Tuning superconductivity in Ge:Ga using ${\mathrm{Ga}}^{+}$ implantation energy

High-fluence gallium $\left({\mathrm{Ga}}^{+}\right)$ implantation at medium energies is proven to be an effective tool in forming superconducting (SC) thin films in germanium (Ge). By changing the post-implantation annealing conditions nanocrystalline to single-crystalline Ge matrices have been produced. Irrespective of crystallinity, such processes have mostly led to supersaturated Ge:Ga films where superconductivity is controlled by the extent of coherent coupling between Ga precipitates. Here we use ${\mathrm{Ga}}^{+}$ implantation energy as a means to tailor the spatial distribution and the coupling energy of the Ga precipitates. By systematic structural and magneto-transport studies, we unravel the complex connection between the internal structure of Ge:Ga films and their global SC parameters. At the shallowest implantation depth, we observe the strongest coupling leading to a robust superconductivity that sustains parallel magnetic fields as high as 9.95 T, above the conventional Pauli paramagnetic limit and consistent with a quasi-2D geometry. Further measurements at mK temperatures revealed an anomalous upturn in perpendicular critical field ${\mathrm{B}}_{\perp }$ vs temperature whose curvature and thus origin may be tuned between weakly coupled SC arrays and vortex glass states with quenched disorder. This warrants future investigations into Ge:Ga films for applications where tunable disorder is favorable, including test-beds for quantum phase transitions and superinductors in quantum circuits.

Figure 1

(a) A schematic detailing the various pathways implanted Ga atoms can take within the Ge matrix, including substituting Ge as a dopant, precipitation within the implanted region, precipitation at the $Si{O}_2/Ge$ interface, and finally diffusion through the $Si{O}_2$ to form Ga surface clusters. The yellow squiggly lines represent the nearest-neighbor coupling between the Ga clusters within the bulk (${\mathrm{J}}_{\mathrm{B}}$) or at the interface (${\mathrm{J}}_{\mathrm{I}}$). (b) One-dimensional simulation of Ga concentration vs depth for various implantation energies from 25 to 100 keV, calculated by TRIM for ${\mathrm{Ga}}^{+}$ fluence of $4\times {10}^{16}{\text{cm}}^{-2}$.

Figure 2

(a) An overview of transport properties, marked by “N,” normal; “SC,” superconducting; and “L.SC,” locally superconducting vs processing conditions used in this study, i.e., implantation energy ${\mathrm{E}}_{\mathrm{IMP}}$ and annealing temperature ${\mathrm{T}}_{\mathrm{DA}}$. (b) Sheet resistance ${\mathrm{R}}_S$ (normalized to sheet resistance at 9K, ${\mathrm{R}}_{\mathrm{N}}$) vs temperature showing SC transitions for four representative processing conditions circled in (a). Transition onset and completion temperatures for the blue curve are marked as ${\mathrm{T}}_1$ and completion ${\mathrm{T}}_2$, respectively. (c) Superconducting transition midpoint ${\mathrm{T}}_{\mathrm{c}}$ (at ${\mathrm{R}}_{\mathrm{S}}$ = $0.5{\mathrm{R}}_{\mathrm{N}}$), onset ${\mathrm{T}}_1$, and completion ${\mathrm{T}}_2$ vs anneal temperature ${\mathrm{T}}_{\mathrm{DA}}$ for samples with complete zero-resistance transitions. The ${\mathrm{T}}_c$ value for $\beta$-Ga is adapted from Ref. [26].

Figure 3

TEM images of cross-sections prepared on Ge:Ga samples with (a) ${\mathrm{E}}_{\mathrm{IMP}}$ = 80 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 700 ${}^{\circ }\mathrm{C}$; (b) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 400 ${}^{\circ }\mathrm{C}$; (c) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 600 ${}^{\circ }\mathrm{C}$; (d) ${\mathrm{E}}_{\mathrm{IMP}}$ = 25 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 600 ${}^{\circ }\mathrm{C}$. The yellow boxes shown in lower magnification images (top row) are visual guides to outline the approximate areas from which the higher magnification images (bottom row) were taken. In (a), the dotted lines denote stacking faults within the Ge after dopant activation annealing. In (b)–(d), “DB” are seen as a result of $\mathrm{Si}{\mathrm{O}}_2$ recoil during the implantation process.

Figure 4

STEM images and EDS elemental Ga maps for cross-sections of Ga-implanted samples with: (a) ${\mathrm{E}}_{\mathrm{IMP}}$ = 80 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 700 ${}^{\circ }\mathrm{C}$; (b) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 400 ${}^{\circ }\mathrm{C}$; (c) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 600 ${}^{\circ }\mathrm{C}$; (d) ${\mathrm{E}}_{\mathrm{IMP}}$ = 25 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 600 ${}^{\circ }\mathrm{C}$. The line traces for [Ga] (solid green lines) and [Si] (dotted gray lines), normalized to $\left[\mathrm{Si}\right]+\left[\mathrm{Ge}\right]$, are shown on the right. The traces are averaged over the width of the areas outlined by the dotted rectangles in the STEM images and maps. The line traces are aligned by setting the $Si{O}_2/Ge$ interface to zero distance. Disturbed bands are marked by red arrows and “DB.”

Figure 5

Normalized resistance vs temperature for four samples before (dash-dotted line) and after etching the $Si{O}_2$ cap (solid line) including: (a) ${\mathrm{E}}_{\mathrm{IMP}}$ = 80 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 700 ${}^{\circ }\mathrm{C}$; (b) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 400 ${}^{\circ }\mathrm{C}$; (c) ${\mathrm{E}}_{\mathrm{IMP}}$ = 35 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 500 ${}^{\circ }\mathrm{C}$; (d) ${\mathrm{E}}_{\mathrm{IMP}}$ = 25 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 600 ${}^{\circ }\mathrm{C}$. For the oxide etch, 15 s dip in 6:1 BOE was followed by 30 s of DI–${\mathrm{H}}_2\mathrm{O}$ rinse.

Figure 6

Sheet resistance maps vs temperature T and magnetic field applied perpendicular ($B_{\perp }$) and parallel ($B_{\parallel }$) to the surface of the samples prepared at: (a) ${\mathrm{E}}_{\mathrm{IMP}}$ = 80 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 700 ${}^{\circ }\mathrm{C}$; (b) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 400 ${}^{\circ }\mathrm{C}$; (c) ${\mathrm{E}}_{\mathrm{IMP}}$ = 25 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 600 ${}^{\circ }\mathrm{C}$. The white overlay plot on each map outlines the normal-superconductor transition boundary, taken at points where ${\mathrm{R}}_{\mathrm{s}}$ = 0.5 ${\mathrm{R}}_{\mathrm{n}}$.

Figure 7

Magnetoresistance and critical field measurements. ${\mathrm{R}}_{\mathrm{s}}$ as a function of magnetic field for SC Ge samples with (a) ${\mathrm{E}}_{\mathrm{IMP}}$ = 80 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 700 ${}^{\circ }\mathrm{C}$ and (b) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 400 ${}^{\circ }\mathrm{C}$ at 1.55–3.85 K. ${\mathrm{B}}_{\mathrm{c}}$ vs temperature extracted from ${\mathrm{R}}_{\mathrm{s}}$(B) measurements at 35 mK – 1.1 K for (c) ${\mathrm{E}}_{\mathrm{IMP}}$ = 80 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 700 ${}^{\circ }\mathrm{C}$ and (d) ${\mathrm{E}}_{\mathrm{IMP}}$ = 45 keV and ${\mathrm{T}}_{\mathrm{DA}}$ = 400 ${}^{\circ }\mathrm{C}$. For all the measurements, the magnetic field is applied perpendicular to the sample surface.