status solidi Structural and electronic properties of ScSb, ScAs, ScP and ScN

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1 physica pss status solidi basic solid state physics b Structural and electronic properties of ScSb, ScAs, ScP and ScN AbdelGhani Tebboune 1, Djamel Rached, AbdelNour Benzair 3, Nadir Sekkal, 5,, and A. H. Belbachir 1 1 Département de physique, Université des Sciences et Technologie Mohamed Boudiaf d Oran, Oran, Algeria Applied Materials Laboratory, Centre de Recherches (ex-cfte), Université de Sidi Bel Abbès, 000 Sidi Bel Abbès, Algeria 3 Département de Physique, Université de Sidi Bel Abbès, 000 Sidi Bel Abbès, Algeria Département de Physique-Chimie, Ecole Normale Supérieure de l Enseignement Technique, BP 153, El M Naouer, Oran, Algeria 5 Computational Materials Science Laboratory, Département de Physique, Institut de Sciences Exactes, Université de Sidi Bel Abbès, 000 Sidi Bel Abbès, Algeria Physia-Laboratory, BP 7 (RP), 000 Sidi Bel Abbès, Algeria Received 10 October 005, revised 1 June 00, accepted June 00 Published online 8 August 00 PACS.0.Dc, Ap, 71.0.Ps The structural and electronic properties of ScSb, ScAs, ScP and ScN III V materials are investigated within a version of the first-principles full potential linear muffin-tin orbitals method (FPLMTO) that enables an accurate treatment of the interstitial regions. At high pressure, the transition from rocksalt (B1) to CsCl (B) structure is found to be possible. The zinc blende phase is also investigated and is found to give a semiconductor behavior with a wide bandgap to all our materials. The latter is direct at X for ScAs, ScSb, ScP. phys. stat. sol. (b) 3, No. 1, (00) / DOI /pssb REPRINT

2 phys. stat. sol. (b) 3, No. 1, (00) / DOI /pssb Structural and electronic properties of ScSb, ScAs, ScP and ScN AbdelGhani Tebboune 1, Djamel Rached, AbdelNour Benzair 3, Nadir Sekkal *,, 5,, and A. H. Belbachir 1 1 Département de physique, Université des Sciences et Technologie Mohamed Boudiaf d Oran, Oran, Algeria Applied Materials Laboratory, Centre de Recherches (ex-cfte), Université de Sidi Bel Abbès, 000 Sidi Bel Abbès, Algeria 3 Département de Physique, Université de Sidi Bel Abbès, 000 Sidi Bel Abbès, Algeria Département de Physique-Chimie, Ecole Normale Supérieure de l Enseignement Technique, BP 153, El M Naouer, Oran, Algeria 5 Computational Materials Science Laboratory, Département de Physique, Institut de Sciences Exactes, Université de Sidi Bel Abbès, 000 Sidi Bel Abbès, Algeria Physia-Laboratory, BP 7 (RP), 000 Sidi Bel Abbès, Algeria Received 10 October 005, revised 1 June 00, accepted June 00 Published online 8 August 00 PACS.0.Dc, Ap, 71.0.Ps The structural and electronic properties of ScSb, ScAs, ScP and ScN III V materials are investigated within a version of the first-principles full potential linear muffin-tin orbitals method (FPLMTO) that enables an accurate treatment of the interstitial regions. At high pressure, the transition from rocksalt (B1) to CsCl (B) structure is found to be possible. The zinc blende phase is also investigated and is found to give a semiconductor behavior with a wide bandgap to all our materials. The latter is direct at X for ScAs, ScSb, ScP. 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Scandium III V based materials have recently received more attention. The most known is the ScN [1 ], which is being fully studied because it contains the nitrogen element and is from the same family as GaN, AlN and InN wide-bandgap nitride materials. The nature of the bandgap of ScN is subject to some controversy. However, recent works [3] show that ScN is a semiconductor in the rocksalt (B1) phase and a semimetal in the CsCl (B) phase. The rocksalt (B1) configuration is found to be the most probable with the possibility of a transition to the CsCl (B) at high pressures. Compared with ScN, less is known about ScAs, ScSb and ScP [, 5 7]. Recent synchrotron X-ray diffraction experimental studies have proved that ScSb can have a phase transition from the NaCl (B1) structure to the CsCl (B) structure []. This is similar to what is predicted for ScN, and it will be shown in this paper that this is also true for ScSb, ScAs and ScP. The main purpose of this work is to investigate simultaneously the electronic and the structural properties of ScSb, ScAs, ScP and ScN because they are expected to be similar. Our aim is to predict the phase-transition pressures for the different components and then to compare their electronic properties. One very interesting result we obtained is that ScSb, ScAs, ScP are found to be wide and direct bandgap semiconductors in the zinc blende (B3) phase. In this phase, the top of the valence band of ScN is at X * Corresponding author: nsekkal@yahoo.fr 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

3 Original Paper phys. stat. sol. (b) 3, No. 1 (00) 789 but the bottom of its conduction band is at W, but this indirect X W gap is very close to the X X gap. For this reason, we have given some attention to this phase even if it is not found to be the ground-state configuration. The present investigations are necessary to predict the possibility of obtaining superlattices and heterostructures from this material family. The paper is organized as follows. The method is briefly commented in Section, the results are discussed in Section 3, and then conclusions are summarized in Section. Theoretical framework Our calculations were performed within the first-principle Savrasov version of the full potential linear muffin-tin orbitals (FPLMTO) method. At the reverse of the previous LMTO methods, the latter treats the interstitial regions on the same footing with the core regions. The nonoverlapping muffin-tin spheres (MTS) potential is expanded in spherical harmonics inside the spheres and Fourier transformed in the interstitial regions [8]. The exchange-correlation energy of electrons is described in the local density approximation (LDA) using the parameterization of Vosko et al. [9]. The available computer code lmtart [8, 10] is used in the present work. Indeed, the present method takes much time for calculation, but provides the best accuracy compared with the atomic spherical approximation (ASA). An unscreened long-range LMTO representation [11] has been used. To eliminate the dependence of radial wave functions from the spin index, radial wave functions have been adjusted to the spin average part of the potential. Both the LMTO basis set and charge density are expanded in spherical harmonics up to l max = for -181, -00,7 Energy (Ryd) Energy (Ryd) -181, -01, Volume (a.u) 3 Volume (a.u) 3 a) b) -0,5-133 Energy (Ryd) Energy (Ryd) -07, Volume (a.u) 3 Volume (a.u) 3 c) d) Fig. 1 Calculated total energy versus relative volume for the relative materials (a) ScSb, (b) ScAs, (c) ScP and (d) ScN. The filled circles are for the B1 phase, the open circles for B, the filled squares for B3 and the open triangles are for B. For reasons of clarity, the present curves do not include all points that have been taken into account in our structural properties calculations. 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

4 790 AbdelGhani Tebboune et al.: Structural and electronic properties of ScSb, ScAs, ScP and ScN Table 1 Structural parameters of ScSb, ScAs, ScP and ScN in the four phases (V 0 is the equilibrium volume, a 0 the lattice constant, B 0 the bulk modulus and B 0 is its pressure derivative). V 0 is taken equal to a 3 / for both zinc blende and NaCl phases, a 3 for the CsCl phase and 1/[a c(3/) 1/ ] for the wurtzite phase for which the volume per unit formula is taken into account. The data under brackets are from the references. parameters NaCl (B1) CsCl (B) zinc blende (B3) wurtzite (B) ScSb V 0 (Å 3 ) a 0 (Å) B 0 (GPa) B 0 u c/a P T (B1 to B), GPa ScAs V 0 (Å 3 ) a 0 (Å) B 0 (GPa) B 0 u c/a P T (B1 to B), GPa ScP V 0 (Å 3 ) a 0 (Å) B 0 (GPa) B 0 u c/a P T (B1 to B), GPa ScN V 0 (Å 3 ) a 0 (Å) B 0 (GPa) B 0 u c/a P T (B1 to B), GPa a) Ref. []; b) Ref. [3] [58 ± 3 a) ] 3.05 [9.5 ± 0.8 a) ] [8 3 a) ] [3. b) ].51 [.5 b) ] 10.3 [01 b) ] 3.15 [3.31 b) ] [31 b) ] 5.83 [37.5 a) ] [3.3 a) ] [.15 b) ].9 [.81 b) ] [170 b) ] [3.7 b) ] [9.09 b) ].939 [.88 b) ] [153 b) ] 3.33 [3.3 b) ] [9.1 b) ] 3.5 [3.9 b) ] [15 b) ] [.1 b) ] [0.38 b) ] [1. b) ] both Sc and As/Sb/P/N. The MTS radius for each atomic position is taken to be different for each case so that the spheres do not overlap. Thus, for each compound, the muffin-tin radii change with the phase. The use of the full potential ensures that the calculation is independent of the choice of the sphere radii. The K-mesh is also set up differently following the case. For ScSb, ScAs and ScP, meshes of,, and 3 3 are utilized for B1, B, B3 and B, respectively, while for these same phases, meshes of, 0 0 0, and are used for ScN. The energy cutoff ranges from 91. Ry to 9.95 Ry for ScSb, ScAs and ScP in B and B. For the B1 phase, it is about Ry, 89. Ry and 93.5 Ry for ScSb, ScAs and ScP, respectively. For the B3 phase, it is approximately the same for both ScSb and ScAs (8.9 Ry) and is 91. Ry for ScP. For ScN the cutoff is nearly the same for all phases (about 101 Ry) except for the B3 phase where it is fixed at 19.5 Ry. In the interstitial region, the s, p and d basis functions are expanded in a number of plane waves determined automatically by the cut-off energies. The number of plane waves involved in the calculations ranges from 3000 to 5000 for B1, B and B3 phases. It reaches 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

5 Original Paper phys. stat. sol. (b) 3, No. 1 (00) plane waves for ScN in the B phase and is up to 0000 for the other compounds in this same phase. 3 Results and discussion First, we have calculated the equilibrium lattice parameters of our four compounds using the habitual minimization procedure. The total energy was calculated for different values of the lattice constant, and the equilibrium corresponds to the lowest value of the total energy. In Fig. 1, and for each compound, we show the minimization curves for the four phases. Volume and energy are per single formula unit. Our calculations show that the ground-state configuration of all these materials is the rocksalt (B1) structure. Nevertheless, depending on the pressure, the CsCl phase (B) can be formed and eventually the zinc blende structure (B3), because the curve corresponding to the B1 structure crosses the curve of both the B and the B3 structures. The difference between the NaCl and CsCl curves minima is so small that the coexistence of these two phases is expected for a range of pressures. We notice also that the minimization curves of ScAs, ScSb and ScP are comparable in the sense that the arrangement of the four phases are similar (B1 then B, followed by B3 then B). The ScN minimization curve looks very differ- Fig. Band structure for (a) ScSb, (b) ScAs, (c) ScP and (d) ScN in the rocksalt (B1) structure. 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

6 79 AbdelGhani Tebboune et al.: Structural and electronic properties of ScSb, ScAs, ScP and ScN 1 1 E F a 5 E F b DOS, st./[ev*cell] 10 8 DOS, st./[ev*cell] Energy (ev) Energy (ev) c 1 d 5 E F 10 DOS, st./[ev*cell] 3 DOS, st./[ev*cell] 8 E F 1 Fig Energy (ev) Energy (ev) Total DOS for (a) ScSb, (b) ScAs, (c) ScP and (d) ScN in the rocksalt (B1) structure. ent. It is clear from Fig. 1d that for ScN, B1 and B are the most favorable phases (B under high pressure), but the B phase becomes more stable than the B3 phase. This is in agreement with Ref. [3] where it is shown that a second local minimum occurs for the B phase, suggesting the existence of a metastable wurtzite structure for ScN. However, in the present work, the difference between the minima of the B and B3 curves is small compared with that of Ref. [3]. We note that our value of the internal parameter u = for the B phase agrees well with that of Ref. [3] (u = 0.38) but not with that of Ref. [1]. Using these minimization curves, the equilibrium volume, the equilibrium lattice constant, the bulk modulus B and its derivative have been calculated by fitting to the Murnaghan equation of state [13]. The results are summarized in Table 1. We have also used the Birch state s equation [1] and we have found almost the same results. We note that all these materials have the same NaCl ground-state configuration and change to the CsCl configuration at high pressures and that the lattice constants for ScAs and ScP are very close for the B1 and B phases which are the most interesting. The lattice mismatch reaches only.18% in the NaCl structure and.1% in the CsCl structure. The same remark can be made for 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

7 Original Paper phys. stat. sol. (b) 3, No. 1 (00) 793 Fig. Band structure for (a) ScSb, (b) ScAs, (c) ScP and (d) ScN in the CsCl (B) structure. ScAs and ScSb in the NaCl structure (mismatch of 5.71%) and the CsCl structure (mismatch of.81%). However, ScSb and ScP have the most important lattice mismatches (7.89% for B1 and.97% for B) and that are still small. In the case of the B3 phase, the lattice mismatches are only.5% for ScAs/ScP, 7.31% for ScAs/ScSb but reaches 9.83% for ScSb/ScP. These lattice mismatches are reasonable and lead us to predict the possibility of the fabrication of superlattices from these compounds in their B1 and B3 phases. On the other hand, even if these materials are not semiconductors in the B1 phase, they can be combined with ScN and can also be combined with zinc blende (Ga,Al,In)As arsenides or (Ga,Al,In)N nitrides to form semiconducting ternary alloys that can be involved in the fabrication of semiconducting superlattices. We note also, that in all phases, ScN presents a very different equilibrium lattice parameter compared with the three other compounds. The line joining the slopes of the B1 and B curves determines the transition pressure of the two phases. Because it is difficult to calculate accurate slopes, and hence to determine the most stable structure at finite pressure and temperature, we have used the free energy G = E + PV TS. Since our calculations do not include temperature effects, we neglect the last term and use directly the enthalpy H = E + PV. From the enthalpy curve crossing of the two structures B1 and B, we obtain the pressure of this phase transition. 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

8 79 AbdelGhani Tebboune et al.: Structural and electronic properties of ScSb, ScAs, ScP and ScN Fig. 5 Band structure for (a) ScSb, (b) ScAs, (c) ScP and (d) ScN in the zinc blende (B3) structure. The obtained values are P T = GPa for ScSb, GPa for ScAs and 330 GPa for ScP. Our results for the transition pressure of ScSb are quite different from those of Ref. [] that found the transition to begin to occur from 8 GPa, the NaCl and the CsCl phases being coexisting until P T reaches 3 GPa. However, the obtained bulk modulus agrees quite well with Ref. []. Table 1 summarizes the results of our calculations. In order to check the validity of the present FPLMTO method, we have also calculated the same parameters for ScN for which data is more available in contrast to the other compounds. Our values were in good agreement with Ref. [3]. In particular, we have found P T = GPa, while Takeuchi [3] has found P T = 31 GPa. In Fig., we show the band structure of these materials in their respective equilibrium volume in the rocksalt (B1) phase. The topology is almost the same and we also note that the top of the valence band is at Γ and the bottom of the conduction band is at X for all these materials. The observed negative bandgap (semimetallic behavior) is probably not only due to the underestimation of the gap by LDA because it is clearly seen from both the band structure and the total density of states (DOS) curves (Fig. 3) that the Fermi level E f crosses the valence bands and that DOS is nonzero at E f. This is very different from what we have found for ScN, where a small indirect Γ X fundamental bandgap is found with the Fermi level at the top of the valence band (the topology is, however, similar). Corrections to LDA may easily show that this gap is greater and we can conclude that ScN is a semiconductor in the rocksalt (B1) phase. This is in agreement with the Ref. []. 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

9 Original Paper phys. stat. sol. (b) 3, No. 1 (00) 795 Figure shows the band structure of these materials in the CsCl (B) phase for the equilibrium volume. The same earlier remarks on the topology are made again. We observe a complete mixing between valence and conduction bands so that some crossings are clearly obtained. These multi-overlap lines between valence and conduction bands indicate a metallic behavior. The same result has been obtained in ScN [] and was checked by us within the present method. The zinc blende (B3) phase has also been investigated. Figure 5 shows the band structure of these materials at their respective equilibrium volume, we can see that the topology is almost the same for all the studied materials. But the most important result is that the B3 phase presents a wide and direct bandgap at X, except for ScN, for which the top of the valence band is at X and the bottom of its conduction band is at W, but this indirect X W gap is close to the X X gap. The direct bandgap is about 1.3 ev for ScSb, 1.7 ev for ScAs and 1.9 ev for ScP. The X X gap is. ev and the X W gap is.3 ev for ScN. The results for ScN in the B3 phase are in agreement with those reported by Noboru for the zinc blende structure of ScN [3]. Conclusions ScSb, ScAs, ScP and ScN have been investigated with the ab initio PLW-FPLMTO method. These materials are found to have a NaCl rocksalt (B1) structure. A transition to the CsCl (B) structure is expected at high pressures. The zinc blende structure is very interesting: all the compounds (ScN also) have a semiconducting behavior with a wide and direct bandgap at X in this phase. It has also been found that in some cases, these materials have similar lattice constants, so that their combination could make possible the fabrication of heterostructures. However, their lattice constants are very different from that of ScN. Acknowledgements One of the authors, N. S. would like to thank the Center of Theoretical and Applied Physics (CTAPS) in Yarmouke University of Irbid in Jordan for their hospitality in 005. The authors thank also B. Amrani and A. Lazreg for valuable discussions and S. Y. Savrasov for his Mindlab software freely available for research and Pr. Malika Benzohra and Pr. Mohamed Benzohra for documentation help. This work has been supported by both CTAPS of Jordan and the ENSET of Oran (Algeria) and by the Algerian National Research Project CNEPRU under number J 311/0/05/0. References [1] C. Stampfl, R. Asashi, and A. J. Freeman, Phys. Rev. B 5, (00). [] W. R. Lambrecht, Phys. Rev. B, (000). [3] N. Takeuchi, Phys. Rev. B 5, (00) and references therein. [] N. Takeuchi and S. U. Uloa, Phys. Rev. B 5, (00). [5] F. Tientega and J. F. Harrison, Chem. Phys. Lett. 3, 0 (199). [] J. Hayashi, I. Shirotani, K. Hirano, N. Ishimasu, O. Shimomura, and T. Kikegaw, Solid State Commun. 15, 53 (003). [7] A. G. Petukhov, W. R. Lambrecht, and B. Segall, Phys. Rev. B 50, 7800 (199). [8] S. Y. Savrasov, Phys. Rev. B 5, 170 (199). [9] S. H. Vosko, L. Wilk, and M. Nussair, Can. J. Phys. 58, 100 (1980). [10] mindlab/. [11] O. K. Andersen, Phys. Rev. B 13, 3050 (1975). [1] N. Farrer and L. Bellaiche, Phys. Rev. B, 0103 (00). [13] F. D. Murnaghan, Proc. Natl. Acad. Sci. (USA) 30, 5390 (19). [1] F. Birch, Phys. Rev. 71, 809 (197). 00 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim