Superconductivity in Group III-V Semiconductor AlN Under High Pressure

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1 ull Paper Orbital: The Electrnic Jurnal f Chemistry j u r n al h m ep ag e: w w w. r b i t al. u f m s. b r ISSN Vl 7 N. 3 July-September Supercnductivity in Grup III-V Semicnductr AlN Under High Pressure G. Selva Dancy a, V. Benaline Sheeba a, C. Nirmala Luis a*, and A. Amalraj b a Research Center in Physics, Hly Crss Cllege, Nagercil, Tamil Nadu, India. b St.Jerme s Cllege, Ananthanadarkudy-6901 Kanya Kumari District, Tamilnadu, India. Article histry: Received: 09 Octber 014; revised: 5 Nvember 014; accepted: 4 January 015. Available nline: 14 September 015. DOI: Abstract: The electrnic prperties f cubic zinc blende type grup III-V semicnductr AlN under pressure is studied using full ptential linear muffin-tin rbital (P-LMTO) methd. At nrmal pressure, AlN is an indirect bandgap semicnductr with band gap value 4.56 ev. When the pressure is increased, there is enhanced verlapping between the wave functins f the neighbring atms. As a result the widths f the valence and empty cnductin bands increase. These changes lead t the narrwing and indirect clsing f the band gaps in AlN (metallizatin). On further increase f pressure, AlN becmes a supercnductr and AlN cmes under the class f electrn-phnn-mediated high pressure supercnductrs. The supercnducting transitin temperatures (Tc) f AlN are btained as a functin f pressure fr the CsCl structure. It is als cnfirmed that the metallizatin, structural phase transitin and nset f supercnductivity d nt ccur simultaneusly in this cmpund. Keywrds: band structure; density f states; phase transitin; metallizatin; supercnductivity; high pressure 1. INTRODUCTION Grup III-V semicnductrs have been extensively studied because it is cnsidered as an imprtant technlgical material in electrnic and pt-electrnic applicatins [1]. Generally aluminum cmpunds (AlN, AlAs) crystallize in zinc blende (ZnS) structure []. The effect f pressure n the electrnic prperties f grup III-V cmpunds can be investigated in many ways [3, 4]. The technlgical applicatins f AlN cmpund require significant prgress in the fundamental understanding f their behavir at nrmal and high pressures [5]. Subjecting AlN t high pressure leads t pressure-induced metallizatin, structural phase transitin, and supercnducting transitin []. Wang et al. [6] presented the mechanical and electrical prperties f twelve III-V semicnductrs, under pressure, using Plane wave Pseudptential methd. Edgar [7] presented the prperties f grup III nitrides using experimental bservatins. Wagner et al. [8] reprted the electrnic and phnn defrmatin ptentials f GaN and AlN using Ab initi calculatins versus experimental values. There are n high pressureinvlving studies related t metallizatin and supercnductivity in AlN. This mtivated us t take up the present investigatin. In this wrk, self-cnsistent full ptential linear muffin tin rbital methd (P- LMTO) is emplyed t study the effect f pressure [9]. We have analyzed the phenmena f metallizatin (NaCl structure) and supercnductivity fr high pressure (CsCl) structure f AlN [1, ]. It is hped that this analysis will enable us t make sme general statement regarding the path t high Tc supercnductivity in cvalent cmpunds.. MATERIAL AND METHODS.1. Band structure and density f states.1.1. Calculative prcedure The electrnic band structure and density f states calculatins were perfrmed fr AlN crrespnding t different reduced vlumes in ZnS, NaCl and CsCl structures, by the first-principle P- LMTO methd with in generalized gradient apprximatin (GGA). The electrnic cnfiguratins f Al and N are [Ne] 3s 3p 1 3d 10 (Z = 13) and [He] s p 3 (Z = 7), respectively. The valence electrnic cnfiguratins chsen in ur calculatins are 3s 3p 1 fr Al, and s p 3 fr N. There are 8 valence electrns * Crrespnding authr. nirmala_luis@yah.c.in

2 cntributing t the valence bands. The final energy cnvergence is within 10 5 Ry. The calculated ttal energies were fit t Murnaghan s equatin f state (EOS), t determine the phase-transitin pressure and ther grund-state prperties [1, ]. Murnaghan s equatin f state is given by the fllwing frmula t btain the equilibrium lattice cnstant and ther grund state prperties. P = 1.5B [(V /V) 7/3 (V /V) 5/3 ] [ (B 1-4) {(V /V) /3-1}] (1) In ur calculatins we have chsen the ZnS structure fr AlN at ambient pressure. The phase stability f the ZnS and NaCl structures f AlN is analyzed using the enthalpic calculatin [1]. The enthalpy H(P) is defined by: H(P) = E tt (P) + PV(P) () ull Paper widened. These changes lead t the narrwing f the band gap under pressure (ig. 3). Table 1. Equilibrium lattice cnstant (a ), bulk mdulus (B ) and its pressure derivative (B 1 ) f AlN in ZnS structure Grund State Prperties Present wrk AlN Experimental wrk [7] Previus theretical wrk [6] a a.u B Mbar B Eg ev and the transitin pressure crrespnding t the phase transitin frm ZnS t NaCl is btained frm the relatin: H ZnS (P) = H NaCl (P) (3) where H ZnS and H NaCl are the enthalpies f the ZnS and NaCl phases, respectively..1.. The Band structure f AlN under pressure The band structures f AlN were cmputed fr varius reduced vlumes ranging frm V/V =1.0 t 0.3 in steps f Even thugh we have btained the band structure fr V/V values frm 1.0 t 0.3, we have presented here the band structures f AlN alng the symmetry directins -X-W-L--K and the crrespnding density f states f AlN (igs.1 t 4). The vlume cmpressins crrespnding t V/V =1.0 and V/V =0.756 fr AlN is given. A single band nearer t the bttm arises frm s electrns f N (ig. 1). The three bands appearing belw the ermi level are due t the 3s, 3p 1 electrns f Al and p 3 electrns f N (ig. 1). The empty cnductin bands abve the ermi level are due t 3p, 3d states f Al and 3d, p states f N (ig. 1). At nrmal pressure, the band gap f AlN is indirect with valence band maximum at pint and cnductin band minimum at X pint with band gap value 4.56 ev. The calculated energy gaps are in agreement with the experimental value f 4.8 ev (Table 1) [7]. As pressure increases the width f the valence band and the empty cnductin band get.1.3. The Density f states under pressure: The density f states (DOS) (states/ry.) calculatins fr all the reduced vlumes have been carried ut. The density f states (DOS) histgram f AlN crrespnding t nrmal pressure is shwn in ig.. At nrmal pressure, the levels arising frm 3s electrns f Al give the lng spike near the rigin. The shrt spikes near the ermi energy are due t s, p 3 electrns f N and 3p 1 electrn f Al. The shrt peaks abve the ermi energy E are due t the 3p, 3d states f Al and 3d, p states f N. The general features f the band structure and density f states (figures 1-4) are similar t that f the ther grup III-V cmpunds [1, ]. igure 1. Band Structure f AlN at V/V = 1 (nrmal pressure). 7 Orbital: Electrn. J. Chem. 7 (3): 6-30, 015

3 igure. Density f states f AlN at V/V = 1 (nrmal pressure). ull Paper transitins are studied frm the ttal energies btained frm ur calculatin. The ttal energy is calculated as a functin f reduced vlume (V/V ) fr ZnS, NaCl, and CsCl phases f AlN [1]. Here, V is the experimental equilibrium vlume crrespnding t the experimental equilibrium lattice cnstant. In Table 1, the equilibrium lattice cnstant (a ), band gap (E g), bulk mdulus (B ) and its pressure derivative (B 1 ) values are cmpared with experimental [7] and previus theretical wrks [6]. The values f reduced vlume, pressure, and lattice cnstant are given in Table. The calculated ttal energies were fit t Murnaghan s equatin f state t btain the equilibrium lattice cnstant and ther grund state prperties. Table. Reduced vlumes, Lattice cnstant and Presssure values f AlN. V/V0 Lattice cnstant(au) Pressure(Mbar) igure 3. Band Structure f AlN at V/V = (metallizatin pressure =1Mbar) Structural phase transitin igure 4. Density f states f AlN at V/V = (metallizatin pressure=1mbar). 3. RESULTS AND DISCUSSION 3.1 Grund state prperties The grund state prperties and structural phase In ur calculatin we have chsen the ZnS structure as the grund state structure fr AlN. The phase stability f the B3 (ZnS), B1 (NaCl), and B (CsCl) structures f AlN is analyzed using the enthalpic calculatin [1]. The phase transitin pressure (P T) and the crrespnding reduced vlume (V/V ) T estimated in ur calculatin are given in Table 3. r AlN, ur calculated phase transitin pressure is in gd agreement with the experimental and previus theretical results [4, 5]. The mechanism fr the phase transitin is a gemetric effect invlving a change in the crdinatin number frm 4 in the ZnS phase t 6 in the NaCl phase and t 8 in the CsCl phase under pressure [1, ]. 3.3 Metallizatin At nrmal pressure, AlN is a semicnductr. 8 Orbital: Electrn. J. Chem. 7 (3): 6-30, 015

4 With the increase f the pressure, the band gap decreases and at a particular pressure, there is a clsing f the band gap. The band structure and density f states crrespnding t the metallizatin f AlN are shwn in figures 3 and 4, respectively. In AlN, the metallizatin ccurs thrugh indirect clsing f the band gap between valence band maximum at pint and cnductin band minimum at X pint. The metallizatin vlume f AlN is V/V =0.756 (NaCl structure), which crrespnds t the pressure P M = 1 Mbar. At the metallizatin pressure, the values fr ull Paper density f states at ermi energy E ) are very small (pseud gap), which indicate that metallizatin has just set in AlN (ig.4). Thereafter E ) increases slwly with pressure and becmes fairly large at a particular value f V/V. The values f E and E ) crrespnding t different V/V are used in studying the pressure variatin f supercnducting transitin temperature. Hwever, there are n experimental nr theretical studies available fr cmparisn at these pressures [1, ]. Table 3. Structural phase transitin pressure fr AlN. Cmpund Structural phase transitin Present study Experiment [4] Previus thery [5] (V/ V )T PT (Mbar) (V/ V )T PT (Mbar) (V/ V )T PT (Mbar) AlN ZnS t NaCl NaCl t CsCl Supercnductivity in AlN under pressure The prmtin f an s electrn t the d shell in slids is ne f the factrs, which will induce supercnductivity. Under very high pressures, aluminum cmpunds are nt nly metals but als supercnductrs. The thery f Gaspari and Gyrffy in cnjunctin with McMillan s frmula is used t calculate Tc [1]. The electrn phnn mass enhancement factr, is: E ) I (4) M where M is the atmic mass, is an average f the phnn frequency square and I is an average (ver the ermi energy) f the electrn phnn matrix element square. I (in Rydbergs) can be written as: I l ( l 1) M (l 1)(l 3) l, l1 Nl ( E ) Nl 1( E ) E ) E ) (5) where l,l+1 = - l l+1 [(D l(e )-1)(D l+1(e )+l+) + (E -V(S))S ] and in this, l is the radial wave functin at the muffin-tin sphere radius crrespnding t the ermi energy, D l is the lgarithmic derivative f the radial wave functin at the sphere bundary, V(S) is the muffin-tin ptential at the sphere bundary, and S is the radius f the muffin-tin sphere. The abve quantities are taken frm the band structure results. pressure The average f the phnn frequency square is: 1 D (6) The variatin f Debye temperature with D (P) is given by: where D, a and quantities. [], E D ( P) D (7) E a a E are nrmal pressure The McMillan s frmula used fr Tc calculatin D 1.04(1 ) exp 1.45 * (1 0.6) Tc (8) gives a gd estimate f the Tc value. Here * is the electrn-electrn interactin parameter which is 9 Orbital: Electrn. J. Chem. 7 (3): 6-30, 015

5 estimated using the relatin, * 0.6 E ) (9) 1 E ) where E ) is the density f levels per atm per ev at E. With the results btained frm the selfcnsistent calculatin, we have cmputed D,, * and Tc as a functin f pressure using Eqs. (4-9). The nset f supercnductivity ccurs at V/V=0.5, with Tc= 0.04K. On further increase f pressure, Tc begins t increase. Our results indicate that AlN is a ne-band rather than a ne-electrn material. The electrn-phnn interactin parameter () and its variatin under pressure shws that AlN is an electrn-phnn mediated supercnductr. In this material, the Tc increases with pressure. It is fund that the Tc(P) fllw the variatin in E ) with pressure. The increase f Tc(P) depends mainly n the rate f increase f s p electrn numbers with pressure fr AlN. At lw pressures the rate f increase f these electrn numbers are increasing with pressure resulting in the increase f Tc. The calculated values at high pressure (CsCl) structure are given in Table 4 fr AlN. As pressure increases ur cmputed value f Tc increases and reaches a maximum value. In ur calculatin, the highest Tc btained in AlN is 8.864K at 7.0 Mbar (Table 4). This reflects the fact that the structural and band gap cnfiguratins play an imprtant rle in the supercnducting (high Tc-max) behavir f these cmpunds under high pressure [1, ]. ull Paper wave functins f the adjacent atms. As a result the widths f the valence and empty cnductin bands increase. These changes lead t the narrwing and clsing f band gaps (metallizatin). On further increase f pressure, AlN becmes a supercnductr, and this material cmes under the class f electrnphnn-mediated high pressure supercnductr. It is als cnfirmed that the metallizatin, structural phase transitin, and nset f supercnductivity d nt ccur simultaneusly in aluminum cmpunds []. 5. REERENCES AND NOTES [1] Amal Raj, A.; Nirmala Luis, C.; Iyakutti, K. J. Ther. Cmput. Chem. 01, 11, 19. [CrssRef] [] Sheeba, V. B.; Nirmala Luis, C. Chem. Mater. Eng. 013, 1, 13. [3] Davydv, S. Yu. Semicnductrs, 00, 36, 41. [CrssRef] [4] Vladimir, A.; Serget, R. Phys. Status Slidi B 007, 44, 43. [5] Christensen, N. E.; Nvikv, D. L.; Alnsn, R. E.; Rdriguez, C. O. Phys. Status Slidi B 1999, 5, 11. [6] Wang, S. Q.; Ye, H. Q. J. Phys.: Cndens. Matter 00, 14, [CrssRef] [7] Edgar, J. H. Electrnic materials infrmatin service, Data Reviews series, 1994, (Institutin f Electrical Engineers, Lndn). [8] Wagner, J. M.; Bechstedt,. Phys. Status Slidi B 00, 34, 965. [9] Andersen, O. K.; Jepsen, O.; Sb, M. In: Electrnic band structure and its applicatins. Yussuff, M., ed. Heidelberg: Springer, Table 4. Variatin f Tc as a functin f pressure fr AlN in CsCl structure. Pressure P Mbar D * Tc K K CONCLUSION In the present investigatin, the pressure dependent band structures and density f states f AlN is cmputed and the results are used t study the metallizatin and supercnductivity under high pressure fr the first time. When the pressure is increased there is enhanced verlapping between the 30 Orbital: Electrn. J. Chem. 7 (3): 6-30, 015