Contribution of the Nanocrystallites and Their Interfaces to the Optical Response of Porous Silicon Layers

1994 ◽  
Vol 358 ◽  
Author(s):  
U. Rossow ◽  
U. Frotscher ◽  
W. Richter ◽  
H. Muender ◽  
M. Thoennissen ◽  
...  
Keyword(s):  
Porous Silicon ◽  
Critical Point ◽  
Dielectric Function ◽  
Spectroscopic Ellipsometry ◽  
Critical Points ◽  
Optical Response ◽  
Electrochemical Process ◽  
Strong Indication ◽  
Lineshape Analysis ◽  
Preparation Conditions

ABSTRACTWe discuss the dependence of the dielectric function on the nanocrystalline size of porous silicon layers. The layers were grown by a standard electrochemical process and characterized by spectroscopic ellipsometry. By a lineshape analysis values of the critical point energies and broadening parameters of the Interband critical points were derived. In order to obtain further information about the nanocrystallites, the preparation conditions were varied (HF concentration, NH4F was added) or the layers were further treated by etching and arsenic deposition. The lineshape analysis values indicate that the layers consist mainly of nanocrystallites, or more accurately, that the electrons are confined to regions of a few nanometers in size. Furthermore, there is strong indication that some preparation conditions may leave these nanocrystallites heavily strained .

Dielectric function and critical points of AlP determined by spectroscopic ellipsometry

2014 ◽  
Vol 587 ◽  
pp. 361-364 ◽  
Author(s):  
S.Y. Hwang ◽  
T.J. Kim ◽  
Y.W. Jung ◽  
N.S. Barange ◽  
H.G. Park ◽  
...  
Keyword(s):  
Dielectric Function ◽  
Spectroscopic Ellipsometry ◽  
Critical Points

Effects of Electron Radiation on the Optical Constants of P-Type Silicon

1993 ◽  
Vol 302 ◽  
Author(s):  
Onofrio L. Russo ◽  
Katherine A. Dumas
Keyword(s):  
Critical Point ◽  
Spectroscopic Ellipsometry ◽  
Critical Points ◽  
Line Shape ◽  
Optical Constants ◽  
Electron Radiation ◽  
Main Structure ◽  
Type Silicon ◽  
Lorentz Line ◽  
P Type

ABSTRACTThe optical constants n and k are determined for p-type silicon at the Eo and El and critical point energies for one MeV electron irradiated samples. The value for fluences of 1014 and 1016 e−/cm2 are compared to samples before irradiation. The real, ε1 and imaginary,ε2 components of the dielectric function, ε, used to find n and k, were obtained by measurement of tanψ and δ using spectroscopic ellipsometry (SE). The data show that changes in δ, in particular, are greater in the region about Eo than of E1. This is consistent with electrolyte electroreflectance (EER) results in which the Lorentz line shape is narrower for Eo than for E1. The value of n is found to increase and k to decrease with e- radiation at the critical points, although, neither does so monotonically. The change in n at the Eo critical point is greater than at the higher energy main structure E1 whereas, k is a slower varying function in this region.

Dielectric function and energy of the E 0 critical point of hexagonal GaN at 26 K studied by using spectroscopic ellipsometry

2012 ◽  
Vol 61 (5) ◽  
pp. 791-794 ◽  
Author(s):  
Tae Jung Kim ◽  
Soon Yong Hwang ◽  
Junho Choi ◽  
Han Gyeol Park ◽  
Jun Seok Byun ◽  
...  
Keyword(s):  
Critical Point ◽  
Dielectric Function ◽  
Spectroscopic Ellipsometry

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

Gold nanoclusters reductively deposited on porous silicon: morphology and electronic structures

1998 ◽  
Vol 76 (11) ◽  
pp. 1707-1716 ◽  
Author(s):  
I Coulthard ◽  
S Degen ◽  
Y -J Zhu ◽  
T K Sham
Keyword(s):  
Gold Nanoparticles ◽  
Porous Silicon ◽  
Photoelectron Spectroscopy ◽  
Gold Nanoclusters ◽  
Gold Complex ◽  
X Ray Diffraction ◽  
Complex Ions ◽  
X Ray ◽  
Preparation Conditions ◽  
P Type

Utilizing porous silicon as a reducing agent and a substrate, gold complex ions [AuCl4]- were reduced from aqueous solution to produce nanoparticles of gold upon the surface of porous silicon. Scanning electron microscopy (SEM) was utilized to study the morphology of the porous silicon layers and the deposits of gold nanoparticles. It is found that preparation conditions have a profound effect on the morphology of the deposits, especially on porous silicon prepared from a p-type wafer. The gold nanoparticles, varying from micrometric aggregates of clusters of the order of 10 nm, to a distribution of nearly spherical clusters of the order of 10 nm, to strings of ~10 nm were observed and compared to bulk gold metal using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and X-ray absorption spectroscopy (XAS). These techniques confirm and complement the SEM findings. The potential for this reductive deposition technique is noted.Key words: gold nanostructures, reductive deposition, porous silicon, morphology, X-ray spectroscopy.

Nitrogen dependence of the GaAsN interband critical points E1 and E1+Δ1 determined by spectroscopic ellipsometry

2000 ◽  
Vol 77 (11) ◽  
pp. 1650-1652 ◽  
Author(s):  
G. Leibiger ◽  
V. Gottschalch ◽  
B. Rheinländer ◽  
J. Šik ◽  
M. Schubert
Keyword(s):  
Spectroscopic Ellipsometry ◽  
Critical Points

Probing Optical Transitions in Porous Silicon by Reflectance Spectroscopy in the Near Infrared, Visible and UV

1994 ◽  
Vol 358 ◽  
Author(s):  
W. Theiβ ◽  
R. Arens-Fischer ◽  
M. Arntzen ◽  
M.G. Berger ◽  
S. Frohnhoff ◽  
...  
Keyword(s):  
Porous Silicon ◽  
Dielectric Function ◽  
Near Infrared ◽  
Solid Phase ◽  
Pore Wall ◽  
Reflectance Spectroscopy ◽  
Wall Material ◽  
Bulk Silicon ◽  
Band Structure Calculations ◽  
Structure Calculations

ABSTRACTReflectance spectroscopy has been used to obtain the dielectric function of the solid phase of porous silicon. The method is based on a fit of a parameterized dielectric function model to measured spectra. A crucial step in the procedure is the 'dielectric averaging' of the microscopic dielectric function of the pore wall material to the macroscopic effective dielectric function which governs the optical properties.Results are given for heavily and moderately p-doped samples of various porosities. For the latter large differences to bulk silicon have been found. The obtained dielectric functions are compared to the results of band structure calculations taken from literature.

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