Ab initio studies of electronic structure of defects on the Te sites in PbTe

Transcription

1 Mater. Res. Soc. Symp. Proc. Vol Materials Research Society 0886-F Ab initio studies of electronic structure of defects on the Te sites in PbTe Salameh Ahmad*, S.D. Mahanti*, and M.G. Kanatzidis** *Department of Physics and Astronomy,** Department of Chemistry Michigan State University, East Lansing, MI ABSTRACT Ab initio electronic structure calculations have been carried out to understand the nature of anionic defect states in PbTe. We find that Te vacancies strongly perturb the electronic density of states (DOS) near the band gap region. New states of predominantly Pb p character appear in the band gap. Iodine is an ideal substitutional defect and a donor. Sulpher and Selenium do not affect the states near the conduction band minimum but suppress the DOS near the valence band maximum. These results have important implications on the thermoelectric properties of PbTe and PbTe x M 1-x (M=S, Se) ternary systems. INTRODUCTION Narrow Band-gap IV-VI binary semiconductors have been of great interest since last four decades because of their fundamental solid state properties and for their practical applications. Lead chalcogenide salts PbTe and PbSe are two IV-VI narrow gap semiconductors whose study has been motivated by their importance in infrared detectors, light-emitting devices, infrared lasers, thermophotovoltaics and thermoelectrics [1, 2, 3]. In fact, PbTe was one of the first materials studied by Ioffe and his colleagues in the middle of the last century when there was a revival of interest in thermoelectricity [4]. This compound, its alloys with SnTe and PbSe, and related compounds called TAGS (alloys of AgSbTe 2 and GeTe) were for many years the best thermoelectric materials at temperatures ~ 700 K [5]. In recent years quantum wells of PbTe/Pb 1- xeu x Te, PbSe 0.98 Te 0.02 /PbTe superlattices [6] and novel quaternary compounds AgSbPb m Te m+2 (m=16, 18) (LAST-m) [7] have attracted considerable attention because of their large thermoelectric figure of merit (FOM). It is well known that the thermoelectric FOM (denoted as ZT where T is the operating temperature T) depends on the thermopower (S) through the relation ZT = σs 2 T/κ, where the σ and κ are the electric and thermal conductivities of the material [8]. Clearly large values of ZT require large values of S. Since S depends sensitively on the nature of the electronic states near the band gap of a semiconductor [8,9], it is important to have a fundamental understanding of the changes in the electronic states near the band gap region in PbTe when it is mixed with other binary and ternary compounds. In our previous work we studied how the conduction and valance band states get modified when one replaces Pb by a vacancy or by other atoms with same and different valance [10]. To make the picture complete we discuss in this paper how the conduction and valence band states of PbTe get modified when one replaces Te by a vacancy or by other anions such as S, Se and I. Naively, one expects to see defect states in the band gap when a Pb or Te atoms is replaced by either a donor or acceptor-like impurity. Shallow and deep defect states in semiconductors are known to profoundly alter their electronic structure near the band gap and control their transport properties. It is believed that in narrow band gap semiconductors like PbTe deep defect states are more likely to occur [11-13]. Unlike shallow impurity levels, which are produced by

2 0886-F the long-range Coulomb potential screened by the dielectric constant of the host semiconductor, deep levels are produced by the short-range atomic-like defects potential and changes in local bonding. A fundamental understanding of the shallow defect states in semiconductors with large band gap traces back to the classic work of Kohn and Luttinger. [14] In this case bound defect states appear below the conduction band bottom (for donor impurities) or above the valence band maximum (for acceptor impurities). The binding energies of these shallow defect states are well described by a hydrogenic model taking proper account of the band effective masses and the dielectric constant of the host. In contrast, the problem of defects in narrow-gap semiconductors, particularly with regard to the physics underlying deep defects states, is not well understood. In this paper we continue our attempts to understand the physics behind the deep defect states in PbTe using self consistent ab initio electronic structure calculations within density functional theory (DFT) and a periodic supercell model. Bilc et. al. have recently reported their results on Ag and Sb substitutional defects in PbTe using all electron full potential linearized augmented plane-wave (LAPW) method and a similar supercell model.[15] In a previous work we extended these studies to a larger class of defects; Pb vacancy, Pb substituted by monovalent atoms (alkali atoms), divalent atoms (Cd).[10] In this paper we address how the conduction and valance band states get modified when one replaces the Te atom by either with a Te vacancy or by other anions (S, Se and I).Our main focus is to develop a systematic understanding (any qualitative trend) of these defect states as one goes across or down the periodic table to select different defects. For our electronic structure calculations we use a supercell model where the defects are periodically arranged in the PbTe lattice. This corresponds to a compound RPb 2n Te 2n-1 (where R is a vacancy, Se, S, I). The arrangement of the paper is as follows. In Sec.II we describe the structural model we have used and discuss briefly the method used to calculate the electronic structure. In Sec.III we present the results of our calculations focusing on the electronic density of states (DOS) with and without the defects. In particular, we give the change in the total and projected DOS caused by different types of defects and discuss the underlying physics. Finally in Sec. IV we give a brief summary. ELECTRONIC STRUCTURE CALCULATIONS To model the impurities and the vacancy we have use a supercell model; 2x2x2 supercells of PbTe containing 64 atoms. We choose the defects to be at the origin of the supercell with separation of two lattice constants (12.908Å) between the defects. Due to the large dielectric constant of the host PbTe we expect long range coulomb effects to be screened out, thereby reducing the impurity-impurity interaction. However, short range interaction is very important [11-13,15]. Electronic structure calculations have been performed within density functional theory and all electron full potential linearized augmented plane-wave (LAPW) plus local orbital method [16]. We have used the generalized gradient approximation (GGA) [17] for the exchange and correlation potential. Scalar relativistic corrections were included and spin orbit interaction (SOI) was incorporated using a second variational procedure [18]. We have used WIEN2K program [19]. Convergence of the self-consistent iterations was performed using 10 k-points inside the reduced Brillouin zones to within Ry (1.36 mev) with a cutoff -6.0 Ry between the valance and the core states. For all calculations we use the experimental lattice constant of PbTe.

3 0886-F Before we present the results of our ab initio calculations let us discuss some basic physics. In PbTe the Pb s-states are quite deep (due to a relativisitic effect) and the valence and conduction bands are formed out of 6p states of Pb and 5p states of Te. The Pb and Te bonds have both covalent and ionic character. The removal of a Te atom (vacancy) or replacing it by other valance atom introduces a local charge disturbance and alters the covalent bonding with the neighboring Pb (denoted as Pb2) p states. As a result, we expect the valance and conduction bands states to get strongly perturbed. Te vacancy in PbTe The total DOS with vacancy, without vacancy and the difference between the two are shown in Fig.1(a,b). For the sake of comparison we shifted the DOS of the PbTe the core bands match perfectly. As we can see the entire valence band and conduction band density of states get modified by the presence of the vacancy. Since transport properties are controlled by the states near the Fermi energy (0 ev in the figure) let us focus on this region. Looking at Fig1.a,b we see that new states appear in the band gap of PbTe in the range 0,-0.5 ev which are predominantly of Pb p character (Fig. 1c). These states are occupied by 2 electrons and the Fermi energy is at the top of this band. Because of Te and Pb hybridization the Te states around -1.0 ev (Fig.1b) also get perturbed strongly. Figure 1: (a) Total DOS with and without Te vacancy; (b) their difference ρ tot ; (c) partial DOS per Pb associated with nearest neighbor Pb atoms S and Se impurities in PbTe S and Se are divalent ions as Te. Thus one expects very little perturbation of the conduction band as can be seen in Fig 2a,b,c and 3a,b.c. The major change occurs in the density of states

4 0886-F near the top of the valence band (Fig. 2c and 3c), a transfer of DOS from the top 0.5 ev of the valence band. S and Se p states appear in the entire valence band region peaqking around ev. Figure 2: (a) Total DOS with and without S impurity; (b) their difference ρ tot ; (c) S partial DOS of p character; (d) partial DOS per Pb associated with nearest neighbor Pb atoms. Figure 3: (a) Total DOS with and without Se impurity; (b) their difference ρ tot ; (c) Se partial DOS of p character; (d) partial DOS per Pb associated with nearest neighbor Pb atoms.

5 0886-F I impurity in PbTe I appears to act as perfect donor in PbTe. It does not perturb the states both near the top of the valence band and the bottom of the conduction band. The major change occurs near the bottom of the valence band around -5.0 ev (predominantly I p character) and near -1.5 ev due to changes in the Pb p hybridization effect. Figure 4: (a) Total DOS with and without I impurity; (b) their difference ρ tot ; (c) I partial DOS of p character; (d) partial DOS per Pb associated with nearest neighbor Pb atoms. SUMMARY In summary, Te vacancy has the strongest effect on the PbTe DOS near the band gap region. New states appear in the band gap which comprise primarily p-states of Pb atoms neighboring the vacancy. Iodine appears to be an ideal donor, it does not change the PbTe DOS near the band gap, just shifts the Fermi energy to the conduction band. The divalent ions S and Se also do not change the DOS near the conduction band minimum. There is however some depletion of the DOS near the valence band maximum. These results should have important implications in the ternary systems PbTe 1-x M x (M=S and Se). ACKNOWLEDGEMENT The work is partially supported by a ONR-MURI program (Contract No. N ).

6 0886-F References 1. G. P. Agrawal and N. K. Dutta in Semiconductor Lasers (New York: Van Nostrand Reinhold) p. 547 (1993); S. Chatterjee and U. Pal Optical Eng (1993). 2. T. K. Chaudhuri, Int. J. Energy Res (1992). 3. J. H. Dughaish, Physica B (2002). 4. A. F. Ioffe, Semiconductor Thermoelements and Thermoelectric Cooling (London: Infosearch) (1957). 5. E. A. Skrabek and D. S. Trimmer in CRC Handbook of Thermoelectrics, ed. D M Rowe (Boca Raton: CRC Press) p 267 (1995). 6. T. C. Harman, D. L. Sprears M. J. and Manfra, 1996 J. Elec. Mater (1996); T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, 2002 Science (2002). 7. K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis and M. G. Kanatzidis, Science (2004). 8. N. P. Blake and H. Metiu, in Chemistry, Physics, and Material Science of Thermoelectric Materials Beyond Bismuth telluride ed. M G Kanatzidis, S D Mahanti and T Hogan (New York: Kluwer Academic/Plenum Publishers) p 259 (2003). 9. S. D. Mahanti, P. M. Larson, D. Bilc and H. Li H, in Chemistry, Physics, and Material Science of Thermoelectric Materials Beyond Bismuth telluride ed. M G Kanatzidis, S D Mahanti and T Hogan (New York: Kluwer Academic/Plenum Publishers) p 227 (2003). 10. S. Ahmad, D. Bilc, S.D. Mahanti, and M.G. Kanatzidis, in Semiconductor Defect Engineering Materials, Synthetic Structures and Devices, edited by S. Ashok, J. Chevallier, B.L. Sopori, M. Tabe, and P. Kiesel (Mater. Res. Soc. Symp. Proc. 864, Warrendale, PA, 2005), E S. T. Pantelides, Deep centers in Semiconductors 2 nd ed. Gordon and breach (Yverdon, Switzerland) (1992); S. T. Pantelides, 1978 Rev. Mod. Phys (1978). 12. C. S. Lent, M. A. Bowen, J. D. Dow, R. S. Allgaiger, O. F. Sankey, and E. S. Ho, Solid State Communications (1987). 13. L. I. Ryabova and D. R. Khokhlov, JETP Letters 80, (2004) and refernces therein. 14. W. Kohn, Solid StatePhysics ed F Seitz and D Turnbull (New York: Academic) vol 5 Chap 4 (1957). 15. Daniel Bilc, S D Mahanti, Eric Quarez, Kuei-Fang Hsu, Robert Pcionek, and M G Kanatzidis, Phys. Rev. Lett (2004); S D Mahanti and Daniel Bilc, J. of Phys., Cond. Matt (2004). 16. D. J. Singh, Planewaves, Pseudopotentials, and the LAPW method (Boston: Kluwer Acadimic)(1994) 17. Perdew J P, Burke K and Ernzerhof M, Phys. Rev. Lett (1996). 18. D. D. Koelling and B. Harmon B J. Phys. C (1980). 19. P. Blaha et al., WIEN2K, An Augmented Plane Wave +Local Orbitals Program for Calculating Crystal Properties, K. Schwarz, Techn. Universitat Wien, Austria (2001).