Codoping Method for Solutions of Doping Problems in Wide-Band-Gap Semiconductors

Transcription

1 phys. stat. sol. (a) 193, No. 3, (2002) Codoping Method for Solutions of Doping Problems in Wide-Band-Gap Semiconductors T. Yamamoto 1 ) Department of Electronic and Photonic System Engineering, Kochi University of Technology, 185 Miyanokuchi, Tosayamada-cho, Kami-gun, Kochi , Japan (Received March 13, 2002; accepted June 3, 2002) PACS: Eq; Gs; Ht We propose a codoping method of using acceptors and donors simultaneously as a solution to the crucial doping problem, or unipolarity, of wide-band-gap semiconductors which exhibit an asymmetry in their ability to be doped as n-type or p-type. The deliberate codoping of donors is essential for the enhancement of acceptor incorporation, decrease of the binding energy of the acceptor impurity and stabilization of the ionic charge distributions in p-type highly doped semiconductors. The donor is not the p-type killer but a good by-player that activates acceptors, i.e., reactive codopant. Confirmation of the applicability of the codoping method to produce low-resistivity p-type GaN, ZnO, and ZnS was sought experimentally. 1. Introduction Wide-band-gap semiconductors, such as diamond with a wide indirect band gap (E g ) of at 295 K, ZnO with a direct E g of ev at 4.2 K and ZnS with a direct E g of 3.68 ev at room temperature, have attracted attention because of their possible application in short-wavelength light-emitting devices. In order to develop such optoelectronic devices based on wide-band-gap semiconductors, one important issue that must be resolved is the fabrication of low-resistivity p- and n-type materials. The semiconductors described above exhibit asymmetry in their ability to be doped as n-type or p-type, which is termed to unipolarity. It is very difficult to obtain lowresistivity n-type diamond, while it has proven to be difficult to dope ZnO and ZnS as p-type. As for ZnO, transparent, electrically conductive n-type Al-doped ZnO films have been investigated more recently and have been found to be very promising as a transparent conducting oxide (TCO) thin film, although there has been no report concerning low-resistivity p-type ZnO. The theoretical prediction for the realization of p-type ZnO by codoping N acceptors and Ga donors in the ratio of N : Ga = 2 :1 [1 4] and ZnS codoped with N acceptors and In donors in the ratio of N :In = 2 :1 was proposed by us [5, 6]. We note that the formation of a cluster, constituting of acceptor-donor-acceptor that occupy the nearestneighbor sites or second-nearest ones, is energetically favorable due to the strong attractive interaction between the dopants and codopants at high doping levels. Subsequent confirmation of the applicability of this codoping in producing p-type ZnO was conducted by Joseph et al. [7]. The fabrication of p-type ZnS with blue Ag emission by the triple-codoping method was reported; The control of compatibility between activator impurity doping for the emission described above and p-type codoping for the control of conductivity was successful [8]. Moreover, the formation of a homo p n junction with a n-zns : In/p-ZnS:(Ag, In, N)/p-GaAs structure was reported [9]. The fabrication 1 ) Phone: ; Fax: ; yamamoto.tetsuya@kochi-tech.ac.jp # 2002 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim /02/ $ 17.50þ.50/0

2 424 T. Yamamoto: Solutions of Doping Problems in Wide-Band-Gap Semiconductors of p-type GaN, ZnO and ZnS is enabling the development of wide-band-gap semiconductor technology. The purpose of this paper is to discuss the necessary ingredients in the codoping effect and investigate how to control the valence electrons in order to change them from localized impurity states to delocalized ones for ZnO and ZnS. 2. Basic Concepts of Codoping Method Here we focus on the fabrication of low-resistivity p-type wide-band-gap semiconductors. We summarize the basic concepts of our codopig method [1 4, 10 12]. The codoping method using acceptors (A) and donors (D) as a reactive codopant, in a ratio of A:D = 2 :1, contributes (i) to enhancing the incorporation of the acceptors because the strong attractive interactions between the acceptor and donor dopants overcome the repulsive interactions between the acceptors, where the driving force is the electrostatic energy gain and (ii) to lowering the energy levels of the acceptors and raising those of the donors in the band gap due to the strong attractive interactions between the acceptor and donor reactive codopants, as shown in Fig. 1. The first mechanism above requires a high affinity between the acceptors and the reactive codopants. For example, we discuss this for the case of ZnO. Considering that the formation enthalpy of kj mol 1 [13] for ZnO is significant lower than that of 20 kj mol 1 for Zn 3 N 2 [14], which could be present as an actual separate phase in the material, the formation of Zn O bonds is energetically favorable compared with that of Zn N bonds. This suggests a low solubility of N into ZnO. For the Zn species, tetrahedral complexes are the most common type and are formed with a variety of O-donor ligands, and more stable ones are formed with N-donor ligands. The cohesive energies per bond for AlN and GaN, which are wurtzite structures like ZnO, are 2.88 and 2.24 ev [15], respectively, being higher than that of 1.89 ev for ZnO [15]. This means there is a higher affinity between Al or Ga and the N species. Thus, both Ga and Al species are eminently suitable for use in codoping with N acceptors. Moreover, we note that the similarity of the Al or Ga N bond distance in their crystals to the Zn O bond distance reduces the elastic contribution to the energy of formation of the N atoms at O (N O ) site acceptors. Nakahara et al. [16] reported that the presence of Ga clearly enhances the incorporation of N into ZnO, at the basis of the analysis of the data obtained by secondary ion mass spectroscopy (SIMS) measurements of ZnO codoped with Ga and N (ZnO :(Ga, N)). Energy Conduction Band acceptor (A) alone Valence Band donor (D) alone Fig. 1. Schematic energy diagram for p-type codoped semiconductors. The acceptor (A) level is lowered and the donor (D) level is raised with the formation of acceptor donor acceptor complexes upon codoping

3 3. Codoping Effects in ZnO Conductive n-type ZnO films have been investigated more recently, and are very promising as a transparent conducting oxide (TCO) thin film. Developing alternatives to indium tin oxide (In 2 O 3 :Sn, ITO) is desirable because of the high cost and scarcity of indium. ZnO is lower in cost and also easier to etch than ITO, so it may replace ITO as a front electrode in some future displays, such as flat-panel displays. To form amorphous-silicon solar cells on transparent conphys. stat. sol. (a) 193, No. 3 (2002) 425 The second mechanism above leads to enhanced impurity ionization. A non-random configuration, such as in A-D-A trimers or trimer-like complexes, is postulated to produce the required reduced ionization energy of the non-compensated acceptor impurities for materials doped with acceptors alone. The postulation will be satisfied by the appropriate choice of the codopant pair under the condition discussed in relation to the first mechanism and the control of the partial pressure for each atom. The estimated acceptor or donor binding energy of the semiconductor based on the Bohr theory of the hydrogen atom, being modified to take into account both the dielectric constant of the medium and the effective mass of an electron or a hole, is given by E B ¼ q4 m eðhþ 2e 2 h 2 ; ð1þ the Bohr radius of the acceptor or donor is a dðaþ ¼ eh2 m eðhþ q 2 : ð2þ The most important factor determining the radius of an impurity orbital is the dielectric constant of the medium. Wide-band-gap semiconductors such as diamond, ZnO, GaN, and ZnS have low dielectric constants, and hence very contracted impurity orbitals. We verified the presence of narrow impurity bands for ZnO:N [1 4] and ZnS :N [5, 6] at a high p-type doping level, where holes are localized by repulsion effects. In order to enhance the Bohr radius of the acceptor, hybridization between p states at acceptor sites and s states at codopant donor sites with a larger Bohr radius and high solubility is very effective. In p-type codoped materials, therefore, acceptor orbitals can overlap sufficiently for good conduction to occur. Below, we present a change from localized impurity states for ZnO or ZnS doped with N alone to delocalized ones for p-type codoped materials. The net doping effect of the majority impurity, which is related to free carrier concentrations, appears to decrease as the codoping method is applied. Noting that the effective mass of holes decreases as the acceptor impurity band width increases, it is very easy to understand the reduced acceptor binding energy due to the codoping using Eqs. (1) and (2). As a result, codoping increases the net doping effect of the majority impurity. Thus, a deliberate codoping of the donors is essential for the enhancement of the solubility of acceptors with the stabilization of the ionic charge distributions and the delocalization of the impurity states at the acceptors, which lead to a reduced acceptor binding energy, in p-type highly doped semiconductors. It should be noted that the donor is not the p-type killer but a good by-player that activates acceptors, which is termed reactive codopant.

4 426 T. Yamamoto: Solutions of Doping Problems in Wide-Band-Gap Semiconductors ductor (TC) superstrates, the TC is exposed to a plasma containing hydrogen atoms. ZnO is much more resistant to hydrogen-plasma reduction and may be preferred for applications such as amorphous-silicon solar cells. ZnO has also attracted attention as a useful material for UV optoelectronic applications. The high excitonic binding energy (60 mev) of ZnO also raises the stimulating possibility of utilizing its excitonic effects in room-temperature devices. In fact, optically pumped UV emission from ZnO films at room temperature has been already reported [17 19]. In order to develop such optoelectronic devices, one important issue that must be resolved is the fabrication of low-resistivity p-type doped ZnO, as well as other wide-band-gap semiconductors such as ZnSe and GaN. However, ZnO is naturally only n-type due to the presence of native n-type defects associated with deviations from perfect stoichiometry, Zn interstitials (Zn i ) and O vacancies (V O ), making the acceptor doping of ZnO difficult. 4. Methodology The results of our band structure calculations for ZnO crystals are based on the local-density approximation (LDA) treatment of electronic exchange and correlation [20 22] and on the augmented spherical wave (ASW) formalism for the solution of effective single-particle equations [23]. For the calculations, the atomic sphere approximation (ASA) with a correction term was adopted. For undoped ZnO crystals, Brillouin zone integration was carried out for 84-k points in an irreducible wedge and for 24-k points for doped and codoped ZnO crystals. For valence electrons, we employed outermost s, p and d orbitals for Zn atoms and s and p orbitals for the other atoms. The Madelung energy, which reflects long-range electrostatic interaction in the system, was assumed to be restricted to a sum over monopoles. We studied the crystal structures of doped and codoped ZnO with periodic boundary conditions by generating supercells that contain the object of interest. 1. For n-type ZnO doped with group III elements (III = B, Al, Ga or In), we replace one of the 16 sites of Zn atoms with a donor site in model supercells. 2. For p-type ZnO doped with N alone, we calculated two cases: a) for ZnO doped with a N concentration of cm 3, we replace one of the 16 sites of O atoms with an acceptor site; b) for ZnO doped with N concentration of cm 3, we replace one of the 64 sites of O atoms by the acceptor site. 3. For ZnO codoped with N and group III elements in a ratio of N : III = 1 :1, (ZnO :(N, III)), we replace one of the 16 sites of the Zn atoms with the donor site and one of the 16 sites of the O atoms with the N atom site. We determined the crystal structure of ZnO :(N, III) by minimizing the total energy. The total energy calculations show that the formation of a pair of the N and III element which occupies the Fig. 2. Crystal structure of a supercell for ZnO : (2N, Ga)

5 phys. stat. sol. (a) 193, No. 3 (2002) 427 nearest-neighbor sites is energetically favorable. 4. For ZnO :(2N, III), we replace one of the remaining 15 sites of the O atoms with the N atom site for ZnO :(N, III) determined above, which is illustrated in Fig Results and Discussion n-type doping of the group III elements, B, Al, Ga and In, results in the broad impurity bands originated due to the large radius of the donor orbital [1]. As a result, the electron has a small effective mass, which yields the rather low impurity ionization energies in ZnO. Moreover, from ab initio electric calculations, we find that the repulsive interactions between the same donor species are very weak compared with those between the N acceptors [1], so that the incorporated donors are very stable in highly n-type doped ZnO crystals. According to the modified Bohr theory of the hydrogen atom, the dielectric constant has the most significant effect on the acceptor energy because it enters as the square, whereas the effective mass enters only as the first power. Considering that AlN, GaN and InN have the same wurtzite structure as ZnO and their dielectric constants are larger than that of ZnO, the group III elements above are eminently suitable for use as reactive codopants with N acceptors. Here, we focus on N species as acceptors because an increase in the Madelung energy for ZnO:N is rather small compared with that for ZnO :Li or ZnO : As, from Table 1. We show the N-site-decomposed densities of states (DOSs) for a) and b) ZnO doped with N alone and c) ZnO :(2N, Ga) in Fig. 3, where the p states at N sites are illustrated. The concentrations of N acceptors for Figs. 3a, b and c are cm 3, cm 3, and cm 3, respectively. Energy is measured relative to the Fermi level (E F ). Figures 3a and b show the formation of an N-impurity band due to the overlap of the N-acceptor orbitals; holes are generated around the top of the valence. For Fig. 3a, the estimated N-impurity band width is almost 0.4 ev; holes in the narrow bands are localized by repulsion effects. The width of the band comes from the overlap of orbitals and depends on their separation. The total energy calculations show that N atoms are well separated from each other by strong repulsive interactions, while the group III elements, Al, Ga and In species, which exhibit as donors, occupy Zn sites at a small distance [1]. The two parts show that the N-impurity bandwidth increases when the concentration of N acceptors increases. In fact, it is very difficult to obtain N concentrations in the order of cm 3 in ZnO crystals or thin films. Next we propose materials design by a codoping method using reactive codopants. We show the crystal structure of supercells for ZnO :(Ga, 2N) crystals shown in Fig. 2. Ab initio total energy calculations revealed the formation of complexes, including the III N pair, which occupy nearest-neighbor sites, and a more distant N, located at the Table 1 Calculated differences in the Madelung energy E Mad (in ev), between undoped and p-type doped ZnO dopant N O As O Li Zn E Mad (ev)

6 428 T. Yamamoto: Solutions of Doping Problems in Wide-Band-Gap Semiconductors DOS (1/eV atom) (a) only N p states 6.5*10 20 cm -3 (b)onlyn p states 2.6*10 21 cm -3 (c) (Ga, 2N) p states 5.2*10 21 cm -3 1st N E F 2nd N Energy (ev) Fig. 3 (online colour). Site-decomposed DOSs for a) and b) ZnO : N and c) ZnO:(2N, Ga). For c), the first N curve indicates the DOS at the N sites close to the Ga site; the second N curve indicates the DOS at the sites of next-nearest-neighbor N atoms (see Fig. 2). For an explanation, see text next-nearest-neighbor site in a layer close to the layer that includes the III N pair, due to the strong repulsive interaction between the N acceptors. Figure 3c for ZnO:(Ga, 2N) shows that the formation of the complexes leads to a mixed state of the hole generated at the top of the valence band originating from the two N acceptors. As a result, we find a change from a narrow band in Fig. 3b to a broad N-impurity band in Fig. 3c; the weight of the p states at the site of N atoms (first N curve) close to the site of the reactive codopant, Ga, shifts towards lower energy regions due to the charge transfer from the Ga to the N atoms. For p-type ZnO:(Ga, 2N), we predict a shallow acceptor with a low effective mass of holes, which is a consequence of the broad band. We summarize the differences in the lattice energy, the Madelung energy, among undoped, n-type doped, p-type doped, and p-type codoped ZnO crystals in Table 2. Table 2 shows that p-type doping using N species causes an increase in the Madelung energy while n-type doping using Al, Ga or In species gives rise to a decrease. It should be noted that the ionic charge distribution in p-type codoped ZnO is stabilized by the codoping. In addition, we discuss the control of carrier concentration for p-type ZnO. From the calculations concerning the three codoped ZnO [1], the delocalization of states of N close to the reactive donors is found to increase in the following order: ZnO:(In, 2N) Table 2 Calculated differences in the Madelung energy E Mad p-type doped codoped ZnO (in ev), between undoped and co-dopant pair (Al, 2N) (Ga, 2N) (In, 2N) E Mad (ev)

7 7. Methodology The results of our band structure calculations for ZnS crystals with zinc-blende structures were based on the local density approximation (LDA) treatment of electronic exchange and correlation [20 22] and on the augmented spherical wave (ASW) formalism for the solution of effective single-particle equations [23]. For valence electrons, we employed the outermost s, p and d orbitals of Zn and S atoms and the outermost s and p orbitals of In and N atoms. The Madelung energy, which reflects the long-range electrostatic interaction within the system, was assumed to be restricted to the sum over monopoles. We studied the crystal structures of doped and codoped ZnS under periodic boundary conditions by generating supercells having 64 atoms that contain the object of interest: 1. for ZnS : In, we replaced one of the 32 sites of Zn atoms with an In site; 2. for ZnS:N, we replaced one of the 32 sites of S atoms with a N site; 3. for ZnS codoped with In and N (ZnS :(In, N)), we replaced one of the 32 sites of S atoms with a N site and one of the 32 sites of Zn atoms with an In site. First, we calculated the total energy for all cases to be considered for ZnS :(In, N). Second, we determined the crystal structure of the material under the condition that the total energy is minimized. We find that an In Zn N S pair which occupies nearest-neighbor sites in the crystal is formed. Finally, to determine the crystal structure of ZnS :(In, 2N), we replaced one of the remaining 31 sites of S with another N site for ZnS : (In, N), as mentioned above. Under the same total energy condition as that of ZnS :(In, N), we determined the crystal structure for ZnS :(In, 2N). The total energy calculations indicate that the formation of the trimer, N S In Zn N S, which occupies the nearest-neighbor sites, is energetically faphys. stat. sol. (a) 193, No. 3 (2002) 429 < ZnO : (Al, 2N) < ZnO:(Ga, 2N). In order to control the carrier concentration in the semiconductor range, it is necessary to apply the triple-codoping method to ZnO crystals using two of the three reactive donors and N acceptors. 6. Codoping Effects in ZnS ZnS with a wide band gap of 3.68 ev at room temperature has the potential of realizing multicolor light-emitting diodes (LEDs) with suitable activator impurity doping. For the development of ZnS-based optoelectronic devices, p n junction formation is essential as is the ZnO discussed above. The realization of p-type ZnS was reported by Iida and coworkers [24, 25]. They prepared N-doped ZnS films by chemical vapor deposition under an ammonia-added flow. Very recently, p-type ZnS:N was fabricated by Svob et al. [26]. The ZnS layers grown by metalorganic vapor phase epitaxy on GaAs substrates showed p-type conductivity with hole concentrations up to cm 3. They found that the energy levels of the N acceptors are about 0.19 ev above the valence band [26]. We have been investigating how to fabricate low-resistivity p-type ZnS thin films with blue Ag emission in order to realize highly efficient blue-led and blue injectionlaser diodes. Ag impurities, which are a Zn-substituting species, are well known to be the blue Ag center (usually called activator ) [27, 28]. In order to realize blue emission of approximately 440 nm (2.81 ev), it is necessary to introduce donors as coactivators into ZnS films. At the same time, ZnS must be doped with acceptors in order to realize p-type ZnS films. We selected N species as acceptor and In as both reactive codopants with N acceptors and coactivators with Ag species. Here we focus on the effects of codoping using In donors on N impurity states.

8 430 T. Yamamoto: Solutions of Doping Problems in Wide-Band-Gap Semiconductors A E F (a) undoped Fig. 4 (online colour). Total DOSs for a) undoped ZnS, b) ZnS : N and c) ZnS :(2N, In) (Ref. [6], Fig. 1) DOS (1/eV cell) (b) N-doped (c) codoped Energy (ev) vorable. The difference in the total energy between the crystal structure having the lowest total energy and the one having the second-lowest total energy, such as the In N pair and another N which occupy the second-nearest neighbor sites from the In sites, is 832 mev. Figure 4 shows the total DOSs for undoped ZnS crystals as a standard reference, for ZnS doped with the N acceptor alone and for ZnS codoped with the N acceptor and In reactive codopants in the ratio of N :In = 2 :1. The S 3s states are included in the calculation as valence states, but those which are located between ev and ev are omitted in Fig. 4. Energy is measured relative to the Fermi level (E F ). For undoped ZnS, zero energy indicates the top of the valence band. Figure 4a shows two groups in the valence band: 1. the first group is bands from 7.01 to 6.16eV with strong d characteristics originating mostly from d states at Zn sites; 2. the second group, located in the upper valence band above approximately 5.61 ev, which corresponds to a high-symmetry point L 1, mainly originates from the S 3p states. The letter A at 4.97 ev refers to a strong interaction between S p states and Zn s states. The lowest conduction bands, antibonding states of the interaction stated above, have a strong Zn 4s contribution; there are charge transfers from Zn 4s to S 3s and 3p due to the mixing between the s and p states at S sites and the s states at Zn sites. As a result, the s and p states of the surrounding Zn shift the center of gravity of the local DOS at the S sites towards the lower energy region. Based on this feature concerning the nature of chemical bonds for ZnS, we also discuss the stability of the ionic charge distributions in ZnS doped with acceptors or donors in terms of the change of the Madelung energy. Figures 4b and c show that a hole is generated at the top of the valence band. The arrow in Fig. 4b at 0.1 ev refers to a sharp DOS peak induced by N doping, whereas, as shown in Fig. 4c, no sharp DOS peak around E F described above is observed, which will be discussed below. The arrow at 3.67 ev in Fig. 4c indicates a DOS peak resulting from the interaction between p states at S sites close to the In site and s states at the Zn sites which occupy the nearest-neighbor sites from the S sites and the second-

9 phys. stat. sol. (a) 193, No. 3 (2002) 431 DOS (1/eV atom) (a) N only p states at N E F Fig. 5. N-site-decomposed DOSs for a) ZnS : N and b) ZnS :(2N, In). p states at the N sites are presented (Ref. [6], Fig. 2) nearest-neighbor sites from the In atoms. 2 Figures 5a and b show N-site-decomposed DOSs for ZnS: N and ZnS:(2N, In), respectively. Based on the analysis of 1 N-site-decomposed DOSs shown in Fig. 5a, we find that the N acceptor heavily doped forms narrow bands with the 5 roughly estimated width of 1.0 ev. This originates in the low static dielectric constant of 8.32 for ZnS [29]. The valence 4 (b) codoped p states at N orbital of N with large electronegativity 3 compared with that of S species is contracted. Thus, the DOS peak below the top of the valence band in both Fig. 4c 2 and Fig. 5a is due to a localized N-impurity state of which the center of gravity of 1 the DOS at N sites is pushed up to a higher energy region due to the strong repulsive potential. This suggests that N doping generates a slightly deeper acceptor level above the valence band, which Energy (ev) explains well the experimental data concerning the N-impurity levels [26]. As shown in Fig. 5b, the center of gravity for the N-impurity band shifts towards lower energy regions compared with that shown in Fig. 5a. We note that In codoping increases the N-impurity bandwidth which is estimated to be more than 2 ev for ZnS:(2N, In). Based on the analysis concerning the DOS at E F for ZnS:N, we determined that the ratio of the partial DOS of p states at the N sites to the total DOS at E F is 22%. The other DOS at E F is the sum of those at the S sites in the vicinity of the N sites. This indicates the small radius of the N-acceptor orbital. On the other hand, for ZnS:(2N, In), from the calculations of the DOS at E F, we determined that the ratio of the sum of partial DOSs of p states at the two N sites to the total DOS at E F is 9.2%; we must note that the partial DOS not only at the S sites in the vicinity of the N sites but also at the more distant S sites contributes to the total DOS at E F. This means that the codoping of In as the reactive codopant into ZnS:N causes the N-acceptor orbital to have a large radius, resulting in a small effective mass of the hole, which is a consequence of the broadened impurity band. Noting the acceptor ionization energy given by Eq. (1), it is reasonable to predict the realization of low-resistivity p-type ZnS:(In, N). Kishimoto et al. [8] reported that Hall effect measurements at room temperature for ZnS :(N, In, Ag) revealed the free hole concentration and mobility

10 432 T. Yamamoto: Solutions of Doping Problems in Wide-Band-Gap Semiconductors values to be ( ) cm 3 and cm 2 /Vs, respectively, for ZnS:(Ag, In and N). Concerning a change of the Madelung energy upon codoping, for ZnS:(In, 2N), we find that it decreases by 30 ev compared with that for ZnS:N, based on the analysis of the calculated results, which is due to a large charge transfer from In to N atoms. Taking into consideration that the ZnS under investigation has not a wurtzite structure, which is favored by more ionic compounds, but a zinc-blende structure, the optimum amount of In to be codoped must be determined in further experiments. 8. Conclusions In conclusion, we have shown that a simultaneous codoping method using an acceptor and a reactive codopant is very effective for the fabrication of lowresistivity p-type wide-band-gap semiconductors, such as ZnO and ZnS. We have developed the codoping method and applied it in the attempt to control the compatibility between activator impurity doping for blue emission and codoping for good p-type conductivity by the triple-codoping method. We have proposed a model for ZnS:(Ag, In, and N), in which some of the In species act as coactivators with Ag activators and other In species act as reactive codopants with N acceptors. Acknowledgements The author thanks Dr. Jürgen Sticht for technical support. We used the ESOCS code of accelrys. The author would like to express sincere thanks to Professor Hiroshi Katayama-Yoshida of Osaka University for fruitful discussions and Professor Akio Hiraki of Kochi University of Technology for his encouragement of this work. The present research was made possible by a grant of a regional consortium from New Energy and Industrial Technology Development Organization (NEDO). References [1] T. Yamamoto and H. Katayama-Yoshida, Jpn. J. Appl. Phys. 38, L166 (1999). [2] T. Yamamoto and H. Katayama-Yoshida, J. Cryst. Growth 214/215, 552 (2000). [3] T. Yamamoto and H. Katayama-Yoshida, Mater. Res. Soc. Proc. 623, 223 (2000). [4] T. Yamamoto and H. Katayama-Yoshida, Physica B 302/303, 155 (2001). [5] T. Yamamoto, S. Kishimoto, and S. Iida, Physica B , 916 (2001). [6] T. Yamamoto, S. Kishimoto, and S. Iida, phys. stat. sol. (b) 229, 371 (2002). [7] M. Joseph, H. Tabata, and T. Kawai, Jpn. J. Appl. Phys. 38, L1205 (1999). [8] S. Kishimoto, T. Hasegawa, H. Kinto, O. Matsumoto, and S. Iida, J. Cryst. Growth 214/215, 556 (2000). [9] S. Kishimoto, A. Kato, A. Naito, Y. Sakamoto, and S. Iida, phys. stat. sol. (b) 229, 391 (2002). [10] T. Yamamoto and H. Katayama-Yoshida, Mater. Res. Soc. Proc. 426, 201 (1996). [11] T. Yamamoto and H. Katayama-Yoshida, Jpn. J. Appl. Phys. 36, L180 (1997). [12] T. Yamamoto and H. Katayama-Yoshida, Jpn. J. Appl. Phys. 37, L910 (1998). [13] D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, and R. L. Nuttall, J. Phys. Chem. Ref. Data 11, Suppl. 2 (1982). [14] P. Pascal, Nouveau traité de Chimie minérale, Tome V, Masson, Paris 1962; Thermodata (Banque de données thermochimiques, BP 66, 38402, Saint-Martin-d Hères, France). [15] W. A. Harrison, Electronic Structure and the Properties of Solids, Dover Publ. Inc., New York 1989 (Chap. 7, Table 7-3). [16] K. Nakahara, H. Takasu, and P. Fons, Appl. Phys. Lett. 79, 4139 (2001). [17] D. C. Reynolds, D. C. Look, and B. Jogai, Solid State Commun. 99, 873 (1996). [18] D. M. Bagnall, Y. F. Chen, M. Y. Shen, Z. Zhu, T. Goto, and T. Yao, Appl. Phys. Lett. 70, 2230 (1997).

11 phys. stat. sol. (a) 193, No. 3 (2002) 433 [19] P. Yu, Z. K. Tang, G. K. L. Wong, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, Solid State Commun. 103, 459 (1997). [20] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). [21] L. Hedin and B. I. Lundquist, J. Phys. C 4, 3107 (1971). [22] U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972). [23] A. R. Williams, J. Kübler, and C. D. Gelatt, Phys. Rev. B 19, 6094 (1979). [24] S. Iida, T. Yatabe, and H. Kinto, Jpn. J. Appl. Phys. (Part 2) 28, L535 (1989). [25] S. Iida, T. Yatabe, H. Kinto, and M. Shinohara, J. Cryst. Growth 101, 141 (1990). [26] L Svob, C Thiandoume, A Lusson, M. Bouanani, Y. Marfaing, and O. Gorochov, Appl. Phys. Lett. 76, 1695 (2000). [27] K. Era, S. Shionoya, and Y. Washizawa, J. Phys. Chem. Solids 29, 1827 (1968). [28] K. Era, S. Shionoya, Y. Washizawa, and H. Ohmatsu, J. Phys. Chem. Solids 29, 1843 (1968). [29] R. K. Watts, Point Defects in Crystals, Wiley, New York 1977 (p. 236).