Determination of the optical constants of metals and semiconductors by combining ellipsometry with electron spectroscopy microscopy and X-ray specular reflection analysis

The optical constants n(λ) and k(λ) of metals and semiconductors can be determined by spectroellipsometry, however, their apparent values are considerably affected by the roughness and oxide overlayer thickness dof the sample. Aluminium thin film samples of high perfection and very low roughness (<1 nm) have been studied by cross-disciplinary experimental methods: X-ray specular reflection analysis for determining the structure and thickness of the natural (hydrated) oxide overlayer and roughness of the substrate; plasmon electron energy loss spectroscopy supplied d. For calibration of the d measurements a special thin film multilayer system was developed, suitable for preparing cross-sectional samples for resolution transmission electron microscopy. Knowing the roughness and d-data, the optical constants n(λ) and k(λ) of aluminium were determined by spectroellipsometry in the spectral range λ=365–633 nm. Experimental results and a nomogram are presented for evaluating n(λ) and k(λ). The dependence of the ellipsometric optical constants on roughness and d is discussed. Very good agreement of the optical constants with the corrected ellipsometric results of Blanco and the synchrotron spectroscopy data of Hagemann was found. The cross-disciplinary methods can be applied to metals and semiconductors covered with an overlayer.     

Infrared reflectivity and dielectric permeability of ultra-thin Cu and Al films

In this report we present an experimental investigation of the reflectivity (R) and the dielectric permeability () for Cu and Al ultra-thin films ranging in thickness from a few monolayers to 12 nm at infrared and visible wavelengths. The metal films were prepared by RF-sputtering on SiO₂ (glass) and Si substrates. IR reflectivity was measured at 9.2 μm, while was measured with the help of laser ellipsometer at a wavelength of 632.8 nm. Two types of oscillations on R(d) and (d) were discovered for two thickness regions determined by the critical thickness value d*. Oscillations at d<d* with periods near 0.3 nm for Al and Cu films were observed on R(d) and (d) due to quantum sized effects (QSEs). At d>d* (thickness between 6–12 nm) we discover a new type of strong oscillation of R(d) and (d) with an oscillating period of 0.2 nm. For thickness larger than 12 nm all the oscillations tend to disappear and R and behave almost as their volume values. A possible explanation for the appearance of these two kinds of oscillations is based on the introduction of the critical film thickness d*.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

4p-4d fano-like resonance in rhodium

Photoemission measurements of Rh films in the photon energy range 40–120 eV show that the 4p-4d intrashell interaction has a Fano-like resonance. The 4d photoemission intensity goes through a sharp dip in the vicinity of the 4p⁶4dⁿ+hv → 4p⁵4dⁿ⁺¹ threshold followed by a resonant enhancement before decreasing again. All parts of the 4d band show the same resonant behavior in contrast to previous resonant photoemission results. The resonant behavior of Rh is compared with Co which is the 3d analog of Rh.     

Structural and optical properties of thermally evaporated Bi2Te3 films

Bi₂Te₃ films were prepared by thermal evaporation technique. X-ray diffraction analysis for as-deposited and annealed films in vacuum at 150 °C were polycrystalline with rhombohedral structure. The crystallite size is found to increase as the film thickness increases and has values in the range 67–162 nm. The optical constants (the refractive index, n, and absorption index, k) were determined using transmittance and reflectance data in the spectral range 2.5–10 μm for Bi₂Te₃ films with different thicknesses (25–99.5 nm). Both n and k are independent on the film thickness in the investigated range. It was also found that Bi₂Te₃ is a high refractive index material (n has values of 4.7–8.8 in the wavelength range 2.5–10 μm). The allowed optical transitions were found to be direct optical transitions with energy gap  eV. The optical conductivities σ₁ = ƒ(hν) and σ₂ = f(hν) show distinct peaks at about 0.13 and 0.3 eV, respectively. These two peaks can be attributed to optical interband transitions.     

Critical dynamics of a stochastic n-vector model below Tc

The dynamic properties of a stochastic n-vector model are investigated for T < T_c in d=4−ε dimensions. Besides the non-conserved order parameter the model involves also the conserved densities of generators of the symmetry group O(n). We calculate the excitation spectra of those conserved densities and the transverse fluctuations of the order parameter to linear order in ε in the hydrodynamic region kξ1. The propagating modes have linear dispersion and quadratic damping in accordance with the phenomenological theory. The relaxing modes, however, exhibit non-hydrodynamic wavenumber dependence with a relaxation rate ω_k ∞ k^d/2.     

Ge-Sb-Se硫系玻璃的折射率和热光系数

Ge-Sb-Se硫系玻璃被认为是极佳的红外传输材料和有潜力的非线性光学材料.在光学设计中,玻璃的线性折射率(n)及其热光系数(ζ)是关键技术参数.以预测和调控Ge-Sb-Se玻璃的n和ζ为目的,考察了玻璃的n,ζ,密度(d)和体积膨胀系数(β)与化学参数dSe和拓扑网络结构参数r的内在联系.研究发现,玻璃的n随d的增加而增大;ζ随β的增大而近似线性减小;β随dSe的减小或r的增大而减小;当Ge含量固定时, d随dSe的减小或r的增大而增大,当Sb含量固定时, d在dSe=0时具有最小值.基于实测d和n,拟合获得了Ge, Sb和Se元素在2—12μm波段的摩尔折射度(R_i),分别为R_(Ge)=10.16—10.50 cm~3/mol,RSb=16.71—17.08 cm~3/mol和RSe=11.15—11.21 cm~3/mol,根据d和R_i计算得到的n与实测值的偏差小于1%.基于实测ζ和β,拟合得到了Ge, Sb和Se元素在2—12μm波段的摩尔折射度温度系数(φ_i),分别为φ_(Ge)=21.1—22.6 ppm/K,φ_(Sb)=7.2—8.4 ppm/K和φ_(Se)=90.2—94.2 ppm/K,根据β和φ_i计算得到的ζ与实测值的偏差小于6 ppm/K.     

Barrier height engineering of Ag/GaAs(100) Schottky contacts by a thin organic interlayer

Thin films of 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) were used as an interlayer for the electronic modification of Ag/n-GaAs(100) Schottky contacts. The electronic properties were investigated recording in situ current–voltage (I–V) and capacitance–voltage (C–V) characteristics. For H-plasma treated substrates the effective barrier height decreases from 0.81 to 0.64 eV as a function of the PTCDA layer thickness (d_PTCDA). In the case of the sulphur passivated GaAs the effective barrier height first increases and then decreases, the overall range being 0.54–0.73 eV. The substrate treatment leads to a different alignment between the band edges of the GaAs and the molecular orbitals of the PTCDA, making it possible to determine the energy position of the LUMO transport level.     

Doppler-shifted cyclotron resonance in thin metal films

The velocities of electrons contained in a thin slab are quantized because the component of momentum transverse to the slab faces is quantized. For a free electron gas the transverse velocity is given by |v_H| = l(/m) (π/d) where l = 1, 2, 3, …. If a magnetic field is applied normal to the slab, the wave number and frequency dependent conductivity consists of a series of resonant terms. The resonances occur at the Doppler-shifted cyclotron resonance frequencies |ω_c| = ω ± p(/m) (π/d)² where l = 1, 2, 3, …. It is shown that these resonances in the conductivity result in an absorption in pure thin films at low temperatures which is periodic in magnetic field. The semi-classical expression for the absorption is in substantial agreement with the corresponding quantum calculation, and has the virtue that it may be readily extended to non-spherical Fermi surfaces.     

Order-disorder criticality, wetting, and morphological phase transitions in the irreversible growth of far-from-equilibrium magnetic films

An exhaustive numerical investigation of the growth of magnetic films in confined (d+1)-dimensional stripped geometries (d=1,2) is carried out by means of extensive Monte Carlo simulations. Films in contact with a thermal bath at temperature T, are grown by adding spins having two possible orientations and considering ferromagnetic (nearest-neighbor) interactions. At low temperatures, thin films of thickness L are constituted by a sequence of well-ordered domains of average length l_DL. These domains have opposite magnetization. So, the films exhibit “spontaneous magnetization reversal” during the growth process. Such reversal occurs within a short characteristic length l_R, such that l_Dl_RL. Furthermore, it is found that for d=1 the system is non-critical, while a continuous order-disorder phase transition at finite temperature takes place in the d=2 case. Using standard finite-size scaling procedures, the critical temperature and some relevant critical exponents are determined. Finally, the growth of magnetic films in (2+1) dimensions with competing short-range magnetic fields acting along the confinement walls is studied. Due to the antisymmetric condition considered, an interface between domains with spins having opposite orientation develops along the growing direction. Such an interface undergoes a localization–delocalization transition that is the precursor of a wetting transition in the thermodynamic limit. Furthermore, the growing interface also undergoes morphological transitions in the growth mode. A comparison between the well-studied equilibrium Ising model and the studied irreversible magnetic growth model is performed throughout. Although valuable analogies are encountered, it is found that the non-equilibrium nature of the latter introduces new and rich physical features of interest.     

Study of some optical properties of evaporated TbCu0.6Al0.4 thin films

Evaporated TbCu_0.6Al_0.4 thin films with different thicknesses, ranging from 26 to 100 nm, were prepared on a glass substrate. The complex refractive index of thin films has been determined for the first time from the measurements of reflectance, R, and transmittance, T, at almost normal incidence in the spectral range of 400–2200 nm. Some micro-characteristics of TbCu_0.6Al_0.4 alloy including free charge concentration, n_c, the relaxation time, τ, the static conductivity, σ, and the electron velocity at the Fermi surface, V_F, have been evaluated using the simplified Drude model.     

Anisotropic percolation and the d-dimensional surface roughening problem

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent δ=0.63±0.01 (d=1+1) and δ=0.48±0.02 (d=2+1) are in good agreement with our recent experiments. The values of δ in higher dimensions (δ=0.38±0.03 in d=4 and δ=0.27±0.05 in d=5) do not support a recent theoretical conjecture.     

Minimal renormalization without ε-expansion: Three-loop amplitude functions of the 0(n) symmetric Φ theory in three dimensions below Tc

We present an analytic three-loop calculation for thermodynamic quantities of the O(n) symmetric Φ⁴ theory below T_c within the minimal subtraction scheme at fixed dimension d = 3. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the three-loop terms of the amplitude functions ƒ_Φ, F₊ and F₋ of the order parameter and the specific heat above and below Tc, respectively, without using the e = 4-d expansion. A Borel resummation for the case n = 2 yields resummed amplitude functions f_Φ and F₋ that are slightly larger than the one-loop results. Accurate knowledge of these functions is needed for testing the renormalization-group prediction of critical-point universality along the λ₋line of superfluid ⁴He. Combining the three-loop result for F₋ with a recent five-loop calculation of the additive renormalization constant of the specific heat yields excellent agreement between the calculated and measured universal amplitude ratio A⁺/A^- of the specific heat of ⁴He. In addition we use our result for f_Φ to calculate the universal combination Rc of the amplitudes of the order parameter, the susceptibility and the specific heat for n = 2 and n = 3. Our Borel-resummed three-loop result for R_c is significantly more accurate than the previous result obtained from the ε-expansion up to O(ε².     

Scaling properties for ordered/disordered 2-D dry froths

We investigate the evolutionary behaviour of a 2-D dry froth with initial ordered/disordered conditions corresponding, respectively, to monodisperse/polydisperse topological networks. Using the direct simulation approach, we discuss the scaling properties of the cell side distribution, f(n), and its second moment, μ₂, for various system sizes and initial structures. For the case of a highly ordered network, the introduction of disorder may be viewed in terms of “seeding” the froth system with a number of defects, d, where for d = 1 previous work has shown that stable conditions are not achieved. We find that the limiting behaviour here depends on the amount of disorder, where this is quantified by the proportion of non-uniform initial cells and the pattern of seeding. Our findings support the view that a quasi-scaling state exists for the highly ordered froth, in contrast to the universal scaling state of the disordered and low-ordered froth. In the light of these results, we briefly reconsider the question of transience for the early results of Aboav (1980).     

Theta-terms in nonlinear sigma-models

We trace the origin of θ-terms in nonlinear σ-models as a nonperturbative anomaly of current algebras. The nonlinear σ-models emerge as a low energy limit of fermionic σ-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic σ-models in space-time dimension (d+1) with chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres. The geometric phases in the first two hierarchies are θ-terms. We emphasize a relation between θ-terms and quantum numbers of solitons.     

Frustrated total internal reflection evanescent switching

The mechanism of frustrated total internal reflection was analyzed according to the theory of optical film. The transmission and reflection functions were developed and the curves of transmission and reflection changing from the relative gap width d/λ, incident angle θ₀, and refraction index n were shown in graphs. We proposed a scheme of experimental device to test the theoretical conclusion. A self-made electronic actuator drove the piezoelectric ceramics of FTIR. Experiments showed that the evanescent of transmission is 80% for He–Ne laser and smaller for YAG laser and Er:glass laser.     

A theoretical analysis of refractive-index grating waveguide structures for integrated optics

Based upon equivalent transmission line method, a perturbation analysis on the guiding properties of refractive-index gratings is presented. By numerical calculation, the leakage parameter which influences the leakage energy into the diffracted orders due to the grating scatter, is achieved as functions of the grating period, thickness of the waveguide and index modulation Δn. Our results reveal that, although the index modulation Δn is much less than that of the etched or deposited grating, refractive-index gratings can still reach a high leakage parameter because of the prominent increase of the grating height.     

Hyperscaling for polymer rings

The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a d-dimensional lattice obeys hyperscaling. The combination p_NR²_N^d/2μ^−N (where p_N is the number of configurations of an oriented and rooted N-step ring, R²_N a typical average size squared, and μ the SAW effective connectivity constant of the lattice) is equal for N å ∞ to a lattice-dependent constant times a universal amplitude A(d). The latter amplitude is calculated directly from the minimal continous Edwards model to second order in 4 − d. The case of rings at the upper critical dimension d = 4 is also studied. The results are checked against field-theoretical calculations, and former simulations. As a consequence, we show that the universal constant λ appearing to second order in in all critical phenomena amplitude ratios is equal to .     

The magnetized d-dimensional ideal paragas

The magnetic properties of a d-dimensional uncharged ideal paragas in a uniform magnetic field are examined. For parastatistics parameter p = ∞ (bosons) there is Bose-Einstein condensation for d/ > 1 with spontaneous magnetization, and for 1<d/2 there is a divergent magnetic susceptibility at zero magnetic field. For finite p (parafermions) we obtained the asymptotic limit behavior of low and high temperature of the magnetic susceptibility. The crossover between these limits is evaluated numerically, observing that the parafermions can be characterized by Fermi-Dirac behavior.     

Multilayer relaxation of Rh(311)

The multilayer relaxation of the Rh(311) surface was investigated by means of LEED structure determination both for vertical and surface parallel (registry) relaxations. Excellent agreement between experimental and calculated spectra could be achieved mirrored by a minimum Pendry R-factor R = 0.174. The first three layer spacings are oscillatorily relaxed by Δd₁₂/d₀ = −14.5 ± 1.8%, Δd₂₃/d₀ = +4.9 ±2.0% and Δd₃₄/d₀ = −1.0 ±2.0%. There seems to be a coherent registry shift of the fir Δs = 0.03 ± 0.07 Å which, however, is within the error limits of the structure determination. Moreover, an energy dependent inner potential is detected. The results are discussed in comparison to equivalent surfaces of other materials as well as for the less open surfaces of rhodium.