Kenneth E. Goodson

Nanoscale thermal transport

Rapid progress in the synthesis and processing of materials with structure on nanometer length scales has created a demand for greater scientific understanding of thermal transport in nanoscale devices, individual nanostructures, and nanostructured materials. This review emphasizes developments in experiment, theory, and computation that have occurred in the past ten years and summarizes the present status of the field. Interfaces between materials become increasingly important on small length scales. The thermal conductance of many solid–solid interfaces have been studied experimentally but the range of observed interface properties is much smaller than predicted by simple theory. Classical molecular dynamics simulations are emerging as a powerful tool for calculations of thermal conductance and phonon scattering, and may provide for a lively interplay of experiment and theory in the near term. Fundamental issues remain concerning the correct definitions of temperature in nonequilibrium nanoscale systems. Modern Si microelectronics are now firmly in the nanoscale regime—experiments have demonstrated that the close proximity of interfaces and the extremely small volume of heat dissipation strongly modifies thermal transport, thereby aggravating problems of thermal management. Microelectronic devices are too large to yield to atomic-level simulation in the foreseeable future and, therefore, calculations of thermal transport must rely on solutions of the Boltzmann transport equation; microscopic phonon scattering rates needed for predictive models are, even for Si, poorly known. Low-dimensional nanostructures, such as carbon nanotubes, are predicted to have novel transport properties; the first quantitative experiments of the thermal conductivity of nanotubes have recently been achieved using microfabricated measurement systems. Nanoscale porosity decreases the permittivity of amorphous dielectrics but porosity also strongly decreases the thermal conductivity. The promise of improved thermoelectric materials and problems of thermal management of optoelectronic devices have stimulated extensive studies of semiconductor superlattices; agreement between experiment and theory is generally poor. Advances in measurement methods, e.g., the 3ω method, time-domain thermoreflectance, sources of coherent phonons, microfabricated test structures, and the scanning thermal microscope, are enabling new capabilities for nanoscale thermal metrology.

Phase Change Memory

In this paper, recent progress of phase change memory (PCM) is reviewed. The electrical and thermal properties of phase change materials are surveyed with a focus on the scalability of the materials and their impact on device design. Innovations in the device structure, memory cell selector, and strategies for achieving multibit operation and 3-D, multilayer high-density memory arrays are described. The scaling properties of PCM are illustrated with recent experimental results using special device test structures and novel material synthesis. Factors affecting the reliability of PCM are discussed.

Thermal Conductance of an Individual Single-Wall Carbon Nanotube above Room Temperature

The thermal properties of a suspended metallic single-wall carbon nanotube (SWNT) are extracted from its high-bias (I-V) electrical characteristics over the 300-800 K temperature range, achieved by Joule self-heating. The thermal conductance is approximately 2.4 nW/K, and the thermal conductivity is nearly 3500 Wm(-1)K(-1) at room temperature for a SWNT of length 2.6 mum and diameter 1.7 nm. A subtle decrease in thermal conductivity steeper than 1/T is observed at the upper end of the temperature range, which is attributed to second-order three-phonon scattering between two acoustic modes and one optical mode. We discuss sources of uncertainty and propose a simple analytical model for the SWNT thermal conductivity including length and temperature dependence.

A benchmark study on the thermal conductivity of nanofluids

This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or “nanofluids,” was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band (±10% or less) about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are (small) systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. [J. Appl. Phys. 81, 6692 (1997)], was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

Nanoscale thermal transport. II. 2003–2012

A diverse spectrum of technology drivers such as improved thermal barriers, higher efficiency thermoelectric energy conversion, phase-change memory, heat-assisted magnetic recording, thermal management of nanoscale electronics, and nanoparticles for thermal medical therapies are motivating studies of the applied physics of thermal transport at the nanoscale. This review emphasizes developments in experiment, theory, and computation in the past ten years and summarizes the present status of the field. Interfaces become increasingly important on small length scales. Research during the past decade has extended studies of interfaces between simple metals and inorganic crystals to interfaces with molecular materials and liquids with systematic control of interface chemistry and physics. At separations on the order of ∼1 nm, the science of radiative transport through nanoscale gaps overlaps with thermal conduction by the coupling of electronic and vibrational excitations across weakly bonded or rough interface...

PHONON SCATTERING IN SILICON FILMS WITH THICKNESS OF ORDER 100 NM

Although progress has been made in the ab initio simulation of lattice dynamics in semiconducting crystals, information about the relaxation of nonequilibrium lattice vibrations remains incomplete. This work studies the relaxation times of room-temperature thermal phonons through measurements of thermal conduction along monocrystalline silicon films of thickness down to 74 nm. A repetitive oxidation and etching process ensures that the purity and crystalline quality of the films are comparable with those of bulk samples. Phonon-interface scattering reduces the thermal conductivity by up to 50% at room temperature. The data indicate that the effective mean-free path of the dominant phonons at room temperature is close to 300 nm and thus much longer than the value of 43 nm predicted when phonon dispersion is neglected. This study indicates that a broad variety of lattice transport characteristics for bulk silicon can be obtained through measurements on carefully prepared silicon nanostructures. The present ...

Thermometry and Thermal Transport in Micro/Nanoscale Solid-State Devices and Structures

We review recent advances in experimental methods for high spatial-resolution and high time-resolution thermometry, and the application of these and related methods for measurements of thermal transport in low-dimensional structures. Scanning thermal microscopy (SThM) achieves lateral resolutions of 50 nm and a measurement bandwidth of 100 kHz: SThM has been used to characterize differences in energy dissipation in single-wall and multi-wall carbon nanotubes. Picosecond thermoreflectance enables ultrahigh time-resolution in thermal diffusion experiments and characterization of heat flow across interfaces between materials; the thermal conductance G of interfaces between dissimilar materials spans a relatively small range, 20<G<200 MW m -2 K -1 near room temperature. Scanning thermoreflectance microscopy provides nanosecond time resolution and submicron lateral resolution needed for studies of heat transfer in microelectronic, optoelectronic and micromechanical systems. A fully-micromachined solid immersion lens has been demonstrated and achieves thermal-radiation imaging with lateral resolution at far below the diffraction limit, <2 μm. Microfabricated metal bridges using electrical resistance thermometry and joule heating give precise data for thermal conductivity of single crystal films, multilayer thin films, epitaxial superlattices, polycrystalline films, and interlayer dielectrics. The room temperature thermal conductivity of single crystal films of Si is strongly reduced for layer thickness below 100 nm. The through-thickness thermal conductivity of Si-Ge and GaAs-AlAs superlattices has recently been shown to be smaller than the conductivity of the corresponding alloy. The 3ω method has been recently extended to measurements of anisotropic conduction in polyimide and superlattices. Data for carbon nanotubes measured using micromachined and suspended heaters and thermometers indicate a conductivity near room temperature greater than diamond.

Heat Generation and Transport in Nanometer-Scale Transistors

As transistor gate lengths are scaled towards the 10-nm range, thermal device design is becoming an important part of microprocessor engineering. Decreasing dimensions lead to nanometer-scale hot spots in the transistor drain region, which may increase the drain series and source injection electrical resistances. Such trends are accelerated by the introduction of novel materials and nontraditional transistor geometries, including ultrathin body, FinFET, or nanowire devices, which impede heat conduction. Thermal analysis is complicated by subcontinuum phenomena including ballistic electron transport, which reshapes the heat generation region compared with classical diffusion theory predictions. Ballistic phonon transport from the hot spot and between material boundaries impedes conduction cooling. The increased surface to volume ratio of novel transistor designs also leads to a larger contribution from material boundary thermal resistance. This paper surveys trends in transistor geometries and materials, from bulk silicon to carbon nanotubes, along with their implications for the thermal design of electronic systems

Measurement and modeling of self-heating in SOI nMOSFET's

Self-heating in SOI nMOSFETs is measured and modeled. Temperature rises in excess of 100 K are observed for SOI devices under static operating conditions. The measured temperature rise agrees well with the predictions of an analytical model and is a function of the silicon thickness, buried oxide thickness, and channel-metal contact separation. Under dynamic circuit conditions, the channel temperatures are much lower than predicted from the static power dissipation. This work provides the foundation for the extraction of device modeling parameters for dynamic operation (at constant temperature) from static device characterization data (where temperature varies widely). Self-heating does not greatly reduce the electromigration reliability of SOI circuits, but might influence SOI device design, e.g., requiring a thinner buried oxide layer for particular applications and scaled geometries. >

Negative Differential Conductance and Hot Phonons in Suspended Nanotube Molecular Wires

Freely suspended metallic single-walled carbon nanotubes (SWNTs) exhibit reduced current carrying ability compared to those lying on substrates, and striking negative differential conductance at low electric fields. Theoretical analysis reveals significant self-heating effects including electron scattering by hot nonequilibrium optical phonons. Electron transport characteristics under strong self-heating are exploited for the first time to probe the thermal conductivity of individual SWNTs (approximately 3600 W m-1 K-1 at T=300 K) up to approximately 700 K, and reveal a 1/T dependence expected for umklapp phonon scattering at high temperatures.