Critical Point Model Research Articles

Ion implantation induced disorder in single‐crystal and sputter‐deposited polycrystalline CdTe characterized by ellipsometry and backscattering spectrometry

AbstractBulk single‐crystal CdTe, sputter‐deposited polycrystalline CdTe films of about 2.5 micron thickness, and single‐crystal Si (c‐Si) have been ion implanted using 350 keV Xe at fluences ranging from 1×1013 to 16×1013 cm–2 so as to create disorder in a controlled way from fully single‐crystalline to fully amorphous material. The general purpose of the investigations is to seek a parameterization of the critical point structures and establish a database for fitting the optical properties of CdTe films having different unknown grain sizes whereby the grain size will be described in terms of an effective defect density. The polycrystalline CdTe samples were magnetron sputtered onto c‐Si followed by CdCl2 and Br2‐methanol treatment to improve properties in terms of grain size and surface smoothness, respectively. The fluences for use in the ion implantation of CdTe were estimated using the SRIM (Stopping and Range of Ions in Matter) software, and cross‐checked by simultaneous implantation of bulk c‐Si samples. The optical properties were characterized by second derivative analysis and by a generalized critical point model. Although the damage created by 350 keV Xe in the simultaneously implanted c‐Si samples, as measured by both spectroscopic ellipsometry and Rutherford backscattering/ channeling spectrometry (RBS/C), agrees well with the expectations based on the SRIM simulation, the damage created in CdTe remains at a very low level even for doses several times higher than the amorphization level estimated by simulation. The character of the dechanneling of the RBS/C spectra indicates extended defects (presumably dislocation loops). This effect was similar in both single‐crystal and thin film polycrystalline CdTe, although less pronounced in thin film samples. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ellipsometric models for vertically inhomogeneous composite structures

AbstractThe optical properties of thin films usually depend on the preparation conditions. For example, the microstructure of ion implantation‐caused damage, the grain size of deposited polycrystalline materials, or the porosity of chemically etched silicon largely depend on the parameters of ion implantation, deposition, and etching, respectively. Generally, as a first approach, these materials can be considered as a mixture of components described by reference dielectric function data from the literature using the effective medium approximation (EMA). Interface roughness and vertical inhomogeneity can be described by the volume fraction of components changing as a function of depth. The EMA models are robust, and provide useful information like damage depth profiles of ion implanted materials, crystallinity and surface roughness of deposited materials, or porosity of chemically etched porous silicon. The requirement for EMA is that the size of the components must be smaller than the wavelength of the measuring light, but large enough to retain their bulk dielectric properties. If the component sizes are large, diffraction and scattering has to be taken into account. For example, surface roughness is routinely modeled by EMA, but in case of rough surfaces with large correlation length EMA may become invalid as approaching small wavelengths in the UV part of the spectrum. If component sizes decrease, it may not be possible to describe the components using bulk reference data, because of size effects or strain. For example, fine grained polycrystalline silicon or highly porous silicon can not be modeled by the usual mixture of single‐crystalline silicon (c‐Si) and amorphous silicon (a‐Si) for polycrystalline silicon, or mixing c‐Si and voids for porous silicon, but a component representing an intermediate structure between c‐Si and a‐Si has to be used to describe the vanishing long‐range order. A less robust but more detailed analysis is provided by parametrization of the dielectric function of the layer or the components in an EMA composition using model dielectric functions, critical point (CP) models, oscillator models, or empirical dispersion equations. In these cases, cross‐correlation, parameter‐coupling, selection of sensitive parameters, local minima, and regression in a multi‐parameter space are crucial issues to be handled properly. Consideration of the optical penetration depth (OPD) is also important, when measuring vertically inhomogeneous semiconductor materials. Obviously, CP analysis in semiconductors is most sensitive around the CP photon energies, but the OPD is the smallest just at this region of the spectrum. In silicon, the OPDs at the E1 and E2 CP energies are about 10 nm and 5 nm, respectively. Consequently, CP analysis of structures below this depth is not possible using ex situ measurement of silicon. This work shows approaches and examples to model multi‐component materials created using different methods including ion implantation, deposition, and electrochemical etching. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparative infrared study of optimally doped and underdopedLa2−xSrxCuO4 single crystals

The temperature dependence of the optical spectra of twoLa2−xSrxCuO4 single crystals was investigated for both in-plane and out-of-plane directions. For the underdoped(x = 0.08) single crystal, the in-plane optical conductivity that was analysed by ageneralized Drude formalism shows a suppression of the scattering rate1/τ(ω) and an increasedeffective mass m* as the temperature decreases at low frequencies. Since this behaviour can be explained by thepseudogap effect, it is concluded that the pseudogap is not present at the optimal doping(x = 0.15). This result isconfirmed by the c-axis optical conductivity, which decreases only for the underdoped single crystal. Theabsence of the pseudogap at the optimal composition is in accord with the quantum criticalpoint model and it can explain the phase diagram of high-temperature superconductors.

First experimental test of X(5) critical-point symmetry in theA~130mass region: Low-spin states and the collective structure ofCe130

Excited, low-spin states in $^{130}\mathrm{Ce}$ are populated in the ${\ensuremath{\beta}}^{+}/\ensuremath{\epsilon}$ decay of $^{130}\mathrm{Pr}$ and studied through off-beam \ensuremath{\gamma}-ray spectroscopy at the Yale moving tape collector. New coincidence data lead to the construction of a substantially revised level scheme. The low-lying states of $^{130}\mathrm{Ce}$ are compared with the predictions of the X(5) critical-point model and the X(5)-${\ensuremath{\beta}}^{4}$ model, and the latter is found to give better agreement with the data in terms of energies. Discrepancies in the relative $B(E2)$ values in $^{130}\mathrm{Ce}$ and the geometrical models suggest that the \ensuremath{\gamma} degree of freedom may play an important role in this mass region.

Dielectric Function and Defect Structure of CdTe Implanted by 350-keV Bi Ions

AbstractIn this work we have developed optical models for the ellipsometric characterization of Bi-implanted CdTe. We have characterized the amount and nature of disorder using Rutherford Backscattering Spectrometry combined with channeling (RBS/C). Samples with a systematically varying degree of disorder were prepared using ion implantation of Bi into single-crystalline CdTe at an energy of 350 keV with increasing doses from 3.75×1013 cm-2 to 6×1014 cm−2. The motivation for use of the high atomic mass Bi ions was that previous studies using lighter ions revealed damage at a low level, even for doses several times higher than the amorphization threshold estimated by simulation [P. Petrik et al., phys. stat. sol. (c) 5, 1358 (2008)]. In contrast, Bi ions create sufficient disorder for investigation of the changes in dielectric function critical point (CP) features in a wider variety of structures from single-crystalline to the disordered state. The CP features can be described by numerous methods starting from the standard CP model, through the parameterization of Adachi [Adachi et al., J. Appl. Phys. 74, 3435 (1993)], and finally to the generalized CP models. The standard CP model has been demonstrated to be a reliable approach for polycrystalline CdTe characterization used in photovoltaic applications [Li et al., phys. stat. sol. (a) 205, 901 (2008)].

Yield loss of lentil caused by Uromyces viciae-fabae

Yield loss in lentil (Lens culinaris Medik.) due to rust (Uromyces viciae-fabae [Pers.] J. Schröt) was determined by assessing crop and disease parameters at different growth stages and leaf canopy layers in field epidemics at Akaki, Ethiopia. The epidemics were created by inoculation of the rust-susceptible cultivar EL-142 with U. viciae-fabae and spraying plots with tebuconazole at different frequencies. The epidemics produced disease progress curves that varied significantly in the rate (rL ) of temporal progression and area under the disease progress curve (AUDPC). The rust epidemic, in particular between early flowering and early pod formation, had a significant influence on seed yield, pods per plant and seed mass. Mean seed yield losses up to 41.6% were recorded. The number of seeds per pod remained unaffected by the disease. The effect of rust on seed yield of lentil can be predicted with AUDPC and critical-point models using disease severity assessed on the upper canopy layer in the early flowering stage. Every 1% increase in rust severity reduced seed yield by 8.4%. Rust severity ≥ 4.7% at the critical early flowering stage significantly reduced seed yield, and hence, any measure that keeps severity below this threshold level would be advisable.

Dimensionality of electronic excitations in organic semiconductors: A dielectric function approach

We present a detailed investigation on the effective dimensionality (associated with the degree of delocalization) of electronic excitations in thin organic films using the dielectric function as obtained from ellipsometry. To this end, we study first the best analytical representation of the optical dielectric function of these materials and compare different approaches found in the literature: (i) the harmonic oscillator approximation, (ii) the standard critical-point model (SCP), (iii) the model dielectric function (MDF), and (iv) the Forouhi-Bloomer model. We use these models to analyze variable angle spectroscopic ellipsometry raw data for a thin poly(9,9-dioctylfluorene) (PFO) film deposited on quartz (taken as an archetypal sample). The superiority of the SCP model for PFO films and a wide range of other spin-coated conjugated polymers (and guest-molecules in polymers) is demonstrated. Moreover, we show how the SCP model can be used to gain physical information on the microscopic structure. As an example, we show that the delocalization of excitons decreases for nonconjugated polymers, such as polymethylmethacrylate and polyimide, while the conjugation length and exciton delocalization are, respectively, enhanced in cases where a planar conformation (e.g., $\ensuremath{\beta}$ phase of PFO) or a high degree of crystallinity [e.g., poly(3-hexylthiophene)] is achieved. As an additional example, we employ the SCP excitonic model to investigate the temperature dependence of the dielectric function of crystalline and glassy PFO films. We propose that the SCP excitonic model should be adopted as the standard choice to model the optical properties of polymer thin films from ellipsometry data.

Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method

Using a combination of Drude and critical points models, we show that the permittivity of several metals can be more efficiently described than using the well-known Drude–Lorentz model. The numerical implementation in a finite-difference time-domain code together with a non-uniform grid enables the study of thin metallic intermediate layers often neglected in simulations but found in realistic resonant structures.

Dielectric functions and critical points of PbTiO3, PbZrO3, and PbZr0.57Ti0.43O3 grown on SrTiO3 substrate

Single crystalline PbTiO3, PbZrO3, and PbZr0.57Ti0.43O3 thin films on SrTiO3 (001) substrates were grown by a combination of molecular beam epitaxy and rf sputtering methods. The authors measured the dielectric functions of the thin films using spectroscopic ellipsometry and determined the interband critical point energies using standard critical point model. They compared the critical point energies to the band structure calculations in the literature. The data suggest that anticrossing behavior occurs between Ea and Eb near Zr=0.17. This phenomenon is attributed to a coupling between X1c and X3c bands caused by intrinsic alloy disorder.

Ellipsometric study of the poling effect on nonlinear-optical side-chain polymers containing disperse red 1

The purpose of this work is to investigate the effect of corona poling on the optical functions of the nonlinear-optical (NLO) polymers. We measured the complex refractive indices of NLO polymers deposited on glasses before and after corona poling using spectroscopic ellipsometry at room temperature at various incidence angles. In addition, we observed the absorption spectral change using ultraviolet-visible spectroscopy after corona poling, which is attributed to the chromophore orientation. In order to make NLO polymers, we attached a NLO active dye and photocrosslinkable moieties as side chains of poly(4-hydroxystyrene), deposited the polymer thin films on glass substrates by spin-coating, and corona-poled it along the surface-normal direction to align the dipoles of the chromophores along the electric field direction. In detail, PSDR1-25 designates a poly(4-hydroxystyrene) where 25% of hydroxyl groups in the side chain are substituted by disperse red 1 (DR1) and PSDR1-50 means the same except for 50% substitution. PSDR1 has the second-order NLO property, which is expected to show an acentric ordering by poling electric field. We used a parametric optical constant model to estimate the complex refractive index of the polymers. We found that the poling induced the uniaxial property of the complex refractive index of the polymers by aligning the chromophores along the poling direction. With increased poling voltage, we found that the oscillator strength of the major peak near the 2.4eV (designated as Ea) peak decreases in the surface-parallel direction (x), whereas that of the surface-normal direction (z) increases. Moreover, a detailed analysis of the dielectric functions using the standard critical point model showed that the poling induced a new peak Ec (∼2.6eV) between dominant Ea (∼2.3eV) and weak Eb (∼2.9eV) peaks for PSDR1-50 polymers. With increased poling voltage, the Ec peak strength increased compared to those of Ea and Eb peaks. We tentatively attribute Ec to lower symmetry, possibly Stark effect, induced in the chromophores by the corona poling.

Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method

We describe the implementation of the critical points model in a finite-difference time domain code dealing with dispersive media through the recursive convolution method. We show that this requires only minor modifications to existing codes able to take the Drude and Lorentz models into account. The use of this model of dispersion over the typical Drude–Lorentz one may be advantageous in specific cases.

Critical-point yield model to estimate yield damage caused by Cercospora zea-maydis in corn

A model to estimate damage caused by gray leaf spot of corn (Cercospora zea-maydis) was developed from experimental field data gathered during the summer seasons of 2000/01 and during the second crop season [January-seedtime] of 2001, in the southwest of Goiás state. Three corn hybrids were grown over two seasons and on two sites, resulting in 12 experimental plots. A disease intensity gradient (lesions per leaf) was generated through application, three times over the season, of five different doses of the fungicide propiconazol. From tasseling onward, disease intensity on the ear leaf (El), and El - 1, El - 2, El + 1, and El + 2, was evaluated weekly. A manual harvest at the physiological ripening stage was followed by grain drying and cleaning. Finally, grain yield in kg.ha-1 was estimated. Regression analysis, performed between grain yield and all combinations of the number of lesions on each leaf type, generated thirty linear equations representing the damage function. To estimate losses caused by different disease intensities at different corn growth stages, these models should first be validated. Damage coefficients may be used in determining the economic damage threshold.

Optical Properties of Black NiO and CoO Single Crystals Studied with Spectroscopic Ellipsometry

Using spectroscopic ellipsometry, we measure the dielectric functions of NiO and CoO single crystals, which are grown by using the Verneuil (flame fusion) process. Taking the 2nd derivative of the dielectric function, we identify several optical structures below and near the band gap. We fit the 2nd derivative of the dielectric function by using an exciton lineshape and the standard critical point (SCP) model. The band gap energies of NiO and CoO are estimated to be 3.87 eV and 5.43 eV, respectively. The optical structures below and near the band gaps are attributed to intra-atomic d-d transitions and are estimated to be 1.2, 1.3, 1.8, 2.6, 2.9, 3.2, 3.4, 3.7, and 4.2 eV for NiO and 1.61, 2.26, 2.72, and 3.6 eV for CoO. Both the band gap and the d-d transition energies of NiO and CoO are compared to the literature values. The derivative spectra show unambiguously the d-d transitions near and above the band gap and those below the band gap. The lineshape fitting using the SCP model provides accurate values for the band gap energy and the d-d transitions. In addition, the SCP analysis verifies the exciton nature of the band gap and the d-d transitions. We attribute this to the formation of Frenkel excitons in NiO and CoO transition metal oxides.

Lifetime measurements of yrast states inYb162andHf166

Lifetime measurements of yrast levels in 162Yb and 166Hf were performed using the recoil distance Doppler-shift method in coincidence mode. Excited states in 162Yb and 166Hf were populated via the reactions 116Cd(50Ti, 4n) and 122Sn(48Ti, 4n), respectively. The resulting B(E2) values are compared with the X(5) critical point model predictions and interacting boson approximation (IBA) model calculations. The X(5) model provides a reasonable description of the yrast B(E2) values in 166Hf, whereas the IBA fails to reproduce the transition strengths from the higher spin levels. In 162Yb, some transitions agree with the X(5) predictions while others are more consistent with the predictions of the IBA or a deformed symmetric rotor.

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.

Visible-ultraviolet spectroscopic ellipsometry of lead zirconate titanate thin films

We measured pseudodielectric functions in the visible-ultraviolet spectral range of Pb(ZrxTi1−x)O3 (x=0.2, 0.56, 0.82) (PZT) grown on platinized silicon substrate using the sol-gel method and also on (0001) sapphire using radio frequency sputtering method. Using a parametric optical constant model, we estimated the dielectric functions of the PZT thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard critical point model, we determined the parameters of the critical points. In the second derivative spectra, the lowest bandgap energy peak near 4eV is fitted as a double peak for annealed PZTs associated with the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest bandgap is fitted as a single peak. We compared the bandgap energies with literature values.

Effects of dry etching processes on optical properties of ZnTe surface layers in ultraviolet region

We report on the ultraviolet reflection measurements of zinc telluride (ZnTe) crystals exposed to CH 4/H 2 gases under different rf plasma powers in combination with the critical points model. The effects of dry etching on optical properties such as dielectric function, refractive index and distinction coefficient in perturbed ZnTe surface layers have been investigated in the photon energy range of 3–6 eV. All of the optical coefficients decrease with the increase of plasma power, which has been explained as the effects of the etch-induced defects. The temperature-dependent ultraviolet reflection measurements on the reactive ion etching (RIE) ZnTe crystals reveal resembled effects while either increasing the rf power or increasing the experimental temperature due to the similar role of the electron–phonon and electron-defect scattering.

Optical properties of ZnSe and Zn 0.87Mn 0.13Se epilayers determined by spectroscopic ellipsometry

The semimagnetic ternary semiconductor material ZnMnSe is a suitable candidate for the use in optoelectronic devices either as a spin aligner or a waveguiding layer. In our work we are studying the optical properties of Zn 1− x Mn x Se layers grown on GaAs (001) substrates by molecular beam epitaxy. We present the complex dielectric function obtained by variable-angle spectroscopic ellipsometry in the photon energy range from 0.75 to 4.5 eV. Between 0.75 and 3.3 eV the experimental data are fitted with a critical-point parametric model. The energies of E 0, E 0+Δ 0, E 1 and E 1+Δ 1 critical points are given for ZnSe and Zn 0.87Mn 0.13Se.

Optical properties of poly 2-methoxy-5-hexyloxy phenylenevinylene and related copolymers

We have measured the dielectric function of poly 2-methoxy-5-hexyloxy phenylenevinylene and the alternating copolymers with N-hexylphenothiazine grown on glass using variable angle spectroscopic ellipsometry and Raman spectroscopy at room temperature. Using the parametric optical constant model, we estimated the dielectric function of each polymer and also determined the band gap parameters, such as threshold energy, broadening, and amplitude. We also determined the band gap parameters by performing lineshape curve-fitting on the second derivative of the fit dielectric function using standard critical point model, and compared to those of the parametric optical constant model. We discussed the shift of band gap parameters and phonon wave numbers in terms of the chemical structures.

Accuracy of the in situ determination of the CdZnTe temperature by ellipsometry before the growth of HgCdTe by MBE

We examine the effects of surface preparation and window birefringence on the determination of Cd 965Zn 035Te temperatures, prior to the deposition of Hg 1− x Cd x Te alloys by molecular beam epitaxy. We find that the different surface morphologies and chemical statuses induced by the substrate preparation recipe are responsible for the large run-to-run changes in the measured temperature. We speculate on the nature of the overlayers produced on the sample surface and obtain the optical constants of Hg chemisorbed on the Te-rich CdZnTe surface. We also investigate the possibility of using a critical point model for the CZT dielectric function in order to decrease the sensitivity of spectroscopic ellipsometry to the presence of overlayers. We prove by a simulation that an instrument capable of measuring at least 400 wavelengths in the range between 2.5 and 4.0 eV is needed to achieve good results with this method. Such instruments are available. Finally, we find that variations in window birefringence due to window baking occur in our system and can be detrimental to the run-to-run accuracy if not taken into account.