Variation of band gap energy and photoluminescence characteristics with Te composition of ZnS1−xTex epilayers grown by hot-wall epitaxy

Applied Surface Science 182 (2001) 159±166

Variation of band gap energy and photoluminescence characteristics with Te composition of ZnS1 x Tex epilayers grown by hot-wall epitaxy Young-Moon Yua, Sungun Nama, Byungsung Oa, Ki-Seon Leea, Yong Dae Choib,*, Jongwon Leec, Pyeong Yeol Yud a Department of Physics, Chungnam National University, Taejon 305-764, South Korea Department of Optical and Electronic Physics, 800, Doan-Dong, Seo-Ku, Mokwon University, Taejon 302-729, South Korea c Department of Materials Engineering, Hanbat National University, Taejon 305-719, South Korea d Department of Physics, Sunchon National University, Sunchon 540-742, South Korea

b

Received 9 April 2001; received in revised form 9 July 2001; accepted 20 August 2001

Abstract ZnS1 x Tex ternary alloy epilayers were grown on GaAs (1 0 0) substrates by hot-wall epitaxy (HWE), and the dependence of their band gap energy and photoluminescence (PL) characteristics on the Te composition x was investigated. The spectrophotometer measurement results demonstrated that the room temperature band gap energy varied with the Te composition x. The band gap energy showed the strong bowing effect given by Eg …x† ˆ 3:73 5:27x ‡ 3:80x2. The PL peaks of ZnS1 x Tex epilayers shifted to the lower energy with increasing Te composition x. For x > 0:69, the PL peak energy was very close to the band gap energy. Bowing parameter, 3.80, was closer to the value of Bernard et al., 3.83, and was a little larger than the previous other results. Strong emission ranging from blue to yellow was observed at room temperature. Also, the relations between Ten …n ˆ 1; 2; 3† atoms of the ZnS1 x Tex epilayers and the exciton emission at room temperature were investigated. # 2001 Elsevier Science B.V. All rights reserved. PACS: 78.20.-e; 78.55.Et; 81.15.Tv Keywords: ZnS1 x Tex epilayers; Hot-wall epitaxy; Band gap energy; Photoluminescence

1. Introduction Zinc chalcogenide alloys have attracted extensive interest because of their large energy gap and particular optical characteristics. ZnS1 x Tex has a direct

*

Corresponding author. Tel.: ‡82-42-829-7552; fax: ‡82-42-823-0639. E-mail address: [email protected] (Y.D. Choi).

band gap ranging from 1.98 to 3.73 eV. For this ternary alloy, the minimum energy gap is smaller than the band gaps of two binary alloys, ZnTe (2.26 eV) and ZnS (3.73 eV), due to the bowing effect. Due to its wide energy gap, ZnS1 x Tex can be used for fabrication of light emitting devices and photodiodes in nearUV to visible range [1±3]. Gupta et al. [4] have prepared the polycrystalline ZnS1 x Tex ®lms on the glass substrates by coevaporating the ZnS and ZnTe powders. They measured the

0169-4332/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 1 ) 0 0 5 5 0 - 5

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Y.-M. Yu et al. / Applied Surface Science 182 (2001) 159±166

optical re¯ectance of the samples using spectrophotometer and showed that the energy band gap of the ®lms varied with the Te composition. They also showed that its bowing parameter b was 1.6, which was substantially different from the experimental value of b ˆ 3:0 obtained by Hill and Richardson [5] and Liu et al. [6]. Sou et al. [1±3,7,8] have grown ZnS1 x Tex epilayers on Si, GaAs and GaP substrates by molecular beam epitaxy (MBE) since 1994, and have fabricated the optoelectronic devices with these materials. When wide-band gap II±VI semiconductors such as ZnS, ZnSe and CdS are mixed with very low concentration of Te, Te atoms act as isoelectronic centers capturing the free excitons [1]. The recombination of these excitons makes a strong luminescent band in the entire visible range. This is attributed to the large difference in the electronegativity of Te and the host atom it replaces. If Te is less electronegative than the host atom it replaces, a hole is strongly localized due to a short-range potential resulting from this difference. An electron is subsequently bound by the coulombic potential of a hole and then forms a localized exciton at isoelectronic center. The emission from the isoelectronic center is usually very strong and wide and shows very large Stokes shift which can be explained by extrinsic self-trapping [9]. The radiative recombination of such excitons can be very ef®cient, because the localization of the carriers is very fast and because non-radiative Auger recombination involving a third particle does not occur [9±14]. Therefore, the light emission ef®ciency of the ZnS1 x Tex epilayer can be greatly enhanced by incorporating Te atoms of low concentration, and it is thus expected that the fabrication of short wavelength light emitting devices of high ef®ciency can be accomplished. In this study, ZnS1 x Tex epilayers have been grown on the GaAs (1 0 0) substrates by hot-wall epitaxy (HWE). The bowing effect and the photoluminescence (PL) characteristics with Te composition of ZnS1 x Tex epilayers were investigated. 2. Experimentals ZnS1 x Tex epilayers were grown on the Cr-doped semi-insulating (1 0 0) GaAs substrates by using an HWE system in a vacuum of about 10 7 Torr. Polycrystalline ZnS and ZnTe powders of 5 N were

used as the source materials. The GaAs substrates were ultrasonically cleaned by trichloroethylene, acetone and methanol in sequence for 5 min each. The GaAs substrates were chemically etched in 608C 3H2SO4:H2O2:H2O for 1 min and rinsed with deionized water and methanol. After dried with Ar gas, they were put on the substrate holder in HWE set-up. Prior to the epilayer growth, the GaAs substrates were preheated for 20 min at 5808C to remove both the oxide layers and the impurities remaining on the substrate surface. Then, the substrates were slowly cooled to the growth temperature of 280±4008C. To control the Te composition of ZnS1 x Tex , ZnS and ZnTe powder were put in a different section of HWE growth tube and heated independently at 450±7508C. Ê /s and the thickness of The growth rate was 1 A epilayers was about 1.5 mm. The surfaces of the ZnS1 x Tex epilayers were observed using a Nomarski interference microscope. The ®lm thickness was calculated by the periodic interference pattern in the re¯ectance spectrum taken by a spectrophotometer. The optical transmission for ZnS1 x Tex epilayers was measured at room temperature after removing the GaAs substrates. The GaAs substrates were mechanically thinned to a thickness of 10±30 mm and then chemically etched in 10H2O2:NH4 OH solution. PL measurement was also performed using a 40 mW He±Cd laser …l ˆ 325 nm† with an interference laser line ®lter and a 0.85-m double monochromator with a charge-coupled device was used. The composition of the epilayer was examined using both Rutherford backscattering spectrometry (RBS) and double crystal X-ray diffractometry (DCXRD). 3. Results and discussion 3.1. Band gap energy and optical bowing parameter To determine the band gap energy of ZnS1 x Tex epilayers, the optical transmission spectrum at room temperature was measured after removing the GaAs substrates. Fig. 1 shows the room temperature transmission spectra of several ZnS1 x Tex epilayers. In general, the transmission spectra showed a sharp increase at the edge indicating that the crystal quality of the epilayer was good. In the lower energy region than the energy band gap, the oscillation of the periodic

Y.-M. Yu et al. / Applied Surface Science 182 (2001) 159±166

161

Fig. 1. Typical transmission spectra of the ZnS1 x Tex epilayers …0  x  1†.

interference fringes was clearly seen. The transmission edges of ZnS1 x Tex epilayers were shown to shift to the lower energy with increasing Te composition x. The band gap energy was determined with optical absorption coef®cients obtained from the transmission spectra using the following formula [15] I ˆ I0 e

at

;

(1)

where I0 is the intensity of the incident light, a the optical absorption coef®cient and t the thickness of the epilayer. (ahn)2 was measured using a obtained from Eq. (1) and was found to vary linearly with photon energy hn, indicating the direct band gap transition. From extrapolation of the straight portion of (ahn)2 line to …ahn†2 ˆ 0, the values of the energy band gaps Eg of ZnS1 x Tex epilayers were determined. It was found that the ternary mixed epilayers of ZnS1 x Tex have variable optical band gaps in this range 1:98 < Eg …ZnSTe† < 3:73 eV, and the values of the energy band gaps of ZnS and ZnTe epilayers were 3.73 and 2.26 eV, respectively. Fig. 2 shows the room temperature band gap energy as a function of Te composition x of ZnS1 x Tex epilayers. The band gap energy shows the non-linearity with the composition given by [16] Eg …x† ˆ ‰xEg …ZnTe† ‡ …1 ˆ 3:73

x†Eg …ZnS†Š 2

5:27x ‡ 3:80x :

bx…1

x† (2)

Fig. 2. Energy band gaps at room temperature as a function of the Te composition of the ZnS1 x Tex epilayers.

The coef®cient of the quadratic term, b, is called an optical bowing parameter. The solid line in Fig. 2 was ®tted to Eq. (2), and b was found to be 3.80. Experimentally observed band gap bowing parameters b (eV) for ZnS1 x Tex ternary alloys are listed in Table 1 to compare our result with previous data. The band gap energy as a function of Te composition x shows a minimum at x ˆ 0:69, which was very similar to other results [1,4]. Van Vechten et al. [21±24] proposed that the origin of the experimental optical bowing parameter b should be the sum of a contribution bI present in an ideal hypothetical alloy (either perfectly substitutionally random or perfectly ordered), modeled within the virtual-crystal approximation, and a contribution bII due to alloy disorder. They obtained bI ˆ 0:28 and bII ˆ 2:12 for ZnS1 x Tex ternary alloy using dielectric two-band model, and an optical bowing parameter b was found to be bI ‡ bII ˆ 2:4. This is the same result of Larach et al. as listed in Table 1. However, Bernard and Zunger [25] differed from the viewpoint of Van Vechten and Bergstresser [21]. Bernard et al. described the alloys as collections of local atomic arrangements (cluster), each of which occurs with a statistical weight appropriate to the composition. In addition, they explained three contributions to the

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Table 1 Experimentally observed band gap bowing parameter b (eV) for ZnS1 x Tex ternary alloya b (eV)

Sample type

2.4 3.0 3.83 1.6 3.0±3.2

Bulk microcrystals Poly Theoretical value Poly Single

3.0 2.7

Single Single

3.80

Single

Growth method

Experimental method

Temperature (K)

Evaporation

Diffuse reflectance Absorption

300

Evaporation MBE

Reflectance Absorption

MBE Vertical gradient freezing technique HWE

PL Wavelength modulated reflectivity Absorption

10 8 300

Author (year) Larach et al. [17] (1957)b Hill and Richardson [5] (1973) Bernard and Zunger [16] (1986) Gupta et al. [4] Wong et al. [18] (1994), Wei and Zunger [19] (1995) Liu et al. [6] (1998) Seong et al. [20] (1999) Y.-M. Yu et al. (this work)

a

``Single'' and ``poly'' refer to single crystal and polycrystalline, respectively. The temperature at which each bowing parameter was obtained is also listed. Besides, the growth method is given in the footnote below. b Bulk microcrystals produced by heating at 9008C the powdered constituents; diffuse re¯ectance.

optical bowing of the alloy as follows: (i) a volume deformation contribution bVD of the band structure due to the replacement of the lattice constants of the binary constituents by that of the alloy; (ii) a chemicalelectronegativity contribution bCE due to a charge exchange in the alloy relative to its constituent binary subsystems; (iii) a structural contribution bS due to the relaxation of the anion±cation bond lengths in the alloy. The sum bVD ‡ bCE ‡ bS produced a theoretical bowing parameter, b ˆ bVD ‡ bCE ‡ bS ˆ 0:53‡ 1:68 ‡ 2:68 ˆ 3:83 by using the self-consistent band structure techniques for ordered 50±50% alloys in the CuAu-I structure. Our bowing parameter was found to be 3.80, which was closer to the result of Bernard and Zunger [16], 3.83, and was a little larger than the previous other results in Table 1.

means that the PL emission for low Te composition is related to deep level, and for high Te composition to shallow level. The peak energy of PL spectrum decreased as the Te composition x increased, but it

3.2. Photoluminescence Fig. 3 shows the PL spectra measured at 10 K as a function of Te composition x of ZnS1 x Tex epilayers. The epilayers were grown at the substrate temperature of 2808C and had a thickness of about 1.5 mm. The inverted triangles (!) indicate the band gaps of the ZnS1 x Tex epilayer at 10 K. To calculate the band gap of ZnS1 x Tex epilayers at 10 K, ZnTe band gap at 10 K (2.39 eV), ZnS band gap at 10 K (3.84 eV) [26] and the room temperature bowing parameter b (3.80 eV) were used. The difference between the PL peak energy and the band gap energy generally decreased as the Te composition x increased. This

Fig. 3. PL spectra at 10 K as a function of the Te composition of the ZnS1 x Tex epilayers. The inverted triangles (!) represent the band gap energy at 10 K described by Eq. (2).

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increased in the higher Te composition …x > 0:71†. The full width at half maximum (FWHM) of PL spectra generally showed a very wide band (>100 meV) over all the Te compositional range considered in this study, and they decreased with increasing Te composition. The cause of very wide FWHM might be associated with the crystallinity of the epilayers, but it is still necessary to explain this large FWHM in more detail. It could also be seen in Fig. 3 that FWHM of the PL spectrum was small for high Te composition, and large for low Te composition. For the ZnS1 x Tex epilayer with very low Te composition …x < 0:1†, the PL peaks were multiple. This was the weak oscillation in intensity due to the optical interference effect. For ZnS1 x Tex epilayers with high Te composition …x > 0:8†, two PL peaks were observed. The higher energy peak was attributed to the excitons bound to shallow acceptors, and the lower one to the excitons bound to oxygen isoelectronic impurity [27]. Fig. 4 shows the spectra of four ZnS1 x Tex epilayers that showed strong PL emission at room temperature. The inset shows a critical comparison between the

Fig. 4. PL spectra at room temperature as a function of the Te composition of the ZnS1 x Tex epilayers. PL spectra eliminated the interference effects of the ZnS0.99Te0.01 epilayers are depicted by dotted line. Inset shows 300 K-PL spectrum of ZnS epilayer.

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PL spectrum of ZnS epilayer and that of ZnS1 x Tex epilayer at room temperature. The broad excitonic peak (X) and the sharp third-resonant Raman lines (R3LO) are shown around 3.682 eV in ZnS epilayer [28]. Three ZnS1 x Tex epilayers with the Te composition x ˆ 0:01, 0.04 and 0.12 strongly emitted blue, green and yellow luminescence, respectively. Strong near-infrared luminescence emitted by the epilayer with the Te composition x ˆ 0:93 was not visible with naked eyes. ZnS1 x Tex epilayers with small Te composition x ˆ 0:04 and 0.01 show the interference fringes owing to the optical interference effects, as mentioned above. If the interference fringes are eliminated in the spectrum for the Te composition x ˆ 0:01, the net PL spectrum can be depicted by the dotted line as shown in Fig. 4. The optical interference effects can be eliminated by a vertical incidence of excitation light on the surface of the epilayer and the detection of the edge-emission of the epilayer perpendicular to an axis of the excitation light. By eliminating the interference fringes in this way, the two peaks at 2.82 and 2.60 eV can be ®tted to a broad Gaussian curve. PL spectra of ZnS1 x Tex epilayers with Te composition x < 0:7 have some general features at both low temperature and room temperature. First, the FWHM of the PL peaks of ZnS1 x Tex epilayers is much broader than those measured in ZnS and ZnTe epilayers. Second, Stokes shift of PL peak is very large. Third, room temperature PL is very strong. These can be compared with PL of ZnS and ZnTe epilayers. Note that at room temperature, the free exciton intensity of pure ZnS epilayers is very weak and the emission of ZnTe epilayers is not observed. PL characteristics of ZnS1 x Tex epilayers can be well explained by the Te isoelectronic centers induced extrinsic self-trapping effect mentioned above. This isoelectronic self-trapping effect occurs when phonon-coupling effect due to the ionic binding exists as well as when the electronegativity of the impurity atom Te (2.1 eV) differs signi®cantly from that of the host atom S (2.5 eV) it replaces [29,30]. Fig. 5 shows the variation of the PL spectra with Te composition x for the samples with the Te composition x < 0:01 at 300 K. Note that no interference fringes of these spectra are shown since it is the edge-emission detection. Note that the Te composition x for these samples was very small, and thus could not be determined by RBS. Instead, it was determined by the peak

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Fig. 5. PL spectra at room temperature of the ZnS1 x Tex epilayers with the Te composition x < 0:01. Spectrum is ®tted to two dotted curves.

position of DCXRD. Numbers ( ± ) in Fig. 5 show eight different epilayers for the sake of comparison. The Te composition x ˆ 0:01% of spectrum is the smallest and the Te composition x increased with an increase of the number. Spectrum can be ®tted to two dotted curves. In Fig. 5, two distinct differences can be observed as follows. First, although the Te composition x is less than 0.01, the excitonic peaks of pure ZnS epilayers shown in the inset of Fig. 4 are not observed in the ZnS1 x Tex epilayers. Second, the energy separation between the two main peaks at 3.03 and 2.62 eV is about 0.41 eV. The two main peaks at 3.03 and 2.62 eV are marked by ! and 5, respectively. Iseler and Strauss reported that two emission peak energies associated with Te traps in ZnS were 3.1 and 2.7 eV for the zincblende structure [31,32]. The high energy peak at 3.1 eV and the low energy one at 2.7 eV are related to a single Te atom (Te1) and paired Te atoms (Te2) on the nearest-neighbor sites, respectively. Therefore, in Fig. 5, the peaks (!) around 3.03 eVand the peaks (5) around 2.62 eV

are attributed to the single Te-bound exciton (X/Te1) and the paired Te-bound exciton (X/Te2), respectively. These peak energies are nearly the same as those reported by Fukushima and Shionoya [33]. According to their results, only the high energy peak of X/Te1 is observed in the epilayers of the low Te composition x, but X/Te2 in the epilayers of the higher one. The relative intensity of the two emission peaks in Fig. 5 changes with the Te composition x. As the Te composition x increases, the emission peak associated with X/Te1 rapidly decreases and ®nally disappears. Spectrum in Fig. 5 con®rms that the emission peak associated with X/Te2 becomes the main one in the spectra. This can be explained as follows. The distances between the neighboring Te atoms which randomly exist in ZnS become narrow with increasing Te composition x, and the probability of having the neighboring Te atoms accordingly increases. It is then more likely that the excitons are bound to two atoms than to a single Te atom. Fig. 6 shows the energy positions of the PL emission peaks at 10 K as a function of Te composition x of ZnS1 x Tex epilayers. The solid line represents the theoretical band gap energy at 10 K calculated by Eq. (2). The dotted line is ®tted to the data obtained

Fig. 6. PL peak position at 10 K as a function of the Te composition of the ZnS1 x Tex epilayers. (*) and (*) represent the Sou's data [1] and the data obtained in this study, respectively. Solid line represents the theoretical band gap energy at 10 K determined by Eq. (2). Dotted line is ®tted to the data obtained in this study.

Y.-M. Yu et al. / Applied Surface Science 182 (2001) 159±166

in this study. For lower Te composition …x < 0:7†, the difference between the PL peak energy and the band gap energy becomes larger and larger with decreasing Te composition x. However, for high Te composition …x > 0:7†, the PL peak energy is very close to the theoretical band gap energy. This demonstrates that the PL peak energy position for ZnS1 x Tex alloy of low Te composition x cannot necessarily coincide with its band gap energy. Thus, the previous result for the band gap energy of ZnS1 x Tex alloy was not always correct. Yokogawa and Narusawa [34] reported that the band gap energy could be determined by the peak position of cathodoluminescent emission peaks. However, it can be clearly seen from our result that their result is not necessarily right due to the strong compositional dependence of energy band gap of ZnS1 x Tex epilayers. Our data corresponds with the previous result of Sou et al. [1] obtained from the MBE grown samples. As shown in Fig. 6, when the Te composition is low, the PL peak position changes very rapidly with Te composition. It can be explained as follows. As mentioned earlier, at a low concentration of Te, the peak due to Te1 center (3.1 eV) is dominant. With a small increase of Te composition, the PL peak due to Te2 center (2.65 eV) becomes dominant, and ®nally, the peaks (below 2.55 eV) due to the excitons bound to Te3 clusters become predominant. 4. Conclusion Variation of band gap energy and PL characteristics due to the Te composition change in ZnS1 x Tex epilayers were investigated in this study. The transmission spectra were measured to determine the energy band gaps of the ZnS1 x Tex epilayers at 300 K. As a result, the band gap energy of the ZnS1 x Tex epilayers with the Te composition x showed a strong bowing effect in the range 1:98 eV < Eg …ZnSTe† < 3:73 eV. The bowing parameter was found to be 3.80 using our experimental data, which was similar to the value of Bernard et al., 3.83. In the PL spectra of the ZnS1 x Tex …0:01  x† epilayers at 10 K, the PL emission band for small Te composition x was related to deep radiative level, and for large composition x to shallow level. For the

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two PL peaks of the samples with the Te composition x > 0:8, the higher energy peak was attributed to the excitons bound to shallow acceptors, and the lower one to the excitons bound to oxygen isoelectronic impurity. In the PL spectra of the samples with the Te composition x < 0:01 at 300 K, the high energy peak at 3.03 eV and the low energy one at 2.62 eV were related to a single Te atom (Te1) and paired Te atoms (Te2) on the nearest-neighbor sites, respectively. Acknowledgements This work was supported by Korea Research Foundation Grant (KRF-2000-015-DP0158). References [1] I.K. Sou, K.S. Wong, Z.Y. Yang, H. Wang, G.K.L. Wong, Appl. Phys. Lett. 66 (1995) 1915. [2] I.K. Sou, J. Mao, Z. Ma, W.S. Chen, Z. Yang, K.S. Wong, G.K.L. Wong, J. Cryst. Growth 175±176 (1997) 632. [3] I.K. Sou, C.L. Man, Z.H. Ma, Z. Yang, G.K.L. Wong, Appl. Phys. Lett. 71 (1997) 3847. [4] P. Gupta, B. Maiti, S. Chaudhuri, A.K. Pal, Thin Solid Films 227 (1993) 66. [5] R. Hill, D. Richardson, J. Phys. C 6 (1973) L115. [6] N.Z. Liu, G.H. Li, Z.M. Zhu, H.X. Han, Z.P. Wang, W.K. Ge, I.K. Sou, J. Phys. 10 (1998) 4119. [7] I.K. Sou, S.M. Mou, Y.W. Chan, G.C. Xu, G.K.L. Wong, Mater. Res. Soc. Symp. Proc. 340 (1994) 481. [8] I.K. Sou, Z. Yang, J. Mao, Z.H. Ma, K.W. Tong, G.K.L. Wong, Appl. Phys. Lett. 69 (1996) 2519. [9] D. Lee, A. Mysyrowicz, A.V. Nurmikko, B.J. Fitzpatrick, Phys. Rev. Lett. 58 (1987) 1475. [10] A. Reznitsky, S. Permogorov, S. Verbin, A. Naumov, Y. Korostelin, V. Novozhilov, S. Prokov'ev, Solid State Commun. 52 (1984) 13. [11] O. Goede, W. Heimbrodt, T. Lau, G. Matzkeit, B. Selle, Phys. Stat. Sol. (a) 94 (1986) 259. [12] W. Heimbrodt, O. Goede, Phys. Stat. Sol. (b) 135 (1986) 795. [13] T. Yao, M. Kato, J.J. Davies, H. Tanino, J. Cryst. Growth 86 (1988) 552. [14] C.P. Hilton, J.J. Davies, J.E. Nicholls, O. Goede, Phys. Stat. Sol. (b) 151 (1989) 175. [15] C.F. Klingshirn, Semiconductor Optics, 1st Edition, Springer, Berlin, 1995 (Chapter 3). [16] J.E. Bernard, A. Zunger, Phys. Rev. B 34 (1986) 5992. [17] S. Larach, R.E. Shrader, C.F. Stocker, Phys. Rev. 108 (1957) 587. [18] K.S. Wong, H. Wang, I.K. Sou, Y.W. Chan, G.K.L. Wong, in: Proceedings of the 22nd International Conference on the Physics of Semiconductor, World Scienti®c, Singapore, 1994, p. 349.

166

Y.-M. Yu et al. / Applied Surface Science 182 (2001) 159±166

[19] S.-H. Wei, A. Zunger, J. Appl. Phys. 78 (1995) 3846. [20] M.J. Seong, H. Alawadhi, I. Miotkowski, A.K. Ramdas, S. Miotkowska, Solid State Commun. 112 (1999) 329. [21] J.A. Van Vechten, T.K. Bergstresser, Phys. Rev. B 1 (1970) 3351. [22] A. Baldereschi, E. Hess, K. Maschke, H. Neumann, K.R. Schulze, K. Unger, J. Phys. C 10 (1977) 4709. [23] K.E. Newman, J.D. Dow, Phys. Rev. B 27 (1983) 7495. [24] A.B. Chen, A. Sher, Phys. Rev. B 23 (1981) 5360. [25] J.E. Bernard, A. Zunger, Phys. Rev. B 36 (1987) 3199. [26] O. Madelung, M. Schultz, H. Weiss (Eds.), Numerical Data and Function Relationships in Science and Technology, Vol. 17, Springer, Berlin, 1982.

[27] M.J. Seong, H. Alawadhi, I. Miotkowski, A.K. Ramdas, Phys. Rev. B 60 (1999) R16275. [28] S. Nam, B. O, K.-S. Lee, Y.D. Choi, J. Cryst. Growth 194 (1998) 61. [29] D. Lee, A. Mysyrowicz, A.V. Nurmikko, B.F. Fitzpatrick, Phys. Rev. Lett. 58 (1987) 1475. [30] Q. Fu, D. Lee, A.V. Nurmikko, L.A. Koloziejski, R.L. Gunsor, Phys. Rev. B 39 (1989) 3173. [31] G.W. Iseler, A.J. Strauss, J. Lumin. 3 (1970) 1. [32] N.Z. Liu, G.H. Li, Z.M. Zhu, H.X. Han, Z.P. Wang, W.K. Ge, I.K. Sou, J. Phys. 10 (1998) 4119. [33] T. Fukushima, S. Shionoya, Jpn. J. Appl. Phys. 12 (1973) 549. [34] T. Yokogawa, T. Narusawa, J. Cryst. Growth 117 (1992) 480.