Thermal Conductivity Of Superlattices Research Articles

Thermal conductivity measurement of InGaAs/InGaAsP superlattice thin films

The thermal conductivities of InGaAs/InGaAsP superlattices with different period lengths were measured from 100 to 320 K using 3θ method. In this temperature range, the thermal conductivities were found to decrease with an increase in temperature. For the period length-dependant thermal conductivity, the minimum value does exist at a certain period length, which demonstrates that at a short period length, superlattice thermal conductivity increases with a decrease in the period length. When the period is longer than a certain period length, the interface thermal resistance dominates in phonon transport. The experimental and theoretical results confirmed the previous predictions from the lattice dynamics analysis, i.e. with the increase in period length, the dominant mechanisms of phonon transport in superlattices will shift from wave mode to particle mode. This is crucial for the cutoff of the phonons and lays a sound foundation for the design of superlattice structures.

Lattice dynamics investigations of phonon thermal conductivity of Si∕Ge superlattices with rough interfaces

Phonon thermal conductivities in both growth and in-plane directions of Si∕Ge superlattices (SLs) with perfect and rough interfaces are calculated by using a lattice dynamics model. In addition to the general trend, the results show that there exist fluctuations of thermal conductivity in both directions for SLs with even or odd number of layers when the layer thickness is small. Thermal conductivities in both directions of Si∕Ge SLs with rough interfaces are shown to be much lower than those of SLs with perfect interfaces. To understand the influences of rough interfaces, thermal conductivities of homogeneous alloy are further calculated and compared. The results show that along the in-plane direction, the thermal conductivity of SLs with rough interfaces is about the same as that of random alloy, while in the growth direction it is lower than that of the random alloy.

Minimum superlattice thermal conductivity from molecular dynamics

The dependence of superlattice thermal conductivity on period length is investigated by molecular dynamics simulation. For perfectly lattice matched superlattices, a minimum is observed when the period length is of the order of the effective phonon mean free path. As temperature decreases and interatomic potential strength increases, the position of the minimum shifts to larger period lengths. The depth of the minimum is strongly enhanced as mass and interatomic potential ratios of the constituent materials increase. The simulation results are consistent with phonon transmission coefficient calculations, which indicate increased stop bandwidth and thus strongly enhanced Bragg scattering for the same conditions under which strong reductions in thermal conductivity are found. When nonideal interfaces are created by introducing a 4% lattice mismatch, the minimum disappears and thermal conductivity increases monotonically with period length. This result may explain why minimum thermal conductivity has not been observed in a large number of experimental studies.

Thermal conductivity modeling of periodic two-dimensional nanocomposites

In this paper, the phonon Boltzmann equation model is established to study the phonon thermal conductivity of nanocomposites with nanowires embedded in a host semiconductor material. Special attention has been paid to cell--cell interaction using periodic boundary conditions. The simulation shows that the temperature profiles in nanocomposites are very different from those in conventional composites due to ballistic phonon transport at nanoscale. Such temperature profiles cannot be captured by existing models in literature. The general approach is applied to study silicon wire/germanium matrix nanocomposites. We predict the thermal conductivity dependence on the size of the nanowires and the volumetric fraction of the constituent materials. At constant volumetric fraction the smaller the wire diameter, the smaller is the thermal conductivity of periodic two-dimensional nanocomposites. For fixed silicon wire dimension, the lower the atomic percentage of germanium, the lower the thermal conductivity of the nanocomposites. Comparison is also made with the thermal conductivity of superlattices. The results of this study can be used to direct the development of high efficiency thermoelectric materials.

Engineering nanoscale phonon and photon transport for direct energy conversion

Nanostructures have a profound impact on the transport of heat and energy by electrons, phonons, and photons. In this paper, we will discuss some of the nanoscale heat transfer effects on phonon and photon transport and their implications for thermoelectric and thermophotovoltaic energy conversion technologies. For example, low thermal conductivity materials with good electrical properties are required in solid-state refrigerators and power generators to achieve high energy conversion efficiency. Various size effects on carrier transport in nanostructures can be utilized to engineer new structures with improved energy conversion efficiency. The thermal conductivity of superlattices will be used to illustrate the phonon transport characteristics in nanostructures. In another example, we will discuss some nanoscale thermal radiation phenomena, such as interference, tunneling, and surface waves, that can potentially be exploited to improve the efficiency of thermophotovoltaic power generation devices.

Lattice thermal conductivity in superlattices: molecular dynamics calculations with a heatreservoir method

We report on a molecular dynamics study of the cross-plane lattice thermal conductivityin GaAs/AlAs superlattices. The layers of the superlattice are modelled by athree-dimensional face centred cubic lattice with cubic anharmonicity, and with atomicscale roughness at the interfaces. We perform the simulation of heat flow for a section of asuperlattice with high- and low-temperature thermal reservoirs attached to opposite ends.The calculation reproduces qualitatively the features observed experimentally, i.e., thedramatic reduction of the conductivity relative to the conductivity of the bulk constituentmaterials, and the variation of the thermal conductivity with the superlattice repeatdistance. The results are also in agreement with those obtained previously by Daly et al (2002 Phys. Rev. B 66 024301) who determined the thermal conductivity fromthe time taken for an initially inhomogeneous temperature distribution to relax.

Partially coherent phonon heat conduction in superlattices

In this paper, the phonon thermal conductivity of semiconductor superlattices is calculated with the use of a modified lattice dynamics model, in which an imaginary wave vector is added. The mean free path caused by diffuse interface scattering is included in the imaginary wave vector. This model combines the effects of phonon confinement and diffuse interface scattering on the thermal conductivity in superlattices, and is applicable to phonon transport in the partially coherent regime, where bulk and superlattice phonon modes mix up. The theoretical results for the GaAs/AlAs superlattices are compared with the experimental data. The period thickness dependence and temperature dependence of the thermal conductivity in the GaAs/AlAs superlattices can be well explained by this model.

LATTICE DYNAMICS STUDY OF ANISOTROPIC HEAT CONDUCTION IN SUPERLATTICES

Past studies suggest that phonon confinement and the associated group velocity reduction are the causes of the observed drop in the cross-plane thermal conductivity of semiconductor superlattices. In this work, we investigate the contribution of phonon confinement to the in-plane thermal conductivity of superlattices and the anisotropic effects of phonon confinement on the thermal conductivity in different directions, using a lattice dynamics model. The dispersion relation in a free-standing quantum well is calculated and compared with superlattices. We find that the reduced phonon group velocity due to phonon confinement may account for the dramatic reduction in the cross-plane thermal conductivity in superlattices, but the in-plane thermal conductivity drop, caused by the reduced group velocity, is small and cannot explain the reported experimental results. This suggests that the reduced relaxation time due to diffuse interface phonon scattering, dislocation scattering, etc., should make a major contribution to the in-plane thermal conductivity reduction in superlattices.

Conservation of Lateral Momentum in Heterostructure Integrated Thermionic Coolers

ABSTRACTThin film thermionic coolers use selective emission of hot electrons over a heterostructure barrier layer from emitter to collector resulting in evaporative cooling. In this paper a detailed theory of electron transport perpendicular to the multilayer superlattice structures is presented. Using Fermi-Dirac statistics, density-of-states for a finite quantum well and the quantum mechanical reflection coefficient, the currentvoltage characteristics and the cooling power density are calculated. The resulting equations are valid in a wide range of temperatures and electric fields. It is shown that conservation of lateral momentum plays an important role in the device characteristics. If the lateral momentum of the hot electrons is conserved in the thermionic emission process, only carriers with sufficiently large kinetic energy perpendicular to the barrier can pass over it and cool the emitter junction. However, if there is no conservation of lateral momentum, the number of electrons participating in thermionic emission will dramatically increase. The theoretical calculations are compared with the experimental dark current characteristics of quantum well infrared photodetectors and good agreement over a wide temperature range is obtained. Calculations for InGaAs/InGaAsP superlattice structures show that the effective thermoelectric power factor (electrical conductivity times the square of the effective Seebeck coefficient) can be improved comparing to that of bulk material. We will also discuss methods by which the conservation of lateral momentum in thermionic emission process can be altered such as by creating a controlled roughness at the interface of the superlattice barriers. The improvement in the effective power factor through thermionic emission can be combined with the other methods to reduce the phonon thermal conductivity in superlattices and thus obtain higher thermoelectric figure-of-merit ZT.

Phonon engineering in nanostructures for solid-state energy conversion

Solid-state energy conversion technologies such as thermoelectric and thermionic refrigeration and power generation require materials with low thermal conductivity but good electrical conductivity, which are difficult to realize in bulk semiconductors. Nanostructures such as quantum wires and quantum wells provide alternative approaches to improve the solid-state energy conversion efficiency through size effects on the electron and phonon transport. In this paper, we discuss the possibility of engineering the phonon transport in nanostructures, with emphases on the thermal conductivity of superlattices. Following a general discussion on the directions for reducing the lattice thermal conductivity in nanostructures, specific modeling results on the phonon transport in superlattices will be presented and compared with recent experimental studies to illustrate the potential approaches and remaining questions.

Minimum thermal conductivity of superlattices

The phonon thermal conductivity of a multilayer is calculated for transport perpendicular to the layers. There is a crossover between particle transport for thick layers to wave transport for thin layers. The calculations show that the conductivity has a minimum value for a layer thickness somewhat smaller then the mean free path of the phonons.

Lattice Dynamics Study of Anisotropic Heat Conduction in Superlattices

ABSTRACTPast studies on the thermal conductivity suggest that phonon confinement and the associated group velocity reduction are the causes of the observed drop in the cross-plane thermal conductivity of semiconductor superlattices. In this work, we investigate the contribution of phonon confinement to the in-plane thermal conductivity of superlattices and the anisotropic effects of phonon confinement on the thermal conductivity in different directions, using a lattice dynamics model. We find that the reduced phonon group velocity due to phonon confinement may account for the dramatic reduction in the cross-plane thermal conductivity, but the in-plane thermal conductivity drop, caused by the reduced group velocity, is much less than the reported experimental results. This suggests that the reduced relaxation time due to diffuse interface phonon scattering, dislocation scattering, etc, should make major contribution to the in-plane thermal conductivity reduction.

Thermal Conductivity Of Bi/Sb Superlattice

ABSTRACTThe temperature-dependent cross-plane thermal conductivity of a 1-μm thick 50Å Bi / 50Å Sb superlattice on a (111) CdTe substrate was measured, using a differential 3-ω method. This method uses the temperature difference between the superlattice sample and a reference sample to calculate its cross-plane thermal conductivity. However, the substrate thermal conductivity is comparable to or smaller than the superlattice thermal conductivity near room temperature. This results in a very small or negative temperature difference, making the existing data reduction method inapplicable. Based on an improved model, the temperature-dependent thermal conductivity of the Bi/Sb superlattice is obtained and is about half of the literature value of Bi0.5Sb0.5 bulk alloy.

Phonon group velocity and thermal conduction in superlattices

With the use of a face-centered cubic model of lattice dynamics we calculate the group velocity of acoustic phonons in the growth direction of periodic superlattices. Comparing with the case of bulk solids, this component of the phonon group velocity is reduced due to the flattening of the dispersion curves associated with Brillouin-zone folding. The results are used to estimate semiquantitatively the effects on the lattice thermal conductivity in Si/Ge and GaAs/AlAs superlattices. For a Si/Ge superlattice an order of magnitude reduction is predicted in the ratio of superlattice thermal conductivity to phonon relaxation time [consistent with the results of P. Hyldgaard and G. D. Mahan, Phys. Rev. B 56, 10 754 (1997)]. For a GaAs/AlAs superlattice the corresponding reduction is rather small, i.e., a factor of 2--3. These effects are larger for the superlattices with larger unit period, contrary to the recent measurements of thermal conductivity in superlattices.

Phonon superlattice transport

We predict in Si/Ge superlattices a dramatic high-temperature suppression of the perpendicular thermal transport. Total internal reflection confines the superlattice modes and significantly reduces the average group velocity at nonzero in-plane momenta. These consequences of the acoustic mismatch cause at high temperatures an order-of-magnitude reduction in the ratio of superlattice thermal conductivity to phonon relaxation time.

Size and Interface Effects on Thermal Conductivity of Superlattices and Periodic Thin-Film Structures

Superlattices consisting of alternating layers of extremely thin films often demonstrate strong quantum size effects that have been utilized to improve conventional devices and develop new ones. The interfaces in these structures also affect their thermophysical properties through reflection and transmission of heat carriers. This work develops models on the effective thermal conductivity of periodic thin-film structures in the parallel direction based on the Boltzmann transport equation. Different interface conditions including specular, diffuse, and partially specular and partially diffuse interfaces, are considered. Results obtained from the partially specular and partially diffuse interface scattering model are in good agreement with experimental data on GaAs/AlAs superlattices. The study shows that the atomic scale interface roughness is the major cause for the measured reduction in the superlattice thermal conductivity. This work also suggests that by controlling interface roughness, the effective thermal conductivity of superlattices made of bulk materials with high thermal conductivities can be reduced to a level comparable to those of amorphous materials, while maintaining high electrical conductivities. This suggestion opens new possibilities in the search of high efficiency thermoelectric materials.

Thermal Conductivity and Heat Transfer in Superlattices

AbstractUnderstanding the thermal conductivity and heat transfer processes in superlattice structures is critical for the development of thermoelectric materials and devices based on quantum structures. This work reports progress on the modeling of thermal conductivity of superlattice structures. Results from the models established based on the Boltzmann transport equation could explain existing experimental results on the thermal conductivity of semiconductor superlattices in both in plane and cross-plane directions. These results suggest the possibility of engineering the interfaces to further reduce thermal conductivity of superlattice structures.

The Physics of Phonons

Elements of crystal symmetry: Direct lattice Reciprocal lattice Brillouin zone Crystal structure Point groups Space groups Symmetry of the Brillouin zone Jones zone Surface Brillouin zone Matrix representations of point groups. Lattice dynamics in harmonic approximation - semiclassical treatment: Introduction Lattice dynamics of a linear chain Lattice dynamics of three-dimensional crystals - phenomenological models Density of normal modes Numerical calculation of g(w) Lattice heat capacity. Lattice dynamics in the harmonic approximation - ab initio treatment: Introduction The frozen-phonon approach The linear response approach The planar force constant method. Anharmonicity: Introduction Hamiltonian of a general three-dimensional crystal Effect of anharmonicity on phonon states Effects of the selection rules on three-phonon processes Hamiltonian of an anharmonic elastic continuum Evaluation of three-phonon scattering strengths The quasi-harmonic approximation and Grueneisen's constant. Theory of lattice thermal conductivity: Introduction Relaxation-time methods Gree-Kubo linear response theory Second sound and Poiseuille flow of phonons. Phonon scattering in solids: Boundary scattering Scattering by static imperfections Phonon scattering in alloys Anharmonic scattering Phonon-electron scattering in doped semiconductors Phonon scattering due to magnetic impurities in semiconductors Phonon scattering from tunnelling states of impurities Phonon-photon interaction. Analysis of phonon relaxation and thermal conductivity results: Anharmonic decay of phonons Lattice thermal conductivity of undoped semiconductors and insulators Non-metallic crystals with high thermal conductivity Thermal conductivity of complex crystals Low-temperature thermal conductivity of doped semiconductors. Phonons in low dimensional solids: Introduction Surface vibrational modes Attenuation of surface phonons Phonons in superlattices Thermal conductivity of superlattices. Phonons in impure and mixed crystals: Introduction Localised vibrational modes in semiconductors Experimental studies of long-wavelength optical phonons in mixed crystals Theoretical models for long-wavelength optical phonons in mixed crystals Phonon conductivity of mixed crystals. Phonons in quasi-crystalline and amorphous solids: Introduction Phonons in quasi-crystals Structure and vibrational excitations of amorphous solids Vibrational properties of amorphous solids Low-temperature properties of amorphous solids. Phonon spectroscopy: Introduction Heat pulse technique Superconducting tunnel junction technique Optical techniques Phonons from Landau levels in 2DEG Phonon focusing and imaging Frequency crossing phonon spectroscopy Phonon echoes. Phonons in liquid helium: Introduction Dispersion curve and elementary excitations Specific heat Interactions between the excitations Kapitza resistance Quantum evaporation. Appendices: Density functional formalism The pseudopotential method Evaluation of integrals in sections 6.4.1.4 Negative-definitenss of the phonon off-diagonal operator ^D*L. References. Index.

Thermal conductivity of superlattices

The lattice thermal conductivity of superlattices is shown to depend on a new kind of umklapp scattering process, called a mini-umklapp, associated with the mini-Brillouin zone of the superlattice. Expressions for three-phonon mini-umklapp-scattering matrix elements are obtained for superlattices consisting of lattice-matched simple-cubic layers. The temperature dependence of the thermal conductivity is evaluated using an extension of Callaway's phenomenological model.