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Kapitza Resistance of Laser-Annealed Surfaces
Abstract
Our understanding of the phonon processes at the interfaces between two media is still quite rudimentary. Particularly notorious is the helium-solid interface, where the accoustic impedances differ by a large amount. It is well known that the Kapitza resistance, i.e. the thermal boundary resistance between helium and a solid, is usually up to 100 times smaller than predicted by the acoustic theory as formulated by Khalatnikov [1]. However, it was shown by J. WEBER et al. [2] that there was no discrepancy at surfaces of freshly cleaved crystals, i.e. at surfaces of exceptional good quality. Thus it is clear that surface irregularities must be responsible for the anomalous Kapitza resistance. Little progress has been made, however, in the understanding of how these irregularities mediate the anomalously strong phonon transmission.
Solids usually occur as polycrystalline aggregates. Although their macroscopic physical properties may then be averaged over a large number of randomly oriented microcrystals, nevertheless the local environment of almost every individual atom is totally ordered. Thus attempts to understand the physical properties of most solids begin from the model of a single crystal, with the atoms arranged on an infinite lattice. In contrast, a small number of materials occur in an amorphous state with the disordered structure of a glass. Such a structure is not thermodynamically stable and can be visualized as a supercooled liquid that is slowly relaxing back to its equilibrium crystalline state over a long period of time. It is only recently that significant advances have been made in our understanding of amorphous structures as the result, particularly, of low-temperature experiments. We shall review some of the current ideas in §2.6 and §3.5, but the main theme of chapters 2 and 3 refers to crystalline solids.
The phenomenon of desorption has fired the imaginations of scientists for decades, leading them, at times, to the very frontiers of knowledge. For example, the first splitting of the atom — J. J. Thomson’s discovery of the electron in 1896 — was accomplished when he realized he could improve the vacuum in his cathode ray tubes by baking them before they were sealed. Thomson’s insight may have been the first important application of thermal desorption kinetics, a subject we shall explore in some detail. On a more prosaic level, any scientist who has spent lonely and frustrating hours waiting for an experimental system to reach high vacuum was most likely contending with the kinetics of desorption.
Acoustic phonons in the terahertz range, with energies from a few meV to tens of meV interact effectively with various electronic states (electrons, holes, excitons, local states), and thus participate in many electronic processes in semiconductors.
Over the years luminescence has became a powerful technique for the detection of terahertz acoustic phonons in crystals [1], Used mainly in insulators the method is based on the interaction of nonequilibrium phonons with electronic emitting states of “probe” impurities in photoexcited crystals (such as ruby, doped flourite, etc.). The technique has an advantage over the methods using superconducting devices because of a much wider spectral range of phonon frequencies and the lack of the boundary between the crystal and detector.
More than fifty years after its discovery, the Kapitza resistance is still under debate. New information can be obtained from experiments with angular resolution of the phonons emitted into the solid.
It is now well established from cleaving [1] and laser annealing [2,3] experiments that the anomalous Kapitza transmission is caused by surface defects. Furthermore, apparently all experimentally observed phenomena can be described with a phenomonological defect model [4]. This model requires the presence of two-level states at the surface with splittings in the range of typical phonon energies, i.e. about 1 meV.
This chapter presents the investigations on the anomalous Kapitza thermal boundary resistances between liquid 3He and metal particles observed at mK temperatures. The acoustic mismatch (AM) theory is explained in a different manner from the conventional procedure based on phonon transmission and reflection at the solid–liquid He interface. This enables treating in a simple way the Kapitza resistance between a finite-size system such as small particles and liquid 3He. The experimental data for RK both at mK temperatures and above about 1 K are compared with the predictions of the AM theory. The Fermi liquid theory for the Kapitza resistance RK is explained in the chapter, where the emphasis is laid on the theoretical treatment of the heat transfer mechanisms due to both zero-sound excitations and single quasiparticle excitations. The effect of the elastic softening of sintered powders on the anomalous behavior of the Kapitza resistance observed at the liquid 3He-sintered powder interfaces.
Several alternative neutrino detection schemes are described briefly and compared. It is suggested that a ballistic-phonon experiment might be promising. In such an experiment the amplitude received at a bolometer would depend on the distance it is from the neutrino event, and also on the direction because of phonon focusing, so several bolometers suggested to locate the event position from the difference in arrival times. The design of such an experiment is discussed assuming the phonons are detected by conventional superconducting bolometers. Determination of the direction of neutrino flux would be obtained from a study of the distribution of direction of the tracks of recoiling electrons or nuclei. The problem of smearing out the effective source over a distance of approximately a mean free path is addressed, and the need for high-resolution phonon focusing studies is expressed. (LEW)
We have studied the phonon transmission from ultraclean Si(111) surfaces into liquid helium by the phonon pulse technique. Reflection experiments and angular resolving transmission experiments were performed to measure the absolute value of the transmission coefficient and its dependence on the phonon emission angle into the solid. Clean samples etched conventionally in dilute HF show a significant anomalous transmission. An additional etch step in highly buffered HF (i.e., NH4F) with a pH-value of 7.8 reduces the transmission coefficient drastically. Local inhomogeneities of the transmission coefficient caused by the deposition of water molecules on the surface could be visualized by the enhanced transmission. We found that the observed anomalous transmission is caused by mass defects.
Perfect surfaces were prepared by laser annealing of Si in situ at an ambient temperature of 1 K. Gold atoms were deposited onto these surfaces by using a laser-evaporation technique. At the same time, the anomalous Kapitza transmission was probed by measuring the phonon reflection at these surfaces. It is found that the Kapitza anomaly is absent at the laser-annealed surfaces. Coverages as low as 0.02 atomic layer of Au, however, restore the anomaly. The anomalous transmission at the Au-covered surfaces increases weakly with phonon frequency. The data are in very good agreement with the defect model of Kinder if a deformation potential of 0.4 eV and an energy-independent density of states are used as parameters.
A simple model is presented of the thermal impedance encountered in the transfer of heat between a dielectric solid and a superconducting metal containing defects, defects which could be introduced by deformation. The model is consistent with new as well as published data, and in particular explains an anomalously large thermal impedance in superconducting aluminum near 0.1 K.
Grain boundaries play a key role in determining several key properties of polycrystalline laser ceramics. Heat transfer measurements
at low temperature constitute a good tool to probe grain boundaries. We review the results of heat transfer measurements in
polycrystalline Y3Al5O12 garnets as well as Y2O3 and Lu2O3 sesquioxide materials obtained by self-energy-driven sintering of nano-particles. The average phonon mean free path in Y3Al5O12 was found to be significantly larger than the average grain size and to scale with temperature as T
−2 at low temperature. Existing models describing the interaction between phonons and grain boundaries are reviewed. Correct
temperature dependence of the mean free path and order of magnitude of scattering rates were found by assuming the existence
of a grain boundary layer having acoustic properties different from those of the bulk. A different temperature dependence
of phonon mean free path was found for the sesquioxides and was ascribed to the stronger elastic anisotropy of these materials.
The thermal resistance associated to the grain boundaries of laser ceramics was found to be lower than in other dense polycrystalline
ceramic materials reported in the literature.
Triple-point dewetting is a well-known behaviour of molecular hydrogen and other van der Waals systems like noble gases on a solid substrate. Recent theoretical and experimental investigations (Phys. Rev. Lett. 88 (2002) 55702) suggest that it is caused primarily by the roughness of the substrate. Strain induced due to the mismatch of the lattice constant of the substrate and the growing layers of the adsorbed materials is increased by the micro-roughness of the substrate which eventually leads to the growth of only a thin solid film of the adsorbate. The dominating role of the substrate roughness is demonstrated, e.g., by ellipsometric measurements on smooth Si surfaces (rms ), where a thicker solid hydrogen film than the 3 monolayers on “usual” substrates is observed. We present a way to modify and improve the surface quality of substrates for such wetting studies of solid van der Waals films.
The effects of the mode conversion of high-frequency phonons on the diffuse scattering are discussed. The shape of phonon-reflection signals is obtained as a function of time for transverse phonons. The conclusion is that the mode-converted surface phonons are of considerable importance in order to interpret the cause of diffuse scattering of high-frequency phonons.
The Kapitza conductance problem is concerned with phonon transmission between solids and light atoms in both directions through the interface. The heat transfer across solid-solid interfaces is covered by Anderson in chapter 1. The magnitudes of the conduction between different solids can be well understood in terms of classical elasticity however when 3He, 4He, H2 or D2 is one of the materials the heat transfer is much greater than that predicted by classical theory. We shall tend to concentrate on 4He as there is more information available for this material than the others. We shall see that classical transmission does occur with liquid 4He but that there is another channel in parallel with it which carries most of the heat for temperatures ≳0.05K. Although many of the characteristics of this non-classical channel have been measured the microscopic process still remains a mystery. The subject has been reviewed by Pollack (1969) Snyder (1970) Challis (1974, 1975) Anderson (1976) Kinder et al. (1979) and Wyatt (1979).
We point out that our time-resolved measurements show zero phonon transmission for transverse phonons which would not have been observable with the traditional heat-transfer technique.
Monochromatic phonons were generated using superconducting tunneling junctions. These phonons were scattered at a solid surface. The backscattered phonons were detected by two different methods. A tunneling junction was used as a detector with a frequency threshold corresponding to its energy gap and a bolometer was used as a detector which is sensitive to all phonons regardless of frequency. When the scattering surface was exposed to helium gas or bulk liquid the two detector signals changed differently. This qualitative frequency analysis yields evidence for frequency conversion of phonons in the two atomic layers of helium at the surface.
- J Weber
- W Sandmann
- W Dietsche
- H Kinder
J. Weber, W. Sandmann, W. Dietsche, and H. Kinder: Phys. Rev. Lett.~,
1469 (1978)
- H Kinder
H. Kinder: Physica 107B, 549 (1981)
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