Theoretical Calculations of the Nonlinear Dielectric Function of Inhomogeneous thin Films

1989 ◽  
Vol 173 ◽  
Author(s):  
Steven M. Risser ◽  
Kim F. Ferris
Keyword(s):  
Dielectric Function ◽  
Linear Response ◽  
Theoretical Calculations ◽  
Intrinsic Properties ◽  
Inhomogeneous Materials ◽  
Nonlinear Part ◽  
Nonlinear Responses ◽  
Random Microstructure ◽  
Void Shape ◽  
Film Microstructure

ABSTRACTThe dielectric function of inhomogeneous materials is composed of linear and nonlinear responses which are sensitive to the film microstructure as well as the intrinsic properties of the materials. We have developed a method to self-consistently determine the linear and non-linear contributions to the dielectric function of films with random microstructure. This method is based upon a numerical solution of the general electrostatic equations and is applicable to arbitrary shapes and orientations of model defects. This method provides near exact solutions to the linear response of the dielectric function. We have shown that the nonlinear part of the dielectric function is extremely sensitive to the void shape and void fraction.

Quantum to macroscale and linear response

2020 ◽  
pp. 521-540
Author(s):  
Sandip Tiwari
Keyword(s):  
Dielectric Function ◽  
Linear Response ◽  
Linear Response Theory ◽  
Linear Transformations ◽  
Electron Model ◽  
Nonlinear Responses ◽  
The World ◽  
Time Marching ◽  
Linear And Nonlinear ◽  
Damped Oscillator

This chapter focuses on the properties associated with linear response. Reversibility holds in linear transformations. Schrödinger and Maxwell equations are linear, yet the world is irreversible, with time marching forward and dissipation quite ubiquitous. The connections between the quantum and microscopic scale, which are reversible and non-deterministic, to the macroscale, where irreversibility and determinism abounds, arise through interactions where both linear and nonlinear responses can appear. Causality’s implication in linear response is illustrated through a toy example and a quantum-statistical view of response. Linear response theory—using Green’s functions—is applied to develop dispersion relationships and dielectric function. The tie-in between real and imaginary parts is illustrated as one example of the Kramers-Kronig relationship, and the linear response of a damped oscillator and the Lorentz model, together with the oscillating electron model, employed to illustrate the dielectric function implications.

Tailored upconversion emission of Eu3+ in Sr2Ca(W,Mo)O6:Yb3+,Eu3+ by a laser via an electronic polarization mechanism

2015 ◽  
Vol 3 (19) ◽  
pp. 4997-5003 ◽  
Author(s):  
Ye Li ◽  
Tianhui Liu ◽  
Shi Ye ◽  
Tengfei Deng ◽  
Xiong Yi ◽  
...  
Keyword(s):  
Impedance Spectroscopy ◽  
Dielectric Function ◽  
Theoretical Calculations ◽  
Ac Impedance ◽  
Upconversion Emission ◽  
Ac Impedance Spectroscopy ◽  
Electronic Polarization ◽  
Polarization Mechanism

The 5D0 → 7F4 upconversion emission of Eu3+ in Sr2Ca(W,Mo)O6:Yb3+,Eu3+ is tailored by a laser via an electronic polarization mechanism, which is deduced by AC impedance spectroscopy measurements and theoretical calculations of the dielectric function.

Dielectric function modelling and sensitivity forecast for Au–Ag alloy nanostructures

2020 ◽  
Vol 22 (26) ◽  
pp. 14932-14940
Author(s):  
Xiu Wang ◽  
Caixia Kan ◽  
Juan Xu ◽  
Xingzhong Zhu ◽  
Mingming Jiang ◽  
...  
Keyword(s):  
Refractive Index ◽  
Dielectric Function ◽  
Theoretical Calculations ◽  
Experimental Results ◽  
Refractive Index Sensitivity ◽  
Dielectric Data ◽  
Function Modelling ◽  
Alloy Nanostructures ◽  
Fdtd Simulations ◽  
Index Sensitivity

Based on theoretical calculations, FDTD simulations and experimental results, the refractive index sensitivity of Au–Ag alloy nanostructures were investigated, indicating the credibility and feasibility of the modelled dielectric data of alloy.

scholarly journals Macroscale adhesion of gecko setae reflects nanoscale differences in subsurface composition

2013 ◽  
Vol 10 (78) ◽  
pp. 20120587 ◽  
Author(s):  
Peter Loskill ◽  
Jonathan Puthoff ◽  
Matt Wilkinson ◽  
Klaus Mecke ◽  
Karin Jacobs ◽  
...  
Keyword(s):  
Layer Thickness ◽  
Interfacial Adhesion ◽  
Theoretical Calculations ◽  
Van Der Waals ◽  
Adhesion Forces ◽  
Inhomogeneous Materials ◽  
Subsurface Layers ◽  
Adhesion Mechanics ◽  
Van Der Waals Energies ◽  
Theoretical Results

Surface energies are commonly used to determine the adhesion forces between materials. However, the component of surface energy derived from long-range forces, such as van der Waals forces, depends on the material's structure below the outermost atomic layers. Previous theoretical results and indirect experimental evidence suggest that the van der Waals energies of subsurface layers will influence interfacial adhesion forces. We discovered that nanometre-scale differences in the oxide layer thickness of silicon wafers result in significant macroscale differences in the adhesion of isolated gecko setal arrays. Si/SiO 2 bilayer materials exhibited stronger adhesion when the SiO 2 layer is thin (approx. 2 nm). To further explore how layered materials influence adhesion, we functionalized similar substrates with an octadecyltrichlorosilane monolayer and again identified a significant influence of the SiO 2 layer thickness on adhesion. Our theoretical calculations describe how variation in the SiO 2 layer thickness produces differences in the van der Waals interaction potential, and these differences are reflected in the adhesion mechanics. Setal arrays used as tribological probes provide the first empirical evidence that the ‘subsurface energy’ of inhomogeneous materials influences the macroscopic surface forces.

scholarly journals A Generalised Linear Response Theory applied to the Dielectric Function of Coulomb Systems

2000 ◽  
Vol 53 (1) ◽  
pp. 133 ◽  
Author(s):  
H. Reinholz
Keyword(s):  
Dielectric Function ◽  
Linear Response ◽  
Electron Gas ◽  
Three Dimensional ◽  
Coulomb Systems ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Response Theory ◽  
Long Wavelength ◽  
Wave Numbers

A generalised linear response theory is used to derive the dielectric function at arbitrary wave numbers k and frequencies w for interacting quantum systems. The connection to thermodynamic Green functions allows the systematic perturbative treatment going beyond RPA and treating local field corrections as well as the inclusion of collisions on the same footing. Emphasis will be on the demonstration of the formalism. Results will be presented for the three-dimensional as well as two-dimensional case of an interacting electron gas. In the long-wavelength limit, a Drude-type expression with frequency dependent relaxation time is given bridging the theories of dielectric function and electrical conductivity.

Velocity anisotropy observed in wellbore seismic arrivals: Combined effects of intrinsic properties and layering

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 12-20 ◽  
Author(s):  
Ahmed Kebaili ◽  
Douglas R. Schmitt
Keyword(s):  
Incidence Angle ◽  
Theoretical Calculations ◽  
Depth Interval ◽  
Intrinsic Properties ◽  
Velocity Anisotropy ◽  
Incidence Oblique ◽  
Seismic Records ◽  
Intrinsic Anisotropy ◽  
Interval Velocities ◽  
Sonic Logs

A method of estimating velocity anisotropy by the τ-p inversion of seismic traveltimes observed in a multi‐depth and offset VSP experiment is developed. In the method, a set of seismic traces observed at a fixed depth in the wellbore are transformed to the τ-p domain. Incidence‐angle‐dependent interval velocities are extracted from the resulting curves using coherency measures after accounting for the effects of the overlaying layers. To test the method, we obtained seismic records from a shallow borehole drilled through a flat lying sedimentary sequence. One depth interval that consists of a homogeneous bioturbated shale is nearly isotropic. A second interval characterized by an alternation of thin (∼1 m) sands and shales displays an anisotropy of 15% with velocities increasing from the near vertical (0 < 30°) to the oblique (30° < 0 < 55°) angles of incidence. Oblique velocities were always larger. The observation that the shale‐sand depth interval displaying the greatest anisotropy also is the most heterogeneous in the sonic logs suggests that the thin layering produces the anisotropy. The theoretical vertical‐to‐horizontal velocity an isotropy for this interval, computed assuming isotropic layering, is 14.2%. Comparing this theoretical value to the vertical‐to‐oblique value obtained over a smaller range of incidence angles indicates that the theoretical value is too small. This discrepancy is possibly because of the intrinsic anisotropy of the shale layers themselves that is not considered in the theoretical calculations.

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