Superconductivity in doped cubic silicon
Although the local resistivity of semiconducting silicon in its standard crystalline form can be changed by many orders of magnitude by doping with elements, superconductivity has so far never been achieved. The structural, electrical and magnetic experiments was performed at room pressure on a set of B-doped silicon thin layers (from 10 to 120 nm) where boron was incorporated into cubic silicon well above its equilibrium solubility. This was achieved
by Gas Immersion Laser Doping where the precursor gas (BCl3) is chemisorbed on a (001)-oriented silicon wafer prior to each UV laser pulse. During each melting/solidification cycle, boron diffuses into molten silicon, and is incorporated at substitutional sites of the crystal as the liquid/solid interface moves back to the surface of the epilayer. High Resolution XRD analysis of the samples was performed around the (004) Bragg reflection. We observed one or two broad diffraction peaks well separated from the narrow line from the substrate. This indicates
a non-uniform distribution of the strain perpendicular to the surface and thus of the boron content, but confirms the epitaxial single crystal character of the films. The broad maxima detected in samples correspond to a contraction of the lattice parameter a along (001). Assuming that the Si:B alloy retains the elastic properties of bulk silicon, this yields an in-plane tensile stress (”negative” pressure), and isotropic lattice parameter variations of -1.4 and -2.1 %. This corresponds to substitutional boron concentrations of 5.7 and 8.4 at.%.
The temperature dependence below 0.5 K of the electrical resistance and of the ac-magnetic susceptibility is plotted in Figure 1. A sharp drop of the resistance is observed with an onset around 0.4 K. An immeasurably small R value is observed below 150 mK. Similarly as the temperature decreases there is an onset of diamagnetism below 0.34 K, but full magnetic screening is not achieved until 150 mK. These measurements unambiguously demonstrate the occurrence of superconductivity. The foot of the resistive and diamagnetic transitions and the width of the magnetic response are typical of an inhomogeneous superconductor, as detected by XRD. In order to define the phase diagram in the magnetic field-temperature plane, we performed electrical measurements varying the temperature at different magnetic fields and varying magnetic field at different temperatures with the field applied perpendicular to the plane of the film. The transitions remain sharp and no hysteresis or supercooling was seen, which is consistent with the transition to superconductivity under field being of second order. This observation and the relatively high value of the critical field 0.4 Tesla suggests that boron-doped silicon is a type II superconductor.
Figure 1: Superconducting transition of B-doped Si. Temperature dependence of the d.c. electrical resistance R (normalised to its normal state value Rn) and of the real part of the a.c.-susceptibility.
In order to provide some insight into the microscopic pairing mechanism, we performed an abinitio study of the electronic, vibrational and electron-phonon coupling properties of boron-doped silicon. We adopted a supercell approach with one B atom substituted for every 16 silicon atoms arranged in a fcc cell, yielding a 6.25 at.% concentration, close to the values estimated for the superconducting samples. Structural relaxation led to an isotropic contraction of 1.9 % of the lattice parameter compared to the pure Silicon, related to the reduced Si-B bond length, and within the range of values deduced experimentally by XRD. To estimate the superconducting transition temperature, we calculated the electron-phonon coupling function (Eliashberg function), which measures the coupling strength as a function of the phonon energy. We find that Tc is predicted to vary in the range 0.34 - 0.03 K. This suggests that a standard BCS mechanism can account for the observed superconducting transition. Theory as well as experimental results obtained on superconducting B-doped diamond lead us to expect that a higher superconducting transition temperature might be achieved if more boron could be incorporated into the silicon.
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