Magnetoconductance and photoresponse properties of disordered NbTiN films

We report on the experimental study of phonon properties and electron-phonon scattering in thin superconducting NbTiN films, which are intensively exploited in various applications. Studied NbTiN films with sub-10-nm thicknesses are disordered with respect to electron transport, the Ioffe-Regel parameter of $k_F{l}_e=2.5–3.0$ ($k_F$ is the Fermi wave vector, and $l_e$ is the electron mean free path), the inelastic electron-phonon interaction, and the product $q_T{l}_e\ll 1$ ($q_T$ is the wave vector of a thermal phonon). By means of magnetoconductance and photoresponse techniques, we derive the inelastic electron-phonon scattering rate $1/{\tau }_{e\text{-ph}}$ and determine sound velocities and phonon heat capacities. In the temperature range from 12 to 20 K, the scattering rate varies with temperature as $1/{\tau }_{e\text{-ph}}\propto T^{3.45\pm 0.05}$; its value extrapolated to 10 K amounts to approximately 1/16 ps. Making a comparative analysis of our films and other films used in superconducting devices, such as polycrystalline granular NbN and amorphous WSi, we find a systematic reduction of the sound velocity in all these films by about 50% compared to the corresponding bulk crystalline materials. A corresponding increase in the phonon heat capacities in all these films is, however, less than the Debye model predicts. We attribute these findings to reduced film dimensionality and film morphology.

Figure 1

Square resistance vs temperature at zero magnetic field (semilogarithmic scale). Symbols: experimental data; curves: the best fits obtained with Eq. (1) at temperatures where $ln(T/T_{C0})\ll 1$ and extrapolated to higher temperatures. The legend indicates film thicknesses.

Figure 2

(a) Square resistance vs temperature at a set of fixed magnetic fields in steps of 0.5 T for the representative NbTiN film with a thickness of 6 nm. The straight horizontal line drawn at $R_S=R_{\mathrm{SN}}/2$ defines the midpoint transition temperature for each field. (b) Upper critical magnetic field as a function of temperature. The legend indicates film thicknesses. Symbols: experimental data; lines: the best linear fits, which are used to evaluate $D$ and $B_{C2}\left(0\right)$.

Figure 3

Hall voltage divided by the transport current vs magnetic field at 25 K.

Figure 4

Dimensionless magnetoconductance vs magnetic field for a set of fixed temperatures indicated in the legend for the representative NbTiN film with a thickness of 6 nm. Symbols: experimental data; black curves: the best fits with a sum of Eqs. (A1, A2, A3, A4).

Figure 5

(a) Electron dephasing rate vs temperature. Symbols: the best-fit values of ${\tau }_{\varphi }^{-1}\left(T\right)$ obtained by fitting the experimental $\delta G(B,T)$ data; solid curves: the best fits with Eq. (2). Electron-phonon scattering time vs temperature for the NbTiN film with (b) $d=6$ nm and (c) $d=9$ nm in a double-logarithmic scale. Symbols: values of ${\tau }_{e\text{-ph}}\left(T\right)$ obtained from the experimental ${\tau }_{\varphi }^{-1}$ data as ${\tau }_{e\text{-ph}}={({\tau }_{\varphi }^{-1}-{\tau }_{e-e}^{-1}-{\tau }_{e-fl}^{-1})}^{-1}$; solid lines: the best fits with the SM model, Eqs. (B1a) and (B1b).

Figure 6

Normalized voltage transient vs time for microbridges fabricated from the NbTiN film with (a) $d=6$ nm and (b) $d=9$ nm. Solid curves: experimental data; dashed curves: the best fits with the 2T model, Eqs. (9)–(13) in [12]. The inset is a sketch of the microbridge geometry.

Figure 7

The $e$-ph scattering time vs temperature for different Nb fractions in the ${\mathrm{Nb}}_x{\mathrm{Ti}}_{1-x}\mathrm{N}$ compound. The data for NbN and NbTiN were extrapolated to temperatures below 10 K, and those for TiN were extrapolated to temperatures above 4 K (see the main text).

Figure 8

Ratio of experimental (calorimetric) and Debye phonon heat capacities.