Mean Free Path Spectroscopy
Figure 1. Transition from diffusive
to ballistic heat transfer.
Figure 2. Example measurement from MFP spectroscopy: thermal conductivity accumulation
measurements and calculations
versus MFP for silicon 1.
Figure 3. Example reconstructed MFP distribution
Knowledge of phonon mean free paths (MFPs) is essential to
understanding and engineering size effects in nanoscale heat
transfer. Because they largely determine the thermal conductivity
of materials and the figure of merit in thermoelectric devices,
means of measuring this quantity is especially important for
scientific and practical purposes.
Our lab has developed the first experimental method, mean free path spectroscopy, that is able to measure MFPs over a wide range of
length scales and materials1. The technique uses
observations of quasi-ballistic heat transfer, in which thermal
lengths are comparable to MFPs, to determine how much different
phonons contribute to the thermal conductivity as a function of
their MFP. Fig. 1 illustrates the transition from diffusive to
ballistic heat transfer when the size of a heater is decreased.
To implement this technique, an experiment with spatial resolution comparable to MFPs (nanometers to microns) is required. Optical techniques, which offer micron spatial resolution and sub-picosecond time resolution, are well suited for this purpose. We employ several ultrafast optical techniques, including traditional TDTR and TG techniques (see optical techniques).
The experiments yield several thermal conductivity values
that vary with the length scale used to perform the
measurements1. For example, Fig. 2 shows measurements
of silicon MFPs at cryogenic temperatures (symbols) compared to
the predictions of first-principles calculations.
recently, how these measurements are related to the actual MFP
distribution was unclear. However, we have showed that the MFP
distribution can be recovered by solving a common inverse
problem using experimental results as input2. A suppression function that is needed for this inversion is obtained computationally by solving the Boltzmann Transport Equation (BTE) using a variety of methods such as finite differences and Monte Carlo. Recently, we have introduced a theoretical framework based on the BTE that allows the MFP accumulation distribution to be quantitatively reconstructed from thermal measurements from TG experiments3. Fig. 3 shows a numerical example of the reconstruction procedure to obtain the MFP distribution. Thus by using experiment and computation, we are able to measure MFPs in semiconductors, thermoelectrics, and other technologically important materials.
- A. J. Minnich, et al. Phys. Rev. Lett. 107, 095901 (2011)
- A.J. Minnich, Phys. Rev. Lett. 109, 205901 (2012)
- C. Hua, et al., Phys. Rev. B, 89, 094302 (2014)
Figure 1. Illustration of Curiosity on the surface of Mars. The multi-mission radioisotope thermoelectric generator (MMRGT) is used to power Curiosity!
Figure 2. 3D animation of phonons in
from MC simulations.
Thermoelectrics are a solid-state energy conversion technology that can convert heat directly to electricity. Because the devices have no moving parts, they are ideal for space power generation and waste heat recovery (Fig. 1). In fact, thermoelectrics are now powering the newest Mars rover, Curiosity! However, at present thermoelectric devices are too inefficient for commercial use.
Nanoengineered thermoelectrics with nanoscale interfaces have made impressive gains in efficiency and are
close to being commercially viable. This improvement is attributed
to strong interface scattering of phonons, which are the dominant
heat carriers in TE and parasitically transmit unconverted
heat. However, the lack of a detailed understanding of phonon
scattering by nanostructures makes further improvements difficult
In our group, we focus on studying the
microscopic details of these interfacial scattering process using
experiment and computation. Experimentally, we are measuring
the phonon mean free paths and thermal conductivities of
nanocrystalline thermoelectric materials using thermal
conductivity spectroscopy. Computationally, we are using a
variance-reduced Monte Carlo (MC) method1 to simulate
the full complex geometry of the actual materials. Recently, we
have use this MC method to study the impact of the
frequency-dependent grain boundary scattering on the
distribution of heat in the thermal phonon spectrum in
nanocrystalline silicon/silicon-germanium2. Fig. 2
shows the geometry used in our MC algorithm, representing a
realistic 3D grain structure. The computations also give us
access to information not available experimentally, such as how
different types of grain boundaries scatter specific phonon
modes. We have also used optimization methods to study the
best nanoparticle size distribution to scatter the broad thermal
phonon spectrum and yield the minimum thermal conductivity3. To put this knowledge gained into practice, we are working with Dr. Snyder of Caltech, an expert in material synthesis, and scientists at JPL to fabricate high-performance TE materials.
Our work could enable efficient waste heat recovery,
environmentally friendly refrigeration, more capable robots for
space exploration, and many other applications.
- J. P. Peraud, et al., Phys. Rev. B, 84, 205331 (2011)
- C. Hua, et al., arXiv:1404.7847 (2014)
- H. Zhang, et al., arXiv:1404.1438 (2014)
Heat Dissipation in LEDs
Lighting in domestic and industrial buildings consumes a staggering 1.5 trillion kWh (Kilowatt hour) of energy out of the total 27 trillion kWh in the U.S. per year. In a recent study, the U.S. Department of Energy estimated that this proportion could be reduced to less than 50% of its current value if the entire lighting market switched to light emitting diodes (LEDs), which is equivalent to saving more than 600,000 barrels of oil or removing 7 million cars off the road per year1. LEDs are an excellent sustainable alternative to conventional light sources like CFLs and incandescent lamps due to their high efficiency and long lifespan, but their market penetration is low due to their high cost.
To address this issue, our group is studying how to reduce the long-term capital cost of the LEDs by substaintially increasing their lifespan. Recent work has demonstrated a threefold increase in LED lifespan for a mere 11 ℃ reduction in LED junction temperature through efficient thermal management, but a poor understanding of thermal transport in the complex LED structures has impeded efforts to enhance their heat transfer properties. We are using MFP spectroscopy to learn which phonons are responsible for heat conduction in the complex LED structure. In particular, we seek to determine which phonons conduct heat across many interfaces of the quantum-well structure, information that can then be used to minimize the thermal resistance of the interfaces. For this project, we are collaborating with Prof. Lu Na from UNC-Charlotte who fabricates nitride superlattices using MBE and CVD.
- M. Yamada, et. al., U.S. Department of Energy (2013)
Thermal Transport in Organic Semiconductors
Organic semiconductors are under intense investigation for both their electronic and thermal properties due to the potential for cheaper material costs and large-scale production due to the use of Earth-abundant materials and solution-processing techniques1. In particular, polymers are of interest as thermoelectrics due to their low bulk thermal conductivity2,3, but also as possible thermal management materials due to the demonstrated high thermal conductivity of aligned polymer nanofibers and films. However, many aspects of thermal transport in polymers remain poorly understood, partly because of limitations on experimental methods to measure their thermal conductivity.
In our group, we seek to understand thermal transport in these organic materials using both computational and experimental techniques. Computationally, we are using molecular dynamics simulations to determine the mechanisms governing the intrinsic thermal conductivity of single molecular chains. Experimentally, we employ non-contact optical methods to gain a full picture of the thermal transport in anisotropic materials. TDTR (see optical techniques) is a standard technique to measure cross-plane thermal conductivity, but obtaining accurate measurements of in-plane thermal conductivity is a considerable difficulty. We overcome this challenge by using TG spectroscopy for which the in-plane thermal diffusivity is the only unknown parameter (see optical techniques). This technique allows us to quickly and accurately study in-plane thermal transport in thin polymer films, measurements that often are impossible using standard techniques such as TDTR and 3ω. Further, TG requires no smaple preparation other than ensuring the sample is optically smooth, in marked contrast to standard techniques that require metal deposition or microfabrication.
For this project, we collaborate with Professor Chabinyc at UCSB, an expert in fabrication of polymers and polymer themoelectrics, and Dr. Snyder, an expert in thermoelectric materials.
- O. Bubnova, et al., Energy Environ. Sci., 5, 9345-9362 (2012)
- G. H. Kim, et al., Nature Materials, 12, 719-723 (2013)
- O. Bubnova, et al., Nature Materials, 10, 429-433 (2011)
Figure 1. Specific elastic modulus E/ρ vs thermal conductivity Κ. Nanotrusses have the potential to possess combinations of mechanical and thermal properties that do not occur in nature and could be very useful for applications, particularly in the aerospace field.
We are investigating multifunctional materials that possess novel combinations of thermal and mechanical properties. In many applications, particularly aerospace and space applications, materials are required with incompatible properties in multiple physical domains. For example, thermal protection systems on spacecraft require a material that is simultaneously stiff, light, and thermally insulating, a combination that is nearly impossible to achieve using typical bulk materials as shown in Fig. 1. An excellent example of the difficult trade-offs in creating such a material is the ceramic tiles used on the space shuttle, which were low density and thermal insulating but also fragile.
Nanotrusses have the potential to overcome this material limitation. These novel materials consist of hollow beams of thickness from 10-100 nm periodically arranged in a 3D lattice with unit cells of a few microns, and are fabricated using two-photon lithography with the Nanoscribe tool at caltech. Due to their lattice structure they can achieve high strength per unit mass while maintaining exceptionally low thermal conductivity due to porosity. Additional reductions in thermal conductivity are achieved by phonon boundary scattering in the hollow beams. These materials thus have the potential to outperform all existing materials as shown in Fig. 1.
A substantial challenge to studying thermal transport in these materials is measuring their thermal conductivity as the final structures have dimensions of only around 50 microns on a side. We overcome this challenge using TDTR (see optical techniques) to optically measure the thermal conductivity without any physical contact. Additionally, we are using efficient variance-reduced Monte Carlo simulations (see BTE section) to understand the role of boundary scattering in reducing the thermal conductivity of nanotrusses.
In addition to studying phonons, our group also seeks to engineer thermal radiation for energy applications such as solar thermal energy conversion and thermophotovoltaics. In one effort, our group is developing spectrally selective solar absorbers to capture light across the entire solar spectrum in the form of heat while minimizing radiative losses. These materials take advantage of the different surface temperatures and resulting different radiation spectra of the Sun and the Earth. The peak of the solar spectrum occurs in the visible, whereas a black body between 300 K and 500 K, which approximates a hot object on the surface of the Earth, emits primarily in the infrared. To best absorb solar energy and mitigate loss to re-radiation, we are developing materials with high absorptivity in the visible and low emissivity in the infrared. We are using computational methods to calculate and optimize the reflectivity and absorptivity of planar multi-layered materials to determine optimal design. Additionally, we use the Kavli Nanoscience Institute (KNI) at Caltech to fabricate and characterize these selective surfaces.
In our second effort, we are examining how hyperbolic metamaterials may be used to engineer the spectral and directional characteristics of far-field thermal radiation. Presently, we are investigating thermal hyperlenses for radiative cooling. Our calculations show that these cylindrical or spherical hyperbolic metamaterials can dramatically alter the thermal radiation emitted from a nanostructure and could substantially increase the emitted heat flux compared to that of the nanostructure alone.
These efforts are perform as part of the Light-Matter Interactions Energy Frontier Research Center (LMI).
Figure 1. Time-domain transient
Figure 2. Picture of the transient Grating spectroscopy (TG) in our lab.
In our lab, we use several optical techniques to study heat transport at ultrafast timescales and nanometer to micron length scales.
Our first experiment, called time-domain transient thermoreflectance (TDTR), is based on a design that is now implemented in many labs.
In this technique, shown in Fig. 1, a femtosecond pulsed laser beam is split into a pump and probe beams. The pump beam heats up a metal film coated on the sample while the probe detects the change in reflectance due to the pump heating1. The time delay between the pump and probe can be adjusted by changing the path length of the probe using a mechanical delay stage, giving sub-picosecond time resolution. Micron spatial resolution is achieved by focusing the two beams with a microscope objective. Thermal properties are obtained by fitting the measured temperature decay curve to a model, yielding properties like interface conductance and thermal conductivity2.
Our second experiment, called transient grating (TG) spectroscopy,
is an optical pump-probe technique that enables the direct
measurement of the in-plane thermal conductivity of thin film or
bulk material3 . In this experiment, shown in Fig. 2, the sample is impulsively heated with a spatially sinusoidal temperature profile from a pump laser pulse, and a probe laser subsequently observes the in-plane transient thermal decay by measuring the intensity of light diffracted from the sample surface. The shape of the transient decay curve is controlled only by the in-plane thermal diffusivity, and thus the thermal diffusivity can be measured from the exponential time constant of the thermal decay. Unlike other methods used to measure in-plane thermal conductivity such as TDTR or the 3ω method, in TG the thermal diffusivity is the only unknown parameter, removing ambiguities in the fitting procedure.
- Capinski, William S. et al. Rev. Sci. Instrum., 67:2720, 1996.
- D. G. Cahill. Review of Scientific Instruments,
- J. A. Johnson, et al. Journal of Applied Physics,
Boltzmann Transport Equation
Thermal transport at length scales smaller than the phonon MFPs is governed by the Boltzmann transport equation (BTE). This equation has a long history in fields ranging from astronomy to neutron transport and is notoriously difficult to solve because it is an integro-differential equation that depends on real space, phase space, phonon frequency, and time. These challenges have historically restricted even numerical solutions to one spatial dimension and a single phonon frequency, assumptions that do not accurately reflect most situations and prevent us from obtaining a complete picture of thermal transport in realistic devices.
Our group is using a variety of approaches to overcome these
challenges. First, we have demonstrated that analytical
solutions to the BTE in fact exist in simple closed form and can
be used to gain extremely useful insights into nondiffusive heat
conduction1. Second, we have employed novel
variance-reduced Monte Carlo algorithms pioneered by the
Hadjiconstantinou group at MIT 3 to simulate thermal transport in large, 3D structures with complex geometry. For example, we have recently used these algorithms to understand the low thermal conductivities in nanopatterned membranes2. These algorithms, and our efforts to parallelize and optimize our codes, allow us to solve the BTE many orders of magnitude faster than previous algorithms in complex 3D structure without any simplifying approximations and including the full frequency depenedence of phonon properties.
- C. Hua, et al., Phys. Rev. B, 89, 094302 (2014)
- N. Ravichandran, et al., Phys. Rev. B, 89, 205432 (2014)
- J. P. Peraud, et al., Phys. Rev. B, 84, 205331 (2011)