Computational Materials Science 88 (2014) 71–75
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DFT study of electronic and structural properties of Sm:GaN Abdul Majid ⇑, Waqas Akram, Amna Dar Physics Department, University of Gujrat, Gujrat, Pakistan
a r t i c l e
i n f o
Article history: Received 7 December 2013 Received in revised form 13 February 2014 Accepted 22 February 2014
Keywords: DFT GGA-PBE GGA + U VBM CBM Intermediate bands
a b s t r a c t First principle calculations of Sm:GaN carried out using GGA-PBE, mBJ and GGA + U are presented to demonstrate the structural, electronic and magnetic properties of the system. The effects of Hubbard correction (i.e. U) on band structure and location of Sm 4f levels are discussed in detail. The application of U indicated a considerable splitting of occupied and unoccupied 4f band unlike that of GGA and mBJ. The introduction of Sm related gap states caused narrowing of band gap which is expected to facilitate the tuning of optical transitions. The results also indicated the production of intermediate bands in the band gap of host material which points to possible use of this material in photovoltaic cell generation. The observed spin polarization of 4f and 5d and 6s states of Sm shows possibility of ferromagnetic exchange interactions in the material for spintronic devices. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction A signiﬁcant attention has been given to the study of III-nitrides due to their exceptional physical and chemical properties. These properties make them promising candidates for application in electronic, optoelectronic and bio-chemical sensing devices, e.g., light emitting devices, display devices operating at all practical wavelengths, transistors, detectors, high power ampliﬁers . Among the nitrides family, GaN is a prototype member which has earned enormous research and industrial interests after Si and GaAs. GaN indeed deserves to earn this fascination among its counterpart semiconductors because it holds the peculiarities of wide direct band gap, strong bonding, chemo stability, high thermo conductivity and potentials for use in future photonic and spintronic devices . The electronic and magnetic properties in Transition metal (TM) doped GaN have been reported by a number of groups [3–5]. It has been convincingly reported that TM doped GaN is a potential dilute magnetic semiconductors (DMS) material for high Curie temperature with high value of magnetic moment [5,6]. However, there are some reports which pointed out the limitations of TM doped III-nitrides because of precipitate formation at high temperatures [7,8]. In order to counter this short coming of TM:GaN, several groups tested the potential of rare earth (RE) doped GaN as alternate DMS materials [9–13].
⇑ Corresponding author. Tel.: +92 3328009610. E-mail address: [email protected]
(A. Majid). http://dx.doi.org/10.1016/j.commatsci.2014.02.039 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
RE based crystalline materials, due to unﬁlled 4f shells, have potential for the production of strong permanent magnets for use in a wide range of electronic, optical and electro-luminescent devices, high-power lasers, solid state microwave devices for radar and communications systems, gas mantles, and in the ceramic, photographic and textile industries . The emission of visible light in narrow bands (red, green and blue) has been reported in RE:GaN . Due to the unoccupied 4f shells of RE elements, it is difﬁcult to get exact description of the electronic structure of RE doped compounds. It is reported that RE 4f bands are generally very narrow, signiﬁcantly different from the bands exhibited by s, p and d states and hence leading to strong on-site Coulomb repulsion between the highly localized f-electrons . Photoemission resonances for various RE (Gd, Er, Yb) doped GaN provides an accurate picture of the occupied 4f state position within the GaN . The optical properties of GaN doped with Pr, Sm, Eu, Dy, Er, Tm and electronic properties of GaN doped with Ce, Eu, Tm, Yb have been reported in literature [18–21]. Despite few experimental reports on spectroscopic properties of Sm doped GaN, the literature is still lacking on its study using ﬁrst principle calculations. Sm doped GaN is reported as a strong candidate for its potential applications in 3D optical memory devices. For tri positive Sm ion: L = 5, S = 5/2, J = 5/2, g = 2/7 and hence (g 1)2J(J + 1) = 4.46 points to signiﬁcant paramagnetic behavior in Sm at the temperature of 1450 K although melting point of Sm is 1347 K . Besides this, interesting feature of polarization of conduction electrons and magnetic moments arranged ferromagnetically in pairs has also been observed for Sm. Luminescence contribution by trivalent
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Sm ions is reported for far red (730 nm) and infrared (810 nm) emission with the suggestion of Sm3+ applications in LEDs . In order to explore the use of semiconductors diluted with RE ions in optical or electronic devices, a complete understanding of impurity induced states is required. The computational approaches have extensively been employed for prediction of impurity states in the band structure of host materials. As REs are important for their partially ﬁlled strongly and correlated 4fn levels so local density approximation (LDA) fails to explain the electronic structures of Sm:GaN correctly. The alternate approaches like GGA-PBE were initially found successful in explaining the electronic structures of RE doped GaN but fundamental problems of this technique in describing the conﬁguration of strongly correlated 4f levels motivated the users to search for other methods [20,24–26]. Another worthwhile recommendation is use of Hubbard correction method in the form of DFT + U for the corrections of on-site Coulomb interactions with the terms of the effective on-site Coulomb and exchange parameters. This correction affects the position of d and f electron states reasonably and often adjusted to reach agreement with experimental results . In the current work, besides using the conventional GGA, we used GGA(+U) for eliminating the underestimation and overestimation problems of routine functionals, because the same has nicely worked as per our previous experience . In this study we are presenting the structural, electronic and magnetic properties of Sm:GaN using ﬁrst principle calculations based on density functional theory (DFT) implemented in Amsterdam Density Functional (ADF) simulation package. It is shown that Sm 4f states contribute in the narrowing of band gap of GaN and are successfully explained by GGA + U, which are efﬁcient and popular method for strongly correlated systems. 2. Computational details Density functional theory based calculations for the electronic structure of pure and Sm doped Wurtzite GaN were carried out using ADF-BAND package . The calculations were performed using GGA-PBE, MBJ and GGA + U exchange correlation functionals. Linear combination of atomic orbital with triple zeta double polarization (LCAO + Tz2P) was used as basis set. Sm has been reported to exhibit its state between 2+ and 3+ up to end 1970s  which make exaggeration to either use Sm2+ or Sm3+. However, Lang et al.  found large values of energy for Sm required to transfer a 4f electron to Fermi level illustrating that Sm has stable trivalent conﬁguration neglecting valence variation in bulk which encouraged us to use Sm3+ in our calculations. In current study, after starting with experimental lattice constants, the lattice constants for geometrically optimized Wz-GaN structure are a = 3.184 Å and c = 5.184 Å, which are in good agreement with literature . Supercell approach was used to avoid the change in the structure of host material so that electronic and structural properties can be studied. A 2 2 1 supercell was used which shows impurity concentration of 6.25% when one atom of dopant is added. As it is well known that band gap and location of 4f levels is underestimated by GGA so GGA + U calculations were performed in which impurity was added in k point grid of 2 2 2 Monkhorst–Pack mesh with impurity concentration of 3.12% . In this study k-space points mesh in irreducible Brillouin zone was used in spin polarization mode. Fermi level was determined by the Brillouin zone integration technique. Moreover frozen core approximation was used in which Ga [4s2,3d10,4p1], N [2s2,2p3] and Sm [5s2,5p6, 4f5,5d1,6s2] were used as valence electrons while rest of electrons are kept frozen. Ga1 xSmxN with x = 0.0625 (Ga7Sm1N8) containing 16 atoms super cell were employed for GGA-PBE and MBJ calculations whereas 32 atoms supercell Ga1 xSmxN with x = 0.0312 (Ga15Sm1N16) was used for GGA + U calculations. The value of U
was taken as 5.6 eV . Strong on-site coulomb repulsion was observed due to the narrow band of localized f electrons which is in good agreement with literature . All the structures were fully relaxed before running the calculations. The values of bond lengths were found as Ga–N:189.5 pm, Sm–Ga:331.3 pm and Sm–N:228.6 pm for optimized structures. Only substitutional defects were considered in the present study because RE elements show strong preference to occupy Ga-sublattice instead of N . 3. Result and discussion The calculations for wurtzite GaN were performed using GGA, MBJ and GGA + U functionals. GGA and mBJ were employed for pure material but all three functional were used for Sm doped GaN. 3.1. Pure GaN The DOSs of pure GaN (not shown) illustrated that the valence band (VB) consists of three portions. The top of the VB consists of N 2p with little contribution of Ga 4s orbital while middle part of VB has main contribution of Ga 3d orbital with minor contribution of N 2s, N 2p and Ga 4s. The bottom portion of VB was formed mainly due to N 2s and Ga 4s states with minor contribution of Ga 3d and 4p. The value of calculated band gap from GGA-PBE is 2.08 eV and Fermi level located near valance band which is in agreement with the literature [31–33]. It is very well known that GGA-PBE underestimates the band gap of pure material due to the well known limitation of GGA . Same calculation for pure GaN were also performed using mBJ which show the value of band gap is 2.80 eV with shifting of Fermi level towards edge of the conduction band (CB) which is in well agreement with the intrinsic n-type nature of pure material . The main features calculated for pure GaN as obtained from both GGA and mBJ are similar. In all these calculations valence band has major contributions from N 2p and conduction band has main character from Ga 4p. 3.2. Sm:GaN (GGA and mBJ calculations) To study the effects of Sm doping on electronic and structural properties of GaN by GGA and mBJ, the band structure (not shown) and DOSs of Sm:GaN were calculated. Fig. 1 illustrates GGA based total and partial DOSs of Sm:GaN with all contributions of different
Fig. 1. GGA calculated total and PDOS for Sm:GaN.
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orbitals. The majority of the band structure remained same as discussed in the pure GaN but majority of dopant (Sm) states appeared localized in the band gap of the host and some in resonance with host CB. The VBM consists of only spin up energy states and all spin down are merged with CB. The localized gap states indicate very weak hybridization of 4f electron with the host VB. The spin down Sm levels shifted away from Fermi level as compared to that of up levels. Sm 6s, 4f and 5d states are plotted in Fig. 2 to discuss the contribution of dopant levels individually. It is very clear that the top of valance band is formed by 6s, 4f and 5d states of Sm along with N 2p states of host. On the other hand the bottom of conduction band showed a major contribution of Sm 5d with minor contribution from Sm 6s. It can be observed from Fig. 1 that DOS of occupied states has greater band width as compared to that of unoccupied states. The hybridization of Sm 6s, 5d and 4f spin up states with top of valance band is observed whereas spin down stats of Sm 4f and 6s show their contribution in lower part of conduction band. Sm 5d level is also found in resonance with the host CB. The valance band maximum (VBM) shifted towards the higher energy region and conduction band minimum (CBM) shifted towards the lower energy regions from the Fermi level as compared to the pure material. It points to band gap narrowing (BGN) in Sm doped GaN. The band gap reduced from value of 2.08 eV for pure GaN to 1.63 eV for Sm doped material. The observed BGN is due to merging of impurity states with host conduction band. The VBM and CBM being located at different k-points shows the indirect band gap nature for doped material. It is in agreement with experimental result according to which Sm:GaN gives the luminescence in far infrared region . Sm doping has a remarkable inﬂuence on the electronic band structure of host material. The Sm states provide reasonable contribution for magnetic behavior of the new material as both occupied and unoccupied states had not the symmetric contribution. Spin polarization can be clearly observed in the VB. Sm has 5 unpaired 4f spin up electrons in charge state Sm+3 in case of SmGa in GaSmN. The bonding conﬁguration of GaN requires three electrons for SmGa, it is satisﬁed by available three electrons of Sm to form Sm3+ (4f5) charge state. If Sm being in Sm2+ (4f6) gives two electrons then third one to complete the octet may be taken from a donor site. It is possible because the Fermi level generally lays near CBM in GaN. It is also observed that the spin down 4f levels of Sm couple weakly with its 6s states in CB. But 5d and 6s states of Sm strongly couple with each other in host CB. Sm 4f and 5d levels coupling can also be observed on edge of CB. The localized
4f levels below Fermi level indicates that 4f electrons are not affected by local crystal environment. The absence of possible electronic DOS at Fermi level rules out the prospect of carrier-mediated magnetism. The possible mechanism of observed ferromagnetism is that 4f spin up electrons of Sm polarize their 5d levels which in turn polarize the host CB. The low DOS at bottom of CB may facilitate the energy transfers from host to Sm impurity. There has been great interest in ﬁnding the methods that predict electronic and spectroscopic properties with improved computational efﬁciency using standard DFT. In this view, Tran and Blaha have developed a semi-local functional based on a modiﬁcation of the Becke–Johnson (mBJ) functional. This is not a signiﬁcantly hybrid functional therefore provides much improved band gaps for a variety of insulators, including semiconductors, oxides, rare gas solids and lithium halides as reported . The main objective of this part of the work is to study the Sm:GaN with improved results as compared to GGA. The comparison of DOSs leads to the obvious conclusion that GGA-PBE and MBJ calculations produce quantitatively different results. MBJ based calculations of doped material (not shown here) make clear that the contribution of different orbital’s regarding the bands formation remain the same as described in GGA section. The location of Sm states, energy gap and magnetic contributions are slightly different but the splitting between the impurity induced peaks is much more pronounced in MBJ calculated DOSs. However, all impurity related contributions observed in GGA-TDOS are also present in MBJ-DOS with same orbital composition and the relative positions in the band gap showing little variation in their widths and positions. The location of 4f levels of RE dopent is very sensitive to explain the electronic conﬁguration of the material. As the magnetic properties are concerned; Sm:GaN presented ferromagnetic behavior in both cases i.e. GGA-PBE and mBJ due to spin polarization of Sm 4f, 5d and 6s states. The magnetic moment of single Sm atom without doping in any material is reported as 1.55lB . However the value of magnetic moment calculated from our calculation is approximately above 2lB. This is an approximate value for one Sm atom in GaN material. The results calculated using GGA-PBE are compared with that of MBJ for bulk Sm:GaN. According to GGA calculations unoccupied Sm 4f states are positioned mainly at the very top of the valence band. This fact is in accordance with the experimental results . In spite of providing reasonable agreement with results generated using GGA-PBE, mBJ seems to be lacking in true description of positions of two spin up Sm 4f states. Therefore, we adopted alternate approach of Hubbard correction for complete description of the system. 3.3. Sm:GaN (GGA + U calculations)
Fig. 2. GGA calculated total and PDOS of Sm for Sm:GaN.
GGA could give the accurate picture of strongly correlated system due to self interaction error whereas mBJ has silently eaten the expected two 4f electronic states. In case of half ﬁlled band, local spin density approximation (LSDA) depicts localization affects as a transition to a magnetic state . However, in general, this approach is unable to explain the localization effects, though self interaction correction (SIC) can do that . In order to account for onsite coulomb repulsion Hubbard correction ‘U’ is employed in DFT calculations of electronic properties of such strongly correlated systems. Yu et al. and Zhong et al. also reported RE elements that execution of ‘U’ greatly modiﬁes PDOS of 4f-electrons [24,40]. Therefore, we made calculations of Sm:GaN using GGA + U approach to overcome the problems associated with GGA-PBE and mBJ calculated results. Fig. 3 gives DOS of Sm:GaN calculated using GGA + U according to which the composition of host bands remains same but impurity states suffered a change in comparison to the results found using GGA and mBJ.
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Fig. 5. Energy level diagram (scaled) of Sm:GaN showing Sm 4f levels, extracted from GGA + U calculations. Fig. 3. GGA + U calculated total and partial DOS of Sm for Sm:GaN.
It was observed that Sm 4f electrons are transferred to the states near Fermi level due to the repulsion of surrounding extended energy states thus giving birth to electronic states in the band gap of host material. This weak binding of RE 4f states has also been experimentally observed by Lang et al. . The unoccupied spin up and spin down states of Sm 4f are found in the bottom and inside the CB. The detailed picture of electrons in Sm 4f states is discussed in following section. Fig. 4 shows seven degenerate Sm 4f levels. Five spin up 4f states are localized and shifted towards Fermi level unlike nine unoccupied states (two spin up and seven spin down). These ﬁve occupied 4f spin up levels form intermediate bands (IBs) in band gap at edge of Fermi level. Zhong et al. have also observed formation of Sm 4f levels at edge of Fermi level . Moreover, appearance of spin down levels buried deeply in the host CB and location of Fermi level at the edge of VB are also consistent with the literature . The appearance of 4f states on the edge of Fermi level is important for describing electronic properties of the system. It is worth mentioning that the results calculated using GGA and mBJ. An energy level diagram showing f levels in band structure of Sm:GaN, extracted on the basis of GGA + U, is sketched in Fig. 5.
It was observed that Sm 5d have very smaller contribution in the valence band while it appears mainly to contribute in the formation of conduction band along with smaller hybridization with Sm 4f in the lower part of CB. Smaller f–s hybridization was observed in GGA but the same was not seen for GGA + U ruling out the possibility of ferromagnetic exchange interaction due to f–s hybridization. However the f–d hybridization was observed in present case. 4. Summary In summary, GGA and GGA + U based ﬁrst principle calculations for exploring electronic structure of Sm doped GaN are presented. The observed band gap narrowing and hybridization of 4f levels with host are discussed. Newly born levels and intermediate bands were observed in the band gap of doped material which belongs to the 4f levels of impurity atom. The appearance of Intermediate bands and spin polarizations points to possible use of Sm:GaN in photovoltaic cells and spintronic devices. References                   
Fig. 4. Seven 4f degenerate levels for Sm:GaN.
S. Nakamura, Solid State Commun. 102 (1997) 237. S.S. Khludkov, I.A. Prudaev, O.P. Tolbanov, Russ. Phys. J. 55 (2013) 8. J. Kang, K.J. Chang, Physica B 376 (2006) 635. Y. Li, W. Fan, H. Sun, X. Cheng, P. Li, X. Zhao, M. Jiang, J. Solid State Chem. 183 (2010) 2662. Abdul Majid, Amna Dar, Azeem Nabi, Abdul Shakoor, Najmul Hassan, Arshad Junjua, Zhu Jianjun, Mater. Chem. Phys. 136 (2012) 809. S.J. Pearton, Y.D. Park, C.R. Abernathy, M.E. Overberg, G.T. Thaler, J. Kim, F. Ren, J.M. Zavada, R.G. Wilson, Thin Solid Films 447–448 (2004) 493. K. Sato, P.H. Dedericsand, H. Katayama-Yoshida, Euro Phys. Lett. 61 (2003) 403. S. Dhar, O. Brandt, A. Trampert, L. Daweritz, K.J. Friedland, K.H. Ploog, J. Keller, B. Beschoten, G. Gutherodt, Appl. Phys. Lett. 82 (2003) 2077. L. Perez, G.S. Lau, S. Dhar S, O. Brandt, K.H. Ploog, Phys. Rev. B74 (2006) 195207. J.K. Hite, R.M. Frazier, R. Davies, G.T. Thaler, C.R. Abernathy, S.J. Pearton, J.M. Zavada, Appl. Phys. Lett. 89 (2006) 092119. S. Dhar, O. Brandt, M. Ramsteiner, V.F. Sapega, K.H. Ploog, Phys. Rev. Lett. 94 (2005) 037205. Abdul Majid, Javed Iqbal, Akbar Ali, J. Supercond. Novel Magn. 24 (2011) 585. Abdul Majid, Sabeen Fatima, Amna Dar, Comput. Mater. Sci. 79 (2013) 929. Stephen David Barrett, Sarnjeet S. Dhesi, The Structure of Rare-earth Metal Surfaces, London Imperial College Press, 2001. A.J. Steckl, J.C. Heikenfeld, D.S. Lee, M.J. Garter, C.C. Baker, Y. Wang, R. Jones, J. Sel. Top. Quantum Electron. 8 (2002) 749. P.W. Anderson, Rev. Mod. Phys. 50 (1978) 191. Lu Wang, Wai-Ning Mei, S.R. McHale, J.W. McClory, J.C. Petrosky, J. Wu, R. Palai, Y.B. Losovyj, P.A. Dowben, Semicond. Sci. Technol. 27 (2012) 115017. J.B. Gruber, B. Zandi, H.J. Lozykowski, W.M. Jadwisienczak, J. Appl. Phys. 91 (2002) 2929. K. Lorenz, U. Wahl, E. Alves, E. Nogales, S. Dalmasso, R.W. Martin, K.P. O’Donnell, M. Wojdak, A. Braud, T. Monteiro, T. Wojtowicz, S. Ruffenach, O. Briot, Opt. Mater. Express 28 (2006) 750. Amna Dar, Abdul Majid, J. Appl. Phys. 114 (2013) 123703.
A. Majid et al. / Computational Materials Science 88 (2014) 71–75  D.W. Palmer, Compr. Semicond. Sci. Technol. 4 (2011) 390.  J. Jensen, Allan R. Mackintosh, Rare Earth Magnetism: Structure and Excitations, Clarendon press, Oxford, 1991.  E. Guziewicz, B.J. Kowalski, B.A. Orlowski, A. Szczepanska, Z. Golacki, I.A. Kowalik, I. Grzegory, S. Porowski, R.L. Johnson, Surf. Sci. 551 (2004) 132.  Guohua Zhong, Kang Zhang, Fan He, Xuhang Ma, Lanlan Lu, Zhuang Liu, Chunlei Yang, Physica B 407 (2012) 3818.  R.O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61 (1989) 689.  J.K. Lang, Y. Baer, P.A. Cox, J. Phys. F: Met. Phys. 11 (1981) 121.  G.T. Velde, F.M. Bickelhaupt, E.J. Baerends, C.F. Guerra, S.J.A. Van Gisbergen, J.G. Snijders, T. Ziegler, J. Comput. Chem. 22 (2001) 931.  M. Campagna, G.K Wertheim, Y. Baer, Topics in Applied Physics, vol. 27, Springer, Berlin, 1979.  K. Lawniczak-Jablonska, T. Suski, I. Gorczyca, N.E. Christensen, K.E. Attenkofer, D.L. Ederer, Z. Liliental Weber, R.C.C. Perera, E.M. Gullikson, J.H. Underwood, Phys. Rev. B 61 (1999) 24.  H.J. Monkhorst, J. Pack, Phys. Rev. B 13 (1976) 5188.
 X.Y. Cui, J.E. Medvedeve, B. Delley, A.J. Freeman, C. Stampﬂ, Phys. Rev. B 75 (2007) 155205.  P. Chao, S. Jun-Jie, Z. Yan, K.S.A. Butcher, T.L. Tansley, J.E. Downes, S. Jia-Xiang, Chin. Phys. Lett. 24 (2007) 2048.  C. Stampﬂ, Phys. Rev. B 59 (1999) 55521.  D.S. Sholl, J.A. Steckel, Density Function theory: A practical Introduction, John Wiley & Sons, Inc., 2009.  S.E. Park, H.J. Lee, Y.C. Cho, S.Y. Jeong, C.P. Cho, S. Cho, Appl. Phys. Lett. 80 (2002) 4187.  F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401.  J.Li. Juan, W.X. Liang, X.H. Ling, W.Z. Guo, F. Chun, Z.M. Lan, T. Jian, Chin. Phys. Lett. 26 (2009) 077502.  A. Savane, N.E. Christensen, L. Petit, Z. Szotek, W.M. Temmerman, Phys. Rev. B 74 (2006) 165204.  A. Svane, O. Gunnarsson, Phys. Rev. B 37 (1988) 9919.  Yu Fu, Z. Huang, X. Wang, L. Ye, J. Phys.: Condens. Matter 15 (2003) 1437.