F. A. Modine

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%.

Two-modulator generalized ellipsometry: theory

A new ellipsometer is described that uses two photoelastic modulator-polarizer pairs, where the photoelastic modulators are operating at differing resonant frequencies. The time-dependent intensity of the light beam is extremely complicated but can be analyzed so that all elements of the sample Mueller matrix are obtained. For a given configuration, nine of the Mueller matrix elements can be measured at any one time; the other seven elements are accessible when the azimuthal angles of the photoelastic modulators are changed. The single-configuration measurement is often sufficient to characterize a number of real situations completely, such as film growth in a vacuum environment, anisotropic samples, and simple depolarization.

Two-channel polarization modulation ellipsometer

A new wavelength-scanning two-channel polarization modulation ellipsometer is described, where a photo-elastic modulator is used and the analyzed light is separated into orthogonally polarized beams using a Wollaston prism. Both beams are detected using phototubes whose bias voltage is dynamically controlled for constant dc. The dc from each phototube is measured with a digital voltmeter, and the fundamental and second harmonic of the phototube current are measured using individual lock-in amplifiers. All three of the associated ellipsometric parameters (N = cos2psi, S = sin2psi sindelta, and C = sin2psi, cosDelta) can be determined simultaneously in a single scan. The versatility of the instrument is demonstrated by the determination of the optical functions of Si from 238 to 652 nm (5.3-1.9 eV).

Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO(2)).

Two-modulator generalized ellipsometry is applied to determination of the optical functions of uniaxial rutile. For a nondepolarizing sample the two-modulator generalized ellipsometer determines all the elements of the normalized Jones matrix with one measurement and thereby totally characterizes light reflecting from the sample. If a uniaxial crystal is appropriately aligned, then determining its optical functions requires only a single measurement. We have used this new instrument to obtain optical functions of rutile that are the most accurate available for optical energies above the band edge.

Voronoi network model of ZnO varistors with different types of grain boundaries

Electrical transport in zinc oxide varistors is simulated using two‐dimensional Voronoi networks. The networks are assumed to contain randomly distributed grain boundaries of three electrical types: (1) high nonlinearity (i.e., ‘‘good’’) junctions; (2) poor nonlinearity (i.e., ‘‘bad’’) junctions; and (3) linear with low‐resistivity (i.e., ohmic) junctions. These type classifications are those found in experimental measurements. By varying the type concentrations, the simulated current density versus electric field (J–E) characteristics can be made to conform to the different experimentally observed characteristics of ZnO varistors. These characteristics include the sharpness of switching at the transition between ohmic and nonlinear J–E response (i.e., knee region), as well as the degree of nonlinearity. It is shown that the reduction of the nonlinearity coefficient of bulk varistors, relative to that of isolated grain boundaries, can be explained only by the presence of ‘‘bad’’ varistor junctions.

Influence of ohmic grain boundaries in ZnO varistors

A realistic model of transport properties of zinc oxide varistors is constructed from two‐dimensional Voronoi networks and studied via computer simulations. In agreement with experimental microcontact measurements made on individual junctions, the networks are assumed to contain randomly distributed microjunctions of two types: (1) electrically active with highly nonlinear current‐voltage (I‐V) characteristics and (2) ohmic, i.e., with linear I‐V characteristics. Effects of the ohmic grain boundaries in the network are simulated for various concentrations and resistivities. Shapes of the simulated I‐V characteristics and current dependence of the coefficient of nonlinearity of the network are in good agreement with those experimentally observed for thin varistor samples and in the measurements employing various surface electrode patterns. It is found that the breakdown voltage of the networks increases with the number of the ohmic grain boundaries, except when their resistivity is so low that it becomes c...

New varistor material

A composite varistor material containing silicon carbide, a conductor, and an insulator has been developed. The material has rubberlike flexibility and is easily formed. A higher leakage resistivity (∼1012 Ω cm) and greater nonlinearity (∼10) than for silicon carbide varistors permit the material to be used as a gapless surge suppressor. The breakdown voltage (1–10 kV/cm) and other properties of the material vary with composition. High current capability (>200 A/cm2) and good energy absorption (>40 J/cm3) are obtained. Also, the material exhibits a low‐temperature coefficient (∼4×10−3/K) and a low dielectric constant (∼10) with no observed loss peak.

High frequency polarization modulation method for measuring birefringence

A high frequency modulation method utilizing a photoelastic polarization modulator for the measurement of optical birefringence is described and discussed. Although the apparatus has the high sensitivity required to measure very small retardations, the accurate measurement of larger retardations is emphasized and a particularly simple null detection technique for such measurements is described. Results obtained for some common uniaxial crystals are presented and compared with previously obtained results.