Daniel P. Sellan

Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance

Non-metallic crystalline materials conduct heat by the transport of quantized atomic lattice vibrations called phonons. Thermal conductivity depends on how far phonons travel between scattering events-their mean free paths. Due to the breadth of the phonon mean free path spectrum, nanostructuring materials can reduce thermal conductivity from bulk by scattering long mean free path phonons, whereas short mean free path phonons are unaffected. Here we use a breakdown in diffusive phonon transport generated by high-frequency surface temperature modulation to identify the mean free path-dependent contributions of phonons to thermal conductivity in crystalline and amorphous silicon. Our measurements probe a broad range of mean free paths in crystalline silicon spanning 0.3-8.0 μm at a temperature of 311 K and show that 40±5% of its thermal conductivity comes from phonons with mean free path >1 μm. In a 500 nm thick amorphous silicon film, despite atomic disorder, we identify propagating phonon-like modes that contribute >35±7% to thermal conductivity at a temperature of 306 K.

Cross-plane phonon transport in thin films

We predict the cross-plane phonon thermal conductivity of Stillinger-Weber silicon thin films as thin as 17.4 nm using the lattice Boltzmann method. The thin films are modeled using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. We use this approach, which considers all of the phonons in the first Brillouin-zone, to assess the suitability of common assumptions. Specifically, we assess the validity of: (i) neglecting the contributions of optical modes, (ii) the isotropic approximation, (iii) assuming an averaged bulk mean-free path, and (iv) the Matthiessen rule. Because the frequency-dependent contributions to thermal conductivity change as the film thickness is reduced, assumptions that are valid for bulk are not necessarily valid for thin films.

Size-dependent model for thin film and nanowire thermal conductivity

We present an analytical model for the size-dependence of thin film and nanowire thermal conductivity and compare the predictions to experimental measurements on silicon nanostructures. The model contains no fitting parameters and only requires the bulk lattice constant, bulk thermal conductivity, and an acoustic phonon speed as inputs. By including the mode-dependence of the phonon lifetimes resulting from phonon-phonon and phonon-boundary scattering, the model captures the approach to the bulk thermal conductivity of the experimental data better than gray models based on a single lifetime.

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.

Microsecond-sustained lasing from colloidal quantum dot solids

Colloidal quantum dots have grown in interest as materials for light amplification and lasing in view of their bright photoluminescence, convenient solution processing and size-controlled spectral tunability. To date, lasing in colloidal quantum dot solids has been limited to the nanosecond temporal regime, curtailing their application in systems that require more sustained emission. Here we find that the chief cause of nanosecond-only operation has been thermal runaway: the combination of rapid heat injection from the pump source, poor heat removal and a highly temperature-dependent threshold. We show microsecond-sustained lasing, achieved by placing ultra-compact colloidal quantum dot films on a thermally conductive substrate, the combination of which minimizes heat accumulation. Specifically, we employ inorganic-halide-capped quantum dots that exhibit high modal gain (1,200 cm−1) and an ultralow amplified spontaneous emission threshold (average peak power of ∼50 kW cm−2) and rely on an optical structure that dissipates heat while offering minimal modal loss.

Assessment of the Holland model for silicon phonon-phonon relaxation times using lattice dynamics calculations

We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dynamics data. Instead, we introduce a simple method based on using cumulative thermal conductivity functions to obtain better predictions of the frequency-dependence of relaxation times.We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dy...

Assessment of Fourier-Based Thermal Models Used in Frequency-Domain Thermoreflectance Data Analysis

We assess a Fourier-based thermal model used in frequency-domain thermoreflectance data analysis. The Boltzmann transport equation (BTE) is first used to simulate sub-continuum phonon transport in a semi-infinite solid. We then compare the BTE-predicted temperature profiles to those predicted by an analytical solution of the Fourier-based conduction equation. The two models agree well when ωτ 1.Copyright

A Transient Modified Fourier-Based Approach for Thermal Transport Modelling in Sub-Continuum Regime

The presence of sub-continuum effects in nano-scale systems, including size and boundary effects, causes the continuum-level relations (e.g., Fourier heat equation) to break down at such scales. The thermal sub-continuum effects are manifested as a temperature jump at the system boundaries and a reduced heat flux across the system. In this work, we reproduce transient and steady-state results of Gray lattice Boltzmann simulations by developing a one-dimensional, transient, modified Fourier-based approach. The proposed methodology introduces the following two modifications into the Fourier heat equation: (i) an increase in the sample length by a fixed length at the two ends, in order to capture the steady-state temperature jumps at the system boundaries, and (ii) a size-dependent effective thermal diffusivity, to recover the transient temperature profiles and heat flux values. The predicted temperature and heat flux values from the proposed modified Fourier approach are in good agreement with those predicted by the Gray lattice Boltzmann simulations.Copyright

SIZE-DEPENDENT MODEL FOR THIN FILM THERMAL CONDUCTIVITY

We present a closed-form classical model for the size dependence of thin film thermal conductivity. The model predictions are compared to Stillinger-Weber silicon thin film thermal conductivities (in-plane and cross-plane directions) calculated using phonon properties obtained from lattice dynamics calculations. By including the frequency dependence of the phonon-phonon relaxation times, the model is able to capture the approach to the bulk thermal conductivity better than models based on a single relaxation time.Copyright

Enhanced Thermal Map Prediction and Floor Plan Optimization in Electronic Devices Considering Sub-Continuum Thermal Effects

In current and next-generation semiconductor electronic devices, sub-continuum heat transfer effects and non-uniform power distribution across the die surface lead to large temperature gradients and localized hot spots on the die. These hot spots can adversely affect device performance and reliability. In this work, we propose an enhanced method for thermal map prediction that considers sub-continuum thermal transport effects and show their impact in floor plan optimization. Sub-continuum effects are expressed in terms of an effective thermal conductivity. We introduce and calibrate a 2D thermal model of the die for fast simulation of thermal effects under non-uniform power generation scenarios. The calibrated 2D model is then used to study the impact of the effective thermal conductivity on the thermal map prediction and floor plan optimization. Results show that sub-continuum effects radically change both the predicted thermal performance and the optimal floor plan configurations.Copyright