Phonon Mean Free Path Spectrum Research Articles

Nanostructured planar-type uni-leg Si thermoelectric generators

We demonstrate the power enhancement of planar-type uni-leg poly-Si thermoelectric generators by nano-patterning. The thermoelectric generators were fabricated on an SOI wafer by a conventional lithography-based process. The size of the phononic nano-patterning (300 nm in period) was designed based on the thermal phonon mean free path spectrum. The thermal conductivity of the Si membrane was reduced by 60% compared with an unpatterned one, which resulted in the doubled thermoelectric figure-of-merit. The nano-patterning increased the temperature gradient in the Si membrane and resulted in a four times higher voltage and ten times larger power density.

Determining phonon mean free path spectrum by ballistic phonon resistance within a nanoslot-patterned thin film

At microscales to nanoscales, classical size effects in heat conduction play an important role in suppressing the thermal transport process. Such effects occur when the characteristic lengths become commensurate to the mean free paths (MFPs) of heat carriers that are mainly phonons for non-metallic crystals. Beyond existing experimental efforts on thin films using laser-induced thermal gratings, this work provides the theoretical analysis for a new approach to extract the effective phonon MFP distribution for the in-plane heat conduction within a thin film or flake-like sample. In this approach, nanoslots are patterned on a suspended thin film. Phonons will transport ballistically through the neck region between adjacent nanoslots if the phonon MFPs are much longer than the neck width. The associated ‘ballistic thermal resistance’ for varied neck dimensions can then be used to reconstruct the phonon MFP distribution within the film. The technique can be further extended to two-dimensional materials when the relaxation time approximation is reasonably accurate.

Modified Ballistic–Diffusive Equations for Obtaining Phonon Mean Free Path Spectrum from Ballistic Thermal Resistance: II. Derivation of Integral Equation Based on Ballistic Thermal Resistance

ABSTRACTRebuilding phonon mean free path (MFP) spectra from experimental data is integral to phonon MFP spectroscopy. However, being based on effective thermal conductivity, the current integral equation for this precludes the use of certain heat sources of convenient shapes, such as a cylindrical nanoline. Herein, to enable using diverse specimens exhibiting a ballistic effect, we develop a ballistic thermal resistance-based integral equation, utilizing the ease and accuracy of the modified ballistic–diffusive equations demonstrated in the companion paper. The availability of more diverse shapes of specimens will enhance further development and widen use of phonon MFP spectroscopy.

Modified ballistic–diffusive equations for obtaining phonon mean free path spectrum from ballistic thermal resistance: I. Introduction and validation of the equations

ABSTRACTPhonon mean free path (MFP) spectra are essential for the accurate prediction and utilization of the classical size effect. Rebuilding an MFP spectrum from experimental data remains challenging. It requires solving the thermal transport phenomenon of a heat source of a given shape across the entire size range. Herein, to do this for a heat source embedded in an infinite medium, we derive a new set of modified ballistic–diffusive equations by analyzing the cause of the erroneous results observed in a steady-state solution of the original ballistic-diffusive equations. We demonstrate their ease and accuracy by obtaining the effective thermal conductivity for a spherical nanoparticle embedded in an infinite medium in an explicit closed-form and comparing it with that obtained by the Boltzmann transport equation (differences estimated as <3%).

Thermal Properties and Phonon Spectral Characterization of Synthetic Boron Phosphide for High Thermal Conductivity Applications.

Heat dissipation is an increasingly critical technological challenge in modern electronics and photonics as devices continue to shrink to the nanoscale. To address this challenge, high thermal conductivity materials that can efficiently dissipate heat from hot spots and improve device performance are urgently needed. Boron phosphide is a unique high thermal conductivity and refractory material with exceptional chemical inertness, hardness, and high thermal stability, which holds high promises for many practical applications. So far, however, challenges with boron phosphide synthesis and characterization have hampered the understanding of its fundamental properties and potential applications. Here, we describe a systematic thermal transport study based on a synergistic synthesis-experimental-modeling approach: we have chemically synthesized high-quality boron phosphide single crystals and measured their thermal conductivity as a record-high 460 W/mK at room temperature. Through nanoscale ballistic transport, we have, for the first time, mapped the phonon spectra of boron phosphide and experimentally measured its phonon mean free-path spectra with consideration of both natural and isotope-pure abundances. We have also measured the temperature- and size-dependent thermal conductivity and performed corresponding calculations by solving the three-dimensional and spectral-dependent phonon Boltzmann transport equation using the variance-reduced Monte Carlo method. The experimental results are in good agreement with that predicted by multiscale simulations and density functional theory, which together quantify the heat conduction through the phonon mode dependent scattering process. Our finding underscores the promise of boron phosphide as a high thermal conductivity material for a wide range of applications, including thermal management and energy regulation, and provides a detailed, microscopic-level understanding of the phonon spectra and thermal transport mechanisms of boron phosphide. The present study paves the way toward the establishment of a new framework, based on the phonon spectra-material structure relationship, for the rational design of high thermal conductivity materials and nano- to multiscale devices.

Phonon Boltzmann Transport Equation based modeling of time domain thermo-reflectance experiments

Time Domain Thermo-Reflectance (TDTR) experiments have been recently identified as a viable pathway toward extracting the phonon mean free path spectrum of semiconductor materials. However, this requires an intervening model. It is now widely believed that the frequency and polarization dependent phonon Boltzmann Transport Equation (BTE) is the most suitable model for this purpose. In this article, TDTR experiments are simulated using large-scale parallel computations of the phonon BTE in a two-dimensional computational domain. Silicon is used as the candidate substrate material. Simulations are performed for multiple pulse and modulation cycles of the TDTR pump laser. This requires resolution of a picosecond laser pulse within a computational timeframe that spans several hundreds of nanoseconds. The metallic transducer layer on top of the substrate is modeled using the Fourier law and coupled to the BTE within the silicon substrate. Studies are conducted for four different laser spot sizes and two different modulation frequencies. The BTE results are fitted to the Fourier law, and effective thermal conductivities are extracted. It is demonstrated that the time delay of the probe laser could have a significant impact on the fitted (extracted) thermal conductivity value. The modulation frequency is found to have negligible effect on the thermal conductivity, while the spot size variation exhibits significant impact. Both trends are found to be in agreement with experimental observations. The thermal conductivity accumulation function is also computed, and the effect of the mean free path spectrum on the thermal conductivity suppression is delineated.

Thermal conduction in Si and SiGe phononic crystals explained by phonon mean free path spectrum

Thermal phonon transport in single-crystalline Si, amorphous SiGe, and poly-SiGe nanostructures was investigated experimentally at room temperature. The characteristic length dependence of thermal conductivity was compared across these three materials by changing the shortest distance between the circular holes of phononic crystals formed in the membranes. The dependences clearly differ for these materials, and these differences can be explained by the thermal phonon mean free path spectra of the three materials. Nanostructuring has a larger impact on thermal conductivity reduction when the characteristic length is comparable to that in the region where the thermal phonon mean free path spectrum is dense. The results suggest that thermal phonon mean free path spectra can be estimated qualitatively by thermal conductivity measurements with characteristic length sweeps.

Quenched phonon drag in silicon nanowires reveals significant effect in the bulk at room temperature.

Existing theory and data cannot quantify the contribution of phonon drag to the Seebeck coefficient (S) in semiconductors at room temperature. We show that this is possible through comparative measurements between nanowires and the bulk. Phonon boundary scattering completely quenches phonon drag in silicon nanowires enabling quantification of its contribution to S in bulk silicon in the range 25-500 K. The contribution is surprisingly large (∼34%) at 300 K even at doping of ∼3 × 10(19) cm(-3). Our results contradict the notion that phonon drag is negligible in degenerate semiconductors at temperatures relevant for thermoelectric energy conversion. A revised theory of electron-phonon momentum exchange that accounts for a phonon mean free path spectrum agrees well with the data.

Systematic Studies of Periodically Nanoporous Si Films for Thermoelectric Applications

ABSTRACTAs the major heat carriers in dielectrics and semiconductors, phonons are strongly scattered by boundaries and interfaces at the nanoscale, which can lead to a significantly reduced lattice thermal conductivity kL. In recent years, such phonon size effects have been used to enhance the thermoelectric performance of various nanostructured materials. With dramatically reduced kL and bulk-like electrical properties, high thermoelectric performance has been demonstrated for nanoporous Si films at room temperature. Despite these encouraging results, however, challenges still exist in the theoretical explanation of the observed low kL values. Existing studies mainly attribute the observed low kL to phononic effects and/or amorphous pore edges. These two effects can be separated when the specific heat of the film can be measured along with kL to provide more insight into the phonon dispersion modification. In this work, both the specific heat and k of a suspended nanoporous Si film is extracted from the 3ω measurements. The result is compared to the reported kL values of various porous Si films. The influence of employed phonon mean free path spectrum on the data analysis is discussed.

Phonon mean free path spectrum and thermal conductivity for Si1−xGex nanowires

We reformulate the linearized phonon Boltzmann transport equation by incorporating the direction-dependent phonon-boundary scattering, and based on this equation, we study the thermal conductivity of Si1−xGex nanowires and derive their phonon mean free path spectrum. Due to the severe suppression of high-frequency phonons by alloy scattering, the low frequency phonons in Si1−xGex nanowires have a much higher contribution to the thermal conductivity than pure silicon nanowires. We also find that Si1−xGex nanowires possess a stronger length-dependent, weaker diameter-dependent, and weaker surface roughness-dependent thermal conductivity than silicon nanowires. These findings are potentially useful for engineering Si1−xGex nanowires for thermoelectric applications.

Universal phonon mean free path spectra in crystalline semiconductors at high temperature

Thermal conductivity in non-metallic crystalline materials results from cumulative contributions of phonons that have a broad range of mean free paths. Here we use high frequency surface temperature modulation that generates non-diffusive phonon transport to probe the phonon mean free path spectra of GaAs, GaN, AlN, and 4H-SiC at temperatures near 80 K, 150 K, 300 K, and 400 K. We find that phonons with MFPs greater than 230 ± 120 nm, 1000 ± 200 nm, 2500 ± 800 nm, and 4200 ± 850 nm contribute 50% of the bulk thermal conductivity of GaAs, GaN, AlN, and 4H-SiC near room temperature. By non-dimensionalizing the data based on Umklapp scattering rates of phonons, we identified a universal phonon mean free path spectrum in small unit cell crystalline semiconductors at high temperature.

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.