# Effect of Impurity Scattering on Percolation of Bosonic Islands and Superconductivity in Fe Implanted NbN Thin Films

^{*}

## Abstract

**:**

## 1. Introduction

_{1−x}Ga

_{x}N templates and substrates has emerged as an alternative [42,43,44,45] and can serve as the basis for all nitride-integrated superconductor/semiconductor devices [46]. The Si substrates are commonly employed to grow superconducting NbN films intended for single photon detection and hot bolometer applications, due to the advantages in device processing and relatively low losses at THz frequencies. The significant lattice mismatch between Si and NbN generally results in polycrystalline films with ${T}_{\mathrm{c}}\le 10$ K for layers ∼(5–10) nm thick. The lattice matched substrate MgO presents challenges in device processing, due to its hydrophobic nature and sensitivity to alkaline solutions that are used during the fabrication processes [42]. Since the crystallographic orientation of the NbN films does not affect their superconducting properties, the c-plane of hexagonal wurtzite template/buffer layers is also suitable for NbN growth, provided that the lattice parameter ${a}_{\mathrm{hkl}}^{\mathrm{w}}$ of the wurtzite template matches the one of NbN along the (111) plane, i.e., ${a}_{111}^{\mathrm{NbN}}=\frac{{a}_{100}^{\mathrm{w}}}{\sqrt{2}}$. Thus, the epitaxial relation $\left[111\right]\left(\mathrm{NbN}\right)\Vert \left[100\right]\left(\mathrm{GaN}\right)$ is established between the NbN and c-plane wurtzite template [42,45,46].

## 2. Materials and Methods

#### 2.1. Growth and Structure

_{2}O

_{3}(0001) substrates by means of metal organic vapor phase epitaxy is taken as the template for the deposition of the NbN thin films. The GaN templates are cut into $\left(\right)$ cm

^{2}specimens for the sputtering of the NbN layers. The polycrystalline thin films are grown in an ultrahigh vacuum (UHV) chamber with a base pressure of $(2\times {10}^{-9})$ mbar. A high purity (99.99%) Nb target is employed for the reactive magnetron sputtering process under a plasma consisting of Ar:N

_{2}in the ratio 10:5 standard cubic centimeters per minute (sccm) with a power $P=40$ W and at a constant substrate temperature ${T}_{\mathrm{sub}}=500{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}$C.

^{56}Fe using powdered Fe

_{3}O

_{4}as the source for Fe ions. The implantation is carried out at room temperature at a base pressure of $(1\times {10}^{-6})$ mbar. Half of the surface of the $\left(\right)$ cm

^{2}samples is covered with a brass mask, and the uncovered part of the NbN layers is exposed to the Fe ion beam for implantation. The energy and ion dose are selected after simulating the stoppage and range of ions in the matter (SRIM). The simulation of the ion distribution is considered for ion energies of 35 keV and 50 keV, respectively. A low ion current ∼100 nA is required to ignite the plasma and for the subsequent ion extraction. The ion current is kept constant by tuning the filament current and ion beam focus during the entire implantation process. The Fe implantation dose used in this work is kept constant at $\left(\right)$ atoms/cm

^{2}. After implantation, the samples are not subjected to any thermal annealing, in order to avoid precipitation of secondary Fe or FeN phases and also to preserve the defects generated by the implanted ions. The $\left(\right)$ cm

^{2}samples are then cut into $\left(\right)$ mm

^{2}specimens for further measurements and characterization. In the following, a representative as-grown NbN layer sample A (#A), is considered, while a 35 keV Fe implanted NbN layer is taken as sample B (#B). Both the as-grown NbN and Fe implanted NbN are studied using X-ray diffraction (XRD) and the high crystallinity of the sputtered films is confirmed [49]. An overview of the relevant growth parameters for #A and #B is provided in Table 1.

_{2}O

_{3}(0006) as reported in literature [42]. No secondary Bragg peaks of precipitated or clustered Fe and Fe

_{4}N are detected, pointing out the homogeneous incorporation of the implanted Fe in the cubic NbN crystal lattice.

#### 2.2. Magnetotransport

^{2}specimens are achieved using electrically conducting Ag epoxy and are bonded with Au wires of diameter 25 $\mathsf{\mu}$m. The magnetotransport experiments are carried out in a Janis Super Variable Temperature 7TM-SVM cryostat (Janis Cryogenics, Westerville, OH, USA) equipped with a 7 T superconducting magnet. A lock-in amplifier (LIA) ac technique is employed for measuring the magnetotransport properties of the NbN and of the Fe:NbN thin films. The constant current ${I}_{\mathrm{ac}}$ is sourced from a Stanford Research SR830 LIA via a resistance decade box, while the longitudinal voltage ${V}_{\mathrm{xx}}$ is measured in a phase-locked mode. The lock-in expand function is employed to enhance the sensitivity of the LIA. All measurements have been performed at a frequency of 127 Hz, while ${I}_{\mathrm{ac}}=1$ μA for all measurements. The low input current minimizes the thermal drift due to Joule heating of the samples. The magnetic fields are varied between $-7$ T and $+7$ T for the magnetoresistance measurements.

## 3. Results

^{3}results in a highly diluted Fe doped system, restricting the Fe-Fe interaction to the dilute magnetic limit. Since after implantation #B is not thermally treated, the Fe ions are incorporated into the NbN lattice randomly. Moreover, the incorporation efficiency of implanted Fe ions is different for NbN grains with different crystallographic orientations. The disorder of the Fe implanted NbN system stems from an extrinsic granularity and an intrinsic one. The disorder due to the polycrystalline texture and grain boundaries of the Fe:NbN lattice is the extrinsic granularity. On the other hand, the electronic disorder due to the randomly implanted Fe ions results in modulations of the chemical potential and thus in intrinsic electronic granularity. The intrinsic granularity plays a significant role in defining the observed electronic properties of #B.

## 4. Conclusions

_{3}O

_{4}as the source for Fe ions. An implantation energy of 35 keV and a dose of $\left(\right)$ at/cm

^{3}result in a highly dilute Fe doped system, restricting the Fe-Fe interaction to the dilute magnetic limit. Low-T/high-${\mu}_{0}H$ magnetotransport measurements confirm that the Fe doping does not suppress the superconductivity of the sputtered NbN thin films, but decreases the superconducting transition temperature. A reentrant resistive BI phase is observed in the Fe doped NbN samples, which is explained by an empirical model of a competition between the percolation of bosonic conduction channels at the expense of fermionic conduction channels and by the scattering of the BI as a result of intrinsic granularity due to the random Fe dopants. The observation of a robust superconductivity in the dilute magnetic conventional superconductor Fe:NbN mediated via the percolation of bosonic insulator states is foreseen to violate the symmetry of electron-like and hole-like excitations due to the formation of subgap bound Andreev states in the vicinity of magnetic impurities, leading to giant thermoelectric effects [66]. A system such as the one reported in this work is expected to find applications in zero-biased thermoelectric bolometers with reduced power dissipation in large scale multi-pixel arrays and in hybrid quantum interference devices (HyQUID) [67]. Moreover, these systems are the workbench for understanding quantum emergent phenomena, including gapless superconductivity, triplet Cooper pairings, YSR states and odd frequency superconductivity [68,69].

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

YSR | Yu-Shiba-Rusinov |

FFLO | Fulde-Ferrell-Larkin-Ovchinnikov |

S | Superconductors |

F | Ferromagnets |

BKT | Berezinskii-Kosterlitz-Thouless |

UHV | Ultrahigh vacuum |

sccm | Standard cubic centimeters per minute |

SRIM | Stoppage and range of ions in matter |

LIA | Lock-in amplifier |

SMU | Source-measure unit |

FC | Field cooled |

ZFC | Zero field cool |

BI | Bosonic islands |

HyQUID | Hybrid quantum interference device |

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**Figure 3.**ZFC and FC ${\rho}_{xx}$ as a function of T under the application of ${\mu}_{0}{H}_{\perp}$ = 0 T, 1 T, 3 T, 5 T and 7 T measured for samples (

**a**) #A and (

**b**) #B. Transverse ${\rho}_{\mathrm{xx}}$ as a function of ${\mu}_{0}{H}_{\perp}$ recorded at different T for samples (

**c**) #A and (

**d**) #B.

**Figure 4.**The behavior of the characteristic temperatures ${T}_{\mathrm{loc}}^{\mathrm{onset}}$, ${T}_{\mathrm{d}}$, ${T}_{\mathrm{peak}}$, $T={T}^{*}$ and ${T}_{\mathrm{glo}}^{\mathrm{offset}}$ as a function of (

**a**) ${\mu}_{0}{H}_{\perp}$. (

**b**) ${\mu}_{0}{H}_{\Vert}$. (

**c**) Evolution of ${T}_{\mathrm{loc},\perp /\Vert}^{\mathrm{onset}}$ recorded for #B.

**Figure 5.**ZFC ${\rho}_{\mathrm{xx}}$ as a function of T. The six electronic phases and the phase boundaries of #B. are evidenced.

**Figure 6.**Schematic of the empirical model to describe the N-BI-S transition in #B. The connector lines connecting the ellipses and dumbbells represent fermionic conduction channels and bosonic conduction channels, respectively. The normal state fermions and the Cooper pairs are shown by ellipses and dumbbells, respectively, while the Fe impurities are depicted by solid circles. The electronic phase transitions taking place as the sample #B is cooled from $T>{T}_{\mathrm{loc}}^{\mathrm{onset}}$ down to $T\le {T}_{\mathrm{loc}}^{\mathrm{onset}}$ are: (

**a**) Phase EP-1 for $T>{T}_{\mathrm{loc}}^{\mathrm{onset}}$. (

**b**) Phase EP-2 for ${T}_{\mathrm{d}}<T<{T}_{\mathrm{loc}}^{\mathrm{onset}}$. (

**c**) Phase EP-3 for ${T}^{\mathrm{peak}}<T<{T}_{\mathrm{d}}$. (

**d**) Phase EP-4 for ${T}_{\mathrm{Peak}}\le T\le {T}^{*}$. (

**e**) Phase EP-5 for ${T}^{*}\le T\le {T}_{\mathrm{glo}}^{\mathrm{offset}}$ and (

**f**) Phase EP-6 for $T\le {T}_{\mathrm{glo}}^{\mathrm{offset}}$.

Sample | Material | Template | Nominal ${\mathit{d}}_{\mathbf{NbN}}$ (nm) | Ar:N_{2} Ratio | P (W) | T_{sub} (°C) | Implanted Ion | ${\mathit{E}}_{\mathbf{ion}}$ (keV) | Dose (at/cm^{3}) |
---|---|---|---|---|---|---|---|---|---|

A | NbN | wz-GaN | 100 | 10:5 | 40 | 500 | - | - | - |

B | Fe:NbN | wz-GaN | 100 | 10:5 | 40 | 500 | Fe | 35 | $1\times {10}^{14}$ |

**Table 2.**Characteristic temperatures of samples #A and #B recorded for ZFC ${\rho}_{\mathrm{xx}}(T)$.

Sample | ${\mathit{T}}_{\mathbf{loc},\mathbf{ZFC}}^{\mathbf{onset}}$ (K) | ${\mathit{T}}_{\mathbf{d},\mathbf{ZFC}}$ (K) | ${\mathit{T}}_{\mathbf{peak},\mathbf{ZFC}}$ (K) | ${\mathit{T}}_{\mathbf{ZFC}}^{*}$ (K) | ${\mathit{T}}_{\mathbf{glo},\mathbf{ZFC}}^{\mathbf{offset}}$ (K) | $\mathbf{\Delta}\mathbf{T}$ (K) |
---|---|---|---|---|---|---|

A | 15.72 | - | - | 15.27 | 15.05 | 0.67 |

B | 15.1 | 14.71 | 14.60 | 14.305 | 13.5 | 1.6 |

**Table 3.**The full width and half maxima of the ${T}_{\mathrm{Peak}}$ and $\Delta {T}_{\mathrm{c}}$ estimated for samples #A and #B recorded for ${\mu}_{0}{H}_{\Vert}$ and ${\mu}_{0}{H}_{\perp}$.

${\mathit{\mu}}_{0}{\mathit{H}}_{\Vert /\perp}$ (T) | $\mathbf{\Delta}{\mathbf{T}}_{\mathbf{Peak}}^{\mathbf{A}}(\mathbf{K})$ | $\mathbf{\Delta}{\mathbf{T}}_{\mathbf{Peak}}^{\mathbf{B}}(\mathbf{K})$ | $\mathbf{\Delta}{\mathbf{T}}_{\mathbf{c}}^{\mathbf{A}}(\mathbf{K})$ | $\mathbf{\Delta}{\mathbf{T}}_{\mathbf{c}}^{\mathbf{B}}(\mathbf{K})$ | ||||
---|---|---|---|---|---|---|---|---|

${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\perp}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\Vert}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\perp}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\Vert}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\perp}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\Vert}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\Vert}$ | ${\mathbf{\mu}}_{\mathbf{0}}{\mathbf{H}}_{\Vert}$ | |

0 | - | - | 0.0653 | 0.0653 | 0.67 | 0.67 | 1.6 | 1.6 |

1 | - | - | 0.1376 | 0.1337 | 0.72 | 0.94 | 1.64 | 1.71 |

2 | - | - | 0.0858 | 0.1514 | - | - | 1.5 | 1.34 |

3 | - | - | - | 0.1392 | 0.74 | 0.94 | 1.25 | 1.54 |

4 | - | - | - | 0.0841 | - | - | 1.23 | 1.25 |

5 | - | - | - | - | 0.8 | 0.96 | 1.12 | 1.37 |

6 | - | - | - | - | - | - | 1.31 | 1.05 |

7 | - | - | - | - | 0.78 | 0.91 | 0.96 | 1.18 |

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**MDPI and ACS Style**

Adhikari, R.; Faina, B.; Ney, V.; Vorhauer, J.; Sterrer, A.; Ney, A.; Bonanni, A.
Effect of Impurity Scattering on Percolation of Bosonic Islands and Superconductivity in Fe Implanted NbN Thin Films. *Nanomaterials* **2022**, *12*, 3105.
https://doi.org/10.3390/nano12183105

**AMA Style**

Adhikari R, Faina B, Ney V, Vorhauer J, Sterrer A, Ney A, Bonanni A.
Effect of Impurity Scattering on Percolation of Bosonic Islands and Superconductivity in Fe Implanted NbN Thin Films. *Nanomaterials*. 2022; 12(18):3105.
https://doi.org/10.3390/nano12183105

**Chicago/Turabian Style**

Adhikari, Rajdeep, Bogdan Faina, Verena Ney, Julia Vorhauer, Antonia Sterrer, Andreas Ney, and Alberta Bonanni.
2022. "Effect of Impurity Scattering on Percolation of Bosonic Islands and Superconductivity in Fe Implanted NbN Thin Films" *Nanomaterials* 12, no. 18: 3105.
https://doi.org/10.3390/nano12183105