D. E. Aspnes

Optical properties of thin films

Abstract In this paper we discuss the connection between the microstructure of a heterogeneous thin film and its macroscopic dielectric response e. Effective medium theory is developed from a solution of the Clausius-Mossotti problem from basic principles. The solution is generalized to obtain the Lorentz-Lorenz. Maxwell Garnett and Bruggeman expressions. The connection between microstructure and absolute limits to the allowed values of the dielectric response of two-phase composites is reviewed. The form of these limits for two-phase composites of known composition and two- or three-dimensional isotropy can be used to derive simple expressions for e and also for the average fields within each phase. These results are used to analyze dielectric function spectra of semiconductor films for information about density, polycrystallinity and surface roughness. Examples illustrating the detection of unwanted overlayers and the real-time determination of nucleation growth are also given.

Third-derivative modulation spectroscopy with low-field electroreflectance

Abstract The theoretical basis and experimental procedures are reviewed for third-derivative modulation spectroscopy, which is the same as low-field electroreflectance. The physical origin of the third-derivative behavior is discussed in terms of the effect of a uniform electric field on the translational symmetry of the unperturbed crystal. The relationship between the low-field and the Franz-Keldysh electroreflectance theories is discussed. In the lowfield range, both intraband and interband electric-field effects can be treated by first-order perturbation techniques, leading to great simplifications in the more general theory. By formulating the expression for the experimentally measured relative reflectivity change, ΔR R , in complex-variable form, effects due to experimental field inhomogeneities, the electron-hole interaction, and the optical constants of the material can be described by complex coefficients multiplying a theoretically calculated complex lineshape, thereby simplifying the analysis of experimental spectra. We also review the commonly used experimental configurations, and discuss procedures for determining experimentally the low-field range in a given experimental situation. The linearized third-derivative (LTD) technique, which makes use of specific properties of fully depleted space-charge regions, is discussed in detail. Finally, the application of third-derivative spectroscopy in the measurement of weak spectroscopic features and the determination of band structure parameters is demonstrated with specific examples.

Differential reflection spectroscopy of very thin surface films

Abstract The influence of thin adsorbed films on the reflectance properties of two-phase systems is discussed. It is shown that the linear approximation to the normalized reflectivity change ΔR R reduces the complicated reflectivity expressions for multiphase stratified systems to a simple form which gives direct physical insight into the properties of these systems. Several interfacial systems of physical interest are examined in detail, and the results are generalized to include attenuated total reflection, fractional coverage, and interfaces with smoothly varying optical properties.

Optical properties of AlxGa1−x As

We report pseudodielectric function 〈e〉 data for AlxGa1−xAs alloys of target compositions x=0.00–0.80 in steps of 0.10 grown by liquid‐phase epitaxy and measured by spectroellipsometry. Cleaning procedures that produce abrupt interfaces between the technologically relevant alloys x≤0.5 and the ambient are described. The 〈e2〉 data are corrected near the fundamental direct absorption edge by a Kramers–Kronig analysis of the 〈e1〉 data to circumvent a limitation of the rotating‐analyzer ellipsometric technique. The results and the associated pseudooptical functions 〈n〉, 〈R〉, and 〈α〉 are listed in tabular form. Accurate values of the E0 and E1 threshold energies are determined from these spectra by Fourier methods. From these values, and from similar values for a GaAs‐capped AlAs sample grown by organometallic chemical vapor deposition, the dependencies of the E0 and E1 interband critical point energies on nominal composition are obtained. Cubic polynomial representations of these dependences are determined to...

High Precision Scanning Ellipsometer

We describe the design, construction, alignment, and calibration of a photometric ellipsometer of the rotating-analyzer type. Data are obtained by digital sampling of the transmitted flux with an analog-to-digital converter, followed by Fourier transforming of the accumulated data with a dedicated minicomputer. With an operating mechanical rotation frequency of 74 Hz, a data acquisition cycle requires less than 7 msec. The intrinsic precision attainable is high because precision is limited only by shot noise or intrinsic source instabilities, even when relatively weak continuum lamps are used as light sources. Precision may be improved by accumulating the data for consecutive cycles at a fixed wavelength. The system allows complex reflectance ratios to be determined as continuous functions of wavelength from the near infrared to the near ultraviolet spectral range. Data reduction programs can be modified to calculate complex refractive index or dielectric function spectra, or film thicknesses and refractive indices, as well as the usual ellipsometric parameters tanpsi, cosDelta.

Local‐field effects and effective‐medium theory: A microscopic perspective

Standard textbook derivations of the Clausius–Mossotti (Lorentz–Lorenz) relation tend to obscure the physical origin of local‐field effects by proceeding from the macroscopic dielectric function of the equivalent homogeneous system to the microscopic parameters of the model. The microscopic and macroscopic aspects can be made clearer by reversing the order, that is, by first obtaining the microscopic solution and then implementing the definition of macroscopic quantities as averages of their microscopic counterparts. This approach also leads naturally into a treatment of effective‐medium theory and the description of the dielectric response of heterogeneous materials.

Application of reflectance difference spectroscopy to molecular‐beam epitaxy growth of GaAs and AlAs

We perform an accuracy analysis of several possible reflectance–difference (RD) configurations that are compatible with standard molecular‐beam epitaxy (MBE) growth chambers, and describe in detail an optical‐bridge system that can determine relative changes in RD signals as small as 5×10−5 under standard growth conditions. Using this system, we determine the RD response of GaAs for changes in surface conditions at different wavelengths and correlate these to simultaneously measured reflection high‐energy electron diffraction (RHEED) intensities. Maximum anisotropies are found at 2.0–2.5 and 3.5 eV for Ga on GaAs and Al on AlAs, respectively, providing a way of spectrally distinguishing Ga–Ga and Al–Al dimers for surface‐chemical investigations, and suggesting that these photon energies are also optimal for modifying growth by light. At photon energies well removed from these anisotropy maxima, RD signals follow changes in surface structure, as RHEED. Our RD‐RHEED correlations provide insight concerning c...

Effects of As+ ion implantation on the Raman spectra of GaAs: ‘‘Spatial correlation’’ interpretation

We have studied Raman scattering from 〈100〉 GaAs samples implanted with 270‐keV As+ ions with various fluences up to 3.2×1014 cm−2. In addition to phonon density of states effects, we observe a softening and asymmetric broadening of the allowed LO phonon while the small symmetry forbidden TO phonon remains almost unchanged. The behavior of the LO and TO modes can be explained quantitatively on the basis of a ‘‘spatial correlation’’ model related to q‐vector relaxation induced by the damage. Our interpretation is quite general and makes it possible to use Raman spectra to evaluate an average size of undamaged regions in semiconductors.

Precision Bounds to Ellipsometer Systems

The theoretical precision attainable from a number of types of ideal null and photometric ellipsometers is investigated quantitatively. Photometric and modulated null ellipsometer systems are shown to be approximately comparable with respect to precision when operating under shot-noise limited conditions. Differences are due principally to intrinsic detector noise levels, which are more significant in null designs. The equations derive can be used to estimate practical measurement limits or to choose components to achieve a specific objective.

Recombination at semiconductor surfaces and interfaces

Abstract The present state of understanding of recent work on recombination processes at semiconductor surfaces and interfaces is assessed. The derivation of the phenomenological Stevenson-Keyes expression is outlined to indicate basic mechanisms and assumptions and to provide the theoretical framework for interpreting recombination data. Trends in recombination velocities with bulk doping are shown to be an important diagnostic tool in the absence of explicit information about the surface Fermi level. The significantly greater photoluminescent efficiency of InP relative to GaAs, the improvement of photoluminescent efficiencies in GaAs by Ru treatment, and the sensitivity of the photoluminescent efficiencies of InP are all shown to be consistent with changes in the position of the surface Fermi level within the Spicer unified defect model, although alternative explanations are also possible. In general, independent measurements of the surface Fermi level by, e.g., surface photovoltage measurements could provide the necessary information to decide among alternative interpretations.