PHYSICAL REVIEW B VOLUME 61, NUMBER 19 15 MAY 2000-I Clathrates as effective p-type and n-type tetrahedral carbon semiconductors M. Bernasconi, S. Gaito, and G. Benedek Istituto Nazionale per la Fisica della Materia and Dipartimento di Scienza dei Materiali, Università degli Studi di Milano-Bicocca, Via Cozzi 53, I-20125 Milano, Italy 共Received 17 February 2000兲 Based on ab initio calculations, we predict that a carbon clathrate compound 共hexagonal C40) is suitable to be n doped by Li insertion and p doped by substitutional boron. This material represents an example of n- and p-type tetrahedral carbon semiconductor, alternative to the n-doped diamondlike films whose realization is still in progress. Although this compound has not been synthesized so far, its study can also provide insights into the properties of nanostructured carbon thin films, grown by supersonic cluster beam deposition techniques that display local morphologies similar to the channels and fullereniclike cages present in the system here investigated. The potential application of diamondlike carbon in electronic devices operating at high temperature has stimulated a great deal of experimental and theoretical research on the doping properties of diamondlike films.1,2 Considerable efforts have been directed mainly to the doping of crystalline diamond, synthesized by chemical vapor deposition technique 共CVD兲,2–5 and of tetrahedral amorphous carbon films, grown by implantation of energetic carbon ions on a substrate.6 In the latter system, boron, nitrogen, and phosphorus doping7 have been studied, but they have not yet reached sufficient efficiency for device applications. The doping mechanism itself is still controversial. On the other hand, it is well established that a boron atom can be incorporated in crystalline diamond to form a shallow acceptor level 共0.35 eV above the top of the valence band兲 making diamond an effective p-type semiconductor.2,5 Conversely n-type doping in CVD diamond is still a challenging problem. Incorporation of group-V and -VI elements in diamond have been studied extensively. Nitrogen is well-known to induce a deep level 1.7 eV below the conduction band,2 while only very recently, phosphorus4 and sulfur3 have been reported to induce shallow acceptor levels in CVD diamond films 共0.56 and 0.38 eV below the conduction band for phosphorus and sulfur impurities, respectively兲. However, the realization of n-type diamondlike films with electrical properties suitable for device applications is still far from being accomplished. In this paper we propose an alternative form of tetrahedral carbon suitable to be both p-type and n-type doped. Based on ab initio calculations, we show here that the hexagonal C40 carbon clathrate8 共hex-C40 hereafter兲 is a tetrahedrally bonded carbon material, p dopable by boron substitution and n dopable by lithium insertion. The n doping is realized by inserting the lithium atoms in the large cages of the clathrate structure. The guest ion fully ionizes by donating its outermost electron to the host frame, which becomes metallic. In fact, it is conceivable that the realization of cagelike structures is the route to the incorporation in a tetrahedral carbon frame of ionized donor impurities that would otherwise bond covalently to the host. The clathrates are tetrahedrally bonded crystals that precisely provide such a frame. 0163-1829/2000/61共19兲/12689共4兲/$15.00 PRB 61 The synthesis of silicon and germanium clathrates dates back to the 1960s.9 Their structures are analogous to type-I and -II clathrate hydrates. Silicon and germanium clathrates, doped by insertion of groups-IA and -IIA metal ions, have recently attracted considerable interest for their superconductive properties10 and as potential thermoelectric materials.11 The carbon analogs of the Si and Ge clathrates have not been synthesized so far. However, recent progress in the synthesis of carbon films by supersonic cluster beam deposition 共SCBD兲 共Ref. 12兲 have shown that carbon nanostructured thin films, grown by this technique, display a variety of morphologies,13 which can be locally modeled as schwarzites14 and eventually as clathrate structures. In fact, the crystalline clathrates could be described as produced by the coalescence of fullereniclike cages, which is reminiscent of the growth conditions of carbon thin films produced by cluster assembling in the SCBD technique. The study of the electronic properties of carbon clathrates could therefore provide insights also on the properties of the nanostructured, albeit disordered, thin films grown by SCBD. In this perspective we have chosen to study the hexagonal clathrate hex-C40 , proposed theoretically in Ref. 8, and shown in Fig. 1. It belongs to the space group P6/mmm and has 40 atoms per unit cell, the symmetry independent atoms being five. The structure can be seen as resulting from the coalescence 共by sharing hexagonal and pentagonal rings兲 of two C26 , two C24 , and three C20 per unit cell, which gives rise to a hexagonal array of parallel tubes, each tube being an infinite pile of C24 cages. The tubes in turn are held together by rings of C26 and C20 cages arranged on alternate planes normal to the tubes. We have computed the structural and electronic properties of the pure, Li- and B-doped compounds within densityfunctional theory in the local spin-density approximation 共LSDA兲.15,16 Only valence electrons are treated explicitly and electron-ion interactions are described by normconserving pseudopotentials for carbon17 and boron18 in the Kleinman-Bylander form.19 Nonlinear core corrections have been added for lithium.20 The Kohn-Sham orbitals are expanded in plane waves up to a kinetic cutoff of 35 Ry. Geometry optimization have been performed either by simulated annealing in the Car-Parrinello molecular dynamics21 12 689 ©2000 The American Physical Society 12 690 BRIEF REPORTS FIG. 1. Structure of the clathrate hex-C40 . 共a兲 View of the plane perpendicular to the c axis. Chains of C24 cages form channels running along the c direction, arranged in a hexagonal array in the plane. 共b兲 Side view of one channel. 共c兲 Top view of one channel. The position of the Li atom at the center of one of the C24 cages and the most stable site for boron substitution in the largest hexagonal ring of the C24 cage are shown. The position of the five symmetryindependent atoms in Cartesian coordinates 共Å兲 are (⫺1.529,0,0), (⫺2.451,0,1.269), (⫺2.2,⫺1.27,2.106), (⫺1.446,⫺0.835,3.404), (⫺1.539,⫺3.359,0.767). or by using the Broyden-Fletcher-Goldfarb-Shanno algorithm.22 The simulation cell is the unit cell of the pure system containing 40 atoms. The equation of state of the pure and doped system have been computed by restricting the Brillouin zone 共BZ兲 integration at the ⌫ point only. Refinement of the internal geometry at the equilibrium volume, and band-structure calculations have then been performed by extending the BZ integration over a uniform grid of 27 k points in the irreducible part. This mesh turns out to be sufficient also to describe the structure of the metallic system doped by lithium. The c/a ratio of the hexagonal structure has been optimized at the equilibrium volume obtained in previous tight-binding calculations8,23 共6.65 Å3 /atom兲 and then held fixed to the resulting value of c/a⫽1.014 in the PRB 61 FIG. 2. Electronic energy bands of the Lix C40 compounds. 共a兲 the undoped clathrate. 共b兲 LiC40 with a Li ion at the center of one C24 cage 关cf. Figs. 1共b兲 and 1共c兲兴. 共c兲 Li7C40 . A Li ion is at the center of all the fullereniclike cages 共three C20 , two C24 , and two C26 per unit cell兲. The Fermi level in panel 共a兲 is at the top of the valence band at the ⌫ point 共9 eV兲. The reference zero of energy corresponds to the average electrostatic potential as usual in bandstructure calculations. The band structure is reported along the highsymmetry lines of the irreducible Brillouin zone of the hexagonal P6/mmm space group following the notation of Ref. 31. calculation of the equation of state. The equation of state has been fitted by a Murnaghan function,24 which gives an equilibrium volume25 of 6.65 Å3 /atom 共0.855 times the density of diamond兲 which coincides with the result of previous tightbinding calculations.8 The bulk modulus is B⫽365 GPa and the derivative of B with respect to pressure at equilibrium is B ⬘ ⫽3.486. We have then optimized the internal structure at the equilibrium volume by sampling the irreducible BZ over 27 k points. The resulting atomic positions differ by less than 0.01 Å with respect to the ⌫-point optimization. The cohesive energy of the clathrate turns out to be 0.17 eV/atom smaller than the cohesive energy of diamond as computed in the same framework and at convergence in the BZ integration,26 a value not too far from the 0.214 eV obtained in previous tight-binding calculations.8 The electronic band structure along the high-symmetry directions of the BZ is reported in Fig. 2共a兲. The clathrate is a wide band-gap insulator. The ⌫-A indirect band gap 共3.13 eV兲 is only 0.04 eV narrower than the direct gap at ⌫. The real band gap is expected to be larger than the value reported here, due to the PRB 61 BRIEF REPORTS well-known underestimation of band gaps in LSDA. We then turned to study the doping properties of the clathrate by first considering p-type doping by insertion of substitutional boron, which is known to be an effective p dopant in diamond. We considered a boron concentration of one boron per unit cell, i.e., the compound B1C39 . Among the five possible inequivalent sites for boron substitution, we find that boron preferentially lies in the larger hexagonal ring as shown in Fig. 1共b兲. The boron insertion induces the formation of an acceptor state in the gap, 0.53 eV above the top of the valence band. The acceptor state is mostly localized on the boron atom and on the two first neighbors of boron, which do not lie on the hexagonal ring.27 The bonds with the latter atoms also display the largest changes in length with respect to the pure system 共up to 0.15 Å兲. Therefore boron is an effective p dopant in the hex-C40 clathrate as well. In the search of possible n dopant, we inserted lithium in the cages of the clathrate hex-C40 , in analogy with the insertion of groups-IA and -IIA metal ions already realized experimentally in the germanium and silicon clathrates.11 Electron transfer from alkali metals to the host carbon frame is demonstrated in intercalated s p 2 structures such as graphite28 and fullerite.29 Here, we investigate the possibility to observe a similar charge transfer in the clathrate structure, which, as opposed to the formerly studied intercalated carbon compounds,28,29 is a wide band-gap insulator and fully sp 3 hydridized. As already mentioned, there are three different types of cages in the hex-C40 structure: the C20 共three per unit cell兲, C24 , and C26 cages 共two per unit cell, each兲. Therefore, we can easily study the lithium doping in the concentration range from one to seven lithium atoms per unit cell, by still using as a simulation cell the unit cell of the pure system. By geometry optimization we find that the most favorable site for Li insertion is at the centers of the largest C26 cages. However, the other site at the center of the C24 cages is only 0.08 eV higher in energy. The position at the center of the C24 cage is indicated in Figs. 1共b兲 and 1共c兲. The Li ion is confined in the cages by a very high energetic barrier for diffusion across the hexagonal rings. For instance, the energy barriers for the diffusion across the large and small hexagonal rings of the C24 cages are 1.97 and 3.97 eV, respectively. The large energy barriers prevent Li diffusion up to very high temperature and therefore assure the thermal stability of the Li doping. On the other hand, the presence of high diffusion barriers imply that Li, and a fortiori larger alkali ions, cannot be inserted by electrochemical means, but must be implanted or introduced in the growth process as done for instance in the synthesis of the Si and Ge clathrates. We computed the equation of state of the system with a Li ion in one or two C24 cages and with seven Li ions per unit cell occupying the centers of all the available cages. The c/a ratio and the equilibrium volumes are essentially unaffected 共the changes are less than 1%兲 by increasing the Li concentration. Analogously, B decreases only slightly by increasing Li content from 358 GPa 共one Li/cell兲 down to 356 GPa 共seven Li/cell兲. The electronic band structures of the LiC40 compound with Li ions at the center of the C24 cages is shown in Fig. 2共b兲. The band structure of the Li7C40 compound is shown instead in Fig. 2共c兲. The reference zero of energy corresponds to the average electrostatic potential as usual in band- 12 691 structure calculations. At low Li content (LiC40), the band structure does not change significantly with respect to the pure compound, but for the shift of the Fermi level inside the conduction bands and a small downward shift in energy of the lowest conduction band at the ⌫ point. Therefore, the electronic properties of the system at low Li content can be described in the rigid-band approximation where the Li is fully ionized and donates its outermost electron to the host without changing the band structure. This picture is a fortiori valid at Li content lower than those studied here. The insertion of Li thus makes the clathrate metallic. At low Li content the electronic conductivity is mainly due to a pocket of electrons at the A points of the BZ 关cf. Fig. 2共b兲兴. In conclusion, Li can be considered an effective n dopant in the clathrate hex-C40 . A similar charge transfer from the guest ion to the host has been proposed also for the Nax Si136 silicon clathrate.30 However, in the latter compound a Jahn-Teller distortion is expected to drive a metallic-insulator transition and a breakdown of the rigid-band approximation. At high Li content the rigid-band approximation is inadequate for hex-C40 as well: also when the smaller C20 cages are filled, the shape of the lowermost conduction bands are drastically modified with respect to the pure compound indicating a stronger Lihost interaction 关cf. Fig. 2共c兲兴. By increasing the Li content the Madelung energy is expected to decrease, at fixed ionicity of Li. In fact, the insertion energy 共computed as the difference between the sum of the energies of the pure hex-C40 and of isolated Li atoms and the energy of Lix C40) increases from 0.87 eV/atom in LiC40 to 1.13 eV/atom in Li2C40 when only the C24 cages are filled. In Li7C40 the insertion energy is still 1.2 eV, the latter value coming, however, from an average over all the different sites. While the computed change in the insertion energy with Li content is expected to be quantitatively correct, an error of the order of 0.1 eV is expected for the absolute values 共cf. Ref. 15, p. 715兲. This is due to the well-known deficiencies of the LSDA in the calculation of the cohesive energies that mainly come from an overestimation of the total energy of the isolated atoms. Nevertheless, the insertion energy quoted above 共0.87 eV兲 is so much lower than the cohesive energy of metallic Li (⬃1.7 eV, cf. Ref. 15, p. 715兲 that we can safely expect that the insertion by electrochemical means from a metallic Li anode is energetically disfavored, besides the kinetical hindrances already mentioned. Lithium should therefore be introduced by implantation. In this respect the hex-C40 structure might be a more suitable choice than the cubic clathrates.9 In fact, channeling along the tubular structures might reduce the implantation damage in hex-C40 . In conclusion we have shown that the theoretically proposed carbon clathrate hex-C40 is suitable to be n doped by Li insertion and p doped by substitutional boron. Therefore this material represents an example of n- and p-type tetrahedral carbon semiconductor. These findings can help in the study of the doping properties of the nanostructured carbon thin films grown by SCBD techniques that display similar channels and fullereniclike cages, able to host intercalant ions. This work was partially supported by the INFM Advanced Research Project CLASS and by MURST, through COFIN99. 12 692 1 BRIEF REPORTS R. E. Clausing et al., Diamond and Diamondlike Films and Coatings 共Plenum, New York, 1991兲. 2 A. T. Collins, in Properties and Growth of Diamond, edited by G. Davies 共INSPEC, Institution of Electrical Engineers, London, 1993兲, p. 263. 3 I. Sakaguchi et al., Phys. Rev. B 60, 2139 共1999兲. 4 N. Fujimori et al., in Diamonds, Silicon Carbide and Related Wide Bandgap Semiconductors, edited by J. T. Glass et al., MRS Symposia Proceedings No. 162 共Materials Research Society, Pittsburgh, 1990兲, p. 23; A. E. Alexenko and B. V. Spitsyn, Diamond Relat. Mater. 1, 705 共1992兲; S. Koizumi et al., Appl. Phys. Lett. 71, 1065 共1997兲; T. Saito et al., Jpn. J. Appl. Phys., Part 2 37, L543 共1998兲; N. Nesládek et al., Phys. Rev. B 59, 14 852 共1999兲. 5 B. A. Fox et al., Diamond Relat. Mater. 4, 622 共1995兲; S. Yamanaka et al., Jpn. J. Appl. Phys., Part 2 37, L1129 共1998兲. 6 D. R. Mckenzie, D. A. Muller, and B. A. Pailthorpe, Phys. Rev. Lett. 67, 773 共1991兲; D. R. McKenzie, Rep. Prog. Phys. 59, 1611 共1996兲. 7 M. Chhowalla et al., Appl. Phys. Lett. 69, 2344 共1996兲; C. A. Davis et al., J. Non-Cryst. Solids 170, 46 共1994兲; B. Kleinsorge et al., Diamond Relat. Mater. 7, 472 共1998兲; C. Ronning et al., ibid. 4, 666 共1995兲; V. S. Veerasamy et al., Phys. Rev. B 48, 17 954 共1993兲; A. Gambirasio and M. Bernasconi, ibid. 60, 12 007 共1999兲; Th. Köler, G. Jungnickel, and Th. Frauenheim, ibid. 60, 10 864 共1999兲. 8 G. Benedek et al., Chem. Phys. Lett. 244, 339 共1995兲; G. Benedek and L. Colombo, in Cluster Assembled Materials, edited by K. Sattler 共Trans. Tech., Winthertur, 1997兲, p. 1; G. Benedek et al., in The Physics of Diamond, Proceedings of the International School of Physics ‘‘Enrico Fermi,’’ Course CXXXV, edited by A. Paoletti and A. Tucciardone 共IOS, Amsterdam, 1997兲, p. 575. 9 J. S. Kasper et al., Science 150, 1713 共1965兲; C. Cros et al., C. R. Acad. Sci. 共Paris兲 260, 4764 共1965兲; Bull. Soc. Chim. Fr. 11, 379 共1971兲; 7, 2737 共1968兲; C. Cros et al., J. Solid State Chem. 2, 570 共1970兲. 10 H. Kawaji et al., Phys. Rev. Lett. 74, 1427 共1995兲; S. Saito and A. Oshiyama, Phys. Rev. B 51, 2628 共1995兲. 11 G. S. Nolas et al., Appl. Phys. Lett. 73, 178 共1998兲; J. L. Cohn et al., Phys. Rev. Lett. 82, 779 共1999兲. 12 P. Milani et al., J. Appl. Phys. 82, 5793 共1997兲; P. Milani and S. Iannotta, Cluster Beam Synthesis of Nanostructured Materials, PRB 61 Springer Series in Cluster Physics 共Springer-Verlag, Berlin, 1999兲. 13 C. Lenardi et al., J. Appl. Phys. 85, 7159 共1999兲; E. Barborini et al., Chem. Phys. Lett. 300, 633 共1999兲; D. Donadio et al., Phys. Rev. Lett. 83, 776 共1999兲. 14 D. Vanderbilt and J. Tersoff, Phys. Rev. Lett. 68, 511 共1992兲; M. O’Keefe et al., ibid. 68, 2325 共1992兲; S. Gaito, L. Colombo, and G. Benedek, Europhys. Lett. 44, 525 共1998兲. 15 R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 共1989兲. 16 We used the code CPMD, developed by J. Hutter et al., MaxPlanck-Institut für Festkörperforschung and IBM Research Laboratory, 1990–1999. 17 W. Andreoni, D. Sharf, and P. Giannozzi, Chem. Phys. Lett. 173, 449 共1990兲. 18 R. Stumpf, X. Gonze, and M. Scheffler 共unpublished兲. 19 L. Kleinman and D. M. Bylander, Phys. Rev. Lett. 48, 1425 共1982兲. 20 S. G. Louie, S. Froyen, and M. L. Cohen, Phys. Rev. B 26, 1738 共1982兲. 21 R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 共1985兲. 22 W. H. Press et al., Numerical Recipes 共Cambridge University Press, Cambridge, 1992兲. 23 The c/a ratio has been optimized at fixed volume by computing the stress tensor and choosing the c/a value which gives an isotropic pressure. The residual difference in the diagonal elements of the stress tensor is less than 0.15 GPa. 24 D. Murnaghan, Proc. Natl. Acad. Sci. USA 30, 244 共1944兲. 25 Due to the limited BZ sampling, the equation of state had to be smoothed by correcting for the discontinuities in the basis set as a function of volume following the prescription given by Francis et al. 关G. P. Francis and M. C. Payne, J. Phys.: Condens. Matter 2, 4395 共1990兲兴. 26 We used ten special points 关H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 共1976兲兴 in the irreducible BZ of diamond. 27 The localization properties have been analyzed by projecting the Kohn-Sham orbitals on the atomic minimal basis set obtained from the atomic pseudo-wave functions. 28 M. S. Dresselhaus and G. Dresselhaus, Adv. Phys. 30, 139 共1981兲. 29 S. Saito and A. Oshiyama, Phys. Rev. Lett. 66, 2637 共1991兲. 30 V. E. Smelyansky and J. S. Tse, Chem. Phys. Lett. 264, 459 共1997兲. 31 J. Zak, Irreducible Representation of the Space Groups 共Benjamin, New York, 1969兲.
