Relative Contributions of Inelastic and Elastic Diffuse Phonon Scattering to Thermal Boundary Conductance Across Solid Interfaces

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Patrick E. Hopkins ◽  
Pamela M. Norris
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Debye Temperature ◽  
Diffuse Scattering ◽  
Phonon Scattering ◽  
Interfacial Transport ◽  
Thermal Boundary Conductance ◽  
Dielectric Interfaces ◽  
Scattering Events

The accuracy of predictions of phonon thermal boundary conductance using traditional models such as the diffuse mismatch model (DMM) varies depending on the types of material comprising the interface. The DMM assumes that phonons, undergoing diffuse scattering events, are elastically scattered, which drives the energy conductance across the interface. It has been shown that at relatively high temperatures (i.e., above the Debye temperature) previously ignored inelastic scattering events can contribute substantially to interfacial transport. In this case, the predictions from the DMM become highly inaccurate. In this paper, the effects of inelastic scattering on thermal boundary conductance at metal/dielectric interfaces are studied. Experimental transient thermoreflectance data showing inelastic trends are reviewed and compared to traditional models. Using the physical assumptions in the traditional models and experimental data, the relative contributions of inelastic and elastic scattering to thermal boundary conductance are inferred.

Effects of Inelastic Scattering on Thermal Boundary Conductance at Metal-Dielectric Interfaces

2007 ◽  
Author(s):  
Patrick E. Hopkins ◽  
Pamela M. Norris ◽  
Robert J. Stevens
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Debye Temperature ◽  
High Temperatures ◽  
Interfacial Transport ◽  
Thermal Boundary Conductance ◽  
Dielectric Interfaces ◽  
Scattering Events

The accuracy of predictions of thermal boundary conductance using traditional models such as the diffuse mismatch model (DMM) varies depending on the types of material comprising the interface. These traditional models assume that phonons are elastically scattered which drives the energy conductance across the interface. It has been shown that at relatively high temperatures (i.e., above the Debye temperature) inelastic scattering events can drive interfacial transport. In this case, the predictions from traditional models become highly inaccurate. In this paper, the effects of inelastic scattering on thermal boundary conductance at metal/dielectric interfaces are studied. Experimental transient thermoreflectance data showing inelastic trends are reviewed and compared to traditional models. Using the physical assumptions in the traditional models and the experimental data, the relative contributions of inelastic and elastic scattering on thermal boundary conductance is inferred.

scholarly journals Contributions of Anharmonic Phonon Interactions to Thermal Boundary Conductance

2011 ◽  
Author(s):  
Patrick E. Hopkins ◽  
John C. Duda ◽  
Pamela M. Norris
Keyword(s):  
Inelastic Scattering ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Transmission Model ◽  
Material Interfaces ◽  
Physical Consideration ◽  
Interfacial Transport ◽  
New Model ◽  
Thermal Boundary Conductance ◽  
Scattering Events

Continued reduction of characteristic dimensions in nanosystems has given rise to increasing importance of material interfaces on the overall system performance. With regard to thermal transport, this increases the need for a better fundamental understanding of the processes affecting interfacial thermal transport, as characterized by the thermal boundary conductance. When thermal boundary conductance is driven by phononic scattering events, accurate predictions of interfacial transport must account for anharmonic phononic coupling as this affects the thermal transmission. In this paper, a new model for phononic thermal boundary conductance is developed that takes into account anharonic coupling, or inelastic scattering events, at the interface between two materials. Previous models for thermal boundary conductance are first reviewed, including the Diffuse Mismatch Model, which only consdiers elastic phonon scattering events, and earlier attempts to account for inelastic phonon scattering, namely, the Maximum Transmission Model and the Higher Harmonic Inelastic model. A new model is derived, the Anharmonic Inelastic Model, which provides a more physical consideration of the effects of inelastic scattering on thermal boundary conductance. This is accomplished by considering specific ranges of phonon frequency interactions and phonon number density conservation. Thus, this model considers the contributions of anharmonic, inelastically scattered phonons to thermal boundary conductance. This new Anharmonic Inelastic Model shows excellent agreement between model predictions and experimental data at the Pb/diamond interface due to its ability to account for the temperature dependent changing phonon population in diamond, which can couple anharmonically with multiple phonons in Pb.

Anharmonic Phonon Interactions at Interfaces and Contributions to Thermal Boundary Conductance

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Patrick E. Hopkins ◽  
John C. Duda ◽  
Pamela M. Norris
Keyword(s):  
Inelastic Scattering ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Transmission Model ◽  
Material Interfaces ◽  
Physical Consideration ◽  
New Model ◽  
Thermal Boundary Conductance ◽  
Anharmonic Coupling ◽  
Scattering Events

Continued reduction in characteristic dimensions in nanosystems has given rise to increasing importance of material interfaces on the overall system performance. With regard to thermal transport, this increases the need for a better fundamental understanding of the processes affecting interfacial thermal transport, as characterized by the thermal boundary conductance. When thermal boundary conductance is driven by phononic scattering events, accurate predictions of interfacial transport must account for anharmonic phononic coupling as this affects the thermal transmission. In this paper, a new model for phononic thermal boundary conductance is developed that takes into account anharmonic coupling, or inelastic scattering events, at the interface between two materials. Previous models for thermal boundary conductance are first reviewed, including the diffuse mismatch model, which only considers elastic phonon scattering events, and earlier attempts to account for inelastic phonon scattering, namely, the maximum transmission model and the higher harmonic inelastic model. A new model is derived, the anharmonic inelastic model, which provides a more physical consideration of the effects of inelastic scattering on thermal boundary conductance. This is accomplished by considering specific ranges of phonon frequency interactions and phonon number density conservation. Thus, this model considers the contributions of anharmonic, inelastically scattered phonons to thermal boundary conductance. This new anharmonic inelastic model shows improved agreement between the thermal boundary conductance predictions and experimental data at the Pb/diamond and Au/diamond interfaces due to its ability to account for the temperature dependent changing phonon population in diamond, which can couple anharmonically with multiple phonons in Pb and Au. We conclude by discussing phonon scattering selection rules at interfaces and the probability of occurrence of these higher order anharmonic interfacial phonon processes quantified in this work.

Influence of Inelastic Scattering at Metal-Dielectric Interfaces

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Patrick E. Hopkins ◽  
Pamela M. Norris ◽  
Robert J. Stevens
Keyword(s):  
Inelastic Scattering ◽  
High Temperatures ◽  
Experimental Testing ◽  
Phonon Transport ◽  
Dynamic Simulations ◽  
Interfacial Transport ◽  
Thermal Boundary Conductance ◽  
Dielectric Interfaces ◽  
Transport Channels

Thermal boundary conductance is becoming increasingly important in microelectronic device design and thermal management. Although there has been much success in predicting and modeling thermal boundary conductance at low temperatures, the current models applied at temperatures more common in device operation are not adequate due to our current limited understanding of phonon transport channels. In this study, the scattering processes across Cr∕Si, Al∕Al2O3, Pt∕Al2O3, and Pt∕AlN interfaces were examined by transient thermoreflectance testing at high temperatures. At high temperatures, traditional models predict the thermal boundary conductance to be relatively constant in these systems due to assumptions about phonon elastic scattering. Experiments, however, show an increase in the conductance indicating inelastic phonon processes. Previous molecular dynamic simulations of simple interfaces indicate the presence of inelastic scattering, which increases interfacial transport linearly with temperature. The trends predicted computationally are similar to those found during experimental testing, exposing the role of multiple-phonon processes in thermal boundary conductance at high temperatures.

Examining Interfacial Diffuse Phonon Scattering Through Transient Thermoreflectance Measurements of Thermal Boundary Conductance

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Pamela M. Norris ◽  
Patrick E. Hopkins
Keyword(s):  
Inelastic Scattering ◽  
Phonon Scattering ◽  
Experimental Studies ◽  
Thermal Boundary Conductance ◽  
Debye Temperatures ◽  
Wide Range ◽  
Dielectric Interfaces ◽  
Order Of Magnitude ◽  
Atomic Mixing ◽  
Insight Into

Today’s electronic and optoelectronic devices are plagued by heat transfer issues. As device dimensions shrink and operating frequencies increase, ever-increasing amounts of thermal energy are being generated in smaller and smaller volumes. As devices shrink to length scales on the order of carrier mean free paths, thermal transport is no longer dictated by the thermal properties of the materials comprising the devices, but rather the transport of energy across the interfaces between adjacent materials in the devices. In this paper, current theories and experiments concerning phonon scattering processes driving thermal boundary conductance (hBD) are reviewed. Experimental studies of thermal boundary conductance conducted with the transient thermoreflectance technique challenging specific assumptions about phonon scattering during thermal boundary conductance are presented. To examine the effects of atomic mixing at the interface on hBD, a series of Cr/Si samples was fabricated subject to different deposition conditions. The varying degrees of atomic mixing were measured with Auger electron spectroscopy. Phonon scattering phenomena in the presence of interfacial mixing were observed with the trends in the Cr/Si hBD. The experimental results are reviewed and a virtual crystal diffuse mismatch model is presented to add insight into the effect of interatomic mixing at the interface. The assumption that phonons can only transmit energy across the interface by scattering with a phonon of the same frequency—i.e., elastic scattering, can lead to underpredictions of hBD by almost an order of magnitude. To examine the effects of inelastic scattering on hBD, a series of metal/dielectric interfaces with a wide range of vibrational similarity is studied at temperatures above and around materials’ Debye temperatures. Inelastic scattering is observed and new models are developed to predict hBD and its relative dependency on elastic and inelastic scattering events.

The measurements of the elastic-inelastic multiple scattering electron intensity in EELS

1995 ◽  
Vol 53 ◽  
pp. 300-301
Author(s):  
S. C. Cheng ◽  
Y. Y. Wang ◽  
V. P. Dravid
Keyword(s):  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Multiple Scattering ◽  
Electron Spectroscopy ◽  
Collective Excitation ◽  
Interband Transition ◽  
Single Scattering ◽  
Simple Relationship ◽  
Momentum Range ◽  
Scattering Events

The Electron energy loss function in the low energy range is determined by collective excitation of valence electrons and charge carriers, i.e. plasmons, as well as interband and intraband excitations. The explicit dependence of the cross-section on the momentum transfer q allows the observation of nonvertical interband transition and a measurement of the dispersion of plasmon excitations. The drawback of the momentum resolved electron spectroscopy is the multiple scattering, which often obscure the single scattering events. Under relatively small scattering angles, both strong elasticinelastic multiple (E-I-M) scattering and elastic scattering events compared to the inelastic scattering have been reported. In order to find out in what momentum range the E-I-M scattering intensity can be ignored in the momentum resolved electron spectroscopy, we have measured the angular dependency of the intensities of the E-I-M scattering electrons Ie+in. The intensities of the elastic scattering electrons Ie as well as of the inelastic scattering electrons Iin were also measured and are presented in this paper together. A simple relationship between Ie and Ie+in is found.

Symmetry analysis of extinction rules in diffuse-scattering experiments

2010 ◽  
Vol 66 (3) ◽  
pp. 315-322 ◽  
Author(s):  
R. L. Withers ◽  
M. I. Aroyo ◽  
J. M. Perez-Mato ◽  
D. Orobengoa
Keyword(s):  
Experimental Data ◽  
Inelastic Scattering ◽  
Diffuse Scattering ◽  
Computer Programs ◽  
Symmetry Analysis ◽  
Specific Structure ◽  
Scattering Data ◽  
Disordered Materials ◽  
Space Groups ◽  
The Individual

Structured diffuse-scattering intensities, whether of compositional or of pure displacive origin, static or dynamic, contain important information about the symmetry of the individual compositional and/or displacive modes responsible for the observed intensities. However, the interpretation of the experimental data is very often impeded by the lack of a symmetry-based approach to the analysis of the structured diffuse-scattering distributions. Recently, we have demonstrated the existence of systematic phonon selection rules for diffuse scattering that depend on the symmetries of the mode and the scattering vector, and not on the specific structure. Here, we show that such symmetry analysis can be successfully extended and also applied to structure-dependent diffuse scattering associated with `disordered' materials: the combination of theoretically determined, diffuse-scattering extinction conditions with the concept of non-characteristic orbits proves to be very useful in the interpretation of the observed diffuse-scattering extinctions. The utility of this approach is illustrated by the analysis of diffuse-scattering data from ThAsSe, FeOF and FeF2. The essential part of the associated calculations are performed by the computer programs NEUTRON (systematic phonon extinction rules in inelastic scattering) and NONCHAR (non-characteristic orbits of space groups) that are available on the Bilbao crystallographic server (http://www.cryst.ehu.es).

scholarly journals The scattering of electrons in thin films

1933 ◽  
Vol 140 (840) ◽  
pp. 159-178
Keyword(s):  
Experimental Data ◽  
Thin Films ◽  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Atomic Number ◽  
General Problem ◽  
Absolute Intensity ◽  
Experimental Investigations ◽  
The Absolute ◽  
Theoretical Side

The laws governing the single elastic scattering of electrons by atoms have been fully investigated from the theoretical side. The more general problem which includes inelastic scattering has also been investigated, but the results are not readily applicable to experimental data. The nature of the results of experimental investigations varies considerably; for the most part electron energies of at least 40 kilovolts and comparatively thick foils have been used. The results of these experiments, which are not wholly in accord for different investigators, indicate that the variation of scattering with voltage and with angle follows the Rutherford law. The absolute intensity is in all cases too large, and it appears to vary with the atomic number of the scattering atom more rapidly than predicted.

Measurement of Thermal Boundary Conductance of a Series of Metal-Dielectric Interfaces by the Transient Thermoreflectance Technique

2005 ◽  
Vol 127 (3) ◽  
pp. 315-322 ◽  
Author(s):  
Robert J. Stevens ◽  
Andrew N. Smith ◽  
Pamela M. Norris
Keyword(s):  
Elastic Scattering ◽  
Thermal Model ◽  
Room Temperature ◽  
Optical Technique ◽  
Thermal Boundary Conductance ◽  
Prepared Sample ◽  
Scattering Mechanisms ◽  
Sample Series ◽  
Phonon Spectra ◽  
Dielectric Interfaces

Measurement of the thermal boundary conductance (TBC) by use of a nondestructive optical technique, transient thermoreflectance (TTR), is presented. A simple thermal model for the TTR is presented with a discussion of its applicability and sensitivity. A specially prepared sample series of Cr, Al, Au, and Pt on four different substrates (Si, sapphire, GaN, and AlN) were tested at room temperature and the TTR signal fitted to the thermal model. The resulting TBC values vary by more than a factor of 3 0.71×108-2.3×108 W/m2 K. It is shown that the diffuse mismatch model (DMM) tended to overpredict the TBC of interfaces with materials having similar phonon spectra, while underpredicting the TBC for interfaces with dissimilar phonon spectra. The DMM only accounts for diffuse elastic scattering. Other scattering mechanisms are discussed which may explain the failure of the DMM at room temperature.

The Resolution and Contrast in Biological Sections Determined by Inelastic and Elastic Scattering

1973 ◽  
Vol 31 ◽  
pp. 224-225
Author(s):  
D. L. Misell
Keyword(s):  
Electron Microscopy ◽  
Adverse Effect ◽  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Amorphous Carbon ◽  
Polymeric Materials ◽  
Chromatic Aberration ◽  
Image Resolution ◽  
Quantitative Estimates ◽  
Elastic Ratio

In the electron microscopy of biological sections the adverse effect of chromatic aberration on image resolution is well known. In this paper calculations are presented for the inelastic and elastic image intensities using a wave-optical formulation. Quantitative estimates of the deterioration in image resolution as a result of chromatic aberration are presented as an alternative to geometric calculations. The predominance of inelastic scattering in the unstained biological and polymeric materials is shown by the inelastic to elastic ratio, I/E, within an objective aperture of 0.005 rad for amorphous carbon of a thickness, t=50nm, typical of biological sections; E=200keV, I/E=16.

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