Length Scale of Diffusive Phonon Transport in Suspended Thin Silicon Nanowires

Abstract

Recent experimental advances have revealed that the mean free path (mfp) of phonons contributing significantly to thermal transport in crystalline semiconductors can be several microns long. Almost all of these experiments are based on bulk and thin film materials and use techniques that are not directly applicable to nanowires. By developing a process with which we could fabricate multiple electrically contacted and suspended segments on individual heavily doped smooth Silicon nanowires, we measured phonon transport across varying length scales using a DC self-heating technique. Our measurements show that diffusive thermal transport is still valid across O(100) nm length scales, supporting the diffuse nature of phonon-boundary scattering even on smooth nanowire surfaces. Our work also showcases the self-heating technique as an important alternative to the thermal bridge technique to measure phonon transport across short length scales relevant to mapping the phonon mfp spectrum in nanowires.

Quasi-Ballistic Heat Conduction due to Lévy Phonon Flights in Silicon Nanowires

“…To conclude, heat conduction in silicon nanostructures is more ballistic than it is common to assume 8,[13][14][15] . Our experiments and simulations show that quasi-ballistic heat conduction occurs even in micron-long NWs up to room temperature and should be even more pronounced at the shorter length scales.…”

“…Thus, we should also examine the length dependence of the thermal resistance per unit area, given by A / K, where A is the cross-section area and K is the thermal conductance. Figure 3 shows that the data points for the long NWs (L > 2.5 μm) form a linear trend for both types of NWs and at all temperatures, which implies that heat conduction in the long NWs is diffusive 8,15,16 . This linear trend extrapolates precisely to zero resistance at zero length ( Supplementary Fig.…”

Thermal conductivity of Si nanowires with δ-modulated dopant distribution by self-heated 3ω method and its length dependence

“…To clarify whether the phenomenon is related to the contact effect, we further studied the temperature dependence of the nanowire thermal conductivity at varied length scales. 30 If the thermal resistance in measurement is dominated by the thermal contact, they will then follow the monotonic and linear length dependence at all temperatures. 30 Figure 5 displays the temperature dependence of thermal conductivity and thermal resistance for nanowires from 0.7 to 2.6 lm (note because of the TCR restriction, the j measurements do not cover the same temperature range).…”

Radial dependence of thermal transport in silicon nanowires

“…In most of them there is a deviation from Fourierʼs law [9]. Among the main methods for measuring the thermal conductivity of nanowires one finds the bridge technique [10][11][12] and the tip methodology [13]. While in the first method the nanowires are attached in their extremities and a cold and a hot reservoir are imposed, thus the total thermal conductivity is measured, in the second methodology a hot AFM tip approaches the nanowire in a certain position and the thermal conductivity is deduced from the contact with the external layer.…”