Selenium solubility in solid zinc selenide

ISSN 0020-1685, Inorganic Materials, 2016, Vol. 52, No. 7, pp. 643–649. © Pleiades Publishing, Ltd., 2016. Original Russian Text © Khanh Cong Tran, E.N. Mozhevitina, K.A. Potapova, B.N. Levonovich, I.Ch. Avetissov, 2016, published in Neorganicheskie Materialy, 2016, Vol. 52, No. 7, pp. 699–705. Selenium Solubility in Solid Zinc Selenide Khanh Cong Tran, E. N. Mozhevitina, K. A. Potapova, B. N. Levonovich, and I. Ch. Avetissov Mendeleev University of Chemical Technology, Miusskaya pl. 9, Moscow, 125047 Russia e-mail: aich@rctu.ru Received May 5, 2015; in final form, November 12, 2015 Abstract—Selenium solubility in solid s-ZnSe ( F 43m ) under mono- and divariant equilibrium conditions has been determined by a direct physicochemical method in the temperature range 850–1173 K. The maximum concentration of excess selenium is 3.76 × 10–4 mol of excess Se per mole of ZnSe at 1173 K. The homogeneity range of the s-ZnSe phase has been shown to be characterized by retrograde solubility at its Se-rich phase boundary. A model has been proposed for defect formation in nonstoichiometric s-ZnSe at temperatures in the range 963–1173 K and pSe 2 pressures in the range 1.05 × 10 4 to 5.01 × 105 Pa according to which the dissolution of excess Se is accompanied by the formation of electrically neutral associated vacancy defects in the zinc sublattice. Keywords: zinc selenide, nonstoichiometry, selenium solubility, point defects DOI: 10.1134/S0020168516070037 INTRODUCTION Owing to its unique physicochemical properties, zinc selenide has found wide application in optoelectronic devices, in particular as a substrate material for blue light-emitting diodes (LEDs); in X-ray detectors; and in the fabrication of optical components, such as windows, lenses, mirrors, and prisms, operating in the IR spectral region in specialized optical systems and CO2 laser optics. Structure-sensitive properties of the materials in question are determined by both doping and native point defects. The presence of native point defects, due to thermal disorder and deviations of the composition of phases from stoichiometry [1], is thermodynamically unavoidable at temperatures above absolute zero. Availability of reliable information about the pi– T–x phase diagram of the Zn–Se system, including information about the homogeneity range of zinc selenide, is a necessary condition for successful development of technologies of poly- and single crystals with controlled composition. Despite the extensive studies of zinc selenide due to its practical importance, no consistent data on the homogeneity range of ZnSe are available in the literature. The wurtzite–sphalerite (3C–2H) polymorphic transformation, which occurs near the maximum melting point of zinc selenide, is still unclear in a number of aspects [2]. A scheme of this transformation was proposed by Okada and Kawanaka [3] based on differential thermal analysis (DTA) results. In this study, we made an attempt to clarify the question of selenium solubility in solid ZnSe and locate the homogeneity range of zinc selenide by a direct physicochemical method. EXPERIMENTAL Analysis of the purity of zinc selenide samples. To study the nonstoichiometry of ZnSe, we used s-ZnSe powder with an average particle size of 50 ± 20 μm. The starting ZnSe powder (ELMA, 5N, sphalerite structure) was further purified by vacuum resublimation. The impurity composition of the samples was determined by inductively coupled plasma mass spectrometry (ICP-MS) with a NexION 300D ICP-MS system (PerkinElmer, USA) and by secondary ion mass spectrometry (SIMS) with a MiniSIMS system (Millbrook, UK) under conditions meeting the requirements of the Russian Federation State Standard GOST 12997-76. The samples were prepared in a laboratory room that met the ISO 7 cleanroom requirements. The measurements were performed by the Total Quant method using a collision cell in kinetic energy discrimination (KED) mode in order to eliminate spectral interferences. According to the measurement results, the purity of the resublimed material (with allowance for gas-forming impurities) was 99.9991+ wt % (Fig. 1). Procedure for the synthesis of nonstoichiometric sZnSe samples. Nonstoichiometric s-ZnSe samples were synthesized in silica glass ampules. The ampules were produced using extrapure-grade silica tubes 643 644 KHANH CONG TRAN et al. С, wt % 10–2 10–3 10–4 10–5 10–6 10–7 Resublimed s-ZnSe, 99.9991 wt % Starting s-ZnSe powder, 99.997 wt % Be C O Na Al P Cl Ca Ti Cr Fe Ni Ga As Rb Y NbRu Pd Cd Sn Te Cs La Pr SmGdDy Er Yb Hf W Os Pt Hg Pb Th Fig. 1. Impurity analysis data for the s-ZnSe samples. (Russian Federation Purity Standard TU 5932-0I400288679-01) having a smooth surface and free of visible flaws, 10–12 mm in inner diameter. To prevent oxygen diffusion across the walls of the ampules at synthesis temperatures above 1150 K, the inner surface of the ampules was graphitized through the pyrolysis of extrapure-grade acetone (Company Specification STP TU COMP 2-001-06). s-ZnSe powder samples and elemental selenium (Russian Federation Purity Standard TU 6-09-252177) were loaded into an ampule through a silica funnel. Next, the ampules containing the s-ZnSe samples were pumped down to a residual gas pressure of 10–2 Pa or lower and hermetically sealed. High-temperature annealings of the s-ZnSe samples were carried out under monovariant (Ss-ZnSeL(Se)V) and divariant (Ss-ZnSeV) equilibrium conditions (Fig. 2) in a two-zone resistance furnace with a controlled temperature profile and 1-K temperature stability, and were followed by the “quenching” of the high-temperature equilibrium reached [4]. To prevent the liquid phase from reaching the sample being synthesized when the process was carried out under Ss-ZnSeL(Se)V monovariant equilibrium conditions, the sample was spatially isolated from the heterophase mixture that determined the monovariant equilibrium conditions. Superheating the s-ZnSe sample to 2–5 K above the temperature of the monovariant system did not cause its composition to differ significantly from the true equilibrium value [4]. Under Ss-ZnSeV divariant equilibrium conditions, the addition of an inert gas to a quasi-closed system helps to equalize the selenium vapor partial pressure over the pure Se component and that over the ZnSe compound [1]. To evaluate the vapor pressure over solid s-ZnSe, we proceeded from mechanical stability of a closed system, used reference data on the composition and vapor pressure of various selenium molecules [5] and the dissociation constant of ZnSe, and solved Eq. (1) for pSe 2 : 8   12 (ki pSe 2 ) 2/ i   k diss pSe 2 + pSe 2 +   i =1, i ≠ 2  T1 8   0l pSe =  , i   i =1 T2 ∑ (1) ∑ where kdiss is the dissociation constant of solid zinc selenide according to the reaction ZnSes → Zn v + 1 Sev2 2 0l [6], pSe 2 is the partial pressure of the i-th molecular selenium species in the vapor phase over pure liquid selenium at temperature T2, and ki is the constant of equilibrium between the i-th molecular selenium species and Se2 molecules in the vapor phase at temperature T1. Determination of the excess component concentration. The concentration of excess components in the “quenched” s-ZnSe samples was determined by an extraction method. The basic physicochemical principles of the method were described in detail by Avetissov et al. [7]. The method builds on the vacuum extraction of the excess component from solid ZnSe into the vapor phase in a temperature gradient, transfer of the vapor into the “cold” part of the ampule, vapor condensation on the ampule walls, and subsequent determination of the condensate composition by chemical analysis. We experimentally determined conditions that ensured a detection limit for excess selenium at a level of 4 × 10–8 mol of excess Se per mole of ZnSe: TZnSe = 773 K, Tcondensate = 500 K, and extraction time of 65 h. After annealing, the ampule was cooled and cut, the condensate was dissolved in extrapure-grade nitric acid (Russian Federation Standard GOST 11125-84), and the composition of the condensate was determined quantitatively by ICP-MS with a selenium detection limit of 1 × 10–8 g/mL and zinc detection limit of 2 × 10–8 g/mL. INORGANIC MATERIALS Vol. 52 No. 7 2016 SELENIUM SOLUBILITY IN SOLID ZINC SELENIDE 645 log pSe2 log pSe2 V 0l pSe 2 sZn Se L -Z nS eL V 0l pSe 2 0s pSe 2 S Ss 0s pSe 2 Ss -Z nS e Ss = -Z nS e V 1/T T1 T2 = V T1 T2 1/T Ss-ZnSe + LSe T ZnSes ∆T ≃ 5K lg p Sel ptotal рinert gas pSe2 T2 T1 l Ss-ZnSe pZn Fig. 2. Schematics illustrating the synthesis of a nonstoichiometric s-ZnSe phase under Ss-ZnSeL(Se)V monovariant (left panels) and Ss-ZnSeV divariant (right panels) equilibrium conditions. RESULTS AND DISCUSSION Nonstoichiometry can be quantified in a great diversity of ways [7]. In this study, the superstoichiometric (excess) selenium content of s-ZnSe was calculated as ex X Se = mSe M Se − mZn M Zn , mZnSe M ZnSe where MSe, MZn, and MZnSe are the molecular weights of zinc, selenium, and zinc selenide, respectively; mZnSe is the weight of the nonstoichiometric s-ZnSe sample; and mZn and mSe are the weights of the zinc and selenium in the condensate after the completion of the extraction process, respectively. The results obtained by determining the phase boundaries of s-ZnSe under Ss-ZnSeL(Se)V monovariant equilibrium conditions in the temperature range 850– 1173 K (Table 1) demonstrate that, as the temperature is raised from 850 to 1173 K, the excess selenium concentration increases by more than a factor of 7: from (5.29 ± 0.18) × 10–5 to (37.65 ± 0.87) × 10–5 mol of excess Se per mole of ZnSe. INORGANIC MATERIALS Vol. 52 No. 7 2016 The homogeneity range of ZnSe was shown to include its stoichiometric composition. The solidus has a retrograde character at both the Zn-rich [2] and Se-rich phase boundaries of zinc selenide (Fig. 3). The solubility of excess selenium in zinc selenide was studied as a function of selenium partial pressure, log XSe = f( pSe 2 ), using s-ZnSe samples synthesized under Ss-ZnSeV divariant equilibrium conditions at temperatures of 963, 1078, and 1173 K (Table 2). m M Se − mZn M Zn meas calc In Table 2, X Se = Se , and X Se = mZnSe M ZnSe k 2n[(V 2n )×2n ] is the nonstoichiometry value calculated by Eq. (3) (see below). In the isothermal solubility curves for Se in s-ZnSe (Fig. 4), the data points at the maximum pressures max characterize the solubility of excess selenium pSe 2 under Ss-ZnSeL(Se)V monovariant equilibrium conditions. We failed to measure the concentration of free charge carriers in “quenched” single-crystal samples synthesized in parallel with the powder samples at a ∑ n =1 646 KHANH CONG TRAN et al. Table 1. Deviation from stoichiometry in nonstoichiometric s-ZnSe samples synthesized under Ss-ZnSeL(Se)V monovariant equilibrium conditions T, K Time, h mZnSe, g mZn, μg synthesis 1173 1127 1078 977 879 850 120 120 144 144 144 144 mSe, μg analysis 0.8626 1.4694 1.6167 0.7782 0.8429 1.2463 detection limit of 1012 cm–3 in our electrical measurements, which corresponds to an excess selenium concentration at a level of 10–11 mol of excess Se per mole of ZnSe. This leads us to conclude that, at temperatures from 963 to 1173 K and selenium pressures pSe 2 = 1.05 × 10 4 to 5.01 × 105 Pa, Se dissolution in nonstoichiometric s-ZnSe results in predominant formation of electrically neutral defects. This conclusion is consistent with current views of defect formation in ex X Se × 10 5, mol of excess Se per mole of ZnSe 1.43 ± 0.03 179.36 ± 4.15 37.65 ± 0.87 0.38 ± 0.01 0.40 ± 0.03 0.11 ± 0.02 0.14 ± 0.04 0.10 ± 0.03 91.69 ± 2.27 84.08 ± 3.19 31.13 ± 0.95 29.21 ± 1.25 36.18 ± 1.53 11.40 ± 0.28 9.45 ± 0.36 7.28 ± 0.22 6.30 ± 0.26 5.29 ± 0.18 undoped zinc selenide [11]. By analogy with other II– VI compounds [12], we assume that, in the case of selenium dissolution in s-ZnSe, defect formation most likely follows the vacancy mechanism represented by the reaction scheme × v × n Se 2 → 2n Se Se + (V Zn )2n, K (V × Zn ) 2 n = [(V Zn )×2n ] , n pSe 2 (2) Temperature, K w-ZnSe 1700 1700 1500 1500 1300 1300 s-ZnSe 1100 1100 900 900 1 700 2 3 4 10–3 10–4 10–5 10–6 10–7 XZn, mol of excess Zn per mole of ZnSe δ=0 10–6 10–5 10–4 10–3 XSe, mol of excess Se per mole of ZnSe 700 Fig. 3. Homogeneity range of zinc selenide and assumed scheme of the 3C–2H polymorphic transformation [3]: (1) this work, (2) [8], (3) [9], (4) [10]. INORGANIC MATERIALS Vol. 52 No. 7 2016 Table 2. Solubility of excess selenium in s-ZnSe under Ss-ZnSeV divariant equilibrium conditions meas X Se × 10 6 mZn, μg calc X Se × 10 6 [(V Zn )×2 × 10 6 ] [(V Zn )×4 × 1011] [(V Zn )×8 ] mSe, μg meas X Se calc − X Se calc mol of excess Se per mole of ZnSe Vol. 52 1.73 1.1275 0.29 ± 0.02 3.46 ± 0.19 5.04 ± 0.27 2.39 1.2317 0.44 ± 0.02 6.90 ± 0.41 9.45 ± 0.56 2.75 0.7147 0.33 ± 0.03 9.71 ± 0.69 23.8 ± 1.6 5.01 0.8626 1.43 ± 0.03 179.36 ± 4.15 376.5 ± 8.7 0.104 1.0123 2.70 ± 0.10 4.90 ± 0.50 2.96 ± 0.50 2.99 0.168 1.0561 3.57 ± 0.14 6.73 ± 0.51 4.19 ± 0.59 0.168 1.4674 3.35 ± 0.16 8.89 ± 1.62 6.04 ± 1.78 0.376 1.2174 2.91 ± 0.12 15.42 ± 0.91 17.9 ± 1.2 0.509 1.0954 3.28 ± 0.08 15.26 ± 1.14 1.610 1.6167 0.40 ± 0.03 0.117 1.0163 0.188 5.57 × 10–7 11.6 16.0 1.92 2.01 × 10–6 –69.9 28.1 2.54 3.52 × 10–6 –18.2 8.45 3.89 × 10–5 17.2 1.50 4.61 × 10–11 –1.06 4.82 2.41 3.11 × 10–10 –15.1 4.82 2.41 3.11 × 10–10 20.2 10.8 5.39 7.76 × 10–9 39.4 18.9 ± 1.7 14.8 7.29 2.60 × 10–8 21.6 84.08 ± 3.19 94.5 ± 3.6 66.7 2.30 2.59 × 10–6 29.4 0.12 ± 0.02 8.62 ± 0.50 15.2 ± 0.8 15.8 7.91 –3.83 1.2388 3.49 ± 0.28 21.80 ± 0.35 26.0 ± 0.2 25.4 12.7 2.07 0.266 1.0312 0.15 ± 0.02 21.45 ± 0.38 37.7 ± 0.6 36.0 18.0 4.70 0.298 1.1401 0.21 ± 0.05 28.95 ± 0.52 46.0 ± 0.7 40.3 20.1 12.4 0.557 0.7782 0.41 ± 0.04 30.48 ± 0.41 70.5 ± 0.9 75.3 37.7 –6.83 1173 No. 7 311 2016 1078 963 647 1.01 4.46 ,% X Se SELENIUM SOLUBILITY IN SOLID ZINC SELENIDE INORGANIC MATERIALS TZnSe, K pSe 2 , mZnSe, g Pa × 10–5 log XSe [mol of excess Se per mole of ZnSe] 648 KHANH CONG TRAN et al. associates of two, four, and eight vacancies. The degree of vacancy association was found to rise with increasing temperature and increasing selenium vapor partial pressure. To ensure an adequate description of a (V Zn )×2 defect associate, we determined basic values of the enthalpy and entropy of its formation ( Δ H (V )× = –116.4 kJ/mol and Δ S (V )× = Zn 2 Zn 2 290.6 J/(mol K)) and increments that determine the increase in enthalpy and entropy with increasing associate size (δh = –116.4 kJ/mol and δs = 515.5 J/(mol K)) using the equations –3.0 1173 K 1078 K 963 K –3.5 –4.0 –4.5 –5.0 –5.5 –6.0 4.0 4.2 4.4 4.6 4.8 5.0 5.2 log pSe2 [Pа] 5.4 5.6 5.8 Fig. 4. Isothermal solubility of excess selenium in zinc selenide as a function of selenium partial pressure. The data points represent the experimental data and the solid lines represent calculation by Eq. (3). where n is 1/2, 1, 2, 3, or 4 according to quasichemical defect formation theory [13] and selenium vapor composition [5]. ex The excess selenium concentration X Se in s-ZnSe is given by k ex X Se = ∑( p ni Se 2 exp i =1 (ΔRTH + ΔRS )). i i (3) Each term on the right-hand side of Eq. (3) determines the concentration of vacancy defects with the i-th degree of association. As a crystalline phase approaches its maximum melting point, such vacancy associates (clusters) lead to complete disintegration of the crystal and, eventually, to its melting. This hypothesis was first put forward by Frenkel [14] and is supported by increasing experimental evidence provided by studies of modern nonstoichiometric phases: a variety of phases have been reported to have an anomalously broad homogeneity range in the immediate vicinity of their maximum melting point. Analysis of the present data on selenium solubility in ZnSe indicates that reaction (2) is exothermic. We were able to adequately describe all of the data with a 17% average relative uncertainty in excess selenium concentration by taking into account the formation of + δ h n − 1, n (4) n − 1. Δ S n = Δ S (V )× + δ S Zn 2 n The increments are not directly proportional to the associate size but follow an n − 1 law, with increasing n decrease as the degree of association, n, increases (see Eq. (2)). The present experimental data can be adequately described under the assumption that, with increasing temperature, the cluster size, or the degree of vacancy association, increases (Fig. 4, Table 3). This means that, with increasing temperature, the degree of disorder in the crystals increases, which is consistent with Frenkel’s hypothesis [14] that disordering of crystals follows a vacancy mechanism as their melting point is approached. Note that an approach to melting is here taken to mean not only a rise in temperature but also a displacement of the system from divariant equilibrium to monovariant one. This is particularly clear at T = 1173 K, where increasing the selenium vapor pressure and bringing the system closer to monovariant equilibrium causes associates of eight defects (n = 4) to prevail (see Table 3). Δ H n = Δ H (V × Zn ) 2 CONCLUSIONS The present results demonstrate that the homogeneity range of ZnSe includes its stoichiometric composition in the temperature range 850–1173 K. The solidus line has a retrograde character at both the Znrich and Se-rich phase boundaries. Analysis of the present experimental data on selenium solubility in nonstoichiometric s-ZnSe in terms of quasichemical defect formation theory indicates that they can be ade- Table 3. Thermodynamic parameters of the reactions underlying the formation of (V Zn )×2n vacancy associates as a result of Se dissolution in nonstoichiometric s-ZnSe at different temperatures T, K n1 ∆H1, kJ/mol ∆S1, J/(mol K) n2 ∆H2, kJ/mol ∆S2, J/(mol K) 963 1078 1173 1 1 2 –116.4 –116.4 –174.6 290.6 290.6 548.4 – 4 4 – –203.7 –203.7 – 677.2 677.2 ni is the degree of vacancy defect association according to Eq. (2). INORGANIC MATERIALS Vol. 52 No. 7 2016 SELENIUM SOLUBILITY IN SOLID ZINC SELENIDE quately described by the sum of exothermic reactions representing the formation of associates (clusters) based on electrically neutral vacancies in the zinc sublattice. The enthalpies and entropies of the reactions underlying the formation of vacancy associates can be described by a simple expression of the form En = Emin + δE n − 1, which takes into account the enthalpy or n entropy of formation of a minimum associate (Emin) and the increment δ E n − 1 determined by the asson ciate size (n). The degree of vacancy association increases with increasing temperature and increasing selenium vapor partial pressure. ( ) ACKNOWLEDGMENTS This research was supported by the Russian Science Foundation, grant no. 15-13-10028. REFERENCES 1. Kröger, F.A., The Chemistry of Imperfect Crystals, Amsterdam: North-Holland, 1964. 2. Rudolph, P., Schtifer, N., and Fukuda, T., Crystal growth of ZnSe from the melt, Mater. Sci. Eng., 1995, vol. 15, pp. 85–133. 3. Okada, H. and Kawanaka, T., Study on the ZnSe phase diagram by differential thermal analysis, J. Cryst. Growth, 1996, vol. 165, pp. 31–36. 4. Zlomanov, V.P. and Novoselova, A.V., P–T–x diagrammy sostoyaniya sistem metal–khal’kogen (P–T–x Phase Diagrams of Metal–Chalcogen Systems), Moscow: Nauka, 1987. 5. Kulikov, I.S., Termodinamika oksidov: spravochnoe izdanie (Thermodynamics of Oxides: A Handbook), Moscow: Metallurgiya, 1986. INORGANIC MATERIALS Vol. 52 No. 7 2016 649 6. 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