A General and Predictive Understanding of Thermal Transport from 1D- and 2D-Confined Nanostructures: Theory and Experiment

Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Past experimental and theoretical works exploring nanoscale heat transport in semiconductors addressed known deviations from Fourier's law modeling by including effective parameters, such as a size-dependent thermal conductivity. However, recent experiments have qualitatively shown behavior that cannot be modeled in this way. Here, we combine advanced experiment and theory to show that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be described using a general hydrodynamic heat transport model, contrary to previous understanding of heat flow in bulk silicon. We use a comprehensive set of extreme ultraviolet scatterometry measurements of nondiffusive transport from transiently heated nanolines and nanodots to validate and generalize our ab initio model, that does not need any geometry-dependent fitting parameters. This allows us to uncover the existence of two distinct time scales and heat transport mechanisms: an interface resistance regime that dominates on short time scales and a hydrodynamic-like phonon transport regime that dominates on longer time scales. Moreover, our model can predict the full thermomechanical response on nanometer length scales and picosecond time scales for arbitrary geometries, providing an advanced practical tool for thermal management of nanoscale technologies. Furthermore, we derive analytical expressions for the transport time scales, valid for a subset of geometries, supplying a route for optimizing heat dissipation.

Ballistic Phonons in Ultrathin Nanowires

According to Fourier's law, a temperature difference across a material results in a linear temperature profile and a thermal conductance that decreases inversely proportional to the system length. These are the hallmarks of diffusive heat flow. Here, we report heat flow in ultrathin (25 nm) GaP nanowires in the absence of a temperature gradient within the wire and find that the heat conductance is independent of wire length. These observations deviate from Fourier's law and are direct proof of ballistic heat flow, persisting for wire lengths up to at least 15 μm at room temperature. When doubling the wire diameter, a remarkably sudden transition to diffusive heat flow is observed. The ballistic heat flow in the ultrathin wires can be modeled within Landauer's formalism by ballistic phonons with an extraordinarily long mean free path.

Far-field thermal imaging below diffraction limit

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.

Full-field thermal imaging of quasiballistic crosstalk reduction in nanoscale devices

Understanding nanoscale thermal transport is of substantial importance for designing contemporary semiconductor technologies. Heat removal from small sources is well established to be severely impeded compared to diffusive predictions due to the ballistic nature of the dominant heat carriers. Experimental observations are commonly interpreted through a reduction of effective thermal conductivity, even though most measurements only probe a single aggregate thermal metric. Here, we employ thermoreflectance thermal imaging to directly visualise the 2D temperature field produced by localised heat sources on InGaAs with characteristic widths down to 100 nm. Besides displaying effective thermal performance reductions up to 50% at the active junctions in agreement with prior studies, our steady-state thermal images reveal that, remarkably, 1-3 μm adjacent to submicron devices the crosstalk is actually reduced by up to fourfold. Submicrosecond transient imaging additionally shows responses to be faster than conventionally predicted. A possible explanation based on hydrodynamic heat transport, and some open questions, are discussed.

Collective thermal transport in pure and alloy semiconductors

Suppressing collective effects from momentum-conserving phonon collisions cause fast drop in thermal conductivity at small semiconductor alloy impurity concentrations.

Thermal conductivity of Bi2Te3 nanowires: how size affects phonon scattering

This work provides an in-depth study of how the thermal conductivity of stoichiometric [110] Bi₂Te₃ nanowires becomes affected when reducing its diameter from an experimental and theoretical point of view. The thermal conductivity was observed to decrease more than 70% (from 1.78 ± 0.46 W K^-1 m^-1 to 0.52 ± 0.35 W K^-1 m^-1) when the diameter of the nanowire was reduced one order of magnitude (from 300 nm to 25 nm). The Kinetic-Collective model was used to understand such a reduction, which can be explained by the impact that surface scattering has in acoustic phonons. The smaller the diameter of the nanowires is, the larger the alteration in the mean free path of the low-frequency phonons is. The model agrees well with the experimental data, and the reduction in the thermal conductivity of the nanowires can be explained in terms of an increment of phonon scattering.

Thermal conductivity of group-IV semiconductors from a kinetic-collective model

The thermal conductivity of group-IV semiconductors (silicon, germanium, diamond and grey tin) with several isotopic compositions has been calculated from a kinetic-collective model. From this approach, significantly different to Callaway-like models in its physical interpretation, the thermal conductivity expression accounts for a transition from a kinetic (individual phonon transport) to a collective (hydrodynamic phonon transport) behaviour of the phonon field. Within the model, we confirm the theoretical proportionality between the phonon-phonon relaxation times of the group-IV semiconductors. This proportionality depends on some materials properties and it allows us to predict the thermal conductivity of the whole group of materials without the need to fit each material individually. The predictions on thermal conductivities are in good agreement with experimental data over a wide temperature range.

In-plane thermal conductivity of sub-20 nm thick suspended mono-crystalline Si layers

We measure the thermal conductivity of a 17.5-nm-thick single crystalline Si layer by using a suspended structure developed from a silicon-on-insulator wafer, in which the Si layer bridges the suspended platforms. The obtained value of 19 Wm(-1) K(-1) at room temperature represents a tenfold reduction with respect to bulk Si. This design paves the way for subsequent lateral nanostructuration of the layer with lithographic techniques, to define different geometries such as Si nanowires, nanostrips or phononic grids. As a proof of concept, nanostrips of 0.5 × 10 μm have been defined by focused ion beam (FIB) in the ultrathin Si layer. After the FIB cutting process with Ga ions at 30 kV and 100 pA, the measured thermal conductivity dramatically decreased to 1.7 Wm(-1) K(-1), indicating that the structure became severely damaged (amorphous). Re-crystallization of the structure was promoted by laser annealing while monitoring the Raman spectra. The thermal conductivity of the layer increased again to a value of 9.5 Wm(-1) K(-1) at room temperature, below that of the single crystalline material due to phonon scattering at the grain boundaries.

Robustness of the nonequilibrium entropy related to the Maxwell-Cattaneo heat equation

The connection between the Maxwell-Cattaneo heat transport equation and a nonequilibrium entropy is examined through four different thermodynamic approaches, and it is shown that all of them lead to the same form of the nonequilibrium entropy. Furthermore, it is seen that this form is also consistent with three microscopic formalisms. This robustness underlines the consistency and relevance of the entropy.