HEAT FLOW IN DIELECTRIC MATERIALS IN THE BOUNDARY-SCATTERING LIMIT

1967 ◽  
Vol 45 (2) ◽  
pp. 323-331 ◽  
Author(s):  
P. W. Matthews
Keyword(s):  
Heat Flow ◽  
Diffusion Equation ◽  
Bulk Material ◽  
Correction Term ◽  
Mean Free Path ◽  
Dielectric Materials ◽  
Dielectric Medium ◽  
Boundary Scattering ◽  
High Frequencies ◽  
Steady State Heat

The theory of Casimir (1938) for steady-state heat flow in the boundary-scattering limit for cylindrical samples is extended to include time-dependent effects. This shows that a term of the form (∂3T/∂x2∂t) is the first correction term which should be added to the usual thermal diffusion equation, the range of validity of the theory being restricted by the condition that the wavelength of the disturbance, [Formula: see text], where L is the mean free path of phonons in the bulk material and a is the radius of the cylinder. The dispersion relation is derived, and, as an example, dispersion curves are computed for liquid helium as the dielectric medium, contained in a tube of 1-cm radius. At high frequencies the velocity of the temperature wave is reduced below the value predicted by the diffusion equation.

Light scattering by phonons in the presence of a heat flow

1968 ◽  
Vol 46 (24) ◽  
pp. 2843-2845 ◽  
Author(s):  
Allan Griffin
Keyword(s):  
Light Scattering ◽  
Heat Flow ◽  
Temperature Gradient ◽  
Free Path ◽  
Mean Free Path ◽  
Photon Scattering ◽  
The Mean ◽  
Anti Stokes

If the temperature in an insulating crystal decreases in the z-direction, there are more phonons with momentum qz > 0 than with qz < 0. The resulting difference between the Stokes and anti-Stokes Brillouin intensities is proportional to the mean free path of the phonon involved and to the temperature gradient. The effect should be observable by either neutron or photon scattering.

Thermal Design of Highly-Efficient Thermoelectric Materials With Atomic-Scale Three-Dimensional Phononic Crystals

2007 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Bulk Material ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Dispersion Curves ◽  
Phononic Crystals ◽  
Thermal Design ◽  
Atomic Scale ◽  
Thermal Insulating

Owing to their thermal insulating properties, superlattices have been extensively studied. A breakthrough in the performance of thermoelectric devices was achieved by using superlattice materials. The problem of those nanostructured materials is that they mainly affect heat transfer in only one direction. In this paper, the concept of canceling heat conduction in the three spatial directions by using atomic-scale three-dimensional (3D) phononic crystals is explored. A period of our atomic-scale 3D phononic crystal is made up of a large number of diamond-like cells of silicon atoms, which form a square supercell. At the center of each supercell, we substitute a smaller number of Si diamond-like cells by other diamond-like cells, which are composed of germanium atoms. This elementary heterostructure is periodically repeated to form a Si/Ge 3D nanostructure. To obtain different atomic configurations of the phononic crystal, the number of Ge diamond-like cells at the center of each supercell can be varied by substitution of Si diamond-like cells. The dispersion curves of those atomic configurations can be computed by lattice dynamics. With a general equation, the thermal conductivity of our atomic-scale 3D phononic crystal can be derived from the dispersion curves. The thermal conductivity can be reduced by at least one order of magnitude in an atomic-scale 3D phononic crystal compared to a bulk material. This reduction is due to the decrease of the phonon group velocities without taking into account that of the phonon average mean free path.

scholarly journals Reconstructing bottom water temperatures from measurements of temperature and thermal diffusivity in marine sediments

2014 ◽  
Vol 11 (5) ◽  
pp. 2391-2422
Author(s):  
F. Miesner ◽  
A. Lechleiter ◽  
C. Müller
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Water Temperature ◽  
Marine Sediments ◽  
Bottom Water ◽  
Measured Data ◽  
Temperature History ◽  
Artificial Data ◽  
Bottom Water Temperature ◽  
Steady State Heat

Abstract. Temperature fields in marine sediments are studied for various purposes. Often, the target of research is the steady state heat flow as a (possible) source of energy but there are also studies attempting to reconstruct bottom water temperature variations to understand more about climate history. The bottom water temperature propagates into the sediment to different depths, depending on the amplitude and period of the deviation. The steady state heat flow can only be determined when the bottom water temperature is constant while the bottom water temperature history can only be reconstructed when the deviation has an amplitude large enough or the measurements are taken in great depths. In this work, the aim is to reconstruct recent bottom water temperature history such as the last two years. To this end, measurements to depths of up to 6 m shall be adequate and amplitudes smaller than 1 K should be reconstructable. First, a commonly used forward model is introduced and analyzed: knowing the bottom water temperature deviation in the last years and the thermal properties of the sediments, the forward model gives the sediment temperature field. Next, an inversion operator and two common inversion schemes are introduced. The analysis of the inversion operator and both algorithms is kept short, but sources for further reading are given. The algorithms are then tested for artificial data with different noise levels and for two example data sets, one from the German North Sea and one from the Davis Strait. Both algorithms show good and stable results for artificial data. The achieved results for measured data have low variances and match to the observed oceanographic settings. Lastly, the desired and obtained accuracy are discussed. For artificial data, the presented method yields satisfying results. However, for measured data the interpretation of the results is more difficult as the exact form of the bottom water deviation is not known. Nevertheless, the presented inversion method seems rather promising due to its accuracy and stability for artificial data. Continuing to work on the development of more sophisticated models for the bottom water temperature, we hope to cover more different oceanographic settings in the future.

Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors

1999 ◽  
Author(s):  
Per G. Sverdrup ◽  
Y. Sungtaek Ju ◽  
Kenneth E. Goodson
Keyword(s):  
Diffusion Equation ◽  
Free Path ◽  
Temperature Rise ◽  
Mean Free Path ◽  
Channel Length ◽  
Silicon On Insulator ◽  
Heat Diffusion ◽  
Boltzmann Transport ◽  
Heat Diffusion Equation ◽  
Silicon Devices

Abstract The temperature rise in compact silicon devices is predicted at present by solving the heat diffusion equation based on Fourier’s law. The validity of this approach needs to be carefully examined for semiconductor devices in which the region of strongest electronphonon coupling is narrower than the phonon mean free path, Λ, and for devices in which Λ is comparable to or exceeds the dimensions of the device. Previous research estimated the effective phonon mean free path in silicon near room temperature to be near 300 nm, which is already comparable with the minimum feature size of current generation transistors. This work numerically integrates the phonon Boltzmann transport equation (BTE) within a two-dimensional Silicon-on-Insulator (SOI) transistor. The BTE is coupled with the classical heat diffusion equation, which is solved in the silicon dioxide layer beneath a transistor with a channel length of 400 nm. The sub-continuum simulations yield a peak temperature rise that is 159 percent larger than predictions using only the classical heat diffusion equation. This work will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.

The anomalous skin effect

1952 ◽  
Vol 215 (1123) ◽  
pp. 481-497 ◽  
Keyword(s):  
Free Path ◽  
Low Temperatures ◽  
Skin Effect ◽  
Mean Free Path ◽  
Skin Depth ◽  
Surface Conductance ◽  
High Frequencies ◽  
Surface Imperfections ◽  
Anomalous Skin Effect ◽  
Cadmium Lead

The anomalous skin effect arises in good conductors at low temperatures and high frequencies when the electronic mean free path becomes comparable with or greater than the classically calculated skin depth. Measurements have been made on a number of metals at frequencies of 1200 and 3600 Mc/s, and the form of variation of r. f. surface conductance with d. c. conductivity agrees well with that predicted theoretically by Reuter & Sondheimer, assuming that the electrons are scattered diffusely when they hit the surface of the metal. From the results, estimates are made of the effective value of σ/ l , the ratio of d. c. conductivity to mean free path, and hence of the free surface area of the occupied region of k -space. The estimate for copper agrees well with that expected theoretically; those for silver and gold are rather lower than the theoretical values. For the other metals investigated, tin, cadmium, lead and aluminium, no theoretical estimates are available. The results are very sensitive to the presence of surface imperfections; the effect of these is discussed.

Electrochemically Prepared Pore Arrays for Photonic-Crystal Applications

MRS Bulletin ◽  
2001 ◽  
Vol 26 (8) ◽  
pp. 623-626 ◽  
Author(s):  
R.B. Wehrspohn ◽  
J. Schilling
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystals ◽  
Electromagnetic Waves ◽  
Porous Alumina ◽  
Dielectric Materials ◽  
Dielectric Medium ◽  
Geometrical Parameters ◽  
Quarter Wavelength ◽  
Physically Based ◽  
1D Photonic Crystal

In the last few years, photonic crystals have gained considerable interest due to their ability to “mold the flow of light.” Photonic crystals are physically based on Bragg reflections of electromagnetic waves. In simple terms, a one-dimensional (1D) photonic crystal is a periodic stack of thin dielectric films with two different refractive indices, n1 and n2. The two important geometrical parameters determining the wavelength of the photonic bandgap are the lattice constant, a = d1(n1) + d2(n2), and the ratio of d1 to a (where d1 is the thickness of the layer with refractive index n1, and d2 is the thickness of layer n2). For a simple quarter-wavelength stack, the center wavelength λ of the 1D photonic crystal would be simply λ = 2n1d1 + 2n2d2. In the case of 2D photonic crystals, the concept is extended to either airholes in a dielectric medium or dielectric rods in air. Therefore, ordered porous dielectric materials like porous silicon or porous alumina are intrinsically 2D photonic crystals.

The Lifetime of Polar-Optical Modes in Semiconductors

2009 ◽  
Vol 1221 ◽  
Author(s):  
Brian K Ridley ◽  
Angela Dyson
Keyword(s):  
Raman Scattering ◽  
Bulk Material ◽  
Phonon Modes ◽  
High Frequencies ◽  
Power Semiconductor ◽  
Power Semiconductor Devices ◽  
Optical Modes ◽  
Electronic Performance ◽  
Anharmonic Decay

AbstractAn enduring problem in the engineering of high-power semiconductor devices is how to mitigate the effect of heating. Heating means the proliferation of phonons, and phonons, interacting with electrons directly affect the electronic performance of the device. Nowhere is this more evident than the role of hot polar-optical phonons in reducing the drift velocity in the channel of an HFET and hence reducing its performance at high frequencies. The task of describing hot-phonon effects is complicated by the coupling to plasma modes. We present a theory of coupled plasmon-phonon modes in GaN, how they interact with electrons and how their lifetime becomes density-dependent. Raman scattering in bulk material shows a reduction of lifetime with increasing density and we offer an explanation for this in terms of the frequency dependence of the anharmonic decay mechanism. Hot-phonon effects, however, involve modes with wave-vectors beyond those probed by Raman scattering. By adopting a single-pole approximation for these modes we have obtained the lifetime dependence on wave vector, electron temperature and density.

Sign in / Sign up

Export Citation Format

Share Document