Heat Conduction In Thin Films Research Articles

Surface phonons limit heat conduction in thin films

Understanding microscopic heat conduction in thin films is important for nano/micro heat transfer and thermal management for advanced electronics. As the thickness of thin films is comparable to or shorter than a phonon wavelength, phonon dispersion relations and transport properties are significantly modulated, which should be taken into account for heat conduction in thin films. Although phonon confinement and depletion effects have been considered, it should be emphasized that surface-localized phonons (surface phonons) arise whose influence on heat conduction may not be negligible due to the high surface-to-volume ratio. However, the role of surface phonons in heat conduction has received little attention thus far. In the present work, we performed anharmonic lattice dynamics calculations to investigate the thickness and temperature dependence of in-plane thermal conductivity of silicon thin films with sub-10-nm thickness in terms of surface phonons. Through systematic analysis of the influences of surface phonons, we found that anharmonic coupling between surface and internal phonons localized in thin films significantly suppresses overall in-plane heat conduction in thin films. We also discovered that specific low-frequency surface phonons significantly contribute to surface--internal phonon scattering and heat conduction suppression. Our findings are beneficial for the thermal management of electronics and phononic devices and may lead to surface phonon engineering for thermal conductivity control.

Specular reflection leads to maximum reduction in cross-plane thermal conductivity

In contrast to established work that uses diffuse surface scattering as the mechanism to lower the in-plane thermal conductivities, we show that the largest reduction of heat conduction in thin films is achieved via specular scattering under cross-plane heat transport. Our results create a new perspective for heat conduction manipulation since smooth surfaces—in contrast to rough surfaces—are shown to be more effective in suppressing thin film heat conduction.

Exact harmonic solution to ballistic type heat propagation in thin films and wires

The system of hyperbolic type differential equations is considered for non–Fourier heat transfer in thin films and wires. Structures of the harmonic solutions for telegrapher equation and for Guyer–Krumhansl equation are identified and compared with each other. The exact harmonic solution is obtained; the influence of the phonon heat transfer is explored. The maximum principle violation is demonstrated. Frequency dependence of the solution for Guyer–Krumhansl equation is shown. The exact analytical solution is derived for the inhomogeneous ballistic–diffusion set of differential equations, governing heat propagation in thin films. The contribution of the ballistic, wave and diffusive heat transfer components as well as the influence of the initial conditions and of the Knudsen number on heat conduction in thin films and wires are investigated. The cases of identical and different from each other Knudsen numbers for ballistic and diffusive components are explored. The examples of exact solutions for the heat transfer in each case are demonstrated.

Cross-plane heat conduction in thin films with ab-initio phonon dispersions and scattering rates

We present a first-principles study of the cross-plane thermal conductivity κ⊥ in a wide variety of semiconductor thin films. We introduce a simple suppression model that matches variance-reduced Monte Carlo simulations with ab-initio phonon dispersions and scattering rates within ≤5% even for anisotropic compounds. This, in turn, enables accurate κ⊥ reconstruction from tabulated cumulative conductivity curves κΣ(Λ⊥). We furthermore reveal, and explain, a distinct quasiballistic regime characterised by a fractional thickness dependence κ⊥∼L2−α in alloys (where α is the Lévy exponent) and logarithmic dependence κ⊥∼ln(L) in single crystals. These observations culminate in the formulation of two compact parametric forms for κ⊥(L) that can fit the first-principles curves across the entire ballistic-diffusive range within a few percent for all investigated compounds.

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

Influence of size effect and boundary conditions on temperature overshooting in nanoscale thermal conduction

The temperature overshooting phenomenon in one-dimensional nanoscale heat conduction in thin films is studied for various boundary conditions. The results show that when ballistic heat transport strongly affects the heat transport process, temperature overshooting is more likely to occur. A sudden increase of temperature on only one surface of a thin film cannot trigger temperature overshooting, while symmetric boundary temperature perturbations lead to the largest temperature overshooting. Two-dimensional heat conduction is also studied in a nanoscale area. The analytic results show that Fourier’s law may severely underestimate the temperatures in nanofilms as well as in nanoareas when temperature overshooting occurs.

Anisotropy of the Thermal Conductivity in GaAs/AlAs Superlattices

We combine the transient thermal grating and time-domain thermoreflectance techniques to characterize the anisotropic thermal conductivities of GaAs/AlAs superlattices from the same wafer. The transient grating technique is sensitive only to the in-plane thermal conductivity, while time-domain thermoreflectance is sensitive to the thermal conductivity in the cross-plane direction, making them a powerful combination to address the challenges associated with characterizing anisotropic heat conduction in thin films. We compare the experimental results from the GaAs/AlAs superlattices with first-principles calculations and previous measurements of Si/Ge SLs. The measured anisotropy is smaller than that of Si/Ge SLs, consistent with both the mass-mismatch picture of interface scattering and with the results of calculations from density-functional perturbation theory with interface mixing included.

Micro- and nanoscale thermal phenomena in thin-film magnetic recording heads

As the magnetic data storage industry continues to pursue aggressive miniaturization of sensors and write elements in thin-film recording heads, it faces serious thermal management challenges. The present work develops theoretical models of heat conduction and power dissipation in current-in-plane and current-perpendicular-to-plane sensors to highlight key physics and help examine the influence of various parameters. Fundamental physics of heat conduction in thin films and across interfaces is discussed to facilitate systematic exploration of novel high thermal conductivity materials and methods to minimize the thermal interface resistance. Experimental techniques for thermal characterization of recording heads and constituent thin films are also presented.

MOLECULAR DYNAMICS SIMULATION OF THERMAL CONDUCTIVITY OF NANOSCALE THIN SILICON FILMS

Molecular dynamics simulations are performed to explore the thermal conductivity in the cross-plane direction of single-crystal thin silicon films. The silicon crystal has diamond structure, and the Stillinger-Weber potential is adopted. The inhomogeneous nonequilibrium molecular dynamics (NEMD) scheme is applied to model heat conduction in thin films. At average temperature T = 500 K, which is lower than the Debye temperature ΘD = 645 K, the results show that in a film thickness range of about 2–32 nm, the calculated thermal conductivity decreases almost linearly as the film thickness is reduced, exhibiting a remarkable reduction as compared with the bulk experimental data. The phonon mean free path is estimated and the size effect on thermal conductivity is attributed to the reduction of phonon mean free path according to the kinetic theory.

Phonon Heat Conduction in Thin Films: Impacts of Thermal Boundary Resistance and Internal Heat Generation

The measured thermal resistance across a thin film deposited on a substrate often includes the internal thermal resistance within the film and the thermal boundary resistance (TBR) across the film-substrate interface. These two resistances are frequently lumped and reported as an equivalent thermal conductivity of the film. Two fundamental questions should be answered regarding the use of this equivalent thermal conductivity. One is whether it leads to the correct temperature distribution inside the film. The other one is whether it is applicable for thin films with internal heat generation. This paper presents a study based on the Boltzmann transport equation (BTE) to treat phonon heat conduction inside the film and across the film-substrate interface simultaneously, for the cases with and without internal heat generation inside the film. Material systems studied include SiO2 and diamond films on Si substrates, representative of thin-film materials with low and high thermal conductivity. It is found that for a SiO2 film on a Si substrate, the film thermal conductivity and TBR can be treated independently, while for a diamond film on a Si substrate, the two are related to each other by the interface scattering. When the free surface behaves as a black phonon emitter, the TBR for thin diamond films with internal heat generation is the same as that without the internal heat generation. When the free surface is adiabatic, however, the TBR increases and approaches the value of the corresponding black surface as the film thickness increases. Results of this study suggest that great care must be taken when extending the effective thermal conductivity measured for thin films under one experimental condition to other application situations.

Phonon Wave Heat Conduction in Thin Films and Superlattices

Heat conduction in thin films and superlattices is important for many engineering applications such as thin-film based microelectronic, photonic, thermoelectric, and thermionic devices. Past modeling efforts on the thermal conductivity of thin films were based on solving the Boltzmann transport equation that treats phonons as particles. The effects of phonon interference and tunneling on the heat conduction and the thermal conductivity of thin films and superlattices remain to be explored. In this work, the wave effects on the heat conduction in thin films and superlattices are studied based on the consideration of the acoustic wave propagation in thin film structures and neglecting the internal scattering. A transfer matrix method is used to calculate the phonon transmission and heat conduction through these structures. The effects considered in this work include the phonon interference, tunneling, and confinement. The phonon dispersion is considered by introducing frequency-dependent Lamb constants. A ray-tracing method that treats phonons as particles is also developed for comparison. Sample calculations are performed on double heterojunction structures resembling Ge/Si/Ge and n-period superlattices similar to Ge/Si/n(Si/Ge)/Ge, It is found that phonon confinements caused by the phonon spectra mismatch and by the total internal reflection create a dramatic decrease of the overall thermal conductance of thin films. The phonon interference in a single layer does not have a strong effect on its thermal conductance but for superlattice structures, the stop bands created by the interference effects can further reduce the thermal conductance. Tunneling of phonon waves occurs when the constituent layers are 1–3 monolayer thick and causes a slight recovery in the thermal conductance when compared to thicker layers. The thermal conductance obtained from the ray tracing and the wave methods approaches the same results for a single layer. For superlattices, however, the wave method leads to a finite thermal conductance even for infinitely thick superlattices while the ray tracing method gives a thermal conductance that decreases with increasing number of layers. Implications of these results on explaining the recent thermal conductivity data of superlattices are explored.

A unified solution for heat conduction in thin films

Mathematical formulations of heat conduction in thin films and subsequent analytical solutions are the subject of this paper. A generalized formulation of the energy equation that allows for local nonequilibrium conditions between the heat carriers is valid for a broad spectrum of materials from conductors to nonconductors. A unified solution is derived from the classical solution of the energy equation and it is cast as a modification of the Greens function solution for Fourier heat conduction. Numerical examples show the influence of periodic surface heat flux on phase angle and temperature, and the condition for lumped system approximation.

Wave characteristic of femtosecond heat conduction in thin films

The hyperbolic heat conduction equation (HHC) is solved for submicrometer gold film irradiated with a short-pulse laser. The transient temperature profiles are calculated. It is shown that the solutions of HHC and standard heat diffusion equation are significantly different for submicrometer films.