Effect of boron on the superconducting transition of heavily doped diamond
Introduction
The theoretical prediction and discovery of superconductivity in the doped generated semiconductors were an important validation of the recently developed Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity and of the current understanding of electron–electron and electron–phonon interactions [1], [2], [3]. At the time, both the experimentally observed [2], [3] and theoretically expected [1] superconducting transition temperatures for the diamond-structure semiconductors were below 0.5 K. The recent discovery of the superconductivity at 4 K (» 0.5 K) in heavily boron (B)-doped polycrystalline diamond, which was synthesized at high temperature under high pressure [4], and the observation of the superconductivity at 7 K in the heavily B-doped polycrystalline diamond films, which deposited on a silicon (001) substrate using microwave plasma-assisted CVD method [5], have motivated research into both the experimental and theoretical study of the electronic properties being responsible for the superconductivity transition in the heavily B-doped diamond [3], [6], [7], [8], [9], [10], [11], [12], [13].
According to the BCS theory of superconductivity [14], the superconductivity–transition critical temperature Tc is dominated by the strength of the electron–phonon interaction callipered by the coupling parameter of λ = VN(EF), where N(EF) is the density of states (DOS) around EF. Since the discovery of the diamond superconductivity [4], there has been a series of theoretical studies [6], [8], [9], [10] to investigate the origin and nature of this phenomenon in heavily B-doped diamond (semiconductor). The different studies [8], [10] within the framework of analyzing the strength of the electron–phonon interaction of λ = VN(EF) pointed out the important role of holes in the valence band ignoring the doped band. Very recently, Yokoya et al. [13] conformed that the holes in the diamond bands play an essential part in determining the metallic nature of the heavily boron-doped diamond semiconductor by means of angle-resolved photoemission spectroscopy. It indicated that the doped holes enter into the top of the diamond valence band accompanied by a shift of Fermi level (EF), which is different from the recent X-ray absorption spectroscopy studies interpreting holes in the valence band located at 1.3 eV below the valence band maximum, regardless of the doping level [12]. Baskaran [6] suggested a discrepancy view that the superconductivity driven by electron correlation occurs in a tight binding and half-filled narrow B impurity band, the electronic states of which are localized and the superconductivity mechanism is corresponding to the type of insulator-to-superconductor transition. Therefore, an accurate description of the electronic properties is extremely important for understanding the superconducting transition mechanism of the heavily B-doped diamond [13].
The study of boron as a p-type dopant in diamond has a long history and its importance is growing [15], [16], [17], [18], [19], [20], [21], [22], [23]. The experiments confirmed that a substitutional B impurity has an acceptor level with binding energy 0.37 eV [4], [13] for low B concentration and that the heavily B-doped diamond with a concentration greater than about 1020–1021 cm− 3 shows a metallic behavior [7], [17], [24]. Obviously, boron plays an important role in the electronic behavior transition in diamond. Most of theoretical researches have reported the electronic structure of B-related complexes [20], [21], [22]. In this work, we present the calculation results of the electronic structure for a series of clusters and supercell structures simulating the heavily B-doped materials by means of DFT to reveal the electronic origin and nature of the superconductivity in this wide-gap semiconductor. Our calculations demonstrate that the interaction among B-centers may play an important role in the position of the Fermi level EF. The result analyses support a mechanism of metal–superconductor transition occurring due to the overlapping between the impurity and the valence bands and the Fermi level lying in the valence bands for the heavily B-doped diamond and indicate that the critical temperature Tc may increase with the B concentration increasing.
Section snippets
Methods and models
In the DFT [25] calculations using atomic cluster method, the triple-zeta polarized (TZP) basis sets were employed. The 2s, 2p orbital of C, B and 1s orbital of H are considered as valence shells. The exchange-correction functionals used are VWN plus Becke88 and Perdew86 [25]. The relative error of the numerical integration for single point energy is 10–6. In the geometry optimization, the displacement is converged at 10–3 bohr, the gradient at 10–3 hartree/bohr and the energy at 10–6 hartree,
Results and discussion
In order to research the effect of the interaction among boron centers on the electronic feature in heavily doped diamond, we use firstly the cluster method to study the electronic feature of an isolated B impurity in heavily doped diamond. The electronic structure of the five pairs of clusters C17 and C16B1, C29 and C28B1, C47 and C46B1, C59 and C58B1, and C71 and C70B1 are calculated and shown in Fig. 2 (for simplicity, only the energy levels near band edges are plotted for every group of
Conclusions
Based on the DFT electronic structure calculation for diamond with cluster and supercell model methods, it is concluded that in heavily B-doped diamond, the interaction among B-centers plays an important role in the location of EF and the electronic behavior, which determines directly the density of holes; the superconducting transition is the type of metal-to-superconductor when the temperature drops to Tc. The critical temperature Tc is related to the B concentration.
Acknowledgements
This work was supported by the National Science foundation of China under Grant 10374060, 60377041, and the Natural Science Foundation of Shandong Province under Grant Number Y2003A01.
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