- Email: [email protected]
Theoretical investigations on electronic and optical properties of rock-salt gallium nitride
Thin Solid Films 515 (2006) 2433 – 2436 www.elsevier.com/locate/tsf
Theoretical investigations on electronic and optical properties of rock-salt gallium nitride Z.W. Chen, M.Y. Lv, L.X. Li, Q. Wang, X.Y. Zhang, R.P. Liu ⁎ State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China Received 21 November 2005; received in revised form 13 April 2006; accepted 8 June 2006 Available online 11 July 2006
Abstract The electronic and optical properties of rock-salt gallium nitride (GaN) have been investigated using the first principles method based on the plane–wave basis set. Analysis of band structure suggests that the rock-salt GaN is a middle gap indirect semiconductor with the conduction band minimum and the valence band maximum locating at X point and Σ direction respectively. Within the screen-exchange local density approximation, the bandgap is predicted to be 1.83 eV. The optical properties including dielectric function, reflectivity, absorption and energy-loss function with some special features are obtained and analyzed. The calculated pressure coefficients of the indirect bandgaps at Γ, X and L points are very small, with the value of the smallest indirect bandgap determined to be 26 meV/GPa. © 2006 Elsevier B.V. All rights reserved. Keywords: Electronic structure; Optical properties; Rock-salt phase; Gallium nitride
1. Introduction The GaN phase with a wurtzite structure is a wide direct bandgap semiconductor and a prospective material for optical devices such as light-emitting diodes, laser diode, and UV detectors, owing to its low compressibility, high thermal conductivity and high breakdown fields [1]. Due to these properties, it is also ideal for high-power and high-temperature devices. Stimulated by these applications, much attention has been given to the exploration of the other GaN phases. A metastable zincblende structure that lies close in enthalpy (less than 50 meV) to the common wurtzite form was proved to be possible by epitaxial techniques [2]. Furthermore, the structural transition to a new rock-salt phase was reported to take place at the pressure of about 52 GPa. This structural transition does not change the semiconducting nature of the GaN [3,4]. To date, there has been an increasing interest in stabilizing the high-pressure phases with particular properties, such as the high-pressure semiconducting phases of AlN and ZnO, by means of epitaxial growth or nanocrystallites [5]. It has been suggested that the nonequilibrium rock-salt phase of GaN, which may find its appli⁎ Corresponding author. Tel./fax: +86 335 8074723. E-mail address: [email protected] (R.P. Liu). 0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.06.005
cations in transistor-based strained heretostructures, can be retained to ambient conditions as a metastable phase by appropriate template layers [6]. The changes in symmetry together with the altered density and the band hybridization may bring some unusual optical properties and potential applications [7]. In recent experiments, progress has been made in the synthesis of nanoparticles of the rock-salt GaN phase [8,9] and the strained layer of the rock-salt GaN phase grown on sapphire substrates by metalorganic vapor phase epitaxy [10]. Although much work has been done on the synthesis and stabilization of this phase, less is known about its exact physical properties. Thus, it is of great importance to explore the electronic structure and optical properties of the rock-salt GaN phase, which may be useful in indicating the future technological applications. In this article, we performed a detailed investigation on the electronic and optical properties of rock-salt GaN together with the pressure shift character of the energy gap (dEg / dp) using the first-principles method. 2. Calculation method First-principles calculations are performed with Cambridge Serial Total Energy Package (CASTEP) [11] operated within the Materials Studio® software environment (Accelrys Software Inc.). A plane-wave basis set for the electron wave functions
2434
Z.W. Chen et al. / Thin Solid Films 515 (2006) 2433–2436
Fig. 1. Band structure of rock-salt GaN. Zero energy is defined to be the maximum of the valence band. The valence band maximum locates at point (0.1875, 0.1875, 0.375) in Γ − K direction owing to the upwards dispersion of p bands induced by p − d repulsion. Since the conduction band minimum locates at X point, an indirect bandgap is obtained.
expansion up to a kinetic energy cut-off of 500 eV is used with periodic boundary conditions. The ultra-soft pseudopotential [12] is employed for electron–ion interaction, and the generalized gradient approximation (GGA) of Perdew et al. [13] for electron– electron interaction. Pseudo atomic calculations are performed for N 2s22p3 and Ga 3d104s24p1 by treating d-electron as valence electrons in Ga, since d-electron relaxation was found to have a profound effect on the calculated band structure and its pressure dependence in previous calculation on ZnO [5]. A previous study shows that such a method reproduces very well the structures and properties of GaN under high pressure [14]. The k points integrations over the Brillouin zone (BZ) are performed using the Monkhorst and Pack mesh [15]. Here, 8 × 8 × 8 mesh parameters grid is taken in the irreducible wedge of BZ for the rock-salt GaN phase. During the structure optimizations, the total energy is minimized by varying lattice constants under the restriction of the given symmetry, and all forces on atoms are converged to less than 0.001 eV/Å. The pressure coefficient of an interband transition in a semiconductor is easily calculated which is given by dEg / dp, and is related to the volume deformation potential dE / dlnV and the bulk modulus by the formula dEg / dp = −(1/ B) * dEg / dlnV in the cubic structure. 3. Results and discussion For confirmation of the validity of the present calculation method, the lattice constant of the zincblende GaN is calculated, which is 4.53 Å, almost the same as the experimental value of 4.52 Å [16]. The lattice constant of the rock-salt GaN is determined to be 4.252 Å, which is also very close to the experimental value of 4.234 Å [17]. The calculated bulk modulus of the rocksalt GaN is 204 GPa. This value is higher than the bulk modulus of both the zincblende structure and the wurtzite structure, 178 GPa, which is underestimated compared to the experimental data, 204 GPa [18]. It is common to have an underestimated value when GGA approximation is used. Thus the actual bulk modulus of the rock-salt structure is probably higher than 204 GPa. Given the underestimation of the GGA approximation for calculation of the bandgap [19], here the screen-exchange local
density approximation (sX-LDA) is applied, for which the computation work is much less demanding than the quasiparticle approximation. It is reported that the bandgaps calculated with the sX-LDA are in very good agreement with experimental values especially for the narrow and medium bandgap materials [20,21]. Band dispersions along high symmetry lines of the rock-salt GaN in the BZ are shown in Fig. 1. The valence band maximum (VBM) is at the point (0.1875, 0.1875, 0.375) which locates between Γ and K points. In the Γ − K (or Σ) direction, the p and d states hybridize and the resulting p − d repulsion leads to the upwards dispersion of p bands. This is consistent with the results of Limpijumnong [22,23] and Christensen [24]. The topmost valence band at L and Γ are only slightly lower than VBM with energy differences 0.15 and 0.66 eV. On the other hand, the conduction band minimum locates at X point. Therefore, the rocksalt GaN has an indirect bandgap of 1.83 eV, close to the value of 1.69 eV given by Limpijumnong [22] and obviously smaller than that of wurtzite structure (3.47 eV) and zincblende structure (3.28 eV) [16,25]. In the energy band structure, the valence band consists of 9 energy levels range from 0 to −17.2 eV. The highest three levels degenerate into two levels at L and X points with the higher one doublet, while they degenerate into one at Γ. The upmost valence bands are relatively flat, suggesting large hole effective masses, and some unusual transport properties for ptype semiconductor may be expected. The band gaps between the lowest conduction band energies at Γ, X and L points and the VBM are listed respectively in Table 1. These indirect bandgaps show nearly a linear increase with applied pressure. The pressure coefficient of the energy gap between X and VBM is determined to be 26 meV/GPa, which is much smaller in comparison with the value of wurtzite GaN, 42 meV/GPa [25]. Dielectric function ε(ε), which relates to the interaction of photons with electrons, is used to describe the linear response of the system to an electromagnetic radiation [26]. Its imaginary part ε2(ε) can be given by calculating the momentum matrix elements between the occupied and unoccupied wave functions within selection rules. As the bandgap calculated with sX-LDA is used and the bandgap correction of 1.63 eV is taken into account in the present case, resulting in the onset of the calculated ε2(ω) shifts upwards in photon energy. Accordingly, its real part ε1(ω) can be derived from ε2(ω) according to the Kramer–Kronig relationship. For optical property calculations, the norm-conserving pseudopotential [27] is used. It is important to use a sufficient number of k points in the BZ in optical matrix element calculations. The matrix element changes more rapidly within the BZ than electronic energies themselves. To integrate this property accurately, more k points are required than those needed for an ordinary self-consistent field calculation, and a denser 10 × 10× 10 k points grid are generated. Table 1 Bandgap energies relative to the valence band maximum and the corresponding pressure coefficients calculated with sX-LDA approximation
Σ − Xc Σ − Lc Σ − Γc
Bandgaps (eV)
Pressure coefficients (meV/GPa)
1.83 6.06 3.59
26 18 41
Z.W. Chen et al. / Thin Solid Films 515 (2006) 2433–2436
2435
Fig. 2. Optical properties of rock-salt GaN. An identical value 0.5 of the instrumental smearing for Gaussian broadening is specified: (a) Dielectric function with the dash and solid lines representing the real and imaginary parts respectively; (b) energy-loss function; (c) absorption spectra with the arrow indicating the transition energy corresponding to the absorption edge; and (d) reflectivity.
Meanwhile, enough conduction states are essential for accuracy and 12 empty bands in addition to the occupied bands are included in the calculation. The changes of the optical properties with the number of conduction bands and k points in the optical matrix elements calculation are tested to ensure convergence. The dielectric function curves to the photon energy are displayed in Fig. 2(a) in the range of 0–60 eV, where the dashed and solid lines represent the real part ε1(ω) and the imaginary part ε2(ω) respectively. The real part exhibits a peak at 6 eV due to the interband transitions that originate from the VBM to the bottom of the conduction band at the L point, and it reduces to a minimum at 8.3 eV subsequently. For the imaginary part of the dielectric function, the absorption starts at about 3.5 eV which is related to the transition from VBM to Γ1c, and two prominent peaks at about 6.8 and 13.5 eV are presented mainly due to the interband tranv sitions from Γ15 to L1c and from X5v to X3c respectively. From the real and imaginary parts of the complex dielectric response function, the other related functions such as the reflectivity and energy-loss functions can easily be obtained. Fig. 2 (b) displays the electron energy-loss function, which is the imaginary part of the reciprocal of the complex dielectric function. The energy-loss function describes the energy loss of a fast electron traversing in the material and is usually large at the plasma energy whose position corresponds to ε1(ω) = 0, provided ε2(ω) is reasonably smooth [28]. Three wide peaks can be observed in the curve. This is consistent to the features of ε1(ω), for which three regions with ε1(ω) <0 exist. The absorption spectrum
starting from a lossless region (0–3.5 eV) is shown in Fig. 2(c). In the lossless region, the reflectivity, as shown in Fig. 2(d), is lower than 30%, which indicates that the material is transmitting for frequencies less than 3.5 eV. 4. Conclusion A detailed study is performed on the electronic and optical properties of rock-salt GaN together with the pressure coefficients of bandgaps. An indirect bandgap induced by the transition from Σ to X is presented, with its value of 1.83 eV within the sX-LDA approximation. The band calculations are demonstrated to be in good agreement with the available theoretical data. From the calculated band structure, the dielectric function, reflectivity, absorption and energy-loss function are obtained. The relations of the optical properties to the interband transitions are also elucidated. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 50325103) and by the National Basic Research Program of China (Grant No. 2005CB724400). References [1] Z. Dridi, B. Bouhafs, P. Ruterana, New J. Phys. 4 (2002) 1.1. [2] A. Mujica, A. Rubio, A. Muñoz, R.J. Needs, Rev. Mod. Phys. 75 (2003) 863.
2436
Z.W. Chen et al. / Thin Solid Films 515 (2006) 2433–2436
[3] R. Pandey, J.E. Jaffe, N.M. Harrison, J. Phys. Chem. Solids 55 (1994) 1357. [4] A. Munoz, K. Kunc, Phys. Rev., B Rapid Commun. 44 (1991) 10372. [5] A. Segura, J.A. Sans, F.J. Manjón, A. Muñoz, M.J. Herrera-Cabrera, Appl. Phys. Lett. 83 (2003) 278. [6] V. Pankov, M. Evstigneev, R.H. Prince, Appl. Phys. Lett. 80 (2002) 4142. [7] J.E. Jaffe, R. Pandey, A.B. Kunz, Phys. Rev., B 43 (1991) 14030. [8] Y. Xie, Y. Qian, W. Wang, S. Zhang, Y. Zhang, Science 272 (1996) 1926. [9] F. Xu, Y. Xie, X. Zhang, S. Zhang, L. Shi, New J. Chem. 27 (2003) 565. [10] M. Lada, A.G. Cullis, P.J. Parbrook, M. Hopkinson, Appl. Phys. Lett. 83 (2003) 2808. [11] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys., Condens. Matter 14 (2002) 2717. [12] D. Vanderbilt, Phys. Rev., B 41 (1990) 7892. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] X.-R. Chen, L.-Yu. Lu, Y. Cheng, J.-Z. Zhao, Solid State Commun. 136 (2005) 152. [15] H.J. Monkhorst, J.D. Pack, Phys. Rev., B 13 (1976) 5188. [16] I. Akasaki, H. Amano, in Properties of Group III Nitrides (edited by Edgar, J. H.), EMIS Data reviews Series, No. 11, (1994), an INSPEC publication, pp. 30–34.
[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
H. Xia, Q. Xia, A.L. Ruoff, Phys. Rev., B 47 (1993) 12925. P. Boguslawski, E.L. Briggs, J. Bernholc, Phys. Rev., B 51 (1995) 17255. A. Seidl, A. Görling, P. Vogl, J.A. Majewski, Phys. Rev., B 53 (1996) 3764. J.A. Majewski, S. Birner, A. Trellakis, M. Sabathil, P. Vogl, Phys. Status Solidi (c) 1 (2004) 2003. R. Asahi, W. Mannstadt, A.J. Freeman, Phys. Rev., B 59 (1999) 7486. S. Limpijumnong, W.R.L. Lambrecht, Phys. Rev., B 63 (2001) 104103. S. Limpijumnong, W.R.L. Lambrecht, Phys. Rev. Lett. 86 (2000) 91. N.E. Christensen, I. Gorczyca, Phys. Rev., B 50 (1994) 4397. H. Morkoç, S. Strite, G.B. Gao, M.E. Lin, B. Sverdlov, M. Burns, J. Appl. Phys. 76 (1994) 1363. J. Sun, H.-T. Wang, N.-B. Ming, J.L. He, Y.J. Tian, Appl. Phys. Lett. 84 (2004) 4544. D.R. Hamann, M. Schluter, C. Chiang, Phys. Rev. Lett. 43 (1979) 1494. C.S. Wang, B.M. Klein, Phys. Rev. 24 (1981) 3417.
Theoretical investigations on electronic and optical properties of rock-salt gallium nitride Z.W. Chen, M.Y. Lv, L.X. Li, Q. Wang, X.Y. Zhang, R.P. Liu ⁎ State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China Received 21 November 2005; received in revised form 13 April 2006; accepted 8 June 2006 Available online 11 July 2006
Abstract The electronic and optical properties of rock-salt gallium nitride (GaN) have been investigated using the first principles method based on the plane–wave basis set. Analysis of band structure suggests that the rock-salt GaN is a middle gap indirect semiconductor with the conduction band minimum and the valence band maximum locating at X point and Σ direction respectively. Within the screen-exchange local density approximation, the bandgap is predicted to be 1.83 eV. The optical properties including dielectric function, reflectivity, absorption and energy-loss function with some special features are obtained and analyzed. The calculated pressure coefficients of the indirect bandgaps at Γ, X and L points are very small, with the value of the smallest indirect bandgap determined to be 26 meV/GPa. © 2006 Elsevier B.V. All rights reserved. Keywords: Electronic structure; Optical properties; Rock-salt phase; Gallium nitride
1. Introduction The GaN phase with a wurtzite structure is a wide direct bandgap semiconductor and a prospective material for optical devices such as light-emitting diodes, laser diode, and UV detectors, owing to its low compressibility, high thermal conductivity and high breakdown fields [1]. Due to these properties, it is also ideal for high-power and high-temperature devices. Stimulated by these applications, much attention has been given to the exploration of the other GaN phases. A metastable zincblende structure that lies close in enthalpy (less than 50 meV) to the common wurtzite form was proved to be possible by epitaxial techniques [2]. Furthermore, the structural transition to a new rock-salt phase was reported to take place at the pressure of about 52 GPa. This structural transition does not change the semiconducting nature of the GaN [3,4]. To date, there has been an increasing interest in stabilizing the high-pressure phases with particular properties, such as the high-pressure semiconducting phases of AlN and ZnO, by means of epitaxial growth or nanocrystallites [5]. It has been suggested that the nonequilibrium rock-salt phase of GaN, which may find its appli⁎ Corresponding author. Tel./fax: +86 335 8074723. E-mail address: [email protected] (R.P. Liu). 0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.06.005
cations in transistor-based strained heretostructures, can be retained to ambient conditions as a metastable phase by appropriate template layers [6]. The changes in symmetry together with the altered density and the band hybridization may bring some unusual optical properties and potential applications [7]. In recent experiments, progress has been made in the synthesis of nanoparticles of the rock-salt GaN phase [8,9] and the strained layer of the rock-salt GaN phase grown on sapphire substrates by metalorganic vapor phase epitaxy [10]. Although much work has been done on the synthesis and stabilization of this phase, less is known about its exact physical properties. Thus, it is of great importance to explore the electronic structure and optical properties of the rock-salt GaN phase, which may be useful in indicating the future technological applications. In this article, we performed a detailed investigation on the electronic and optical properties of rock-salt GaN together with the pressure shift character of the energy gap (dEg / dp) using the first-principles method. 2. Calculation method First-principles calculations are performed with Cambridge Serial Total Energy Package (CASTEP) [11] operated within the Materials Studio® software environment (Accelrys Software Inc.). A plane-wave basis set for the electron wave functions
2434
Z.W. Chen et al. / Thin Solid Films 515 (2006) 2433–2436
Fig. 1. Band structure of rock-salt GaN. Zero energy is defined to be the maximum of the valence band. The valence band maximum locates at point (0.1875, 0.1875, 0.375) in Γ − K direction owing to the upwards dispersion of p bands induced by p − d repulsion. Since the conduction band minimum locates at X point, an indirect bandgap is obtained.
expansion up to a kinetic energy cut-off of 500 eV is used with periodic boundary conditions. The ultra-soft pseudopotential [12] is employed for electron–ion interaction, and the generalized gradient approximation (GGA) of Perdew et al. [13] for electron– electron interaction. Pseudo atomic calculations are performed for N 2s22p3 and Ga 3d104s24p1 by treating d-electron as valence electrons in Ga, since d-electron relaxation was found to have a profound effect on the calculated band structure and its pressure dependence in previous calculation on ZnO [5]. A previous study shows that such a method reproduces very well the structures and properties of GaN under high pressure [14]. The k points integrations over the Brillouin zone (BZ) are performed using the Monkhorst and Pack mesh [15]. Here, 8 × 8 × 8 mesh parameters grid is taken in the irreducible wedge of BZ for the rock-salt GaN phase. During the structure optimizations, the total energy is minimized by varying lattice constants under the restriction of the given symmetry, and all forces on atoms are converged to less than 0.001 eV/Å. The pressure coefficient of an interband transition in a semiconductor is easily calculated which is given by dEg / dp, and is related to the volume deformation potential dE / dlnV and the bulk modulus by the formula dEg / dp = −(1/ B) * dEg / dlnV in the cubic structure. 3. Results and discussion For confirmation of the validity of the present calculation method, the lattice constant of the zincblende GaN is calculated, which is 4.53 Å, almost the same as the experimental value of 4.52 Å [16]. The lattice constant of the rock-salt GaN is determined to be 4.252 Å, which is also very close to the experimental value of 4.234 Å [17]. The calculated bulk modulus of the rocksalt GaN is 204 GPa. This value is higher than the bulk modulus of both the zincblende structure and the wurtzite structure, 178 GPa, which is underestimated compared to the experimental data, 204 GPa [18]. It is common to have an underestimated value when GGA approximation is used. Thus the actual bulk modulus of the rock-salt structure is probably higher than 204 GPa. Given the underestimation of the GGA approximation for calculation of the bandgap [19], here the screen-exchange local
density approximation (sX-LDA) is applied, for which the computation work is much less demanding than the quasiparticle approximation. It is reported that the bandgaps calculated with the sX-LDA are in very good agreement with experimental values especially for the narrow and medium bandgap materials [20,21]. Band dispersions along high symmetry lines of the rock-salt GaN in the BZ are shown in Fig. 1. The valence band maximum (VBM) is at the point (0.1875, 0.1875, 0.375) which locates between Γ and K points. In the Γ − K (or Σ) direction, the p and d states hybridize and the resulting p − d repulsion leads to the upwards dispersion of p bands. This is consistent with the results of Limpijumnong [22,23] and Christensen [24]. The topmost valence band at L and Γ are only slightly lower than VBM with energy differences 0.15 and 0.66 eV. On the other hand, the conduction band minimum locates at X point. Therefore, the rocksalt GaN has an indirect bandgap of 1.83 eV, close to the value of 1.69 eV given by Limpijumnong [22] and obviously smaller than that of wurtzite structure (3.47 eV) and zincblende structure (3.28 eV) [16,25]. In the energy band structure, the valence band consists of 9 energy levels range from 0 to −17.2 eV. The highest three levels degenerate into two levels at L and X points with the higher one doublet, while they degenerate into one at Γ. The upmost valence bands are relatively flat, suggesting large hole effective masses, and some unusual transport properties for ptype semiconductor may be expected. The band gaps between the lowest conduction band energies at Γ, X and L points and the VBM are listed respectively in Table 1. These indirect bandgaps show nearly a linear increase with applied pressure. The pressure coefficient of the energy gap between X and VBM is determined to be 26 meV/GPa, which is much smaller in comparison with the value of wurtzite GaN, 42 meV/GPa [25]. Dielectric function ε(ε), which relates to the interaction of photons with electrons, is used to describe the linear response of the system to an electromagnetic radiation [26]. Its imaginary part ε2(ε) can be given by calculating the momentum matrix elements between the occupied and unoccupied wave functions within selection rules. As the bandgap calculated with sX-LDA is used and the bandgap correction of 1.63 eV is taken into account in the present case, resulting in the onset of the calculated ε2(ω) shifts upwards in photon energy. Accordingly, its real part ε1(ω) can be derived from ε2(ω) according to the Kramer–Kronig relationship. For optical property calculations, the norm-conserving pseudopotential [27] is used. It is important to use a sufficient number of k points in the BZ in optical matrix element calculations. The matrix element changes more rapidly within the BZ than electronic energies themselves. To integrate this property accurately, more k points are required than those needed for an ordinary self-consistent field calculation, and a denser 10 × 10× 10 k points grid are generated. Table 1 Bandgap energies relative to the valence band maximum and the corresponding pressure coefficients calculated with sX-LDA approximation
Σ − Xc Σ − Lc Σ − Γc
Bandgaps (eV)
Pressure coefficients (meV/GPa)
1.83 6.06 3.59
26 18 41
Z.W. Chen et al. / Thin Solid Films 515 (2006) 2433–2436
2435
Fig. 2. Optical properties of rock-salt GaN. An identical value 0.5 of the instrumental smearing for Gaussian broadening is specified: (a) Dielectric function with the dash and solid lines representing the real and imaginary parts respectively; (b) energy-loss function; (c) absorption spectra with the arrow indicating the transition energy corresponding to the absorption edge; and (d) reflectivity.
Meanwhile, enough conduction states are essential for accuracy and 12 empty bands in addition to the occupied bands are included in the calculation. The changes of the optical properties with the number of conduction bands and k points in the optical matrix elements calculation are tested to ensure convergence. The dielectric function curves to the photon energy are displayed in Fig. 2(a) in the range of 0–60 eV, where the dashed and solid lines represent the real part ε1(ω) and the imaginary part ε2(ω) respectively. The real part exhibits a peak at 6 eV due to the interband transitions that originate from the VBM to the bottom of the conduction band at the L point, and it reduces to a minimum at 8.3 eV subsequently. For the imaginary part of the dielectric function, the absorption starts at about 3.5 eV which is related to the transition from VBM to Γ1c, and two prominent peaks at about 6.8 and 13.5 eV are presented mainly due to the interband tranv sitions from Γ15 to L1c and from X5v to X3c respectively. From the real and imaginary parts of the complex dielectric response function, the other related functions such as the reflectivity and energy-loss functions can easily be obtained. Fig. 2 (b) displays the electron energy-loss function, which is the imaginary part of the reciprocal of the complex dielectric function. The energy-loss function describes the energy loss of a fast electron traversing in the material and is usually large at the plasma energy whose position corresponds to ε1(ω) = 0, provided ε2(ω) is reasonably smooth [28]. Three wide peaks can be observed in the curve. This is consistent to the features of ε1(ω), for which three regions with ε1(ω) <0 exist. The absorption spectrum
starting from a lossless region (0–3.5 eV) is shown in Fig. 2(c). In the lossless region, the reflectivity, as shown in Fig. 2(d), is lower than 30%, which indicates that the material is transmitting for frequencies less than 3.5 eV. 4. Conclusion A detailed study is performed on the electronic and optical properties of rock-salt GaN together with the pressure coefficients of bandgaps. An indirect bandgap induced by the transition from Σ to X is presented, with its value of 1.83 eV within the sX-LDA approximation. The band calculations are demonstrated to be in good agreement with the available theoretical data. From the calculated band structure, the dielectric function, reflectivity, absorption and energy-loss function are obtained. The relations of the optical properties to the interband transitions are also elucidated. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 50325103) and by the National Basic Research Program of China (Grant No. 2005CB724400). References [1] Z. Dridi, B. Bouhafs, P. Ruterana, New J. Phys. 4 (2002) 1.1. [2] A. Mujica, A. Rubio, A. Muñoz, R.J. Needs, Rev. Mod. Phys. 75 (2003) 863.
2436
Z.W. Chen et al. / Thin Solid Films 515 (2006) 2433–2436
[3] R. Pandey, J.E. Jaffe, N.M. Harrison, J. Phys. Chem. Solids 55 (1994) 1357. [4] A. Munoz, K. Kunc, Phys. Rev., B Rapid Commun. 44 (1991) 10372. [5] A. Segura, J.A. Sans, F.J. Manjón, A. Muñoz, M.J. Herrera-Cabrera, Appl. Phys. Lett. 83 (2003) 278. [6] V. Pankov, M. Evstigneev, R.H. Prince, Appl. Phys. Lett. 80 (2002) 4142. [7] J.E. Jaffe, R. Pandey, A.B. Kunz, Phys. Rev., B 43 (1991) 14030. [8] Y. Xie, Y. Qian, W. Wang, S. Zhang, Y. Zhang, Science 272 (1996) 1926. [9] F. Xu, Y. Xie, X. Zhang, S. Zhang, L. Shi, New J. Chem. 27 (2003) 565. [10] M. Lada, A.G. Cullis, P.J. Parbrook, M. Hopkinson, Appl. Phys. Lett. 83 (2003) 2808. [11] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys., Condens. Matter 14 (2002) 2717. [12] D. Vanderbilt, Phys. Rev., B 41 (1990) 7892. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] X.-R. Chen, L.-Yu. Lu, Y. Cheng, J.-Z. Zhao, Solid State Commun. 136 (2005) 152. [15] H.J. Monkhorst, J.D. Pack, Phys. Rev., B 13 (1976) 5188. [16] I. Akasaki, H. Amano, in Properties of Group III Nitrides (edited by Edgar, J. H.), EMIS Data reviews Series, No. 11, (1994), an INSPEC publication, pp. 30–34.
[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
H. Xia, Q. Xia, A.L. Ruoff, Phys. Rev., B 47 (1993) 12925. P. Boguslawski, E.L. Briggs, J. Bernholc, Phys. Rev., B 51 (1995) 17255. A. Seidl, A. Görling, P. Vogl, J.A. Majewski, Phys. Rev., B 53 (1996) 3764. J.A. Majewski, S. Birner, A. Trellakis, M. Sabathil, P. Vogl, Phys. Status Solidi (c) 1 (2004) 2003. R. Asahi, W. Mannstadt, A.J. Freeman, Phys. Rev., B 59 (1999) 7486. S. Limpijumnong, W.R.L. Lambrecht, Phys. Rev., B 63 (2001) 104103. S. Limpijumnong, W.R.L. Lambrecht, Phys. Rev. Lett. 86 (2000) 91. N.E. Christensen, I. Gorczyca, Phys. Rev., B 50 (1994) 4397. H. Morkoç, S. Strite, G.B. Gao, M.E. Lin, B. Sverdlov, M. Burns, J. Appl. Phys. 76 (1994) 1363. J. Sun, H.-T. Wang, N.-B. Ming, J.L. He, Y.J. Tian, Appl. Phys. Lett. 84 (2004) 4544. D.R. Hamann, M. Schluter, C. Chiang, Phys. Rev. Lett. 43 (1979) 1494. C.S. Wang, B.M. Klein, Phys. Rev. 24 (1981) 3417.