Superconductivity in single-crystalline aluminum- and gallium-hyperdoped germanium

Superconductivity in group IV semiconductors is desired for hybrid devices combining both semiconducting and superconducting properties. Following boron-doped diamond and Si, superconductivity has been observed in gallium-doped Ge; however, the obtained specimen is in polycrystalline form [Phys. Rev. Lett. 102, 217003 (2009)]. Here we present superconducting single-crystalline Ge hyperdoped with gallium or aluminum by ion implantation and rear-side flash lamp annealing. The maximum concentration of Al and Ga incorporated into substitutional positions in Ge is 8 times higher than the equilibrium solid solubility. This corresponds to a hole concentration above ${10}^{21}\mathrm{c}{\mathrm{m}}^{-3}$. Using density functional theory in the local-density approximation and pseudopotential plane-wave approach, we show that the superconductivity in $p$-type Ge is phonon mediated. According to the ab initio calculations, the critical superconducting temperature for Al- and Ga-doped Ge is in the range of 0.45 K for $6.25\mathrm{at}.\%$ of dopant concentration, being in qualitative agreement with experimentally obtained values.

Figure 1

The Ga and Al depth distribution in Ge obtained by the srim code for an ion-implantation fluence of $2\times {10}^{16}\mathrm{c}{\mathrm{m}}^{-2}$ (a) and simulated temperature distribution at the implanted surface during 20 ms FLA from the front side (f-FLA, black curve) and from the rear side (r-FLA, red curve) (b).

Figure 2

The RBS/R and RBS/C spectra obtained from Al- and Ga-hyperdoped Ge. The RBS/C spectrum recorded from virgin Ge is shown as well. The concentrations of Al and Ga in Ge are at the level of $2\times {10}^{21}\mathrm{c}{\mathrm{m}}^{-3}$.

Figure 3

PIXE spectra of Al- (a) and Ga-hyperdoped Ge (b) followed by rear-side FLA for 20 ms.

Figure 4

(a), (c) Cross-sectional bright-field TEM images obtained from Al- and Ga-hyperdoped Ge, respectively, (b), (d) superimposed Ge (green), O (red), and Al or Ga (blue), respectively, element distributions obtained by spectrum imaging analysis based on EDXS in scanning TEM mode for a representative surface region of each sample, as exemplarily marked by the white square in (a).

Figure 5

Temperature dependence of the longitudinal resistance for different samples: (a) low-temperature part of ${\mathrm{R}}_{xx}$ vs T of superconducting Ge with 6% Al (a) and Ga (b).

Figure 6

The electronic structure of Al- (a) and Ga-hyperdoped (b) Ge with the corresponding total density of electronic states $N\left(E_{\mathrm{F}}\right)$.

Figure 7

Phonon band structure with corresponding phonon DOS for Al-hyperdoped Ge (a) and for Ga-hyperdoped Ge (b). The unit of phonon DOS (PHDOS) is states/($\mathrm{c}{\mathrm{m}}^{-1}\times \mathrm{supercell}$). Blue solid circles indicate the partial electron-phonon coupling strength ${\lambda }_{\mathrm{vq}}$ at the Γ point. (c, d) show the Raman spectra obtained from Al- and Ga-hyperdoped Ge, respectively. The Raman spectrum of virgin undoped Ge is shown for comparison.

Figure 8

The total and projected Eliashberg spectral function $\left[{\alpha }^2\mathrm{F}\left(\omega \right)\right]$ for Al-hyperdoped Ge (a) and for Ga-hyperdoped Ge (b). The red dashed curves represent the integrated electron-phonon coupling constant λ (ω).