New dispersion model for band gap tracking

We grow Zn1−xMnxO∕Al2O3 (0⩽x⩽0.08) thin films on sapphire (0001) using radio-frequency sputtering deposition method with Ar and various N2 flow rates. We examine the effect of N2 codoping on the band gap and Mn-related midgap absorption of (Zn,Mn)O. Using spectroscopic ellipsometry, we measure pseudodielectric functions in the spectral range between 1 and 4.5eV. Using the model of Holden et al. [T. Holden et al., Phys. Rev. B 56, 4037 (1997)], we determine the uniaxial (Zn,Mn)O dielectric function and the E0 band-gap energy. The fitted band gap does not change appreciably with increasing Mn composition up to 2%. We find a very large broadening of both the E0 band gap and its exciton partner E0x peaks even for less than 2% of optically determined Mn composition. In ellipsometric spectra, we also find Mn-related 3eV optical structure. In particular, optical absorption spectra with varying N2 gas flow rate show that the Mn-related peak intensity decreases with increasing N2 flux. The decrease of the 3eV Mn-related peak intensity is attributed to increasing N2 flow rate and Mn–N hybridization.

The band gap and optical properties (dielectric functions and optical constants) of Ge thin films with various thicknesses below 50 nm, which were synthesized with electron beam evaporation technique, have been determined using spectroscopic ellipsometry and UV-visible spectrophotometry. The optical properties are well described with the Forouhi–Bloomer model. Both the band gap and optical properties show a strong dependence on the film thickness. For film thickness smaller than ∼10 nm, a band gap expansion is observed as compared to bulk crystalline Ge, which is attributed to the one-dimensional quantum confinement effect. However, a band gap reduction was observed for thickness larger than ∼10 nm, which is explained in terms of the amorphous effect in the Ge layers.

In spectroscopic ellipsometry (SE), appropriate modeling of surface roughness structures is critical for the accurate characterization of optical constants. In particular, when a simple SE analysis is performed for rough surfaceRough surfaces with dimensions comparable to the SE measurement wavelengths (>300 nm), the optical response of the rough surfaces cannot be expressed properly, leading to serious overestimation of absorption coefficients of solar cell materials. Accordingly, extra care is necessary when samples with rough surfaces are analyzed. Large discrepancies observed between reported dielectric functions of CuInSe2 and CH3NH3PbI3 are found to originate from underestimated roughness contributions, induced primarily by oversimplification of optical modelsOversimplification of optical model. Quite fortunately, analysis errors generated by the roughness components can be corrected rather easily based on a simple procedure, referred to as extra roughness correction. When this correction scheme is applied, all the dielectric functions and absorption spectra show excellent agreement. It is further demonstrated that the analytical treatment of roughness in SE influences the optical simulation result of solar cells. In this chapter, we will examine the effect of roughness on SE results and discuss the proper SE analysis method for solar cell materials.

Tailoring properties of nanostructured MoO3−x thin films by aqueous solution deposition

Parameterization of the dielectric function of semiconductor nanocrystals

Characterization of textured SnO2:F layers by ellipsometry using glass-side illumination

Spectroscopic ellipsometry (SE) [1, 2] is a powerful non-destructive technique to determine the structure of silicon-based materials such as amorphous silicon (a-Si) and hydrogenated amorphous silicon (a-Si :H). In analyzing the SE spectra, the Bruggeman effective medium approximation (EMA) [3, 4] is usually used to model a thin film as a mixture of amorphous silicon and voids. In these models, however, precise knowledge of the dielectric functions of the various components is required in order to obtain reliable estimation of the structural parameters. This requirement is particular critical to the amorphous component because the structure of amorphous silicon is known to depend considerably on the preparation procedures [5]. So far, the dielectric functions used for modeling a-Si1 x :Hx have been based on certain dielectric functions without consideration of the preparation method. It may not be clear, particularly for thin films of amorphous silicon prepared by novel method, whether it is relaxed or unrelaxed dielectric functions which are appropriate for the modeling. In the present work the scope of the problem is assessed by constructing dielectric functions for relaxed and unrelaxed a-Si1 x :Hx thin films using measured a-Si dielectric functions, and fitting, respectively, using simulated dielectric functions for bulk unrelaxed and relaxed a-Si1 x :Hx on the surface roughness and void concentration parameters. The tetrahedron model [3, 4] is applied to construct the complex dielectric functions for relaxed (e 1⁄4 e1r þ ie2r) and unrelaxed (e 1⁄4 e1ur þ ie2ur) a-Si1 x :Hx, by using the dielectric functions for relaxed and unrelaxed a-Si [5], respectively. For details we refer to the work of Mui and Smith [3], [4]. The complex dielectric functions constructed for relaxed and unrelaxed a-Si1 x :Hx components with various hydrogen concentrations are shown in Fig. 1. It is seen that the relaxed and unrelaxed spectra exhibit different peak position and amplitude. Moreover, as the hydrogen content increases, the complex dielectric functions shift to higher photon energy with lower peak values. The complex dielectric functions for the relaxed (unrelaxed) a-Si1–x :Hx film are constructed using a three-layer structure: the first layer is a surface roughness layer, modeled using the EMA, consisting of 50% voids, 50% layer 2. Layer 2 is modeled using the EMA, consisting of a mixture of relaxed (unrelaxed) a-Si1 x :Hx and voids. The substrate is smooth silicon dioxide (SiO2). Fractional void concentrations in layer 2 are varied from 0.01 to 0.26 in the simulations. The thickness of layer 1 is set to be 0.001 mm, while the film thickness (layer 2) is fixed at 1 mm. The incidence angle is set to be 75 . The constructed complex dielectric functions for relaxed a-Si1 x :Hx films are then fitted using unrelaxed a-Si :H spectra, applying a nonlinear regression based on the Levenberg-Marquardt method [6], and vice-versa. In order to avoid interference caused by the interface, the fits are done above 1.75 eV. We denote the void concentration and the thickness of the surface roughness by Cvoid and TR respectively. The fitting error of the void concentration and the thickness of surface roughness are denoted by DCvoid and DTR, respectively, i.e. Cvoid 1⁄4 Cconstructed void Cfit void , similarly for DTR. In order to reveal the quality of the modeling, we define

Free carrier plasma edge and plasmonic excitations in heavily doped surface grated n-type Si

Composition-dependent electronic structure and optical properties of Hf1−xSixOy (0.1≤x≤0.6) gate dielectrics on Si at 450 °C grown by UV-photo-induced chemical vapor deposition (UV-CVD) have been investigated via x-ray photoemission spectroscopy and spectroscopy ellipsometry (SE). By means of the chemical shifts in the Hf 4f, Si 2p, and O 1s spectra, the Hf–O–Si bondings in the as-deposited films have been confirmed. Analyses of composition-dependent band alignment of Hf1−xSixOy/Si gate stacks have shown that the valence band (VB) offset (ΔEv) demonstrates little change; however, the values of conduction band offset (ΔEc) increase with the increase in the silicon atomic composition, resulting from the increase in the separation between oxygen 2p orbital VB state and antibonding d states intermixed of Hf and Si. Analysis by SE, based on the Tauc–Lorentz model, has indicated that decreases in the optical dielectric constant and increase in band gap have been observed as a function of silicon contents. Changes in the complex dielectric functions and band gap Eg related to the silicon concentration in the films are discussed systematically. From the band offset and band gap viewpoint, these results suggest that Hf1−xSixOy films provide sufficient tunneling barriers for electrons and holes, making them promising candidates as alternative gate dielectrics.

ABSTRACTCu(In,Ga)Se2 (CIGS) thin films co‐evaporated by 1‐stage, 2‐stage, and 3‐stage processes have been studied by spectroscopic ellipsometry (SE). The disappearance of a Cu2‐xSe optical signature, detected by real time SE during multistage CIGS, has enabled precise endpoint control. Band gap energies determined by SE as depth averages show little process variation for fixed [Ga]/([In] + [Ga]) atomic ratio, whereas their broadening parameters decrease with increasing number of stages, identifying successive grain size enhancements. Refined SE analysis has revealed band gap profiling only for 3‐stage CIGS. Solar cells incorporating these absorbers have yielded increased efficiencies in correlation with phase control, grain size, and band gap profiling. Copyright © 2013 John Wiley & Sons, Ltd.

We review the characterization of optical properties of high‐K gate dielectric films and film stacks. Modern high‐K dielectrics typically incorporate an ultra‐thin oxide interfacial layer designed preserve the channel mobility. High‐K filmstack physical characterization data is presented and correlated to the optical response of the material determined via spectroscopic ellipsometry. In‐line measurement of film physical thickness relies on the optical models used for fitting the dielectric function. Optimal optical models for use in process control are discussed, as well as limitations of spectroscopic ellipsometry to characterize high‐K dielectric/interfacial oxide stacks. We also discuss the application of spectroscopic ellipsometry to characterize high‐K dielectrics on silicon‐on‐insulator substrates.

The authors report the compositional dependence of the direct and indirect band gaps of pseudomorphic Ge1−x−ySixSny alloys on Ge and GaAs with (001) surface orientation determined from deformation potential theory and spectroscopic ellipsometry measurements. The effects of alloying Ge with Si and Sn and the strain dependence of the band gaps at the Γ, Δ, and L conduction band minima are discussed. Deformation potential theory predicts an indirect to direct crossover in pseudomorphic Ge1−y−xSixSny alloys on Ge or GaAs only for very high Sn concentrations between 15% and 20%. No indirect to direct cross-over in pseudomorphic Ge1−ySny alloys (x = 0) on Ge or GaAs was found for practically approachable Sn compositions (y < 25%). The predictions for the compositional dependence of the E0, E1, and E1 + Δ1 band gaps were validated for pseudomorphic Ge1−ySny alloys on Ge using spectroscopic ellipsometry. The complex pseudodielectric functions of pseudomorphic Ge1−ySny alloys grown on Ge by molecular beam epitaxy were determined from Fourier transform infrared and ultraviolet-visible ellipsometry in the 0.1–6.6 eV energy range of Sn contents up to 11%, to investigate the compositional dependence of the band gaps. Critical point energies and related parameters were obtained by analyzing the second derivative spectra of the dielectric function of the Ge1−ySny epilayers. Sn composition, thickness, and strain of the Ge1−ySny epilayers on Ge were characterized by high resolution x-ray diffraction. The E0, E1, and E1 + Δ1 band gaps of pseudomorphic Ge1−ySny alloys on Ge obtained from ellipsometry are in good agreement with the theoretical predictions.

The pseudodielectric functions of electroplated thin films with atomic bismuth content varying from 1.8 to 2.2 were determined using spectroscopic ellipsometry in the energy range of 0.03–3.10 eV. The experimental dielectric functions show differences with the literature bulk single-crystal data which may be explained by a ca. 50% porosity in the electroplated films. In the visible range, the optical constants did not seem to depend on the film composition while in the infrared range a rough tendency can be established: the real part of the dielectric function shifted to lower values with increasing bismuth content while the imaginary part shifted toward higher values. In the infrared range, Tauc–Lorentz combined with Drude dispersion relations were successfully used. The energy bandgap was found to be about 0.11 eV independent of the film composition. This result is related to the minor evolution of the film composition. Moreover, the fundamental absorption edge was described by an indirect optical band-to-band transition. The thickness of the thinner films were estimated, which are comprised between 1.77 and following the samples. Electrical resistivity and energy-independent scattering time were found to be related to the bismuth content.

Optical phonons and the phase transition of relaxor ferroelectric ceramics SrxBa1−xNb2O6 (SBN) and Cay(Sr0.5Ba0.5)1−yNb2O6 (CSBN) with different composition (, ) have been investigated by variable-temperature Raman scattering and spectroscopic ellipsometry. The anomalous temperature dependence of Tauc gap energy (Et) is used to fit the phonon energy dependence of the permittivity, and the Raman intensity of some interesting optical phonons can be ascribed to the phase transition from a ferroelectric to a paraelectric structure. The Curie temperature of SBN decreases from 556 to 359 K with increasing Sr composition, which can be attributed to the substitution of smaller Sr2+ for Ba2+. On increasing the Ca composition, however, the phase transition temperature of CSBN remains nearly unchanged at about 350 K. This could be due to the fact that most doped Ca2+ ions move into the oxygen ion site and exhibit no obvious effect on the vibrational properties. Therefore, the general disorder which results from Sr2+ substituting Ba2+ , dominates the phase transition process for SBN-based ferroelectric oxides. Meanwhile, the dielectric functions from 200 to 600 K have been evaluated with the aid of the Tauc–Lorentz model. The electronic transition is located at about 5 eV and decreases with increasing temperature for all the samples. Moreover, the phase transition temperature range derived from the spectroscopic ellipsometry agrees well with that from the Raman scattering. It reveals that the variation of the fundamental energy gap may be associated with the phase transition of SBN ceramics. Both Raman scattering and spectroscopic ellipsometry are proven to be a effective method of exploring the phase transition of ferroelectric oxides.

Optical properties of multiferroic LuFeO3 ceramics