Taofang Zeng

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 SiO 2 and diamond films on Si substrates, representative of thin-film materials with low and high thermal conductivity. It is found that for a SiO 2 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 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.

Thermal conductivity of skutterudite thin films and superlattices

Experimental results on the temperature-dependent cross-plane thermal conductivity of skutterudite thin films are presented. The films examined include IrSb3, CoSb3, and Ir0.5Co0.5Sb3 single layers, and IrSb3/CoSb3 superlattices that are grown by pulsed-laser deposition. A differential 3ω method is used to measure the cross-plane thermal conductivity of these films from 80 to 300 K. The experimental results show a significant reduction in their thermal conductivity values compared to those of their corresponding bulk samples reported in literature. Possible mechanisms contributing to the thermal conductivity reduction are discussed.

Nonequilibrium phonon and electron transport in heterostructures and superlattices

Electron and phonon transport in nanostructures is characterized by interface effects and can deviate significantly from the assumption of local thermal equilibrium underlying the transport equations at macroscale. In this article, we elucidate some basic nonequilibrium characteristics for phonon and electron transport in thin films and superlattices. Based on a discussion of the thermal boundary resistance at a single interface, the nonequilibrium nature of phonon transport and the consistency of temperature definition are emphasized. Using a consistent definition for temperature, we obtain simplified expressions for phonon transport in thin films and superlattices, and give examples to illustrate the effectiveness of the approximation by comparing the thermal conductivity of thin films and superlattices obtained from solving the Boltzmann equation with the current approximation. Similar nonequilibrium processes occur for the electron transport in nanostructures. An example is given on concurrent electron and phonon transport in double heterojunction structures, considering the nonequilibrium transport processes both within the electron and phonon subsystems and between them. Finally, the ballistic-diffusive equations are introduced as an approximation to the Boltzmann equation. These equations should be applicable to transport problems from nano- to mascroscales, as well as for fast temporal processes.

Phonon heat conduction in micro- and nano-core-shell structures with cylindrical and spherical geometries

This study examines the definition of temperatures at interfaces and within thin films when the phonons are in nonequilibrium, and provides a general solution for the temperature distribution within the micro- and nanocylindrical and spherical shells. By applying the Boltzmann transport equation and the established methods of thermal radiation heat transfer, analytical solutions for the temperature distribution and equivalent thermal conductivity are obtained for micro- and nanocylindrical and spherical shells. The study shows that significant drops in temperature occur at the interfaces of micro- and nanocylindrical and spherical shells. For cylindrical shells, the effective thermal conductivity is determined by both the film thickness and the diameter of the inner cylinder. For spherical shells, the effective conductivity is mainly determined by the size of the inner sphere.

ENERGY CONVERSION IN HETEROSTRUCTURES FOR THERMIONIC COOLING

The energy conversion between electrons and phonons in a heterostructure is studied for thermionic cooling based on the hot electron approximation. An analytical model is established to study the energy transfer of electrons and phonons on the basis of average values of physical properties. In the model, electrons conduct heat, deposit heat to the local phonons and gain energy from the electric field in the thin film. In the hot substrate (anode), electrons lose their energy quickly to the phonons. Calculations show that the coefficient of performance for those heterojunction coolers is low (below 0.8 for the cases calculated), while the maximum temperature difference between the cold side and the hot side can be high. In order to have a high coefficient of performance, the energy exchange rate between electrons and phonons in the thin film should be small, and it should be large in the substrate to better reject the heat generated in the film.

Interplay between thermoelectric and thermionic effects in heterostructures

When electrons sweep through a double-heterojunction structure, there exist thermionic effects at the junctions and thermoelectric effects in the film. While both thermoelectric and thermionic effects have been studied for refrigeration and power generation applications separately, their interplay in heterostructures is not understood. This paper establishes a unified model including both thermionic and thermoelectric processes based on the Boltzmann transport equation for electrons and the nonequilibrium interaction between electrons and phonons. Approximate solutions are obtained, leading to the electron temperature and Fermi level distributions inside heterostructures. These quantities are discontinuous at the interfaces as a consequence of the highly nonequilibrium transport when the film thickness is much smaller than the electron mean free path. The electron temperature and Fermi level discontinuities at the interfaces determine the thermionic effect, while their gradients inside the film govern the...

Nonequilibrium electron and phonon transport and energy conversion in heterostructures

Abstract We establish a unified model dealing with the transport of electrons and phonons in double heterojunction structures with the coexistence of three nonequilibrium processes: (1) nonequilibrium among electrons, (2) nonequilibrium among phonons, and (3) nonequilibrium between electrons and phonons. Using this model, we investigate the energy conversion efficiency based on concurrent thermoelectric and thermionic effects on electrons and size effects on electrons and phonons. It is found that heterostructures can have an equivalent figure of merit higher than the corresponding bulk materials.

Thermal conductivity of Si/Ge superlattices

We report in this paper the thermal conductivity measurement of Si/Ge superlattices as a function of the temperature and the period thickness. The symmetrized Si/Ge superlattices are grown by MBE on Si substrates with a graded buffer layer. A comparative 3/spl omega/ method is used to measure the thermal conductivity of the buffer and the superlattices between 80K-300K. The thermal conductivity is carried out in conjunction with X-ray and TEM sample characterization. The measured thermal conductivity values are lower than that of their corresponding alloys and show a decreasing trend with increasing period thickness which are corroborated with the TEM characterization of the dislocation density.

Nonequilibrium electron and phonon transport in heterostructures for energy conversion

We establish the first unified model dealing with the transport of electron and phonon in double heterojunction structures with the coexistence of three nonequilibrium processes: (1) nonequilibrium among electrons, (2) nonequilibrium among phonons, and (3) nonequilibrium between electrons and phonons. Using this model, we investigate the energy conversion efficiency based on concurrent thermoelectric and thermionic effects on electrons and size effects on electrons and phonons. It is found that heterostructures can have an equivalent figure of merit higher than the corresponding bulk materials.