a solid solution Table 2 High temperature contactless annealing-weight changes and the resulting phases of the crystal and annealing medium for before and after annealing at 800°C for 2.5 days Weight and species
Annealing
Before
After
Sample
Weight(g) Species* Weight(g)
5.3427 112+1711 0.0710
5.3097 112 0.1029
Species*
201
I12+916
Annealing medium
* 112, 1711, 201 and 916 represent AgGaS%, AgGaTSeli, AggGaSe6 and Ag2Se respectively.
(fi) is formed, meaning that the precipitates dissolve in the crystal, in accordance with the modified phase equilibria shown in Fig. 1. The fl solid solution can be thought of as either AgGaSe2 with m tool.% of AgGa7Se11 in solution, or AgGaSe 2 with 3 m mol.% of Ga2Se3 in solution: AgGaSe2 + mAgGa7Sell = (1 + m)AgGaSe2 + 3 m Ga2Se 3
(1)
(c) During annealing, mass is transported through the vapor phase from the crystal to the annealing medium. However, it is not known what the species are. Several possibilities include Ga2Se3, Ga2Se, GaSe and G a + S e atoms [11]. After annealing, a small amount of reddish-black material was found deposited on the ampoule walls. X-ray analysis failed to identify its exact composition. From previous research and current annealing experiments, it is clear that the AgGa7Sezl precipitates in as-grown crystals are eliminated while the crystals lose weight, as the mass transport data in Table 1 and Table 2 show [8]. This means that the weight loss of the crystal is directly related to the combination of two Ga atoms and three Se atoms. Thus, even though the exact transporting species is not known, we can assume that the weight change of the crystal before and after annealing is owing to a unit with composition 2Ga:3Se which we refer to as Ga2S%. (d) The concentration of the precipitate phase in as-grown crystals is estimated from optical measurements to be 0.5 mol.%. (e) There is no solid solubility between Ag2Se and AggGaSe6, or between AggGaSe6 and AgGaSe2, consistent with the modified phase diagram, Fig. 1. (f) When diffusive transport occurs during contact annealing, the number of moles of Ga2Se3 vapor transported to the annealing medium is negligible as compared with the number of moles of Ag2Se3 transported by solid-state diffusion to the crystal. This has been demonstrated clearly in our diffusivity measurements cited previously [7].
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3.1. Low temperature studies Previous research on AgGaSe2 and AgGaS2 has shown that the contact annealing process is significantly faster in reducing precipitate densities than contactless annealing [6,8]. But, as mentioned before, a liquid phase forms at the junction between the crystal and the annealing medium, and this makes it difficult to separate the crystal from the annealing medium in order to measure the resulting weight change and decouple the vapor transport component from the diffusive transport component. Thus, in both the contact annealing case and the contactless case as well, a temperature lower than the eutectic temperature, 670 °C, was used to prevent the formation of a liquid phase. Early research studies [6,8], in which the relative quantities of annealing medium used were in the 0.51.5 mol.% range, resulted in the annealing medium being completely transformed into AgGaSea by the time the heat-treatment process was complete, similar to the experimental results for AgGaS2. This is not true in the general case. The final composition of the crystal and remaining annealing medium depend upon the annealing temperaure, the annealing time, the initial composition of the crystal and the composition and initial relative weight of the annealing medium. In order to determine the kinetics of the heat treatment process, an analysis was carried out for the case where the temperature is fixed at 670 °C and the weights of the crystal and the annealing medium are given in Table 1. Case L When the amount of the annealing medium is just sufficient to compensate for the excess (AgGaTSeix) precipitate phase. From the crystal (c), the excess GazSe3 out-diffuses and volatilizes as follows: AgGaSe2(c) + AgGa7Sei 1(c) = AgGaSe2(c) ÷ Ga2Se3~"
(2)
At the surface of the annealing medium (m), the vapor transported GazSe3 reacts with Ag2Se to form AgGaSe: as follows: Ag2Se(m) + GazSe3(m) = 2AgGaSez(m)
annealing medium
annealing medium
(3)
Case H. When the amount of the annealing medium is more than sufficient to compensate for the excess (AgGavSe11) precipitate phase. (In our experiments the weight of the crystal was made smaller than that of the annealing medium, which is opposite from the usual case during the heat-treatment. This modification was made to increase resolution by enhancing the mass transport effects as much as possible.) The contactless annealing case was analyzed first. For contactless annealing, four parameters (t, m, q and j) are required to analyze the transport processes
crystal
jc
(a)
(b) annealing medium c~'ystal
(j-27m)C +
6zE
(c) annealing medium
~
G
~mD
ann°altng medium
t
crystal
cry
(k+n)C
} (z+q)B
I 3q0*-l(s)
(d)
annealing medium (n-27m)C +
6mE
armealinffmedium crystal [[4(t*m)÷~laokll4l h +
[Ik4qlla] S
(f)
(¢)
Fig. 2. Schematic representation of low temperature heat ~reatment processing. (a), (b), and (c) show the initial stage, mass transfer, and the final stage, respectivelyfor contactless annealing, while (d), (e), (f') and (g) show the initial stage, mass transfer, and intermediate stage, and final equilibrium stage for contaetless annealing. The symbols used are as follows: t: number of moles of AgGaS%; m: number of moles of AgGavSe~ resulting in vapor transport; q: number of moles of AgGaTSe~ reacted with diffused Ag2Se;j: number of moles of initial AgaSe (=n + k); n: number of moles of Ag2Se reacted with vapor transported GazS%; k: number of moles of Ag2Se diffused through the crystal; A: molecular weight of AgGaS%; B: molecular weight of AgGa7Se~; C: molecular weight of Ag'2Se; D: molecular weight of Ga2Se3; E: molecular weight of AggGaSea. as illustrated in Figs. 2(a)-(c). Here, the elimination of the precipitate phase is not allowed to go to completion. Thus, in the crystal, q moles of the precipitate phase still remains after annealing. Since the concentration of the precipitate in as-grown crystals has been estimated to be 0.5 mol.%,
( m + q ) / ( t + m + q ) = 5 x 10 .3
(4)
Table 1 shows the actual weight loss of the annealed crystal after contactless annealing at 670 °C. The data clearly indicate that GazS% moved from the crystal to the annealing medium (which gained a corresponding amount of weight) via vapor transport. The concentration of the precipitate phase after contactless annealing, which is expressed as q/(t + re+q), was found to be 0.3 tool.%. This implies
N.-H. Kim et al. / Materials Science and Engineering B38 (1996) 229-235
that 40% of the precipitate phase in the as-grown crystal was eliminated. For the contact annealing case, three reaction mechanisms must be considered. The first involves vapor phase transport since Ga2S% vapor is transported toward the Ag2Se annealing medium, where compound formation through chemical reaction takes place. The second involves solid-state diffusive transport where Ag2Se diffuses into the crystal. The third involves solid-state diffusive transport where Ga2S% out-diffuses from the crystal and reacts with the Ag2Se annealing medium. However, we have assumed that the concentration of this third mechanism is negligible because of the low effective diffusivities for Ag + measured in a previous study [3,7]. The first two mechanisms have their own rate determining step, and which one predominates depends mainly on the temperature. Five parameters (t, m, q, k and n) are required to analyze the transport process in the contact annealing case, as illustrated in Figs. 2(d)-(f). Since under our experimental conditions, 3q moles of GazS% are much smaller than k moles of AgzSe, all the GazSe3 is transformed into the intermetallic compound Ag9GaSe 6 as the annealing time increases. The concentration of precipitates after contact annealing, expressed as q/(t + m + 4q + k), is found to be 0.08 mol.%. This implies that 84% of the precipitates in as-grown crystals were eliminated. Comparing this case with the previous contactless case, it can be seen clearly that contact annealing is a more efficient method than contactless annealing for eliminating precipitates. Our previously cited diffusivity measurements on chemical interdiffusion between AgGaSe2 and Ag2Se indicated that in this system, diffusion occurs as a cooperative phenomena in which the species move as units having molecular stoichiometry, such as AgzSe and Ga2Se3, in order to preserve electrical neutrality [7]. Furthermore, it was found that the effective diffusivity of Ag2Se into AgGaSe2 is far too low to account for the experimentally determined rate at which the precipitate phase is eliminated from asgrown crystals. The annealing process cannot, therefore, involve diffusion of the AggGaSe6 phase into the AgGaS% phase. We concluded instead that elimination of the precipitate phase most likely occurs by out-diffusion of excess GazSe3 from the crystal. The phases found in both the crystal and the annealing medium as a result of heat-treatment can be compared with what we would expect by applying the lever rule to the Ag2Se-GazS% phase diagram in Fig. 1. Analysis of the possible phases after contact annealing shows that the composition of the crystal after contact annealing for our particular experiment was approximately 40 tool.% AgGaSe2 and 60 tool.%
233
AggGaSe6, and that the final composition of the annealing medium was approximately 99.93 tool.% Ag2Se and 0.07 tool.% AggGaSe6. This particular experiment ended up with the "crystal" far to the left of the b phase boundary, in the middle of the twophase AggGaSe6 + AgGaSe2 system. This was owing to the unusual mass ratio between the test crystal and the annealing medium. Normally, it is desirable that the "crystal" equilibrate as close as possible to the left hand /7 phase boundary to minimize damage caused by formation of the AggGaSe6 phase. From these low temperature heat-treatment studies, we deduce the following: (a) The diffusive transport process can be decoupled from the vapor transport process. (b) The rate at which precipitates are eliminated during contact annealing is much faster than for contactless annealing because the former involves an additional diffusive transport component. Furthermore, the diffusive term becomes predominant as the annealing temperature increases because diffusive transport has an e x p ( - b / T ) dependence, while vapor transport has an e x p ( - a / T ) / T m dependence, where a and b are constants. (c) The annealing processes can be controlled by varying the annealing temperature, annealing time and the amount of the annealing medium. (d) It is, in principle, possible to modify the heattreatment processes by changing the annealing medium. For example, using AggGaSe6 as an annealing medium would prevent continued reaction between the annealing medium and the test crystal once the precipitate phase had been totally eliminated. It might also enhance the rate at which precipitates are eliminated. .3.2. High temperature studies As we indicated earlier, analysis of the transport phenomena occurring during contact annealing is not possible at temperatures higher than the eutectic temperature because a liquid phase forms, this complicates the problem of separating the annealing medium from the test crystal and obtaining accurate weight gain/loss data. It is relatively easy to analyze the transport phenomena at higher temperature in the contactless annealing case, however, since vapor transport is the only mass transport process occuring. Higher temperatures have the added benefit of enhancing the vapor transport process, as indicated. However, while the precipitate phase can, in principle, be eliminated using the contactless annealing process with Ag2Se as the annealing medium, the rate of elimination of the precipitat phase is known to be slow [8] and complete removal has never, to our knowledge, been demonstrated under controlled conditions.
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N.-H. Kim et al. / Materials Science and Engineering B38 (1996) 229-235
Four steps are involved in the.high temperature, contactless annealing case: (i) the dissolution of AgGa7Sex1 precipitates into the /? solid solution, (ii) out-diffusion of GazSe> (iii) transport of GaaSe3 through the vapor phase, and (iv) a chemical reaction between GazSe3 and AgzSe in the annealing medium. The overall reaction rate at high temperature depends on the slowest step. Fig. 3 shows a schematic diagram of the high temperature annealing process. Four parameters (t, m, q and j) are again required to determine the mass transport. This case bears closer resemblance to the commercially used process since the crystal mass is significantly larger than the annealing medium and the annealing temperature is well above the eutectic (800 °C). (There is no direct contact, however.) The chemical reaction between Ga2Se3 vapor and the Ag2Se annealing medium is considered to be spontaneous and irreversible. The rate at which the precipitate phase is eliminated depends, therefore, mainly on outdiffusion of Ga2Se3 and the flux through the vapor phase. The overall reaction between the annealing medium of the GaaSe3(v) follows the AgzSe-Ga2Se3 phase equilibria shown in Fig. 1, and depends on the relative magnitude of j and m. The concentration of the precipitate phase in the crystal after this particular experiment is estimated to have been 0.3 mol.%, and we conclude that 40% of the precipitates had been eliminated. This is consistent with experimental findings in which measurable amounts of the precipitate phase were found routinely in test crystals even after many weeks of heat-treatment. The expected reaction products, AgGaS% and AggGaSe6, were detected in the annealing medium after completion by powder X-ray diffraction analysis. The ratio of AgGaSe2 to AggGaSe6 in the annealing medium, apcrystal tA +
proximately 4:1, was different from that calculated using the lever rule and the phase diagram shown in Fig. 1. One possible reason for the discrepancy might be that this system was not yet in thermodynamic equilibrium. The temperature dependence of the flux owing to vapor transport can be also determined. The evaporation reaction can be expressed as follows: Ga2Se3ts) = Ga2Se3(v?
(5)
A G = A G O+ R T In Po,~2s~3(v~
(6)
At equilibrium, A G O= - R T In PG,2s~3(v)
The flux J tool cm -2 sec- l, based on the Knudsen's equation [12] can be expressed as follows:
1 dn~ .P,o: i J = -S d---[= x / 2 ~ M ~ R T '
where S is the surface area of a crystal, n; is the number of moles transported in the form of vapor, Pi is the partial vapor pressure of the ith species in the vapor, cq is the evaporation constant ( < 1), M t is the molecular weight of the ith species in grams, R is the gas constant in J m o l - a K, and T is the absolute temperature. Here i represents GazSe3 and ~i is a constant close to one. From Eqs. (7) and (8), the flux J can be expressed as follows: Kexp( J--
AH°~ RT/
,/T
where A H °, is the standard enthalpy of vaporization in kJ mol-1 and K is a constant. A H °, and K can be obtained from the data shown in Table 1 and Table 2:
(t+m)A
Thus the flux owing to vapor transport can be expressed as:
qB
(m+q)B
0.0226exp( (b)
(a) crystal medium [(27m-j)/4] A +
qB
(9)
A H ° = 143.6 kJ mol- t
+
+
(8)
crystal
medium
(t+m)A
(7)
[(j-3m)/41E
(c) Fig. 3. A schematic representation of the high temperature heat treatment process: (a), (b), and (c) show the initial stage, mass transfer, and final stage, respectively. The crystal is much larger than the medium and this situation is close to the actual heat treatment process.
J--
~T
and
K = 0.0226
(10)
143.6'~R__T] (11)
The following data support this calculation. Contactless annealing of 600 °C for 7 days with X s = 2.2301 g resulted in a weight change of 0.0015 g, and the experimentally obtained flux was 2.05 x 10-12 mol cm -2 s. (The surface area, 3.22 cm2, was estimated using the density of as-grown AgGaSez single crystal, 5.67 g c m - 3. The sample shape was assumed to be cubic). The estimated flux using Eq. (11) was 1.96 x 10 -lz mot cm -a sec, which is very close to the experimental value. The temperature dependence of the flux is shown in Fig. 4. This, in combination with the out-diffusion of
N.H. Kim et al. / Materials Science and Eng#wering B.38 (1996) 229-2.35 -10.0
t~] - 1 1 . 0
o
-12.0
0.9
1.0
.
.
.
.
.
1.1
.
.
.
1.2
1/T(K -1) x lo ~ Fig. 4. Temperature dependence of the flux due owing to vapor transport. Flux owing to vapor transport increases with annealing temperature.
Ga2Se 3 from the crystal, predicts the kinetics of the contactless heat-treatment process. In addition, it enables us to predict an optimum annealing time once information about the annealing temperature and the density of the precipitate phase in the as-grown crystal is known.
4. Summary and conclusions The kinetics involved in the heat treatment process for eliminating precipitates in as-grown AgGaSe2 crystals have been analyzed for the case where Ag2Se is used as the annealing medium by the development of a chemical mass balance model. Heat treatment at two temperatures was studied; the low temperature case involved both contactless and contact annealing, while the higher temperature case involved only the contactless technique. Quantitative mass transport measurements for three different cases (1) contact annealing, (2) contactless annealing and (3) vacuum annealing without an annealing medium present, permitted us to decouple the diffusive transport component from the vapor transport component, and determine the kinetic differences between the contact and contactless cases. Diffusive transport was found to be significantly faster than vapor phase transport, and this explains why
235
contact annealing appears to be more effective than contactless annealing in eliminating precipitates. The chemical mass balance model and identification of the phases formed during the heat-treatment process, suggest that the mobile species which plays the dominant role in the elimination of the precipitated from asgrown AgGaS% crystals is Ga2S%. The basic mechanism and fundamental constants that control the vapor transport process during contactless heat treatment at high temperature have been determined. These, together with a diffusion model making use of the diffusivity measurements studied previously, comprise a reasonably complete quantitative understanding of the heat treatment process.
Acknowledgements This work was supported in part by DARPA, ARO, ONR, NASA and the National Science Foundation's NSF-MRL program through the Center for Materials Research at Stanford University.
References [1] J.L. Shay and J.H. Wemick, Ternary Chalcopyrite Semiconductors-Growth, Electronic Properties and Applications, Pergamon Press, 1975, Ch. I. [2] R.K. Route, R.S. Feigelson and R.J. Raymakers, J. C~yst. Growth, 24/25 (1974) 390. [3] J.C. Mikkelsen Jr., Mater. Res. Bull., I2 (1977) 497. [4] R.K. Route, R.S. Feigelson, R.J. Raymakers and M.M. Choy, J. Cryst. Growth, .33 (1976) 239. [5] R.S. Feigelson and R.K. Route, Proc. SHE, 567 (I985) 2. [6] R.S. Feigelson and R.K. Route, Optical Eng., 26 (I987) I13. [7] N.H. Kim, R.S. Feigelson and R.K. Route, J. Mater. Res., submitted for publication. [8] R.S. Feigelson and R.K. Route, Mater Res. Bull., 25 (1990) 1503. [9] G.W. Iseler, H. Kildal and N. Menyuk, Inst. Phys. Conf. Ser. No..35, (1977) 73. [10] N.B. Singh, R.H. Hopkins, R. Mazelsky and H.H. Dorman, Mater. Lett., (1986) 357. [I1] David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 72nd edn., CRC Press, 1991. [12] M. Knudsen, Ann. Phys., 47 (I915) 687.