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Nature of energy bands of MgXZn1−XTe mixed crystals near the absorption edge
Journal of Physics and Chemistry of Solids 60 (1999) 799–805
Nature of energy bands of MgXZn1⫺XTe mixed crystals near the absorption edge Sang-Jo Chung a, Youngkyu Kwon a, Chang-Sun Yoon a,*, Byung-Ho Kim a, Deokjoon Cha a, Chang-Dae Kim b, Wha-Tek Kim c, C.U. Hong d a
Department of Physics, Kunsan National University, Kunsan, 573-701, South Korea Department of Physics, Mokpo National University, Mokpo, 534-729, South Korea c Department of Physics, Chonnam National University, Kwangju, 500-757, South Korea d Japan Advanced Institute of Science and Technology (JAIST)-Hokuriku 1-1, Asahidai, Tatsunokuchi, Ishikawa 923-12, Japan b
Received 25 August 1998; accepted 22 November 1998
Abstract Photoluminescence (PL) and excitonic absorption spectra of undoped MgXZn1⫺XTe (0 ⱕ X ⱕ 0.48) mixed crystals were investigated in the near-band-edge region. The PL spectra at 5 K is dominated by the principal bound exciton (PBE) lines, for bound exciton–neutral acceptor complex, which are coupled with one or two LO-phonon replicas. A linear dependence on the composition is observed for both the lattice constant and the excitonic band gap of zincblende MgXZn1⫺XTe. The excitonic band gap as a function of the lattice constant shows a linear dependence in the given composition range. The temperature dependence of the excitonic band gap in zincblende MgXZn1⫺XTe was fitted very well with the Varshni equation, and their temperature coefficients above about 200 K is found to be ⫺ (5.7–6.1) × 10 ⫺4 eV/K. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Alloys; A. Semiconductors; B. Crystal growth; D. Optical properties; D. Semiconductivity
1. Introduction The Mg-based II–VI semiconductors have attracted much attentions because of their potential applications for the optoelectronic devices [1–3]. The incorporation of magnesium in place of the group II elements in ZnTe leads to the ternary MgXZn1⫺XTe mixed crystals, and results in an increase of the band gap and the lattice constant higher than those of the host ZnTe crystals [4,5]. The mixed crystals MgXZn1⫺XTe have the band gap which can be tuned approximately from 2.25–2.27 eV for ZnTe [6–8] to 3.0– 4.7 eV for MgTe [5,9–13] at room temperature. The variation of band gap shows that these alloys are good candidates for light emitting diodes (LED) with green and blue emission in the visible region [5,15,16]. Some of the physical properties of undoped MgXZn1⫺XTe
* Corresponding author. Tel.: ⫹82-654-469-4564; fax: ⫹82654-469-4561. E-mail address: [email protected] (C.-S. Yoon)
mixed crystals have already been studied from band structure [14], luminescence, [5,15,16] reflectivity [8,17] and Raman scattering [18,19] measurements. On the basis of these experiments, the nature of the energy band near the absorption edge for MgXZn1⫺XTe has been investigated by several authors [5,8,11–17]. However, some data previously reported are controversial in relation to the composition and temperature dependence of energy band near the band edge, and energy gap versus lattice constant. The observation and interpretation of the excitonic absorption give useful information concerning the band edge. Except for ZnTe (X 0), there has been no previous investigations of the excitonic absorption in the mixed crystals. In this article, we report the photoluminescence (PL) and the excitonic absorption spectra of zincblende MgXZn1⫺XTe (0 ⱕ X ⱕ 0.48), grown by the Bridgman method, in the nearband-edge region. We present a further study of the photoluminescence near the band edge. We also report the composition dependences of the lattice constant and the excitonic band gap. Finally, we report the temperature dependence of the excitonic band gap of MgXZn1⫺XTe
0022-3697/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(98)00337-0
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Fig. 1. Composition dependence of the lattice constant of zincblende MgXZn1⫺XTe.
observed from the excitonic absorption spectra in the temperature range 4–293 K.
2. Experimental procedure The mixed crystal MgXZn1⫺XTe with the composition rage (0 ⱕ X ⱕ 0.48) were grown from 60% tellurium (Te)-rich solution by the Bridgman method. The crystal growth temperature varied within 1100⬚C and 1150⬚C depending on the Mg concentration. The mixture of the elements (high purity 6N) was sealed inside a quartz ampoule coated with carbon in order to reduce the strong reaction of magnesium with the quartz tube at high temperatures. The sealed ampoules were slowly lowered through the vertical furnace with the temperature gradient of around 0.2–0.3 mm/h.
The alloy compositions of the grown crystals were determined by means of an inductively coupled plasma mass spectroscopy (ICPS) and an electron probe microanalysis (EPMA). Parts of the grown crystals were then powdered and X-ray diffraction (XRD) measurements were performed. The crystal structure and the lattice constant with the Mg concentration were analyzed by XRD. The uniformity in composition of the mixed crystals was also estimated from the lattice constant measured using X-ray diffractometer. The optical absorption spectra were analyzed in the nearband-edge region using a UV-Vis-NIR spectrophotometer (Hitachi, U-3501) and a monochromator (SPEX, 75 cm) system. The non-polarized light beam was always incident perpendicular to the sample surface. Most of the samples were cleaved along (1 1 0) face and the cleaved surfaces were mechanically polished, chemically etched with Brmethanol to remove oxides and rinsed in methanol to prevent hydrolysis. The sample thicknesses for absorption measurements of MgXZn1⫺XTe ranged from 0.1 to 0.3 mm. The PL measurements were made on the natural cleaved (1 1 0) surfaces as the emission intensity for the cleaved surface was stronger than for those polished. Various excitation lines were provided by a Ar-ion and N2 laser systems with wavelength ranging from 337 to 488 nm for exciting PL spectra. The PL was analyzed by a SPEX spectrometer (f 75 cm) and the signal was detected using a photomultiplier tube (R943) or a North Coast EO-817 L germanium detector connected to the data processing system. The sample temperatures were varied in the range 4–300 K using an APD cryogenic system (csw-202).
3. Results and discussion The structure of MgXZn1⫺XTe mixed crystals grown by Bridgman method was found to be zincblende type in the composition rage (0 ⱕ X ⱕ 0.48). Most of the XRD lines of the powdered single crystals shift towards lower diffraction angle with increasing Mg concentration. The lattice constants measured on the samples splitted from various sections of a grown crystal agree with each other within ^ 0.02%. Fig. 1 shows the composition dependence of the
Table 1 The values of the lattice constant, the temperature coefficient (dEex/dT), and the parameters Eex(0), a and b in Eq. (3) for MgXZn1⫺XTe Composition (X)
0.00 0.09 0.16 0.23 0.30 0.48
˚) Lattice constant at 293 K (A
6.103 6.129 6.155 6.183 6.195 6.260
dEex/dT (eV/K)
⫺ 5.7 × 10 ⫺4 ⫺ 5.8 × 10 ⫺4 ⫺ 5.8 × 10 ⫺4 ⫺ 6.0 × 10 ⫺4 ⫺ 6.0 × 10 ⫺4 ⫺ 6.1 × 10 ⫺4
Values of the parameters in Eq. (3) Eex (0)
Eex (293 K)
a
2.381 2.465 2.503 2.550 2.638 2.774
2.260 2.343 2.381 2.426 2.510 2.645
7.273 × 7.300 × 7.305 × 7.400 × 7.619 × 7.625 ×
b 10 ⫺4 10 ⫺4 10 ⫺4 10 ⫺4 10 ⫺4 10 ⫺4
223 222 221 220 219 215
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801
Fig. 4. Composition dependence of the excitonic absorption spectra of MgXZn1⫺XTe at 4.2 K.
Fig. 2. Photoluminescence spectra of MgXZn1⫺XTe at 5 K.
Fig. 3. Composition dependences of the PBE lines (a), and 1LO (b) and 2LO (c) phonon replicas observed from the photoluminescence spectra at 5 K.
lattice constant of zincblende MgXZn1⫺XTe mixed crystals and demonstrates that Vegard’s law, a X 6:103 ⫹ 0:32X, is valid in this alloy system. The lattice constant, obtained ˚ , varies within the accuracy of the measurements ^ 0.002 A ˚ ˚ linearly from 6.103 A (X 0) to 6.260 A (X 0.48) with increasing composition (cf. Table 1). The result obtained is in good agreement with the one reported by Revel et al. [4]. The linear extrapolation of the data in MgXZn1⫺XTe yields ˚ for the zincblende MgTe, which agrees well with 6.423 A ˚ ) obtained from the data in the value (a 6.435 ^ 0.002 A Cd1⫺XMgXTe by Waag et al. [12]. Fig. 2 shows the PL spectra at 5 K of MgXZn1⫺XTe mixed crystals in the near-band-edge region. The PL spectra of all investigated crystals are characterized by intense near-bandedge emissions, which are shifted towards the higher energy region as the composition increases. All emissions are coupled with one or two LO(G)-phonon replicas. The observed phonon energy decreases from 0.026 eV (X 0.0) to 0.023 eV (X 0.48) as the Mg concentration increases. This result is consistent with the behavior of the ZnTe-like LO phonon which has been previously reported by us from the Raman spectra of MgXZn1⫺XTe mixed crystals [19]. For ZnTe (X 0), the principal bound exciton (PBE) line at 2.375 eV appears to result from the annihilation of a bound exciton–neutral acceptor complex [20–22], and this line is coupled with 1LO and 2LO phonon replicas at lower energies. As shown in Fig. 2, PL spectrum for X 0.16 shows a double edge emission, which the energy between two emission peaks is about 0.013 eV. The second emission peak at lower energy disappears above 30 K, which is coupled with LO-phonon replica. The interpretation of this emission requires further study. Fig. 3 shows the
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composition dependences of the PBE lines and their phonon replicas of MgXZn1⫺XTe at 5 K. The energy positions of PBE lines (EPBE) increase linearly from 2.375 eV (X 0.0) and 2.765 eV (X 0.48) as the composition increases. This linear variation can be described by the equation; EPBE(X) 2.375 ⫹ 0.81(X). Fig. 4 shows the excitonic absorption spectra of MgXZn1⫺XTe (0 ⱕ X ⱕ 0.48) near the absorption edge at 4.2 K. The observed absorption spectra show a sharp structure attributed to the free exciton near the fundamental absorption edge. As shown in Table 1, the energetic position of exciton has been shifted from 2.381 eV for X 0 to 2.774 eV for X 0.48 with increasing composition. We have not observed the excited states of exciton in MgXZn1⫺XTe samples. The observed energetic position of exciton at 4.2 K for ZnTe is in good agreement with the one previously reported in the literature [23]. The shift of the energetic position of exciton as a function of the Mg concentration is given in Fig. 5 by the full circles. As excitons are associated with band edges, the data for 4.2 K and 293 K in Fig. 5 have been used to calculate the excitonic band gap (Eex) variation. Only data for the zincblende structure are included. The variation of the excitonic band gap with the alloy composition (X) is described by the equations Fig. 5. Excitonic band gap of MgXZn1⫺XTe as a function of the composition at 4.2 and 293 K.
Fig. 6. Excitonic band gap as a function of the lattice constant for MgXZn1⫺XTe at 293 K.
Eex X 2:381 ⫹ 0:81X
4:2 K;
1
Eex X 2:260 ⫹ 0:81X
293 K:
2
From the linear extrapolation of the data in MgXZn1⫺XTe, excitonic band gaps for the zincblende MgTe (X 1.0) at 4.2 K and 293 K have been found to be about 3.191 and 3.07 eV, respectively. Oh et al. [24] estimated the zincblende band gap of MgTe by extrapolation of Cd1⫺XMgXTe data to be Eg 3.20 eV at 10 K. The zinc-blende band gap of MgTe at room temperature has been also reported to be 2.9 and 3.1 eV from the data of Cd1⫺XMgXTe and MgXZn1⫺XTe, respectively, by Waag et al. [12], and to be 3.0 eV from the data of (CdMg)Te by Waag et al. [13]. However, we note that Parker et al. [5] have investigated the band gap, from band edge luminescence obtained by electron beam bombardment, have two linear relations with the Mg concentration within the regions (0 ⱕ X ⱕ 0.8). They estimated the wurtzite band gap of MgTe by linear extrapolation of MgXZn1⫺XTe data to be about 3.47 eV at 77 K. In order to further discuss, we have investigated the excitonic band gap(Eex) as a function of the lattice constant at 293 K. As shown in Fig. 6, the excitonic band gap varies linearly with increasing the lattice constant in the composition range (0 ⱕ X ⱕ 0.48). From the linear extrapolation of MgXZn1⫺XTe data, the excitonic band gap corresponding to ˚ for the zincblende MgTe the lattice constant a 6.423 A yields Eex 3.07 eV at 293 K. As has been shown by a linear dependence of excitonic band gap versus lattice constant, the bowing effect in the context of the composition
S.-J. Chung et al. / Journal of Physics and Chemistry of Solids 60 (1999) 799–805
803
Fig. 7. Excitonic absorption spectra of ZnTe (X 0) in the temperature range 4.2–293 K.
dependence of the excitonic band gap in MgXZn1⫺XTe can be approximately neglected. In Figs. 7 and 8, we show the excitonic absorption spectra of MgXZn1⫺XTe, X 0.0 and X 0.3, obtained in the temperature range 4.2–293 K. As the temperature increases, the amplitude of exciton peak decreases and the structure is broadened. We note the very fast ionization of the excitonic ground state with increasing the temperature which supports small binding energy. The exciton binding energy at the G point of the Brillouin zone for ZnTe has been estimated as 0.01 eV by Nahory et al. [6]. The energetic position of exciton shifts towards shorter wavelength with decreasing the temperature. Fig. 9 shows the temperature dependence of the excitonic band gap (Eex) for different compositions in the temperature range 4.2–293 K. As excitons are associated with band edges, it can be considered that the variation of
the band gap with temperature is equal to that of the exciton peak. The temperature dependence of the excitonic band gap in MgXZn1⫺XTe mixed crystals was fitted very well with the Varshni equation [25], Eex T Eex 0 ⫺
aT 2 ; T ⫹b
3
where Eex(T) is the excitonic band gap at a given temperature T, Eex(0) is its value at 0 K, and a and b are constants which depend on the particular material. The constant b was interpreted as being related to the Debye temperature u D, with b ⬃ u D. The continuous lines in Fig. 9 represent the theoretical fit according to Eq. (3). As expected according to Eq. (3), the excitonic band gap decreases with increasing the temperature.
Fig. 8. Excitonic absorption spectra of Mg0.3Zn0.7Te in the temperature range 4.2–293 K.
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mixed crystals, with the zincblende structure, grown by the Bridgman method in the composition range (0 ⱕ X ⱕ 0.48). The lattice constant and the excitonic band gap of zincblende MgXZn1⫺XTe are determined. The PL spectra at 5 K is dominated by the principal bound exciton (PBE) lines which are coupled with one or two LO-phonon replicas. A linear dependence on the alloy composition is observed for both the lattice constant and the excitonic band gap of MgXZn1⫺XTe. We also observed a linear dependence of the excitonic band gap on the lattice constant. The excitonic band gap and the lattice constant of zincblende MgTe are ˚ at room extrapolated to be about 3.07 eV and 6.423 A temperature, respectively. We also identified that the temperature dependence of the excitonic band gap in MgXZn1⫺XTe was fitted very well with the Varshni equation. The temperature coefficient of Eex above about 200 K is found to be ⫺ (5.7–6.1) × 10 ⫺4 eV/K in the investigated composition range.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (Grant No. 94-0702-03-01-3).
References Fig. 9. Temperature dependence of the excitonic band gap in MgXZn1⫺XTe. The continuous lines represent the theoretical fit.
For ZnTe (X 0), a good fit of the experimental data has been obtained with Eex(0) 2.381 eV, a 7.273 × 10 ⫺4 eV/K, and b 223 K. Above about 200 K, the excitonic band gap varies linearly with the temperature and the temperature coefficients dEex/dT ⫺ 5.7 × 10 ⫺4 eV/K is in good agreement with the value ( ⫺ 5.5 × 10 ⫺4 eV/K) calculated by the pseudopotential method [26]. In particular, it is found that b 223 K observed in this work is in very good agreement with the Debye temperature (u D 223.2 ^ 5 K) of the zincblende ZnTe reported by Collins et al. [27]. This shows that the temperature variation of the energy gap in MgXZn1⫺XTe can be well described by the equation which Varshni suggested. Table 1 gives the constants a and b in Eq. (3), and the temperature coefficients with the alloy compositions in MgXZn1⫺XTe. We obtain that the temperature coefficients deduced from the linear part above about 200 K are dEex/dT ⫺ (5.7–6.1) × 10 ⫺4 eV/K in the given composition range (0 ⱕ X ⱕ 0.48). As the alloy composition increases, the value of a increases and, that of b in contrast, decreases at X ⱕ 0.48.
4. Conclusions In the present study we investigated the photoluminescence and the excitonic absorption spectra of MgXZn1⫺XTe
[1] J. Petruzzello, J. Gaines, P. van der Sluis, J. Appl. Phys. 75 (1994) 63. [2] S. Itoh, N. Nakayama, S. Matsumoto, M. Nagai, K. Nakano, M. Ozawa, H. Okuyama, S. Tomiya, T. Ohata, M. Ikeda, A. Ishibashi, Y. Mori, Jpn. J. Appl. Phys. 33 (1994) L938. [3] A. Ishibashi, J. Crystal Growth 159 (1996) 555. [4] G. Revel, G.L. Pastol, J.C. Rouchaud, M. Fedoroff, J.C. Guillaume, J. Chevallier, J.F. Rommeluere, J. Electronic Materials 9 (1980) 165. [5] S.G. Parker, A.R. Reinberg, J.E. Pinnell, W.C. Holton, J. Electrochem. Soc. 118 (1971) 979. [6] R.E. Nahory, H.Y. Fan, Phys. Rev. 156 (1967) 825. [7] E. Ebina, M. Yamamoto, T. Takahashi, Phys. Rev. 10 (1972) 3786. [8] D. Barbier, B. Montegu, A. Laugier, Solid State Commun. 28 (1978) 525. [9] G.A. Saum, E.B. Hensley, Phys. Rev. 113 (1959) 1019. [10] A. Kuhn, A. Chevy, M.-J. Naud, J. Crystal Growth 9 (1971) 263. [11] M. Luttmann, F. Bertin, A. Chabli, J. Appl. Phys. 78 (1995) 3387. [12] A. Waag, H. Heinke, S. Scholl, C.R. Becker, G. Landwehr, J. Crystal Growth 131 (1993) 607. [13] A. Waag, G. Bacher, A. Jakobs, A. Forchel, G. Landwehr, J. Appl. Phys. 75 (1994) 5456. [14] A. Laugier, B. Montegu, D. Barbier, J. Chevallier, J.C. Guillaume, K. Somogyi, Phys. Stat. Sol. (b) 99 (1980) 319. [15] F. El Akkad, S. Demian, J. Chevallier, J. Mat. Sci. 20 (1985) 165. [16] K. Somogyi, J. Chevallier, J.F. Rommeluere, J. Marine, B. Schaub, IEEE Trans. on Electron Devices ED-26 (1979) 1198.
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[21] M. Ekawa, Y. Kawakami, T. Taguchi, A. Hiraki, J. Crystal Growth 93 (1998) 667. [22] Y. Oka, M. Carbona, Phys. Rev. B 23 (1981) 4129. [23] R.E. Nahory, H.Y. Fan, Phys. Rev. Lett. 17 (1966) 251. [24] E. Oh, C. Parks, I. Miotkowski, M.D. Sciacca, A.J. Mayur, A.K. Ramdas, Phys. Rev. B 48 (1993) 15040. [25] Y.P. Varshni, Physica 34 (1967) 149. [26] J. Camassel, D. Auvergne, Phys. Rev. 12 (1975) 3258. [27] J.G. Collins, G.K. White, J.A. Birth, T.F. Smith, J. Phys. C: Solid State Phys. 13 (1980) 1649.
Nature of energy bands of MgXZn1⫺XTe mixed crystals near the absorption edge Sang-Jo Chung a, Youngkyu Kwon a, Chang-Sun Yoon a,*, Byung-Ho Kim a, Deokjoon Cha a, Chang-Dae Kim b, Wha-Tek Kim c, C.U. Hong d a
Department of Physics, Kunsan National University, Kunsan, 573-701, South Korea Department of Physics, Mokpo National University, Mokpo, 534-729, South Korea c Department of Physics, Chonnam National University, Kwangju, 500-757, South Korea d Japan Advanced Institute of Science and Technology (JAIST)-Hokuriku 1-1, Asahidai, Tatsunokuchi, Ishikawa 923-12, Japan b
Received 25 August 1998; accepted 22 November 1998
Abstract Photoluminescence (PL) and excitonic absorption spectra of undoped MgXZn1⫺XTe (0 ⱕ X ⱕ 0.48) mixed crystals were investigated in the near-band-edge region. The PL spectra at 5 K is dominated by the principal bound exciton (PBE) lines, for bound exciton–neutral acceptor complex, which are coupled with one or two LO-phonon replicas. A linear dependence on the composition is observed for both the lattice constant and the excitonic band gap of zincblende MgXZn1⫺XTe. The excitonic band gap as a function of the lattice constant shows a linear dependence in the given composition range. The temperature dependence of the excitonic band gap in zincblende MgXZn1⫺XTe was fitted very well with the Varshni equation, and their temperature coefficients above about 200 K is found to be ⫺ (5.7–6.1) × 10 ⫺4 eV/K. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Alloys; A. Semiconductors; B. Crystal growth; D. Optical properties; D. Semiconductivity
1. Introduction The Mg-based II–VI semiconductors have attracted much attentions because of their potential applications for the optoelectronic devices [1–3]. The incorporation of magnesium in place of the group II elements in ZnTe leads to the ternary MgXZn1⫺XTe mixed crystals, and results in an increase of the band gap and the lattice constant higher than those of the host ZnTe crystals [4,5]. The mixed crystals MgXZn1⫺XTe have the band gap which can be tuned approximately from 2.25–2.27 eV for ZnTe [6–8] to 3.0– 4.7 eV for MgTe [5,9–13] at room temperature. The variation of band gap shows that these alloys are good candidates for light emitting diodes (LED) with green and blue emission in the visible region [5,15,16]. Some of the physical properties of undoped MgXZn1⫺XTe
* Corresponding author. Tel.: ⫹82-654-469-4564; fax: ⫹82654-469-4561. E-mail address: [email protected] (C.-S. Yoon)
mixed crystals have already been studied from band structure [14], luminescence, [5,15,16] reflectivity [8,17] and Raman scattering [18,19] measurements. On the basis of these experiments, the nature of the energy band near the absorption edge for MgXZn1⫺XTe has been investigated by several authors [5,8,11–17]. However, some data previously reported are controversial in relation to the composition and temperature dependence of energy band near the band edge, and energy gap versus lattice constant. The observation and interpretation of the excitonic absorption give useful information concerning the band edge. Except for ZnTe (X 0), there has been no previous investigations of the excitonic absorption in the mixed crystals. In this article, we report the photoluminescence (PL) and the excitonic absorption spectra of zincblende MgXZn1⫺XTe (0 ⱕ X ⱕ 0.48), grown by the Bridgman method, in the nearband-edge region. We present a further study of the photoluminescence near the band edge. We also report the composition dependences of the lattice constant and the excitonic band gap. Finally, we report the temperature dependence of the excitonic band gap of MgXZn1⫺XTe
0022-3697/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(98)00337-0
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S.-J. Chung et al. / Journal of Physics and Chemistry of Solids 60 (1999) 799–805
Fig. 1. Composition dependence of the lattice constant of zincblende MgXZn1⫺XTe.
observed from the excitonic absorption spectra in the temperature range 4–293 K.
2. Experimental procedure The mixed crystal MgXZn1⫺XTe with the composition rage (0 ⱕ X ⱕ 0.48) were grown from 60% tellurium (Te)-rich solution by the Bridgman method. The crystal growth temperature varied within 1100⬚C and 1150⬚C depending on the Mg concentration. The mixture of the elements (high purity 6N) was sealed inside a quartz ampoule coated with carbon in order to reduce the strong reaction of magnesium with the quartz tube at high temperatures. The sealed ampoules were slowly lowered through the vertical furnace with the temperature gradient of around 0.2–0.3 mm/h.
The alloy compositions of the grown crystals were determined by means of an inductively coupled plasma mass spectroscopy (ICPS) and an electron probe microanalysis (EPMA). Parts of the grown crystals were then powdered and X-ray diffraction (XRD) measurements were performed. The crystal structure and the lattice constant with the Mg concentration were analyzed by XRD. The uniformity in composition of the mixed crystals was also estimated from the lattice constant measured using X-ray diffractometer. The optical absorption spectra were analyzed in the nearband-edge region using a UV-Vis-NIR spectrophotometer (Hitachi, U-3501) and a monochromator (SPEX, 75 cm) system. The non-polarized light beam was always incident perpendicular to the sample surface. Most of the samples were cleaved along (1 1 0) face and the cleaved surfaces were mechanically polished, chemically etched with Brmethanol to remove oxides and rinsed in methanol to prevent hydrolysis. The sample thicknesses for absorption measurements of MgXZn1⫺XTe ranged from 0.1 to 0.3 mm. The PL measurements were made on the natural cleaved (1 1 0) surfaces as the emission intensity for the cleaved surface was stronger than for those polished. Various excitation lines were provided by a Ar-ion and N2 laser systems with wavelength ranging from 337 to 488 nm for exciting PL spectra. The PL was analyzed by a SPEX spectrometer (f 75 cm) and the signal was detected using a photomultiplier tube (R943) or a North Coast EO-817 L germanium detector connected to the data processing system. The sample temperatures were varied in the range 4–300 K using an APD cryogenic system (csw-202).
3. Results and discussion The structure of MgXZn1⫺XTe mixed crystals grown by Bridgman method was found to be zincblende type in the composition rage (0 ⱕ X ⱕ 0.48). Most of the XRD lines of the powdered single crystals shift towards lower diffraction angle with increasing Mg concentration. The lattice constants measured on the samples splitted from various sections of a grown crystal agree with each other within ^ 0.02%. Fig. 1 shows the composition dependence of the
Table 1 The values of the lattice constant, the temperature coefficient (dEex/dT), and the parameters Eex(0), a and b in Eq. (3) for MgXZn1⫺XTe Composition (X)
0.00 0.09 0.16 0.23 0.30 0.48
˚) Lattice constant at 293 K (A
6.103 6.129 6.155 6.183 6.195 6.260
dEex/dT (eV/K)
⫺ 5.7 × 10 ⫺4 ⫺ 5.8 × 10 ⫺4 ⫺ 5.8 × 10 ⫺4 ⫺ 6.0 × 10 ⫺4 ⫺ 6.0 × 10 ⫺4 ⫺ 6.1 × 10 ⫺4
Values of the parameters in Eq. (3) Eex (0)
Eex (293 K)
a
2.381 2.465 2.503 2.550 2.638 2.774
2.260 2.343 2.381 2.426 2.510 2.645
7.273 × 7.300 × 7.305 × 7.400 × 7.619 × 7.625 ×
b 10 ⫺4 10 ⫺4 10 ⫺4 10 ⫺4 10 ⫺4 10 ⫺4
223 222 221 220 219 215
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801
Fig. 4. Composition dependence of the excitonic absorption spectra of MgXZn1⫺XTe at 4.2 K.
Fig. 2. Photoluminescence spectra of MgXZn1⫺XTe at 5 K.
Fig. 3. Composition dependences of the PBE lines (a), and 1LO (b) and 2LO (c) phonon replicas observed from the photoluminescence spectra at 5 K.
lattice constant of zincblende MgXZn1⫺XTe mixed crystals and demonstrates that Vegard’s law, a X 6:103 ⫹ 0:32X, is valid in this alloy system. The lattice constant, obtained ˚ , varies within the accuracy of the measurements ^ 0.002 A ˚ ˚ linearly from 6.103 A (X 0) to 6.260 A (X 0.48) with increasing composition (cf. Table 1). The result obtained is in good agreement with the one reported by Revel et al. [4]. The linear extrapolation of the data in MgXZn1⫺XTe yields ˚ for the zincblende MgTe, which agrees well with 6.423 A ˚ ) obtained from the data in the value (a 6.435 ^ 0.002 A Cd1⫺XMgXTe by Waag et al. [12]. Fig. 2 shows the PL spectra at 5 K of MgXZn1⫺XTe mixed crystals in the near-band-edge region. The PL spectra of all investigated crystals are characterized by intense near-bandedge emissions, which are shifted towards the higher energy region as the composition increases. All emissions are coupled with one or two LO(G)-phonon replicas. The observed phonon energy decreases from 0.026 eV (X 0.0) to 0.023 eV (X 0.48) as the Mg concentration increases. This result is consistent with the behavior of the ZnTe-like LO phonon which has been previously reported by us from the Raman spectra of MgXZn1⫺XTe mixed crystals [19]. For ZnTe (X 0), the principal bound exciton (PBE) line at 2.375 eV appears to result from the annihilation of a bound exciton–neutral acceptor complex [20–22], and this line is coupled with 1LO and 2LO phonon replicas at lower energies. As shown in Fig. 2, PL spectrum for X 0.16 shows a double edge emission, which the energy between two emission peaks is about 0.013 eV. The second emission peak at lower energy disappears above 30 K, which is coupled with LO-phonon replica. The interpretation of this emission requires further study. Fig. 3 shows the
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composition dependences of the PBE lines and their phonon replicas of MgXZn1⫺XTe at 5 K. The energy positions of PBE lines (EPBE) increase linearly from 2.375 eV (X 0.0) and 2.765 eV (X 0.48) as the composition increases. This linear variation can be described by the equation; EPBE(X) 2.375 ⫹ 0.81(X). Fig. 4 shows the excitonic absorption spectra of MgXZn1⫺XTe (0 ⱕ X ⱕ 0.48) near the absorption edge at 4.2 K. The observed absorption spectra show a sharp structure attributed to the free exciton near the fundamental absorption edge. As shown in Table 1, the energetic position of exciton has been shifted from 2.381 eV for X 0 to 2.774 eV for X 0.48 with increasing composition. We have not observed the excited states of exciton in MgXZn1⫺XTe samples. The observed energetic position of exciton at 4.2 K for ZnTe is in good agreement with the one previously reported in the literature [23]. The shift of the energetic position of exciton as a function of the Mg concentration is given in Fig. 5 by the full circles. As excitons are associated with band edges, the data for 4.2 K and 293 K in Fig. 5 have been used to calculate the excitonic band gap (Eex) variation. Only data for the zincblende structure are included. The variation of the excitonic band gap with the alloy composition (X) is described by the equations Fig. 5. Excitonic band gap of MgXZn1⫺XTe as a function of the composition at 4.2 and 293 K.
Fig. 6. Excitonic band gap as a function of the lattice constant for MgXZn1⫺XTe at 293 K.
Eex X 2:381 ⫹ 0:81X
4:2 K;
1
Eex X 2:260 ⫹ 0:81X
293 K:
2
From the linear extrapolation of the data in MgXZn1⫺XTe, excitonic band gaps for the zincblende MgTe (X 1.0) at 4.2 K and 293 K have been found to be about 3.191 and 3.07 eV, respectively. Oh et al. [24] estimated the zincblende band gap of MgTe by extrapolation of Cd1⫺XMgXTe data to be Eg 3.20 eV at 10 K. The zinc-blende band gap of MgTe at room temperature has been also reported to be 2.9 and 3.1 eV from the data of Cd1⫺XMgXTe and MgXZn1⫺XTe, respectively, by Waag et al. [12], and to be 3.0 eV from the data of (CdMg)Te by Waag et al. [13]. However, we note that Parker et al. [5] have investigated the band gap, from band edge luminescence obtained by electron beam bombardment, have two linear relations with the Mg concentration within the regions (0 ⱕ X ⱕ 0.8). They estimated the wurtzite band gap of MgTe by linear extrapolation of MgXZn1⫺XTe data to be about 3.47 eV at 77 K. In order to further discuss, we have investigated the excitonic band gap(Eex) as a function of the lattice constant at 293 K. As shown in Fig. 6, the excitonic band gap varies linearly with increasing the lattice constant in the composition range (0 ⱕ X ⱕ 0.48). From the linear extrapolation of MgXZn1⫺XTe data, the excitonic band gap corresponding to ˚ for the zincblende MgTe the lattice constant a 6.423 A yields Eex 3.07 eV at 293 K. As has been shown by a linear dependence of excitonic band gap versus lattice constant, the bowing effect in the context of the composition
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Fig. 7. Excitonic absorption spectra of ZnTe (X 0) in the temperature range 4.2–293 K.
dependence of the excitonic band gap in MgXZn1⫺XTe can be approximately neglected. In Figs. 7 and 8, we show the excitonic absorption spectra of MgXZn1⫺XTe, X 0.0 and X 0.3, obtained in the temperature range 4.2–293 K. As the temperature increases, the amplitude of exciton peak decreases and the structure is broadened. We note the very fast ionization of the excitonic ground state with increasing the temperature which supports small binding energy. The exciton binding energy at the G point of the Brillouin zone for ZnTe has been estimated as 0.01 eV by Nahory et al. [6]. The energetic position of exciton shifts towards shorter wavelength with decreasing the temperature. Fig. 9 shows the temperature dependence of the excitonic band gap (Eex) for different compositions in the temperature range 4.2–293 K. As excitons are associated with band edges, it can be considered that the variation of
the band gap with temperature is equal to that of the exciton peak. The temperature dependence of the excitonic band gap in MgXZn1⫺XTe mixed crystals was fitted very well with the Varshni equation [25], Eex T Eex 0 ⫺
aT 2 ; T ⫹b
3
where Eex(T) is the excitonic band gap at a given temperature T, Eex(0) is its value at 0 K, and a and b are constants which depend on the particular material. The constant b was interpreted as being related to the Debye temperature u D, with b ⬃ u D. The continuous lines in Fig. 9 represent the theoretical fit according to Eq. (3). As expected according to Eq. (3), the excitonic band gap decreases with increasing the temperature.
Fig. 8. Excitonic absorption spectra of Mg0.3Zn0.7Te in the temperature range 4.2–293 K.
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mixed crystals, with the zincblende structure, grown by the Bridgman method in the composition range (0 ⱕ X ⱕ 0.48). The lattice constant and the excitonic band gap of zincblende MgXZn1⫺XTe are determined. The PL spectra at 5 K is dominated by the principal bound exciton (PBE) lines which are coupled with one or two LO-phonon replicas. A linear dependence on the alloy composition is observed for both the lattice constant and the excitonic band gap of MgXZn1⫺XTe. We also observed a linear dependence of the excitonic band gap on the lattice constant. The excitonic band gap and the lattice constant of zincblende MgTe are ˚ at room extrapolated to be about 3.07 eV and 6.423 A temperature, respectively. We also identified that the temperature dependence of the excitonic band gap in MgXZn1⫺XTe was fitted very well with the Varshni equation. The temperature coefficient of Eex above about 200 K is found to be ⫺ (5.7–6.1) × 10 ⫺4 eV/K in the investigated composition range.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (Grant No. 94-0702-03-01-3).
References Fig. 9. Temperature dependence of the excitonic band gap in MgXZn1⫺XTe. The continuous lines represent the theoretical fit.
For ZnTe (X 0), a good fit of the experimental data has been obtained with Eex(0) 2.381 eV, a 7.273 × 10 ⫺4 eV/K, and b 223 K. Above about 200 K, the excitonic band gap varies linearly with the temperature and the temperature coefficients dEex/dT ⫺ 5.7 × 10 ⫺4 eV/K is in good agreement with the value ( ⫺ 5.5 × 10 ⫺4 eV/K) calculated by the pseudopotential method [26]. In particular, it is found that b 223 K observed in this work is in very good agreement with the Debye temperature (u D 223.2 ^ 5 K) of the zincblende ZnTe reported by Collins et al. [27]. This shows that the temperature variation of the energy gap in MgXZn1⫺XTe can be well described by the equation which Varshni suggested. Table 1 gives the constants a and b in Eq. (3), and the temperature coefficients with the alloy compositions in MgXZn1⫺XTe. We obtain that the temperature coefficients deduced from the linear part above about 200 K are dEex/dT ⫺ (5.7–6.1) × 10 ⫺4 eV/K in the given composition range (0 ⱕ X ⱕ 0.48). As the alloy composition increases, the value of a increases and, that of b in contrast, decreases at X ⱕ 0.48.
4. Conclusions In the present study we investigated the photoluminescence and the excitonic absorption spectra of MgXZn1⫺XTe
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