Critical Point Parameters Research Articles

Overlayer effects in the critical-point analysis of ellipsometric spectra: Application to InxGa1−xAs alloys

We investigate the effect of incomplete removal of semiconductor overlayers on critical-point (CP) parameters determined from the analysis of ellipsometric spectra. An approximate analytic expression shows that CP energies and broadening parameters should be relatively unaffected for isolated CPs if the dielectric response of the overlayer varies slowly with energy. The results are confirmed by model calculations for InAs, which show that the energies of the E1 and E1+Δ1 CP structures that are commonly used for compositional analysis of semiconductor alloys are relatively unaffected. We also analyze overlayer-removal data for a series of InxGa1−xAs alloy samples. Consistent with the above, the amplitudes and phases are affected significantly for all CPs, while the energies of the well-separated E1 and E1+Δ1 transitions are relatively invariant. The results show that accurate values of composition can be obtained from the analysis of the E1 and E1+Δ1 CP structures, even if complete removal of overlayers is not achieved.

Ellipsometric measurements of quantum confinement effects on higher interband transitions of Ge nanocrystals

AbstractWe studied the dielectric functions of Ge nanocrystals obtained by crystallization of amorphous Ge thin films embedded in SiO2. Partial crystallization of films was induced by thermal annealing. Crystalline regions gave rise to clear spectral features due to interband transitions whose critical point parameters correlated with the initial a‐Ge thickness. These changes were clearly attributed to quantum confinement effects. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A hydrocode equation of state for SiO2

Abstract— The thermodynamic properties of SiO2 are approximated over a range of pressures and temperatures important under the extreme conditions achieved in impacts at typical solar system velocities from 5 to about 70 km/s. The liquid/vapor phase curve and critical point of SiO2 are computed using the equation of state (EOS) program ANEOS. To achieve this goal, two shortcomings of ANEOS are corrected. ANEOS, originally developed at Sandia National Laboratories to describe metals, treats the vapor phase as a monatomic mixture of atoms, rather than molecular clusters. It also assumes a Morse potential for the expanded solid state. Neither of these assumptions is accurate for geologic materials, such as SiO2, that contain molecular clusters in the vapor phase and are better described by a Mie‐type potential in the solid state. Using the updates described here, an EOS adequate for numerical hydrocode computations is constructed that agrees well with shock data at pressures up to at least 600 GPa and temperatures up to 50,000 K. This EOS also gives a good representation of the liquid/vapor transition at much lower pressures and temperatures. The estimated critical point parameters for SiO2 are Pc = 0.19 GPa, Tc = 5400K, ρc = 550 kg/m3.

Fourier 변환을 이용한 ZnCdSe 전이점 연구

타원편광분석법은 반도체 물질의 광 특성과 전이점 연구에 유용하게 쓰이는 기술이다. 측정된 유전율 함수로부터 전이점을 구하기 위해서 전통적으로 이차 미분스펙트럼을 이용하여 분석하는데, 이 방법은 high frequency 의 잡음을 크게 증폭시키는 단점이 있다. 본 연구에서는 역 공간 푸리에 변환 (Fourier transform)을 이용하여 low-, medium-, high-index 의 푸리에 계수로부터 baseline, 정보, high frequency 잡음을 분리하는 방법을 소개하고자 한다. 이 방법을 이용하여 광전자소자에 폭넓게 사용되는 ZnCdSe 화합물 반도체의 <TEX>$E_1,\;E_1+{\Delta}_1$</TEX> 전이점에 대한 연구를 하여 전통적인 이차 미분법과 비교해 보았다. Spectroscopic ellipsometry is an excellent technique for determining dielectric function. To obtain critical point energy, standard analytic critical point expression is used conventionally for second derivatives of dielectric function which might increase high frequency noise than signal. However, reciprocal-space analysis offers several advantages for determining critical point parameters in optical and other spectra, for example the separation of baseline, information, and high frequency noise in low-, medium-, high-index Fourier coefficient, respectively. We used reciprocal Fourier analysis for removing noise and determining critical point of ZnCdSe alloy.

Effect of overlayers on critical-point parameters in the analysis of ellipsometric spectra

As the complete removal of overlayers may not be possible in general, the authors investigate the effect of incomplete removal on critical-point parameters in the analysis of ellipsometric data. Using an approximate analytic expression, they show that energies and broadening parameters are much less affected by overlayers than amplitudes and phases. These conclusions are confirmed by false-data calculations for GaAs and overlayer-removal data for CdTe.

Vacuum UV spectroscopic ellipsometry study on [formula omitted] alloy films

We obtained pseudodielectric function spectra 〈ε〉=〈ε1〉+i〈ε2〉 of III–V based diluted magnetic semiconductor (DMS) Ga1-xCrxN (x=0.004, 0.013, 0.063, 0.101) films grown on GaN buffer layer on the Al2O3 (0001) substrate. The spectra was taken from 0.7 to 9.0eV at room temperature by using vacuum UV spectroscopic ellipsometry (VUVSE). To obtain the critical point (CP) parameters and their concentration dependence we used a standard analytic CP expression to observe linear variation of the E0, E1, and E2 CP energies of Ga1-xCrxN on Cr composition x(0⩽x⩽0.1). By using sp–d hybridization model which explains interaction between 3d levels of transition metal ions and sp levels of band electrons in host semiconductor, we suggested the level of 3d levels of Cr in GaN band structure.

On thermodynamic similarity of the stability boundaries of metastable metal states

The data on the thermodynamic and kinetic stability boundaries of liquid and solid Pb, Li, Al, Cu, and Fe metals over a wide range of pressures and temperatures accumulated by the authors are analyzed and compared. Molecular-dynamics models using the embedded atom and Lennard-Jones potentials are considered. Examples of assuredly absent similarity are given, and the possibility of constructing approximate similarity is discussed. The following variants for constructing dimensionless parameters are considered: the use of critical point parameters (for the liquid phase), the use of Simon parameters, and the use of parameters reached at the stability boundary at zero pressure (the latter variant was most effective for ordering the stability boundaries of crystals).

Survey of Theoretical Work for the Proposed HEDgeHOB Experimental Schemes: HIHEX and LAPLAS

AbstractThis paper presents a review of the theoretical work that has resulted in a scientific proposal on studies of High‐Energy‐Density (HED) states in matter using intense beams of energetic heavy ions that will be available at the future Facility for Antiprotons and Ion Research (FAIR) at Darmstadt [W.F. Henning, Nucl. Inst. Meth B 24 (2003) 725‐729]. The proposal is named HEDgeHOB that stands for High Energy Density Matter Generated by Heavy Ion Beams. Two experimental schemes have been worked out for the HEDgeHOB experimental proposal, namely, HIHEX and LAPLAS. The first scheme allows for studies of HED states by isochoric and uniform heating of matter by an intense heavy ion beam that is followed by isentropic expansion of the heated material. Numerical simulations have shown that using the beam parameters that will be available at the FAIR, one can access all the interesting physical states of HED matter including an expanded hot liquid state, twophase liquid‐gas region, critical point parameters and strongly coupled plasmas for all the materials of interest. The second scheme involves a low‐entropy compression of a test material like hydrogen that is enclosed in a cylindrical shell of a high‐Z material like gold or lead. The target can be driven by a hollow or a circular beam. This compression scheme relies on multiple shock reflection between the hydrogen‐gold (lead) boundary and the cylinder axis. The hydrodynamic stability of the LAPLAS target has also been analyzed that shows that the implosion is completely stable to Rayleigh‐Taylor and Richtmyer‐Meshkov instabilities. LAPLAS implosion using a hollow beam is suitable for studying the problem of hydrogen metallization whereas the one employing a circular focal spot leads to physical conditions that are expected to exist in the interiors of the giant planets. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Thermophysical Properties of a Refrigerant Mixture of R365mfc (1,1,1,3,3-Pentafluorobutane) and Galden® HT 55 (Perfluoropolyether)

This work presents a comprehensive experimental study of various thermophysical properties of an azeotropic refrigerant mixture of 65 mass% R365mfc (1,1,1,3,3-pentafluorobutane) and 35 mass% Galden® HT 55 (perfluoropolyether). Light scattering from bulk fluids has been applied for measuring both the thermal diffusivity and the speed of sound in the liquid and vapor phases under saturation conditions, between 293 K and the liquid–vapor critical point at 450.7 K. Furthermore, the speed of sound has been measured for the superheated-vapor phase along nine isotherms, between 393 and 523 K and up to a maximum pressure of about 2.5 MPa. For temperatures between 253 and 413 K, light scattering by surface waves on a horizontal liquid–vapor interface has been used for simultaneous determination of the surface tension and kinematic viscosity of the liquid phase. With light scattering techniques, uncertainties of less than ±2.0%, ±0.5%, ±1.5%, and ±1.5% have been achieved for the thermal diffusivity, sound speed, kinematic viscosity, and surface tension, respectively. In addition to vapor-pressure measurements between 304 and 448 K, the density was measured between 273 and 443 K using a vibrating-tube method. Here, measurements have been performed in the compressed- and saturated-liquid phases with uncertainties of ±0.3% and ±0.1%, respectively, as well as for the superheated vapor up to a maximum pressure of about 3 MPa with an uncertainty between ±0.3% and ±3%. Critical-point parameters were derived by combining the data obtained by different techniques.

Optical properties of molecular-beam-epitaxy-grown InGaMnAs thin films

The authors have determined the dielectric functions of a series of molecular-beam-epitaxy-grown (In0.5Ga0.5)1−xMnxAs thin films deposited on InP substrates. Two variable angle spectroscopic ellipsometers, covering both the IR and the UV range (0.2–30μm), were used to obtain optical spectra for each of the samples. Using a standard inversion technique, the experimental data were modeled to obtain the dielectric function for each of the quaternary samples. By using a parametric semiconductor model, they deduced the critical point parameters corresponding to the electronic transitions in the Brillouin zone. Their analysis indicates that in this particular quaternary system, while the critical point associated with the fundamental gap, E0, blueshifts as a function of Mn concentration, the E1 critical point shows a redshift with respect to the Mn concentration.

Dielectric functions, elasto-optical effects, and critical-point parameters of biaxially stressed Si1−yCy alloys on Si (0 0 1)

The complex dielectric functions ϵ(ℏω) from 0.74 to 6.6 eV of pseudomorphically strained Si1−yCy (0 < y < 0.014) alloys grown on Si (0 0 1) were determined using spectroscopic ellipsometry. Interference effects due to surface overlayers and multiple reflections at the substrate/epilayer interface were subtracted. We also report the critical-point parameters (amplitude, energy, broadening, phase angle and dimension) of the E′0, E1, E2 and E′1 interband transitions. While the E1 energy gap increases linearly with increasing C content, in good agreement with a continuum elasticity model (taking into account the effects of biaxial stress and alloying with C based on a linear interpolation of the Si and diamond E1 energies), the E′0 gap stays approximately constant and the E2 gap shows a significant decrease. The amplitudes of all critical points decrease by about 50% and the broadenings increase by about 50–80% when adding 1.4% C. The phase angles remain approximately the same as in Si, except for E′1. The changes in the critical-point parameters can be understood due to the lattice relaxation (four Si nearest neighbours move towards C) and the strong alloy scattering, with obvious implications for ultrafast or high-field electronic transport in such alloys. Since the Si1−yCy alloys are under a tensile biaxial stress, the measured ordinary dielectric function is also affected by piezo-optical effects, which were calculated using literature data for bulk Si.

Numerical simulations and theoretical analysis of High Energy Density experiments at the next generation of ion beam facilities at Darmstadt: The HEDgeHOB collaboration

This paper presents detailed numerical simulations and theoretical analysis of different possible experimental schemes to study the thermophysical and transport properties of High Energy Density ( HED) matter generated by the interaction of intense heavy ion beams. The considered beam parameters are those which will be available at the future Facility for Antiprotons and Ion Research ( FAIR) at Darmstadt [W.F. Henneing, Nucl. Instrum. Methods, B214, (2004) 211]. This work has shown that an intense heavy ion beam can be used employing two very different configurations to study HED states in matter. In the first scheme, a sample material is uniformly and isochorically heated by the beam and the heated material is subsequently allowed to expand isentropically. Depending on the specific energy deposited in the material, one may access all the interesting physical states, including that of an expanded hot liquid ( EHL), two-phase liquid–gas ( 2PLG) region, critical point ( CP) parameters as well as strongly coupled plasma ( SCP) states during the expansion. This scheme is named HIHEX ( Heavy Ion Heating and EXpansion). We have considered a 1 GeV/u uranium beam with an intensity, N = 10 10–10 12 ions that are delivered in a single bunch, 50 ns long. The particle intensity distribution in the transverse direction is assumed to be Gaussian with a full width at half maximum (FWHM) in the range of 1–4 mm. We note that the estimated critical temperatures for many metals are very high which are very difficult to access using traditional techniques of shock compression of matter. Employing the proposed HIHEX scheme, one can easily achieve the required temperature by depositing corresponding specific energy in the sample. Solid as well as porous targets have been used in our study. In the second scheme, a sample material like frozen hydrogen that is enclosed in a cylindrical shell of a high- Z material like gold or lead, is imploded by the ion beam. This scheme is specially designed to generate multiple reflection of shocks in the target that leads to a low-entropy compression of the sample material. As a result of this, one achieves super-high densities (up to 30 times solid density) and ultrahigh pressures (3–30 Mbar) in the hydrogen. If one uses a hollow beam with an annular focal spot, hydrogen is not directly heated by the ion beam that leads to a low final temperature (of the order of a few thousand K). This scheme is therefore suitable to study the problem of hydrogen metallization. In case one uses a circular focal spot, although the hydrogen is strongly heated by the beam, one still achieves a very high compression because the pressure in the surrounding shell is orders of magnitude higher than that in hydrogen. However, in this case the final hydrogen temperature is much higher (of the order of a few eV) than in the previous case. This configuration is thus suitable to study the interiors of the giant planets and is named LAPLAS ( LAboratory PLAnetary Science). We have also analyzed the hydrodynamic stability of the LAPLAS target and we find that the Rayleigh–Taylor (RT) and Richtmeyer–Meshkov (RM) instabilities will not pose any serious problems to this scheme.

A new analytical formulation for the generalized corresponding states model for thermodynamic and surface properties in pure fluids

In a previous study [Kiselev, S.B., Ely, J.F., 2003. Generalized corresponding states model for bulk and interfacial properties of pure fluids and fluid mixtures. Journal of Chemical Physics 119(16), 8645–8662] we developed a formulation of the generalized corresponding states (GCS) model which incorporated critical region non-analytic behavior via a parametric crossover function. The parametric variable in that model was obtained from the crossover modification of the sine model originally proposed by Fisher et al. [1999. Trigonometric models for scaling behavior near criticality. Physical Review B 59(22), 14533–14545]. In this work we have developed a new version of the GCS model that incorporates an analytical sine (ANS) model solution which greatly simplifies the application of the resulting equation of state (EOS). Similar to the original GCS/CRS model, the new GCS/ANS model contains the critical point parameters and acentric factor as input and yields a very accurate description of the PVT- and VLE-surfaces of one-component fluids in a wide range of thermodynamic states, including the nearest vicinity of the critical point. The GCS/ANS model reproduces the saturated pressure and liquid density data with an average absolute deviation (AAD) of about 1% and the vapor density with AAD of about 2–3%. In the one phase region for ρ ⩽ 2 ρ c the model reproduces the PVT data with an AAD less then 2% and for liquid densities where ρ ⩾ 2 ρ c with an AAD of about 1–2%. In combination with the density functional theory (DFT), the GCS/ANS–DFT model is also capable of reproducing the surface tension of one-component fluids (polar and non-polar) with high accuracy.

Influence of polydispersity on the critical parameters of an effective-potential model for asymmetric hard-sphere mixtures

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard-sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential [R. Roth, Phys. Rev. E 62 5360 (2000)] designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having a degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q(triple bond)sigma(s)/(-)sigma(b)=0.1 and q=0.05. We find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard-sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.

Simple generalized vapour pressure- and boiling point correlation for refrigerants

A simple generalized vapour pressure equation has been developed to correlate vapour pressures of refrigerants. The proposed vapour pressure equation has one or three adjustable parameters depending on the required accuracy. In the first case the adjustable parameter has been correlated with the reduced triple point temperature. Thus, the proposed vapour pressure equation requires only the fluid-dependent critical and triple point parameters and enables the accurate description of the entire temperature range of pure refrigerants from the triple to the critical point. Another advantage of the proposed correlation is its possibility of being inversed; this way the Boiling point can be calculated from vapour pressures through a single equation. Finally, a predictive method for the triple point pressure is suggested.

Dielectric functions and electronic band structure of lead zirconate titanate thin films

We measure pseudodielectric functions in the visible-deep ultraviolet spectral range of Pb(ZrxTi1−x)O3 (x=0.2,0.56,0.82) (PZT), Pb0.98Nb0.04(Zr0.2Ti0.8)0.96O3, Pb0.91La0.09(Zr0.65Ti0.35)0.98O3, and Pb0.85La0.15Ti0.96O3 films grown on platinized silicon substrates using a sol-gel method and on (0001) sapphire using a radio-frequency sputtering method. Using a parametric optical constant model, we estimate the dielectric functions (ϵ) of the perovskite oxide thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard critical-point model, we determine the parameters of the critical points. In the second derivative spectra, the lowest band-gap energy peak near 4eV is fitted as a double peak for annealed PZTs due to the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest band-gap peak is fitted as a single peak. We also examine the effect of dopants La and Nb, which substitute at Pb and Zr (Ti) sites, respectively. We found three band gaps Ea(∼3.9eV), Eb(∼4.5eV), and Ec(∼6.5eV) in the order of increasing energy. The Ea and Eb band-gap energies were not sensitive to Zr composition. We discuss the change of critical-point parameters for PZTs in comparison to the band-structure calculations based on local-density approximation. The near constancy of the lowest band-gap energy independent of Zr composition is consistent with the band-structure calculations.

Chemical Bonding in the Complexes XeF 5 + XF 6 − (X = P, As, Sb, and Bi)

Ab initio quantum-chemical calculations of the complexes XeF 5 + XF 6 − (X = P, As, Sb, and Bi) were performed with the use of relativistic pseudopotentials for heavy atoms and full-electron basis sets. The chemical bonds were characterized by the parameters of critical points (electron density, its Laplacian, total electron energy, and its kinetic and potential components). It was demonstrated that the interaction between the XeF 5 + cation and the XF 6 − anion in XeF 5 + XF 6 − follows a key-lock scheme involving directed interactions of bridging fluorine atoms Fb → Xe and that the structuring function of the lone electron pair of the Xe atom is to compensate the destabilizing electrostatic interaction between the Xe and X atoms bearing excess positive charges.

Equation of State for Substances that Satisfy the Corresponding States Law

Universal expressions for the free energy of substances that satisfy the law of corresponding states are obtained. The equation of state is constructed using an interpolation between the high temperature Debye approximation and the ideal-gas one. Missing data needed for calculations have been found from the comparison of calculated and tabulated values of entropy and pressure along the phase coexistence curves. The thermodynamics of corresponding states, constructed in this way, allows one to find the triple- and critical-point parameters, as well as the phase coexistence curves with an accuracy that does not exceed the accuracy of the law of corresponding states itself.

Complex dielectric function of biaxial tensile strained silicon by spectroscopic ellipsometry

The complex dielectric function of biaxial tensile strained Si grown on a fully relaxed ${\mathrm{Si}}_{0.81}{\mathrm{Ge}}_{0.19}$ virtual substrate was obtained from spectroscopic ellipsometry measurement in the 2.5--5-eV energy range. Standard critical point (CP) line shapes were fit to numerically obtained second-derivative spectra to extract interband CP parameters. It is shown that the biaxial tensile strain increased the number of ellipsometrically observable CP's from two to three in the ${E}_{0}^{\ensuremath{'}}∕{E}_{1}$ gap region, whereas the CP's in the ${E}_{2}$ region were relatively unaffected. These results compare favorably to previous reports for uniaxially compressed stressed silicon. In particular, the experimentally observed splitting of the ${E}_{1}$ gap---${E}_{1}(1)=3.310\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and ${E}_{1}(2)=3.437\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$---was in reasonable agreement with calculated expectations---${E}_{1}(1)=3.304\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and ${E}_{1}(2)=3.395\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$---using previously reported Si deformation potentials.

Uranium critical point problem

Significant uncertainty of uranium critical point parameters in present knowledge is considered. Paper is to reveal thermodynamic aspects of the problem through comparison of some available theoretical predictions for the uranium critical point parameters as well as to discuss in brief plausible versions to meet existing contradiction. New calculations of gas–liquid coexistence in uranium by modern thermodynamic code are included in the analysis.