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Impurity-stabilized zinc-blende phase of wurtzite compounds
Journal of Physics and Chemistry of Solids 66 (2005) 2008–2010 www.elsevier.com/locate/jpcs
Impurity-stabilized zinc-blende phase of wurtzite compounds Gustavo M. Dalpian *, Su-Huai Wei National Renewable Energy Laboratory, Golden, Colorado 80401, USA
Abstract We propose here a new approach to stabilizing the cubic zinc blende phase of semiconductors that are usually more stable in the hexagonal wurtzite phase. We show that this can be done by taking advantage of the valence and conduction band offsets between the cubic and the hexagonal phases. Due to this band offset, it will cost less energy to insert electrons by shallow donors, or insert holes by 3d acceptors in the zinc blende structure, thus stabilizing the cubic phase. q 2005 Published by Elsevier Ltd.
1. Introduction Most binary semiconductors have a ground state in either a cubic zinc blende (ZB) or hexagonal wurtzite (WZ) phase [1,2]. The two structures are quite similar. They have the same local tetrahedral environment and start to differ only in their third-nearest-neighbor atomic arrangement. Because of these subtle differences, the total energy difference between the WZ and ZB phases is usually very small, on the order of a few meV/atom. In general, a more ionic compound such as GaN will have WZ as ground state at TZ0, because the ideal WZ structure has larger Coulomb interaction energy with a Madelung constant aM(WZ)Z1.6413 compared to aM(ZB)Z 1.6381 for a ZB structure. On the other hand, a more covalent compound such as GaAs or CdTe will prefer the ZB structure because it better preserves the covalent bond characters. Despite the similarity in structural parameters and only a small difference in the total energy, the optical and electrical properties of a compound in the ZB and WZ phases could be very different due to their different crystal symmetries. For instance, in the lower-symmetry WZ phase, the ZB G15v state splits into G6v and G1v states, leading to a repulsion between the G1c and the split G1v state, thus increasing the band gap [1]. For example, ZB GaN has a direct band gap that is about 0.2 eV smaller than that of WZ GaN [3]. The band gap difference could be significantly larger if the material has an indirect band gap, such as in SiC [1]. The upward shift of the G1c state and the crystal field splitting in the valence band of the WZ structure * Corresponding author.
0022-3697/$ - see front matter q 2005 Published by Elsevier Ltd. doi:10.1016/j.jpcs.2005.09.042
also lead to conduction and valence band offsets between the two phases. The band diagram for GaN is shown in Fig. 1. Our calculated valence band offset for GaN is 22 meV, while the conduction band offset is -260 meV. Due to the high symmetry of the cubic phase, ZB compounds usually have more isotropic properties and no spontaneous polarization [4] compared to a WZ compound. The ZB compound is also expected to have smaller effective masses, high carrier mobility, and higher doping efficiency [4], thus making it more suitable for some device applications. Therefore, it is desirable in many cases to stabilize the ZB phase of a WZ compound. The usual way to obtain the ZB phase of a material that has the WZ ground state, such as GaN, is growing it on cubic substrates such as GaAs, b-SiC, or Si [3]. Because of the large strain at the interface, caused by the lattice mismatch between the two materials, the sample quality is usually poor. In this paper, we propose a new methodology for stabilizing the ZB phase of semiconductors that are usually more stable in the WZ phase. This approach is based on injecting electrons or holes into the host by doping the host with appropriate donor or acceptor impurities. We will use GaN as an example through the paper, although our method should work for other materials too. 2. Theoretical model Our approach consists of stabilizing the ZB phase by inserting electrons or holes into the material. This could be done by taking advantage of the band offsets between the WZ and ZB phases, as depicted in Fig. 1. We expect that it will cost less energy to insert electrons into the ZB phase than into the WZ phase, because the conduction band
G.M. Dalpian, S.-H. Wei / Journal of Physics and Chemistry of Solids 66 (2005) 2008–2010
2009
For this, we used the standard approach [8], where the band offset is given by WZ ZB KDEVBM0;C0 C DEC;C0 : DEvWZKZB Z DEVBM;C
Fig. 1. Schematic band structure of the zinc blende and the wurtzite phases of GaN and the calculated band offsets.
Fig. 2. Schematic plot of the valence band offset between ZB and WZ phases of conventional semiconductor before and after doping with 3d acceptor imputities.
minimum (CBM) is lower in the ZB phase. On the other hand, when holes are inserted into both phases, it will cost less energy in the WZ phase than in the ZB phase, unless the natural band offset is reversed. This could be achieved by inserting 3d acceptor impurities such as Mn, Cu, and Zn in the host semiconductor (GaN). This is because the ZB phase has higher symmetry, and therefore the repulsion between the valence band p orbitals and the impurity d orbitals in ZB phase is larger than in the WZ phase, thus reversing the natural valence band offset. As holes are created at the same time, it will cost less energy to create the holes in the ZB phase, thus stabilizing this phase. A schematic drawing of this model can be seen in Fig. 2. Note that, depending on the impurity, the 3d levels can be either inside the band gap or in the valence band. 3. Results and discussions To demonstrate this model, we performed first-principles total energy calculations, based on the density functional theory as implemented in the full potential linearized augmented plane wave code [5,6]. We used the Generalized Gradient Approximation of Perdew and Wang [7] for exchange and correlation potentials. The lattice parameters and atomic positions are fully relaxed. We used a high k-point mesh and high cutoff energies for the basis functions to ensure that the total energies of the WZ and ZB phases are converged within 1 meV. Besides the total energy calculations, we also calculated the band offset between the ZB and WZ phases.
Positive values of DEvWZKZB mean that the valence band maximum (VBM) of the WZ structure is higher. Here, WZ WZ DEVBM;C Z EVBM KECWZ is the core level to VBM energy ZB separation for isolated WZ structure and DEC;C0 Z ECWZ KEC0 is the difference in core level binding energy between each side of the ZB/WZ interface. The band offset between the ZB and WZ phases of pure GaN is DEvWZKZB Z 22 meV, i.e. the VBM of WZ GaN is above that of ZB GaN. After doping GaN with Zn or Cu, the band offset becomes DEvWZKZB ZK41 meV and K45 meV respectively, showing that the impurities can indeed reverse the band offset between WZ and ZB GaN. Our calculations show that the total energy difference between the ZB and WZ phases decreases as Cu, Mn, Zn, or Si are added to the material, substituting at the Ga site. In Table 1 we show the calculated energy difference variation dEZB-WZ/dx, where x is the concentration of the dopant. This was calculated by sampling the energy differences for different impurity concentrations. Through these results, we can also estimate the critical concentration xc, beyond which the ZB phase will become more stable than the WZ phase, as reported in Table 1. Our results show that the best impurities for stabilizing the ZB phase in GaN are Cu and Si. Cu is the best for hole doping because it produces two holes, and because the d levels of Cu are shallower than the other acceptors. Doping by electrons is also efficient for stabilizing the ZB phase of GaN because of the large conduction band offset (Fig. 1). Similar behavior is observed in the delta doping case [8]. In order to verify the role of holes in our model, we performed calculations for the negatively charged Cu in GaN. In this case, instead of having two holes per Cu atom, there will be only one hole. We found that the stabilization of the ZB phase decreased, because fewer holes are present in the system. To verify the role of the d bands, we also performed calculations with Mg-doped GaN. Mg is an acceptor in GaN, but does not have 3d electrons. In this case, there is no VBM reversion, thus no energy gain for the ZB phase. Actually, as the holes are created, the WZ phase is further stabilized.
Table 1 Calculated energy difference variation (dEZB-WZ/dx) and critical concentration (xg) for several impurity configurations System
dEZB–WZ/dx (meV/atom)
xc
GaN:Cu GaN:Cu(–) GaN:Si GaN:Mn GaN:Zn GaN:Mg
K118.4 K90.4 K89.7 K42.7 K39.2 35.2
0.044 0.057 0.058 0.122 0.133 –
2010
G.M. Dalpian, S.-H. Wei / Journal of Physics and Chemistry of Solids 66 (2005) 2008–2010
The hole-mediated stabilization of the ZB phase presented here is supported by previous experimental measurements by Cui et al. [9]. They show that it is possible to obtain cubic GaN during the growth of the hexagonal phase through the deposition of Mn in GaN. We show here that the results of Cui et al. [9] can be successfully explained by our holestabilization model. Although in this paper we report results only for GaN, our model should also work for other semiconductors such as CdS and ZnO [10], where the energy difference between the ZB and WZ phases is small (1 meV/atom and 5 meV/atom, respectively). For these materials, the dopants should be some group I element such as Cu, in the case of acceptors, and group III element such as Al for donors.
4. Conclusions In conclusion, we have proposed a new method to stabilize the cubic ZB phase for compounds that are usually more stable in the WZ phase. We show that this can be done through the addition of shallow donors or 3d acceptor impurities into the host.
Acknowledgements The work at NREL is funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under Contract No. DE-AC36-99GO10337 to NREL. References [1] C.-Y. Yeh, Z.W. Lu, S. Froyen, A. Zunger, Phys. Rev. B 45 (1992) 12130; C.-Y. Yeh, Z.W. Lu, S. Froyen, A. Zunger, Phys. Rev. B 46 (1992) 10086. [2] S.-H. Wei, S.B. Zhang, Phys. Rev. B 62 (2000) 6944. [3] J.I. Pankove, T.D. Moustakas, Gallium Nitride (GaN) I, Academic press, San Diego, CA, 1998. [4] J.R.L. Fernandez, F. Cerdeira, E.A. Meneses, M.J.S.P. Brasil, J.A.N.T. Soares, A.M. Santos, O.C. Noriega, J.R. Leite, D.J. As, U. Kohler, S. Potthast, D.G. Pacheco-Salazar, Phys. Rev. B 68 (2003) 155204. [5] P. Blaha, et al., WIEN2k (Karlheinz Schwarz, Techn. Universitat Wien, Austria), 2001, ISBN 3-9501031-1-2. [6] S.-H. Wei, H. Krakauer, Phys. Rev. Lett. 55 (1985) 1200. [7] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [8] G.M. Dalpian, S.H. Wei, Phys. Rev. Lett. 93 (2004) 216401. [9] Y. Cui, V.K. Lazorov, M.M. Goetz, H. Liu, D.P. Robertson, M. Gajdardziska-Josifovska, L. Li, Appl. Phys. Lett. 82 (2003) 4666. [10] G.M. Dalpian, Y. Yan, S.-H. Wei, in preparation.
Impurity-stabilized zinc-blende phase of wurtzite compounds Gustavo M. Dalpian *, Su-Huai Wei National Renewable Energy Laboratory, Golden, Colorado 80401, USA
Abstract We propose here a new approach to stabilizing the cubic zinc blende phase of semiconductors that are usually more stable in the hexagonal wurtzite phase. We show that this can be done by taking advantage of the valence and conduction band offsets between the cubic and the hexagonal phases. Due to this band offset, it will cost less energy to insert electrons by shallow donors, or insert holes by 3d acceptors in the zinc blende structure, thus stabilizing the cubic phase. q 2005 Published by Elsevier Ltd.
1. Introduction Most binary semiconductors have a ground state in either a cubic zinc blende (ZB) or hexagonal wurtzite (WZ) phase [1,2]. The two structures are quite similar. They have the same local tetrahedral environment and start to differ only in their third-nearest-neighbor atomic arrangement. Because of these subtle differences, the total energy difference between the WZ and ZB phases is usually very small, on the order of a few meV/atom. In general, a more ionic compound such as GaN will have WZ as ground state at TZ0, because the ideal WZ structure has larger Coulomb interaction energy with a Madelung constant aM(WZ)Z1.6413 compared to aM(ZB)Z 1.6381 for a ZB structure. On the other hand, a more covalent compound such as GaAs or CdTe will prefer the ZB structure because it better preserves the covalent bond characters. Despite the similarity in structural parameters and only a small difference in the total energy, the optical and electrical properties of a compound in the ZB and WZ phases could be very different due to their different crystal symmetries. For instance, in the lower-symmetry WZ phase, the ZB G15v state splits into G6v and G1v states, leading to a repulsion between the G1c and the split G1v state, thus increasing the band gap [1]. For example, ZB GaN has a direct band gap that is about 0.2 eV smaller than that of WZ GaN [3]. The band gap difference could be significantly larger if the material has an indirect band gap, such as in SiC [1]. The upward shift of the G1c state and the crystal field splitting in the valence band of the WZ structure * Corresponding author.
0022-3697/$ - see front matter q 2005 Published by Elsevier Ltd. doi:10.1016/j.jpcs.2005.09.042
also lead to conduction and valence band offsets between the two phases. The band diagram for GaN is shown in Fig. 1. Our calculated valence band offset for GaN is 22 meV, while the conduction band offset is -260 meV. Due to the high symmetry of the cubic phase, ZB compounds usually have more isotropic properties and no spontaneous polarization [4] compared to a WZ compound. The ZB compound is also expected to have smaller effective masses, high carrier mobility, and higher doping efficiency [4], thus making it more suitable for some device applications. Therefore, it is desirable in many cases to stabilize the ZB phase of a WZ compound. The usual way to obtain the ZB phase of a material that has the WZ ground state, such as GaN, is growing it on cubic substrates such as GaAs, b-SiC, or Si [3]. Because of the large strain at the interface, caused by the lattice mismatch between the two materials, the sample quality is usually poor. In this paper, we propose a new methodology for stabilizing the ZB phase of semiconductors that are usually more stable in the WZ phase. This approach is based on injecting electrons or holes into the host by doping the host with appropriate donor or acceptor impurities. We will use GaN as an example through the paper, although our method should work for other materials too. 2. Theoretical model Our approach consists of stabilizing the ZB phase by inserting electrons or holes into the material. This could be done by taking advantage of the band offsets between the WZ and ZB phases, as depicted in Fig. 1. We expect that it will cost less energy to insert electrons into the ZB phase than into the WZ phase, because the conduction band
G.M. Dalpian, S.-H. Wei / Journal of Physics and Chemistry of Solids 66 (2005) 2008–2010
2009
For this, we used the standard approach [8], where the band offset is given by WZ ZB KDEVBM0;C0 C DEC;C0 : DEvWZKZB Z DEVBM;C
Fig. 1. Schematic band structure of the zinc blende and the wurtzite phases of GaN and the calculated band offsets.
Fig. 2. Schematic plot of the valence band offset between ZB and WZ phases of conventional semiconductor before and after doping with 3d acceptor imputities.
minimum (CBM) is lower in the ZB phase. On the other hand, when holes are inserted into both phases, it will cost less energy in the WZ phase than in the ZB phase, unless the natural band offset is reversed. This could be achieved by inserting 3d acceptor impurities such as Mn, Cu, and Zn in the host semiconductor (GaN). This is because the ZB phase has higher symmetry, and therefore the repulsion between the valence band p orbitals and the impurity d orbitals in ZB phase is larger than in the WZ phase, thus reversing the natural valence band offset. As holes are created at the same time, it will cost less energy to create the holes in the ZB phase, thus stabilizing this phase. A schematic drawing of this model can be seen in Fig. 2. Note that, depending on the impurity, the 3d levels can be either inside the band gap or in the valence band. 3. Results and discussions To demonstrate this model, we performed first-principles total energy calculations, based on the density functional theory as implemented in the full potential linearized augmented plane wave code [5,6]. We used the Generalized Gradient Approximation of Perdew and Wang [7] for exchange and correlation potentials. The lattice parameters and atomic positions are fully relaxed. We used a high k-point mesh and high cutoff energies for the basis functions to ensure that the total energies of the WZ and ZB phases are converged within 1 meV. Besides the total energy calculations, we also calculated the band offset between the ZB and WZ phases.
Positive values of DEvWZKZB mean that the valence band maximum (VBM) of the WZ structure is higher. Here, WZ WZ DEVBM;C Z EVBM KECWZ is the core level to VBM energy ZB separation for isolated WZ structure and DEC;C0 Z ECWZ KEC0 is the difference in core level binding energy between each side of the ZB/WZ interface. The band offset between the ZB and WZ phases of pure GaN is DEvWZKZB Z 22 meV, i.e. the VBM of WZ GaN is above that of ZB GaN. After doping GaN with Zn or Cu, the band offset becomes DEvWZKZB ZK41 meV and K45 meV respectively, showing that the impurities can indeed reverse the band offset between WZ and ZB GaN. Our calculations show that the total energy difference between the ZB and WZ phases decreases as Cu, Mn, Zn, or Si are added to the material, substituting at the Ga site. In Table 1 we show the calculated energy difference variation dEZB-WZ/dx, where x is the concentration of the dopant. This was calculated by sampling the energy differences for different impurity concentrations. Through these results, we can also estimate the critical concentration xc, beyond which the ZB phase will become more stable than the WZ phase, as reported in Table 1. Our results show that the best impurities for stabilizing the ZB phase in GaN are Cu and Si. Cu is the best for hole doping because it produces two holes, and because the d levels of Cu are shallower than the other acceptors. Doping by electrons is also efficient for stabilizing the ZB phase of GaN because of the large conduction band offset (Fig. 1). Similar behavior is observed in the delta doping case [8]. In order to verify the role of holes in our model, we performed calculations for the negatively charged Cu in GaN. In this case, instead of having two holes per Cu atom, there will be only one hole. We found that the stabilization of the ZB phase decreased, because fewer holes are present in the system. To verify the role of the d bands, we also performed calculations with Mg-doped GaN. Mg is an acceptor in GaN, but does not have 3d electrons. In this case, there is no VBM reversion, thus no energy gain for the ZB phase. Actually, as the holes are created, the WZ phase is further stabilized.
Table 1 Calculated energy difference variation (dEZB-WZ/dx) and critical concentration (xg) for several impurity configurations System
dEZB–WZ/dx (meV/atom)
xc
GaN:Cu GaN:Cu(–) GaN:Si GaN:Mn GaN:Zn GaN:Mg
K118.4 K90.4 K89.7 K42.7 K39.2 35.2
0.044 0.057 0.058 0.122 0.133 –
2010
G.M. Dalpian, S.-H. Wei / Journal of Physics and Chemistry of Solids 66 (2005) 2008–2010
The hole-mediated stabilization of the ZB phase presented here is supported by previous experimental measurements by Cui et al. [9]. They show that it is possible to obtain cubic GaN during the growth of the hexagonal phase through the deposition of Mn in GaN. We show here that the results of Cui et al. [9] can be successfully explained by our holestabilization model. Although in this paper we report results only for GaN, our model should also work for other semiconductors such as CdS and ZnO [10], where the energy difference between the ZB and WZ phases is small (1 meV/atom and 5 meV/atom, respectively). For these materials, the dopants should be some group I element such as Cu, in the case of acceptors, and group III element such as Al for donors.
4. Conclusions In conclusion, we have proposed a new method to stabilize the cubic ZB phase for compounds that are usually more stable in the WZ phase. We show that this can be done through the addition of shallow donors or 3d acceptor impurities into the host.
Acknowledgements The work at NREL is funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under Contract No. DE-AC36-99GO10337 to NREL. References [1] C.-Y. Yeh, Z.W. Lu, S. Froyen, A. Zunger, Phys. Rev. B 45 (1992) 12130; C.-Y. Yeh, Z.W. Lu, S. Froyen, A. Zunger, Phys. Rev. B 46 (1992) 10086. [2] S.-H. Wei, S.B. Zhang, Phys. Rev. B 62 (2000) 6944. [3] J.I. Pankove, T.D. Moustakas, Gallium Nitride (GaN) I, Academic press, San Diego, CA, 1998. [4] J.R.L. Fernandez, F. Cerdeira, E.A. Meneses, M.J.S.P. Brasil, J.A.N.T. Soares, A.M. Santos, O.C. Noriega, J.R. Leite, D.J. As, U. Kohler, S. Potthast, D.G. Pacheco-Salazar, Phys. Rev. B 68 (2003) 155204. [5] P. Blaha, et al., WIEN2k (Karlheinz Schwarz, Techn. Universitat Wien, Austria), 2001, ISBN 3-9501031-1-2. [6] S.-H. Wei, H. Krakauer, Phys. Rev. Lett. 55 (1985) 1200. [7] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [8] G.M. Dalpian, S.H. Wei, Phys. Rev. Lett. 93 (2004) 216401. [9] Y. Cui, V.K. Lazorov, M.M. Goetz, H. Liu, D.P. Robertson, M. Gajdardziska-Josifovska, L. Li, Appl. Phys. Lett. 82 (2003) 4666. [10] G.M. Dalpian, Y. Yan, S.-H. Wei, in preparation.