Heat flow in InAs/InP heterostructure nanowires

The transfer of heat between electrons and phonons plays a key role for thermal management in future nanowire-based devices, but only a few experimental measurements of electron-phonon (e-ph) coupling in nanowires are available. Here, we combine experimental temperature measurements on an InAs/InP heterostructure nanowire system with finite element modeling to extract information on heat flow mediated by e-ph coupling. We find that the electron and phonon temperatures in our system are highly coupled even at temperatures as low as 2 K. Additionally, we find evidence that the usual power-law temperature dependence of electron-phonon coupling may not correctly describe the coupling in nanowires and show that this result is consistent with previous research on similar one-dimensional electron systems. We also compare the strength of the observed e-ph coupling to a theoretical analysis of e-ph interaction in InAs nanowires, which predicts a significantly weaker coupling strength than observed experimentally.

Figure 1

(a) A scanning electron micrograph (SEM) image of the HNW system showing the hot (HC) and cold (CC) Au contacts, and the approximate position of the quantum dot (QD), not visible here. A temperature gradient is applied using an ac heating current $I_{\mathrm{H}}$ through the HC. (b) Closeup SEM image of the two InP barriers within the InAs nanowire. (c) Cross section of the nanowire and contacts along the nanowire axis. $\Delta T_{\text{(HC,CC)}}$ are the heating-induced electron temperature rises above the background temperature $T_0$ in the hot and cold contacts, respectively. $\Delta T_{\text{e,(s,d)}}$ are the source and drain-electron temperature rises measured in the vicinity of the quantum dot. The source and drain portions of the NW are defined by the direction of heat flow, the source being closest to the HC.

Figure 2

Measured source (red filled circles) $\Delta T_{\text{e,s}}$ and drain (blue open circles) $\Delta T_{\text{e,d}}$ electron temperature rises for $T_0=1.228$, 2.2, 2.94, and 4.25 K. The relatively large temperature rise observed for the drain electrons, combined with the low electron conductance of the QD, indicates the presence of phonon-mediated heat flow into the drain-electron reservoir.

Figure 3

(a), (b) Top- and (c) side-view schematics of the simulated area for the Au leads and substrate, called the substrate simulations in the text. The location of where the HNW would be is shown by dashed lines in panels (b) and (c). The outer boundary in (a) and lower boundaries in (c) (blue lines) are set to the background temperature $T_0$. The top boundary in (c) (purple line) is assumed to be a perfect insulator. The red line in panel (b) shows the path of the heating current $I_{\mathrm{H}}$. Panel (d) shows a schematic of the simulated HNW. In panels (c) and (d), $\Delta T_{\mathrm{HC}}^{(\mathrm{e},\mathrm{ph})}$ and $\Delta T_{\mathrm{CC}}^{(\mathrm{e},\mathrm{ph})}$ represent the electron and phonon temperature rises in the HC and CC, respectively, as well as the boundary conditions for the simulated HNW.

Figure 4

Example coupled (dotted-dashed lines) and decoupled (solid lines) electron (thick) and phonon (thin) temperature profiles through the HNW for a measurement of $\Delta T_{\mathrm{e},\mathrm{d}}$. Also shown is a temperature profile (dashed line) between the coupled and decoupled regimes, the transition regime. For the plots shown here, $\lambda \approx 0.9$; note that this value was chosen for demonstration purposes. The hashed region along the HNW position represents the down-current Joule heating due to the voltage drop across the QD. The inset shows how $\Delta T_{\mathrm{e},(\mathrm{s},\mathrm{d})}$ depend on the degree of coupling.

Figure 5

Scatter plot of the optimized $C_{\mathrm{e}}$ and $C_{\mathrm{ph}}$ parameters with linear fits to each $T_0$ parameter set.

Figure 6

(a) Comparison of the optimized $n$ and $\Gamma$ parameter sets from the FEM simulations, theoretical calculations, and literature values (Refs. 11, 12, 13). The $\Gamma$ values here have been normalized by the carrier density to allow for a comparison similar to the power loss per carrier. The theoretical data shown here include both deformation and piezoelectric e-ph scattering; each theory data point represents a different electron temperature between 0.7 and 4.7 K and a background temperature of 2.94 K. (b) Scatter plot of the $\delta$ values, calculated from the optimized FEM parameter sets, as a function of $T_0$.