G. E. Jellison

Parameterization of the optical functions of amorphous materials in the interband region

A parameterization of the optical functions of amorphous semiconductors and insulators is presented in which the imaginary part of the dielectric function e2 is determined by multiplying the Tauc joint density of states by the e2 obtained from the Lorentz oscillator model. The real part of the dielectric function e1 is calculated from e2 using Kramers–Kronig integration. The parameters of this model are fit to n and k data for amorphous Si (2 data sets), SiO, As2S3, and Si3N4. Comparative fits are made with a similar parameterization presented earlier by Forouhi and Bloomer [Phys. Rev. B 34, 7018 (1986)]. In all cases, the new parameterization fits the data better.

Spectroscopic ellipsometry data analysis : measured versus calculated quantities

Abstract Spectroscopic ellipsometry is a very powerful technique for optical characterization of thin-film and bulk materials, but the technique measures functions of complex reflection coefficients, which are usually not of interest per se. The interesting characteristics, such as film thickness, surface roughness thickness and optical functions can be determined only by modeling the near-surface region of the sample Jones matrix. However, the measured quantities are not equivalent to those determined from the modeling. Ellipsometry measurements determine elements of the sample Mueller matrix, but the usual result of modeling calculations are elements of the sample. Often this difference is academic, but if the sample depolarizes the light, it is not. Ellipsometry calculations also include methods for determining the optical functions of materials. Data for bulk materials are usually accurate for substrates, but are not appropriate for most thin films. Therefore, reasonable parameterizations are quite useful in performing spectroscopic ellipsometry data analysis. Recently, there has been an increased interest in anisotropic materials, both in thin-film and bulk form. A generalized procedure will be presented for calculating the elements of the Jones matrix for any number of layers, any one of which may or may not be uniaxial.

Data analysis for spectroscopic ellipsometry

Abstract The modeling of spectroscopic ellipsometry data is reviewed, and is divided into three phases. The first phase involves the calculation of the Fresnel reflection coefficients for a given layer structure; it is shown that the Abeles formalism provides the most flexibility, and can be readily related to the Berreman formalism for calculations involving anisotropic layers. The second phase is to parameterize the optical functions of each individual layer; several models are reviewed, including effective media, the Lorentz oscillator and a recent parameterization of amorphous semiconductors. The final phase involves the fitting of the spectroscopic ellipsometry data to the model, where different figures of merit of the fitting function are discussed. A proper numerical analysis technique requires that the reduced ¢ 2 be used as the figure of merit, which will result in the proper weighting of data points, and in obtaining meaningful error limits and a measure of the goodness of fit.

Optical absorption of silicon between 1. 6 and 4. 7 eV at elevated temperatures

The optical absorption coefficient of silicon for photon energies between 1.65 and 4.77 eV (750– 260 nm) has been determined at elevated temperatures (up to 700 °C) using polarization modulation ellipsometry. For photon energies below ∼3 eV (∼410 nm), the absorption coefficient increases exponentially with temperature from room 24° C to 700 °C, increasing by a factor of approximately 5 over that temperature range. The threshold for direct band‐gap absorption moves to lower energies with increasing temperature.

Optical functions of chemical vapor deposited thin‐film silicon determined by spectroscopic ellipsometry

The optical functions of several forms of thin‐film silicon (amorphous Si, fine‐grain polycrystalline Si, and large‐grain polycrystalline Si) grown on oxidized Si have been determined using 2‐channel spectroscopic polarization modulation ellipsometry from 240 to 840 nm (∼1.5–5.2 eV). It is shown that the standard technique for simulating the optical functions of polycrystalline silicon (an effective medium consisting of crystalline Si, amorphous Si, and voids) does not fit the ellipsometry data.

Optical functions of silicon determined by two-channel polarization modulation ellipsometry

Abstract The optical properties of ( 100 ), ( 111 ), and ( 110 ) silicon have been determined from 234 to 840 nm ( 5.30 to 1.48 eV ) at room temperature using two-channel polarization modulation ellipsometry. The results are tabulated in terms of the refractive index n and extinction coefficient k, including the propagated errors, and are compared with previously published spectroscopic ellipsometry data.

Spectroscopic ellipsometry of thin film and bulk anatase (TiO2)

Spectroscopic ellipsometry (SE) measurements were made on thin-film and single-crystal TiO2 anatase using a two-modulator generalized ellipsometer. The TiO2 films were epitaxially stabilized on a LaAlO3 substrate in the anatase crystal structure using reactive sputter deposition. The films were highly crystalline, possessing a “stepped surface” morphology indicative of atomic layer-by-layer growth. The SE results for the anatase film indicate that the material is essentially oriented with the c axis perpendicular to the substrate, but there is some anisotropy near the interface and the surface. Corrugations of the film surface, as observed using atomic force microscopy, are consistent with a surface structure needed to create cross polarization. Accurate values of the optical functions of crystalline anatase were obtained above and below the band edge using SE. Above the band edge, both the ordinary and extraordinary complex dielectric functions exhibited two critical points.

Optical functions of silicon at elevated temperatures

The optical functions of silicon have been measured accurately at elevated temperatures using the two‐channel spectroscopic polarization modulation ellipsometer. The wavelength region covered is 240–840 nm (5.16–1.47 eV), and the temperature region covered is room temperature to 490 °C. Using this data, the refractive index n and the extinction coefficient k are both parameterized as functions of temperature T and photon energy E for photon energies below the direct band edge of silicon (∼3.36 eV or 370 nm). In this range, n(E,T) can be fit with five parameters, and k(E,T) can be fit with six parameters.

Optical constants for silicon at 300 and 10 K determined from 1. 64 to 4. 73 eV by ellipsometry

Polarization modulation ellipsometry has been used to determine the optical constants of Si for photon energies from 1.64 to 4.73 eV (755 to 262 nm) at 300 as well as 10 K. The results were interpreted using a 2‐boundary, 3‐layer model (air‐SiO2‐Si); the inclusion of an interface layer between the SiO2 and Si did not greatly affect the derived optical constants below ∼3.5 eV. The accuracy of the results has been carefully evaluated, the error in the index of refraction (n) being < 1%, while the error in the extinction coefficient (k) or the absorption coefficient (α) being dependent upon the magnitude, ∼15% at α = 104 cm−1, ∼6% at α = 105 cm−1, and ∼1.5% at α = 106 cm−1. The room temperature absorption coefficient results represent the best spectroscopically available values from ∼2.5 to ∼3.5 eV (∼350 to 500 nm), while results at 10 K represent the best values available over the entire wavelength region measured. A comparison with previously published data is presented.

Two-modulator generalized ellipsometry: experiment and calibration

A two-modulator generalized ellipsometer is described that is capable of measuring all 16 elements of a sample Mueller matrix with four measurements made at different azimuthal orientations of the polarization state generator and polarization state detector. If the sample can be described with a Mueller-Jones matrix, only a single measurement is needed. Only two calibration steps are needed to determine the fundamental operating parameters of the instrument. A reflection measurement from silicon is presented as an example, which illustrates that the elements of the Mueller-Jones matrix can be measured to an accuracy of ~0.1-0.2%.