Observation of Anomalous Non-Ohmic Transport in Current-Driven Nanostructures

Sufficiently large electric current applied to metallic nanostructures can bring them far out of equilibrium, resulting in non-Ohmic behaviors characterized by current-dependent resistance. We experimentally demonstrate a linear dependence of resistance on current in microscopic thin-film metallic wires at cryogenic temperatures, and show that our results are inconsistent with common non-Ohmic mechanisms such as Joule heating. As the temperature is increased, the linear dependence becomes smoothed out, resulting in the crossover to behaviors consistent with Joule heating. A plausible explanation for the observed behaviors is the strongly nonequilibrium distribution of phonons generated by the current. Analysis based on this interpretation suggests that the observed anomalous current-dependent resistance can provide information about phonon transport and electron-phonon interaction at nanoscale. The ability to control the properties of phonons generated by current can lead to new routes for the optimization of thermal properties of electronic nanodevices.

Popular Summary

Joule heating, in which a material’s temperature is increased via electrical currents, is ubiquitous in science and technology. We experimentally demonstrate that, in contrast to macroscopic systems, the effects of electrical current in typical microstructures such as thin-film microwires cannot be described as Joule heating. Phonons generated by the current form a strongly nonequilibrium distribution that cannot be described in terms of temperature, while the quasiballistic flow of phonons from the system cannot be described in terms of heat diffusion. The observed effects are particularly significant at cryogenic temperatures but remain apparent even at temperatures as high as 200 K.

Our findings are relevant to many areas of science and technology. For instance, the effects of current in experiments such as ours provide direct information about electron-phonon interactions, phonon transport, and relaxation at the nanoscale. This can facilitate the design of new materials and structures that more efficiently dissipate heat as well as provide a better understanding of phenomena associated with the electron-phonon interaction, such as superconductivity.

Our results also warrant a reexamination of many experimental observations related to current-induced heating, whose analysis commonly relied on the Joule heating approximation. Furthermore, Joule heating is commonly used in nanoscale heat sources, for example, in studies of thermoelectric phenomena. Our work shows that these effects must be reexamined, which will likely lead to a better understanding of thermoelectric phenomena at nanoscale.

Figure 1

(a) Resistance vs current for a $1\text{−}\mu \mathrm{m}$-long, 500-nm-wide, 5-nm-thick Pt wire deposited on etched Si substrate, at room temperature $T=295\mathrm{K}$. The curve is the best fit to the data with a quadratic function. Inset: Resistivity of Pt deposited on Si substrates vs inverse Pt thickness, at 295 K. (b) Same as (a), at $T=5\mathrm{K}$. Curve is a fit with the linear function $R(I)=R(0)+\alpha |I|$, where $\alpha$ is a fitting parameter. Inset: the dependence of the wire resistance on temperature at $I=0$.

Figure 2

(a) Symbols: $R$ vs $I$ for the same sample as in Fig. 1, at the labeled values of $T$. Curves: best fits with the linear function $R(I)=R_0+\alpha |I|$ convolved with the Gaussian $g(I)=(1/\sqrt{2\pi }\mathrm{\Delta }I)e^{-I^2/2\mathrm{\Delta }{I}^2}$. Some of the data points are omitted for clarity, but fitting is performed for the entire data set. (b),(c) Parameters extracted from the data fitting: the Gaussian width $\mathrm{\Delta }I$ (b) and the slope of the linear dependence (c). The line in (b) is the best linear fit of the data for $T>20\mathrm{K}$.

Figure 3

Effects of the Pt wire geometry. (a),(b) Temperature dependence of the Gaussian broadening width $\mathrm{\Delta }J$ (a) and the linear slope (b) of $\rho (J)$, for 10-nm-thick Pt wires with lengths $L=1$, 3, and $5\mu \mathrm{m}$, as labeled. (c),(d) Same as (a),(b), for $1\text{−}\mu \mathrm{m}$-long Pt wires with thicknesses $d=5$, 7, 10, and 15 nm, as labeled in (c). Inset in (d): Dependence of the phonon relaxation time ${\tau }_{\mathrm{ph}}$ on the Pt thickness, determined from the data at $T=5\mathrm{K}$ using Eq. (6) (symbols), and linear fit with zero intercept (line).

Figure 4

(a) Symbols: resistance vs current for a $1\text{−}\mu \mathrm{m}$-long, 500-nm-wide Au(5) wire on Si substrate, at the labeled values of temperature. Curves: results of the data fitting with a linear function $R(I)=R(0)+\alpha |I|$ convolved with the Gaussian. (b),(c) Parameters extracted from the data fitting: the Gaussian width $\mathrm{\Delta }I$ (b) and the slope of the linear dependence (c). The line in (b) is the best linear fit of the data for $T>20\mathrm{K}$.