Reference Dielectric Function Research Articles

Determination of the Complex Dielectric Function of Ion-Implanted Amorphous Germanium by Spectroscopic Ellipsometry

Accurate reference dielectric functions play an important role in the research and development of optical materials. Libraries of such data are required in many applications in which amorphous semiconductors are gaining increasing interest, such as in integrated optics, optoelectronics or photovoltaics. The preparation of materials of high optical quality in a reproducible way is crucial in device fabrication. In this work, amorphous Ge (a-Ge) was created in single-crystalline Ge by ion implantation. It was shown that high optical density is available when implanting low-mass Al ions using a dual-energy approach. The optical properties were measured by multiple angle of incidence spectroscopic ellipsometry identifying the Cody-Lorentz dispersion model as the most suitable, that was capable of describing the dielectric function by a few parameters in the wavelength range from 210 to 1690 nm. The results of the optical measurements were consistent with the high material quality revealed by complementary Rutherford backscattering spectrometry and cross-sectional electron microscopy measurements, including the agreement of the layer thickness within experimental uncertainty.

Application of a B-spline model dielectric function to infrared spectroscopic ellipsometry data analysis

The flexibility of the Kramers–Kronig-consistent basis spline (B-spline) function provides advantages over traditional physics-based oscillator functions for analyzing infrared spectroscopic ellipsometry data. Oscillator functions require that the user identify the spectral location of every absorption, choose the correct oscillator line shape, and choose the correct number of oscillators (which can be difficult for organic films that have many overlapping absorption peaks). The user must also choose starting parameters sufficiently close to the final values so that the regression fit converges. Weak absorptions can be difficult to identify when they overlap with strong absorption features, or they can be obscured when there are large interference oscillations in the spectroscopic ellipsometry data. The B-spline function’s flexibility allows the user to model the infrared, dielectric-function line shape for any material, and it requires far less user input and judgment to obtain the dielectric function of a material. The user must simply define the spacing of control nodes, which can usually be obtained from a reference dielectric function or by a preliminary fit to a spectral region where the material is transparent. A “wavelength-range-expansion” fit can then be used to obtain the dielectric function for the remaining spectral range.

Optical properties of Zr and ZrO2

Optical properties of Zr and its oxide have been measured on the surface of nuclear fuel cladding tubes. It has been shown that ellipsometry with focusing can routinely be used to measure thin layers and surface properties on Zr tubes with a diameter as small as 9.1mm. Multi-sample and depth profiling models have been used to determine reference dielectric function spectra for both the Zr substrate and its oxide. Temporal behavior of the oxide thickness has been measured for oxidation temperatures of 600°C and 800°C. A vertical inhomogeneity of the oxide properties has been found by the optical measurements as well as by depth-profiling X-ray photoelectron spectroscopy investigations that revealed the formation of sub-oxides at the interface region of Zr and its surface oxide.

Characterization of damage structure in ion implanted SiC using high photon energy synchrotron ellipsometry

The optical properties of ion implantation induced disorder in SiC have been investigated in the photon energy range of 5–9eV using spectroscopic ellipsometry (SE). The most characteristic interband transitions of SiC are located between 5 and 8eV. This photon energy region is extremely important for the sensitive characterization of lattice order in SiC. The dielectric function of the disordered layer has been calculated taking into account the surface overlayer consisting of oxide and roughness using complementary characterization tools. The dielectric function of the damaged region has been analyzed using different techniques like second derivative analysis and effective medium approximation (EMA) based on reference dielectric functions. The disorder determined by SE has been verified by Rutherford backscattering spectrometry combined with channelling (RBS/C). Using derivative lineshape analysis combined with simulations, the track size can be estimated. The results can give insight into the effect of the decreasing characteristic size of the unchanged crystalline regions on the optical properties. We created near-surface damage using heavy ions, since the penetration depth of light at photon energies around the direct interband transitions is very small (in the range of 10nm). We used 100-keV Xe at fluences ranging from a slight damage to full amorphization (between 2.0×1013cm−2 and 1.6×1014cm−2).

Optical characterization of nanocrystals in silicon rich oxide superlattices and porous silicon

We propose to analyze ellipsometry data by using effective medium approximation (EMA) models. Thanks to EMA, having nanocrystalline reference dielectric functions and generalized critical point (GCP) model the physical parameters of two series of samples containing silicon nanocrystals, i.e. silicon rich oxide (SRO) superlattices and porous silicon layers (PSL), have been determined. The superlattices, consisting of ten SRO/SiO2 layer pairs, have been prepared using plasma enhanced chemical vapor deposition. The porous silicon layers have been prepared using short monopulses of anodization current in the transition regime between porous silicon formation and electropolishing, in a mixture of hydrofluoric acid and ethanol. The optical modeling of both structures is similar. The effective dielectric function of the layer is calculated by EMA using nanocrystalline components (nc-Si and GCP) in a dielectric matrix (SRO) or voids (PSL). We discuss the two major problems occurring when modeling such structures: (1) the modeling of the vertically non-uniform layer structures (including the interface properties like nanoroughness at the layer boundaries) and (2) the parameterization of the dielectric function of nanocrystals. We used several techniques to reduce the large number of fit parameters of the GCP models. The obtained results are in good agreement with those obtained by X-ray diffraction and electron microscopy. We investigated the correlation of the broadening parameter and characteristic EMA components with the nanocrystal size and the sample preparation conditions, such as the annealing temperatures of the SRO superlattices and the anodization current density of the porous silicon samples. We found that the broadening parameter is a sensitive measure of the nanocrystallinity of the samples, even in cases, where the nanocrystals are too small to be visible for X-ray scattering. Major processes like sintering, phase separation, and intermixing have been revealed as a function of annealing of the SRO superlattices.

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)

Optical models for the ellipsometric characterisation of porous silicon structures

Thick porous silicon layers were prepared by electrochemical etching on n- and p-type single-crystalline silicon substrate, and characterised by spectroscopic ellipsometry and complementary techniques. The layers were thicker than the penetration depth of light for all wavelengths, so the samples were assumed to be bulk porous material. Best fit was obtained using two-layer models taking into account the surface inhomogeneity. The microstructure of the porous material was characterised using effective medium models with dielectric function reference spectra from the literature or calculated by model dielectric functions (MDF). Using the MDF model, reference dielectric function spectra were generated with different broadening parameters. A good agreement was found between the porosity obtained by ellipsometry and Brillouin scattering. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry

Nanostructured thin oxide films of SnO 2, V 2O 5 and indium tin oxide (ITO) were deposited by conventional and plasma-assisted chemical vapor deposition (CVD, PECVD) on different substrates and at different temperatures. Optical properties of the films were determined by spectroscopic ellipsometry in the energy range 1.5–5.5 eV. A parameterized analysis, based on Lorentzian oscillators combined with the Drude model, along with Bruggeman effective-medium approximation (BEMA) modeling, was used to determine the optical constants of thin films independently from the reference dielectric functions of the bulk materials. In this way, correlation between the optical properties and nanostructure of thin films could be established. In particular, in order to discuss the dependence of optical constants on grain size, SnO 2 nanostructured films have been considered, using a parameterization based on a double Lorentzian oscillator. Nanocrystalline V 2O 5 thin films have demonstrated the correlation between optical constants (described by four Lorentzian oscillators) and crystalline/amorphous volume fractions. Finally, ITO thin film optical properties are described by a combination of a double Lorentzian oscillator with the Drude model; by this analysis, gradients in the structural and optical properties of ITO are demonstrated.

Ellipsometric analysis of polysilicon layers

Results of ellipsometric measurements performed in the UV–vis and NIR spectral range on polysilicon films deposited on SiO2 spacer layers or directly onto silicon are presented. The effective medium approximation (EMA) based on the reference dielectric functions of a-Si and c-Si do not properly fit the ellipsometric spectra of thick polysilicon layers often characterized by large grains and rough surfaces. A multi layer model based on the experimental determined dielectric function of polysilicon measured at thinner layers is presented which fits the ellipsometric spectra well. Spectroscopic ellipsometry in the NIR is especially suitable for the measurement of thicker layers directly deposited on silicon.

Systematic differences among nominal reference dielectric function spectra for crystalline Si as determined by spectroscopic ellipsometry

Results of the first systematic investigation of differences among reference-quality ellipsometrically measured pseudodielectric function 〈ε〉 spectra of crystalline Si are discussed. These data are nominally used to approximate the bulk dielectric function of this material for optical modeling. In addition to the expected influence of residual overlayers, we identify surface-local-field and energy-derivative effects even between spectra obtained for seemingly identical H-terminated surfaces. Model calculations indicate that these effects account for nearly all differences among spectra studied. The isotropic contribution to the surface-local-field effect is also reported.

Dielectric functions of common YBCO substrate materials determined by spectroscopic ellipsometry

Reference dielectric function data for several common YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// (YBCO) substrate materials have been determined by spectroscopic ellipsometry over the range 250 nm 750 nm. These materials include LaAlO/sub 3/, BaZrO/sub 3/, NdGaO/sub 3/, 9.5 mol% Y/sub 2/O/sub 3/-ZrO/sub 2/ (YSZ), LaSrGaO/sub 4/ (LSGO), and (LaAlO/sub 3/)/sub 0.3/-(Sr/sub 2/AlTaO/sub 6/)/sub 0.7/ (LSAT). The precision of the data was confirmed by comparing SE determined data for SrTiO/sub 3/ to published values, Agreement to the third decimal point was shown. These data have been used to characterize interfaces between YBCO and some of these materials by SE.

Spectroscopic ellipsometry of Si1−xGex epilayers of arbitrary composition 0≤x≤0.255

Critical point (CP) transition energies have been calculated for strained Si1−xGex (0≤x≤0.255) between 2.5 and 3.5 eV from Lorentzian fits to the second differential of reference dielectric function spectra. E1 and E′0 transition energies are similar to those of the relaxed alloy. Comparison with deformation potential theory shows E1+Δ1 to be coincident with E′0 due to a strain-induced up shift in the former’s transition energy. The reference spectra and CP transition energies are used in an interpolation procedure to analyze spectroscopic ellipsometry spectra of both uncapped and buried layers of strained Si1−xGex. Compositions and thicknesses are obtained in good agreement with alternative techniques.

In-situ dual-wavelength and ex-situ spectroscopic ellipsometry studies of strained SiGe epitaxial layers and multi-quantum well structures

In-situ dual-wavelength ellipsometry and ex-situ spectroscopic ellipsometry have been used to study strained Si 1−x Ge x Si multilayers. Reference dielectric function spectra of strained Si 1− x Ge x with 0.06 < x < 0.29 have been obtained for the first time and an interpolation procedure based on the strain dependence of the dominant critical point energies developed. Good agreement with composition and thickness values from corroborative techniques was obtained when the effects of strain were taken into account.

Non-destructive characterization of III–V alloy multilayer structures using spectroscopic ellipsometry

Reference dielectric function spectra have been obtained for Al 0.48In 0.53As, In 0.53Ga 0.47As and strained In x Ga 1− x As ( x = 0.1, 0.2). Spectroscopic ellipsometry (SE) data of three- and four-layer lattice-matched and pseudomorphic structures incorporating these materials and InP, GaAs and Al 0.2Ga 0.8As have been characterized, layer thicknesses in excellent agreement with direct techniques being obtained. Doublets due to transitions in single In 0.1Ga 0.9As quantum wells have been observed by SE and photoreflectance.

Spectroscopic ellipsometry of Si1-xGex multi-quantum wells

Spectroscopic Ellipsometry (SE) has been used to characterise a range of strained Si1-xGex/Si multi-quantum well (MQW) samples (x≊0.2) using recently acquired strained Si1-xGex reference dielectric function spectra. SE results for thickness and composition compared well with those from double crystal X-ray diffraction (DCXRD) and cross-sectional transmission electron microscopy (XTEM) for well widths above 50Å. For thinner wells quantum confinement and/or interface effects may be important, invalidating the use of 'bulk' strained Si1-xGex reference dielectric function spectra. Models and procedures appropriate for fitting simulated SE spectra to those measured on MQW samples are discussed in detail. Improvements are seen in fits to some experimental spectra by assuming the period thickness (barrier + well) varies with depth in the MQW.

Spectroscopic ellipsometry study of InP, GaInAs, and GaInAs/InP heterostructures

The dielectric functions of high-purity InP and GaInAs layers grown by metal-organic vapor-phase epitaxy (MOVPE) have been measured in the 2.0–3.5-eV energy range using spectroscopic ellipsometry. Analysis of third derivatives computed from these data gives critical-point (E1 and E1+Δ1 transitions) energies, broadening parameters, and phases. The reference dielectric functions of InP and GaInAs are used to analyze GaInAs/InP and InP/GaInAs heterojunctions fabricated in a MOVPE reactor. The sharpest interface as measured by a multilayer modeling is 30 Å of GaInAsP at the interface of InP grown on GaInAs and 9 Å of InAs for GaInAs grown on InP. Dielectric functions of very thin GaInAs and InP layers (&amp;lt;100 Å) have been extracted from the data measured on heterostructures. It is demonstrated that these extracted dielectric functions are extremely sensitive to the interface quality and give further information about the quality of the MOVPE-grown thin layers of GaInAs and InP.