Superconductivity in Substitutional Ga-Hyperdoped Ge Epitaxial Thin Films

TL;DR

This work demonstrates intrinsic superconductivity in substitutional Ga-doped Ge epitaxial films grown by molecular beam epitaxy, achieving $T_c = 3.5\ \text{K}$ at a high hole density of $n_h = 4.15\times10^{21}\ \text{cm}^{-3}$ with $17.9\%$ Ga substitution. Comprehensive characterization shows Ga occupies substitutional lattice sites, a subtle tetragonal distortion from substrate clamping, and a Fermi-level shift into the valence band that supports a narrow-band heavy-carrier state. First-principles calculations indicate a conventional phonon-mediated pairing mechanism with $\lambda \approx 0.41$ and $T_c \approx 0.77\ \text{K}$, while the observed $T_c$ points to additional narrow-band physics enhancing superconductivity. The results establish Ga:Ge as a low-disorder, epitaxial superconductor-semiconductor platform with coherent interfaces, enabling future vertical Josephson junction devices and scalable quantum technologies in group IV systems.

Abstract

Doping-induced superconductivity in group IV elements may enable quantum functionalities in material systems accessible with well-established semiconductor technologies. Non-equilibrium hyperdoping of group III atoms into C, Si, or Ge can yield superconductivity; however, its origin is obscured by structural disorder and dopant clustering. Here, we report the epitaxial growth of hyperdoped Ga:Ge films and trilayer heterostructures by molecular beam epitaxy with extreme hole concentrations ($n_\textup{h} = 4.15 \times 10^{21}$~cm$^{-3}$, ~17.9\% Ga substitution) that yield superconductivity with a critical temperature of $T_{\textup{c}} = 3.5$~K and an out-of-plane critical field of 1~T at 270~mK. Synchrotron-based X-ray absorption and scattering methods reveal that Ga dopants are substitutionally incorporated within the Ge lattice, introducing a tetragonal distortion to the crystal unit cell. Our findings, corroborated by first-principles calculations, suggest that the structural order of Ga dopants creates a narrow band for the emergence of superconductivity in Ge, establishing hyperdoped Ga:Ge as a low-disorder, epitaxial superconductor-semiconductor platform.

Figures (23)

• Figure 1: Superconductivity in germanium by p-type hyperdoping.a Schematic picture of dopants within a matrix and zone-center $E(k)$ dispersion for a prototypical band insulator in a dilute doping and hyperdoped state. In the dilute doping scenario, dopants with an effective Bohr radius, $a_{0}$, at an average distance between dopants, $\lambda_{d}$, induce mid-gap electronic states at an energy $E_{a}$ above the valence band edge. Increasing dopant concentrations to few-percent levels or higher induces significant hybridization between dopants, giving rise to a low-energy band associated with dopant-dopant hybridization. This defect band is traditionally expected to be non-dispersive due to the stochastic behavior of dopants. However, dopant-dopant hybridization in principle can induce ordering of the dopants on the lattice, giving rise to a narrow heavy band as well. b-e Sheet resistance versus temperature traces for single Ga:Ge layers and Ga:Ge sandwich structures, akin to a Josephson junction along the growth direction. In these structures, the single Ga:Ge layers are held to a constant thickness of roughly 12 nm and the trilayer structures have Ga:Ge layer thicknesses of 10 nm. The insets of each panel present schematic drawings of the sample layer structure. b, c are representative traces where we use Si as the cap and barrier layer material, and d, e are representative traces where Ge replaces the Si-containing layers. The jitter in temperature observed in d during the superconducting transition is an artifact caused by temperature instability during the measurement.
• Figure 2: Ga dopant arrangement in Ge and modulated band structure.a Optimized DFT structures of Ga-doped Ge at the interstitial and substitutional sites, along with the defect formation energies ($E_\textup{Form}$). b Experimental Ga-K-edge spectrum recorded from the Ga:Ge with its corresponding $k^{2}$-weighted $\chi(k)$ EXAFS fit (red line) contained in the inset. c The Fourier-transform ($k^{2}$-weighted) of the EXAFS data (distances have been phase-corrected). An agreeable fit has been made to the experiment using the substitutional doped crystallographic information file (CIF) generated from the optimized DFT calculated structure shown in a.d Calculated band structure for pristine Ge and the substitutionally doped GaGe$_{7}$ structure. The horizontal dashed red line indicates the position of the Fermi level after doping, shifting 1.01 eV into the valence band. e The contribution of each band identified as i, ii, and iii to the 3D Fermi surface with the color map corresponding to the Fermi velocity. The predicted narrow-band condition is observed as small pockets of high-mass carriers in the surface of Band iii at the corners of the Brillouin Zone (R point).
• Figure 3: Cross-sectional electron microscopy reveals coherent crystalline interfaces.a Schematic of the film structure as grown by MBE. b-c Cross-sectional TEM/EDS imaging of the $T_\textup{c}$ = 3.5 K hyperdoped sample presenting the compositional profile across the entire film thickness. d Low-magnification cross-sectional HAADF-STEM image of the film. e Zoom-in on the film/substrate and Ga:Ge/Si interfaces, displaying coherent crystalline interfaces. f Raman back-scattering spectra of undoped (black) and doped (red) structures using 532 nm laser excitation at room temperature. The inset highlights the common emergence of highly anharmonic second-order optical bands, identified as the active LO mode here due to the Raman selection rules for backscattering from a (001) Ge surface. For more details regarding the Raman spectra, please see Figure S12.
• Figure 4: X-ray scattering measurement of tetragonal crystalline distortion.a 2D GISAXS pattern of the Ga:Ge epitaxial film recorded at the critical angle (0.26$^{\circ}$) of the superconducting layer. The intensity map is on a linear scale. b The out-of-plane X-ray reflectivity measurement of the Ga:Ge film with a fit made using the REFLEX software package vignaud_reflex_2019. c Cross-section of the electron scattering length density (ESLD) of the epitaxial stack derived for the fitting model of the fringes in b. d 2D GIWAXS pattern of the Ga:Ge thin film record at the critical angle (0.125$^{\circ}$). The color map is on a log scale. The family of crystallographic planes giving rise to the intense Bragg reflections of the hyperdoped layer are identified with arrows. e Corresponding integrated GIWAXS profile (q$_{xyz}$) and its subsequent structural refinement (Le Bail method). The refined unit cell parameters are displayed and an expansion of the split 220 family of Bragg peaks is shown in the inset to highlight the reduced symmetry of the clamped Ga:Ge epitaxial layer in comparison to the undoped Ge control.
• Figure S1: a Comparison of this study against literature reports for superconducting $T_\textup{c}$ as a function of Hall carriers in Ga-doped germanium. The colored star, square, and triangular points were prepared via ion implantation herrmannsdorfer2009gageprucnal2019sardashti2021 while the black circles (this study) and black diamond strohbeen2023superge are MBE-grown samples. b Representative AFM image of the surface of the sample circled in red in a. We observe an RMS roughness of roughly 1.65 nm, a significant improvement over previous MBE reports strohbeen2023superge. The inset presents the normalized height distribution, $\rho$, across the entire 15 $\mu m \times$15 $\mu m$ image.