superconducting group-iV semiconductors

superconducting group-iV semiconductors

(Parte 1 de 4)

nature materials | VOL 8 | MAY 2009 | w.nature.com/naturematerials 375 progress article Published online: 23 aPril 2009 | doi: 10.1038/nmat2425

It was probably the discovery of a superconducting transition around 40 K in the rather simple MgB2 compound1 that revived interest in a specific class of superconducting materials, belong‑ ing to the ‘covalent metals’2. These superconducting covalent sys‑ tems (see Box 1), including boron‑doped diamond3, silicon4 and silicon carbide5,6, barium‑doped silicon clathrates7,8, alkali‑doped fullerenes9,10 and the CaC6 or YbC6 intercalated graphites11,12, share the specificity of involving at least one relatively light element and of preserving strongly directional covalent bonds in their metallic state. The implications of this covalent character are important in superconductors in which Cooper pairs are coupled through pho‑ nons. The use of perturbation theory to study the renormalization of the electron–electron repulsion by the electron–phonon interaction leads to the ‘Eliashberg equations’13 and to the celebrated McMillan formula13 relating, in an approximate way, the super conducting transition temperature Tc to an average phonon frequency ωln, the electron–phonon coupling parameter λep and the screened and retarded Coulomb repulsion parameter μ*:

hωln –1.04(1 + λep) λep – μ* (1 + 0.62λep)1.2kB Tc =exp (1)

As is well known, low atomic masses lead to high‑frequency phonon modes, which may increase the ωln prefactor and thus Tc. This is the basis of the isotope effect. Furthermore, strong covalent bonding will lead to large phonon frequencies and a large electron–phonon coupling potential Vep = λep/N(EF), with N(EF) the density of states at the Fermi level. Both of these also contribute to increase Tc. Even in a phonon‑mediated coupling scheme, these criteria do not necessarily warrant a large Tc because increasing λep may also lead to a lattice instability, and a large electron–phonon potential Vep may be impaired by a low density, N(EF). However, these simple considerations, as well as more elaborate surveys and predictions14–16 of a larger Tc, have provided much incentive to study this class of materials.

The most familiar covalent systems are certainly diamond and silicon. The former can be considered as the prototype insulating material with unsurpassed incompressibility and hardness, and the latter is the textbook semiconductor, which has laid the grounds for today’s electronic industry. When the doping concentration in semiconductors (or insulators) goes beyond a critical value, a metal–insulator transition (MIT) takes place (see Box 2), turning superconducting group-iV semiconductors Xavier blase1,2*, etienne bustarret1,3, Claude Chapelier4, thierry Klein1,5 and Christophe marcenat4

Despite the amount of experimental and theoretical work on doping-induced superconductivity in covalent semiconductors based on group IV elements over the past four years, many open questions and puzzling results remain to be clarified. The nature of the coupling (whether mediated by electronic correlation, phonons or both), the relationship between the doping concentration and the critical temperature (Tc), which affects the prospects for higher transition temperatures, and the influence of disorder and dopant homogeneity are debated issues that will determine the future of the field. Here, we present recent achievements and pre- dictions, with a focus on boron-doped diamond and silicon. We also suggest that innovative superconducting devices, combining specific properties of diamond or silicon with the maturity of semiconductor-based technologies, will soon be developed.

the host material into a degenerate semiconductor with the Fermi level entering the valence (conduction) bands, in case of p‑type (n‑type) doping, and eventually into a superconductor. Turning diamond into a metal clearly makes this system an ideal candidate for superconductivity as it offers all the qualities listed above, with very directional bonds and optical phonons in the 150‑meV range (compared with a few tens of millielectronvolts in classical metals). This is where recent breakthroughs in the synthesis of highly doped diamond3, silicon4,17 and silicon carbide5,6 samples come in.

From early predictions to recent discoveries The idea that semiconductors doped beyond the MIT could become superconducting was already being discussed in the mid‑1960s (refs 18 and 19). Superconductivity was observed subsequently in reduced SrTiO3 perovskite single crystals20,21 and in Ge1–xTe alloys22. But the interest in superconducting doped semiconductors did not last, probably because of the low critical temperatures (0.5 K at most21).

Here we will not discuss in detail the case of the fullerenes, for which excellent reviews have already been written (see for instance refs 23 and 24). The evolution of the electron–phonon coupling strength with cage curvature, the large value of the ratio ωph/W (coupling phonon frequencies to electronic bandwidth), the prox‑ imity of a MIT driven by electronic correlations (see Box 2) and the local nature of the coupling phonons (Jahn–Teller modes) are, however, aspects that will be relevant to the cases of doped diamond and silicon, as discussed below.

In 1995, it was shown7 that Ba8@Si‑46 clathrates — where @ stands for intercalated inside — undergo a superconducting transi‑ tion around 8 K (see also refs 2 and 8). Silicon clathrates are three‑ dimensional (3D) semi conductors made of face‑sharing Sin clusters (n = 20,24,28) as building blocks25 (see Box 1). Such systems are very close to standard silicon, each atom being fourfold coordinated with a local sp3 tetrahedral environment, but with a cage‑like struc‑ ture that allows large doping by intercalation at the centre of the cages. Ab initio calculations proved that the phonons involved in the transition were mainly the silicon network vibrational modes, and that barium would serve as an n‑type dopant26. This was the first evidence that highly doped column‑IV sp3 covalent insulators, or semiconductors, could be turned into superconductors with Tc exceeding a few kelvin.Institut Néel, CNRS and Université Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France. Laboratoire de Physique de la Matière Condensée et Nanostructures, Université Lyon I, UMR CNRS 5586, F‑69622 Villeurbanne Cedex, France. Departamento de Ciencia de los Materiales, Universidad de Cadiz, 11510 Puerto Real, Spain. CEA, Institut Nanosciences et Cryogénie, SPSMS‑LATEQS, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France. Institut Universitaire de France and Université Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France. *e‑mail: xavier.blase@grenoble.cnrs.fr

376 nature materials | VOL 8 | MAY 2009 | w.nature.com/naturematerials progress articleNaTure maTerIals doi: 10.1038/nmat2425 highly boron‑doped silicon was reported4 with a Tc around 0.35 K for a boron concentration37 of about 8 at%. Finally, a super conducting transition has been observed recently5,6 in boron‑doped SiC with a

Tc of 1.4 K. In all three cases (diamond, Si and SiC), boron was the source of hole‑doping.

Phonon-mediated or correlation-driven mechanism? The question “Where are the electrons?” takes a special twist in doped semiconductors38, because across the MIT, the Fermi level is expected to shift from an impurity band to a degenerate situa‑ tion where it is located in the valence bands (for p‑type doping, see Box 2). The coincidence of the superconducting transition with the MIT in doped diamond has triggered much experimental and theo‑ retical work aimed at understanding the character of the electrons at the Fermi level involved in the superconducting transition, and the origin of the attractive interaction leading to Cooper pairs. Indeed, when the Fermi level is located in a narrow electronic band, the ‘resonant valence band’ model can explain a superconducting transition with a specific pairing mechanism, an alternative to the

On the other hand, research efforts were also intense in the apparently distant field of superhard materials belonging to the B:C:N triangle of chemical composition. Although diamond still stands out as the hardest crystal known, the hardness of other materials such as

B4C, BN or BC2N has stimulated creative synthesis strategies: in 2004, two groups27,28 performed high‑pressure high‑temperature (HPHT) treatments to obtain carbon borides, but also obtained highly doped (2–3 at%) polycrystalline diamond. Then, bridging the gap between the superhardness and superconductivity communities, doped dia‑ mond was found3 to be superconducting around 4 K, paving the way for systematic studies of superhard superconducting materials29. Since then, superconducting polycrystalline, single‑crystal or even nano‑ crystalline boron‑doped diamond samples have been synthesized by a large number of groups using the original HPHT30 techniques or growth techniques using chemical vapour deposition31–35, and transi‑ tion temperatures up to 10 K have been reported36.

In 2006, by using a gas‑immersion laser doping (GILD) tech‑ nique (see Box 3), which allows silicon to be doped well beyond the thermo dynamic solubility limit, a superconducting transition in

It is well known that under ambient conditions, carbon crystallizes mainly in the diamond (sp3) and layered (sp2, graphite) structures.

In its graphite form the Fermi level (EF) lies within the π‑bands formed by 2pz out‑of‑plane orbitals (Fig. B1a). The lateral super‑ position of these orbitals is expected to lead to a small electron– phonon coupling constant. But what makes those systems particu‑ larly interesting is the possibility of modulating their electronic structure by doping. Vibrations perpendicular to the plane, as well as intercalant modes, can for instance couple quite efficiently with the nearly free‑electron‑like band (known as the ζ‑band) that crosses EF in the intercalated CaC6 compound (Fig. B1b), leading to

Tc values of up to 1 K. However, the best coupling constant is expected to be obtained for the lower‑energy σ‑band which arises from in‑plane 2pxy orbitals (sp2 coupling, see Fig. B1c). Indeed, the direct axial superposition of atomic orbitals makes them very sensitive to atomic vibrations, leading to high electron–phonon coupling constants. Bringing the Fermi level into the σ‑band can be achieved either by depleting the π‑band or by merging both π‑ and σ‑bands in the same energy range.

The former is the case for B substitutional doping as in the graphitic

BCx structure (with x < 3). The latter is the case for the MgB2 struc‑ ture (Fig. B1c). Indeed, although isovalent to graphite, in this case the presence of Mg atoms induces a large overlap of π‑ and σ‑bands both crossed by the Fermi level leading to Tc ≈ 39 K. Following the same strategy, a very promising candidate is LixBC in which Tc values of up to 150 K have been predicted but not verified so far.

On the other hand, in 3D sp3 phases such as clathrates (cage structure, Fig. B1d) or diamond (Fig. B1e), states around the gap all present directional σ‑bonds, and the difficulty here is to dope the system in order to place the Fermi level in the valence or conduction bands (see Box 2). Critical temperatures of a few kelvin have already been observed in 3–6% doped diamonds, but several theoretical papers suggest that Tc values could even exceed that of MgB2 in cubic BC5 phases and highly doped diamond (Fig. B1e) up to and including the zinc blende structure (Fig. B1f), and in doped carbon clathrates (F@C‑34, Fig. B1g). So far, only the BC5 structure has been reported experimentally, but evidence for super conductivity is still missing.

Box 1 | Covalent structures.

Figure B1 | symbolic representation of various crystalline superconducting phases. Transition temperatures followed by a question mark indicate hypothetical materials and theoretical predictions. The structures have been grouped according to the electronic states participating in the electron–phonon coupling (sp or sp‑bonds, or interlayer states).

2D p–(sp2)

Ba8@Si-46BC zinc-blende F@C-34

Doped diamond

2D p– 40 K11.5 K m/ CaC6 MgB2Graphiteab c

10 K8 K 60 K (?)

3D p–(sp3) m

fde g 7 K (?)

nature materials | VOL 8 | MAY 2009 | w.nature.com/naturematerials 377 progress articleNaTure maTerIals doi: 10.1038/nmat2425 standard phonon mediation. Besides doped diamond39, such a correlation‑driven mechanism has, for instance, been proposed to occur in doped fullerenes40,41.

Ab initio calculations within density functional theory performed on highly doped diamond42–47, silicon4,48 and silicon carbide49 con‑ sistently led to the picture that for a doping range of a few per cent, the Fermi level lies a few tenths of an electronvolt below the top of the valence bands. These results were obtained either in the virtual crystal approximation (VCA)42–4 or supercell45–49 calculations for various cell geometries and doping concentrations. Furthermore, the effect of disorder on the electronic properties was studied with the coherent potential approximation50 leading again to the picture of a degenerate system with the Fermi level entering valence bands that have been broadened by disorder. This degenerate picture with no signature of an impurity band was rapidly confirmed by experimental angle‑resolved photoemission experiments on dia‑ mond films51. Additional evidence for deep localized states in the gap came from element‑sensitive soft X‑ray emission and absorp‑ tion spectroscopy, together with the conclusion that in the bulk of a superconductive sample, the Fermi level of the normal state lies below the top of the valence band, in a region where boron‑related delocalized states are also present52. But these theoretical and experi‑ mental results were obtained in the very large doping limit, away from the MIT transition, and the question of what happens close to this transition remains open.

In the absence of a narrow impurity band, the best guess for explaining the superconducting transition is the phonon‑mediated mechanism. Ab initio simulations explored this mechanism by

At T = 0, semiconductors are insulators with their highest occupied electronic band and their lowest unoccupied electronic band of delocalized states separated by an energy bandgap with a chemical potential located at midgap. Randomly distributed chemical impu‑ rities or structural defects, leading to localized states within this forbidden gap, may liberate (donor centres) or capture (acceptor centres) electrons. At non‑zero temperature, the number of free carriers in the bands will depend on the ratio of the ionization energy of these centres (respectively Ed and Ea) to the temperature, yielding an activated electrical resistivity intermediate between that of an insulator and that of a metal (see Fig. B2a).

In heavily doped semiconductors, the impurity energy levels begin to aggregate into a narrow range of energy, known as an ‘impurity band’, a misleading term as the wavefunctions remain localized. Moreover, the dispersion of energy levels due to disorder contributes to the spatial localization of electronic states (Anderson localization). At higher concentration, when the impurities are close enough, quantum overlapping of their wavefunctions tends to delocalize them, leading to a metallic behaviour at zero temperature with a Fermi level pinned inside the impurity band (see Fig. B2b). Mott proposed that this simpli‑ fied one‑electron picture may fail, and that the conduction mecha‑ nism would remain thermally activated even if the impurities were regularly spaced102. Indeed, because of strong on‑site correlations, the spin‑degenerate half‑filled impurity band splits into an empty band and a full band (see Fig. B2c). On further doping, these two bands begin to overlap and the metal–insulator transition takes place (see Fig. B2d).

(Parte 1 de 4)

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