Low-field Electroreflectance Research Articles

Theoretical calculations of low-field electroreflectance of ultra-thin hexagonal BN films at the fundamental absorption edge

A theory is developed to describe the electric field effect on the reflectivity of ultra-thin films of hexagonal boron nitride (h-BN) at the fundamental absorption edge. The formulation of the theory is based on the original nonlinear optical approach to electroreflectance (ER) worked out by Aspnes and Rowe (1972 Phys. Rev. B 5 4022). Within the framework of the approach, the electric-field-induced change in the reflectivity in the low-field regime is expressed in terms of the third derivative of the linear optical dielectric function of the system. An explicit closed-form expression for this function is derived within the independent-layer approximation using the tight-binding representation for the π-electron energy bands of h-BN atomic layers. Incorporating this result with the general formalism of Aspnes and Rowe enables the electro-optical response function to be obtained in an explicit analytic form convenient to further numerical analysis for any particular set of input empirical parameters. The results of such an analysis suitable for the ER effect in few-layer h-BN films are presented and discussed in the context of important information they are able to provide for band structure parameters of this material. Our findings (e.g. distinct resonant field-invariant spectral features in the ER near the fundamental bandgap of the material under study) suggest that the ER technique can be used as a sensitive tool to help characterize the electronic structure of atomic hexagonal layers built from boron and nitrogen.

Electroreflectance spectroscopy and scanning electron microscopy study of microrelief silicon wafers with various surface pretreatments

The effect of various pretreatments on the performance of microrelief (textured) Si wafers was studied by the techniques of low-field electroreflectance spectroscopy, scanning electron microscopy, and electron diffraction. Four types of preliminary treatments were employed to prepare microrelief surfaces by anisotropic chemical etching: (i) cutting, (ii) cutting and mechanical polishing with Al 2 O 3 , (iii) cutting and chemical polishing with HNO 3 :HF, and (iv) the standard industrial technique. Using the critical point energy E g at the central point in the Brillouin zone (Γ ∨ 1 25 n Γ C 15 transition) and the phenomenological parameter of broading Γ to characterize the performance of the Si surface, it was found that anisotropic chemical etching performed after cutting produced the surface performance com- parable to that of industrially fabricated wafers, but at a lower cost.

Determination of accurate critical-point energies and linewidths from optical data.

It is not possible to obtain accurate critical-point linewidths or energies directly from spectroscopic ellipsometry, reflectance, or even thermoreflectance or piezoreflectance line shapes without first differentiating those line shapes. On the other hand, the numerical differentiation of experimental line shapes before fitting them to parametrized theoretical functional forms introduces systematic distortion and broadening, which affects the values found for critical-point energies and linewidths. For that reason, low-field electroreflectance, which within the Franz-Keldysh-Aspnes theory is a third-derivative modulation technique, has long been considered a preferable technique for the determination of critical-point energies and linewidths. However, more recently it has been shown that electroreflectance often contains substantial first- and second-derivative contributions and that it is especially sensitive to sample surfaces, interfaces, and highly defectuous regions. For that reason, it may not yield accurate values for bulk critical-point energies and linewidths. Thus, spectroscopic ellipsometry would be the most reliable method for obtaining accurate bulk critical-point energies and linewidths if the systematic distortion and broadening introduced by numerical differentiation and smoothing could be eliminated. In this paper we present a simple method for doing so. We present several examples to show that this method gives accurate undistorted differentiated line shapes and hence accurate values for critical-point energies and linewidths.

Electric field response of a semiconductor superlattice optical mirror from electroreflectance spectra

We report low-field electroreflectance (ER) spectra of an all-semiconductor multilayer optical mirror structure. The structure, consisting of alternating blocks of AlAs/Al0.5Ga0.5 As and Al0.5Ga0.5As/GaAs multiple quantum well layers, was grown by molecular beam epitaxy without wafer rotation. Thickness variations across the wafer produce a position-dependent reflectance spectrum. The observed line shape of the band-edge exciton depends on its wavelength position relative to the mirror spectrum and cannot be explained by ordinary ER theory, due to the rapidly varying background mirror reflectance. Computer simulations, using the matrix method to calculate the reflectance for different layer thicknesses and exciton energies, agree qualitatively with the data. A strong enhancement in ER response is predicted near the minima in the mirror spectrum. This enhancement is important in electo-optic reflectance modulators.

Electroreflectance and wavelength-modulated reflectivity spectra of Zn1−xMnxSe alloys

Low-field electroreflectance (ER) and wavelength-modulated reflectivity (WMR) spectra have been obtained on Zn1−x Mnx Se single crystals in the whole range of composition, 0≤x≤0.57. An analysis of the ER data enabled us to determine the dependence of the fundamental energy gap on temperature (8 K≤T≤300 K) and Mn molar fraction x. In samples with x≥0.35, which crystallize in a wurtzite structure, two or three temperature-dependent features are observed in WMR spectra and in some ER spectra. We identify these peaks with the ground-state excitons for different valence bands in hexagonal Zn1−x Mnx Se. The observed crystal-field splitting is ∼20 meV for x=0.39 and decreases with increasing Mn content.

Excitonic interference phenomena in electrolyte electroreflectance: Application to n-CuInSe2

Excitonic interference effects which may be observed on the low-field electroreflectance response of a semiconductor/electrolyte junction by varying the dc bias voltage at a constant wavelength are discussed in an attempt to generalize current results. Such effects are evaluated in a manner similar to that employed in analyzing conventional interference phenomena, but introducing some simplifying approximations which are also examined. The theoretical response turns out to be periodic in, and damped by, the square root of the band bending at the semiconductor surface in agreement with experimental results. Moreover, the first extremum is a minimum or a maximum according to whether the refractive index of the dead layer is smaller or greater than that of the region containing the excitons. These conclusions are applied to the analysis of the experimental data due to Shen, Siripala, Tomkiewicz, and Cahen [J. Electrochem. Soc. 133, 107 (1986)] concerning n-CuInSe2, a very promising direct-gap material for photoelectrochemical devices. Excitons are shown to exist at room termperature in this compound, in spite of the very small value of the exciton ionization energy. Furthermore, useful information is obtained on basic semiconductor parameters such as the donor concentration, the flatband potential, and the refractive index.

Electroreflectance at the β-ZnP 2/electrolyte interface

The conditions for the Aspnes low-field electroreflectance theory to be applicable have been firmly established for β-ZnP 2 ( E g ≈ 1.5 eV) in the electrolyte surface barrier configuration. For a doping concentration of 2.5 × 10 15 cm −3 the low-field regime extends from near flatband to deep depletion. From the constancy of ΔR / R as a function of the electrode potential it can be inferred that no Fermi level pinning occurs at the β-ZnP 2/aqueous electrolyte interface by surface states with relaxation frequencies above the lowest attainable ER modulation frequency of 12 Hz.

Disorder broadening of E 2 optical spectra in GeSi alloys

he E 2 transitions in GeSi alloys are analyzed quantitatively using low-field electroreflectance data. The model of M 1 saddle point transitions is found to be in fair agreement with differentiated electroreflectance spectra in the whole composttion range. The broadening parameter of pure Ge and Si increases by 0.035 eV in the alloy with equal content of both components.

Electroreflectance studies inMnxCd1−xSe

Low-field electroreflectance (ER) measurements are reported for ${\mathrm{Mn}}_{x}{\mathrm{Cd}}_{1\ensuremath{-}x}\mathrm{Se}$ ($0\ensuremath{\le}x\ensuremath{\le}0.42$) from 1.2 to 2.7 eV. Three different structures are observed in the ER spectra, corresponding to the transition from the crystal-field--- and spin-orbit---split valence bands to the conduction band. The dependence of the energy gap and crystal-field and spin-orbit splitting on the temperature and composition has been obtained from an analysis of the ER data. In the samples with higher Mn content, the high-energy ER structure, which may be due to the excitation of the Mn $3d$ states, is observed. The broadening parameter of the fundamental ER structure yields information about compositional homogeneity of the materials investigated.

Optical determination of Fermi-level pinning using electroreflectance

We have investigated the low-field electrolyte electroreflectance (EER) spectra of matte, polycrystalline, electrodeposited $n$-CdSe in the vicinity of the ${E}_{0}(A,B)$ transitions (direct gap at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=0$. As the applied bias voltage ${V}_{\mathrm{dc}}$ is varied from near flatband to depletion, the EER amplitude for electrodeposited CdSe decreases by a factor of \ensuremath{\sim}40. We interpret this decrease in EER signal as evidence of Fermi-level pinning, which we attribute to the presence of surface states.

Electroreflectance and ellipsometry of silicon from 3 to 6 eV

Using a five-band model, we calculate the effect of the $k$-linear intravalence band coupling term on dielectric function, third derivative, and low-field electroreflectance (ER) line shapes for Si. The $k$-linear term, which was recently shown by Cardona strongly to affect transverse-interband reduced-mass values on the $〈111〉$ symmetry axes, acts to increase the oscillator strength of the upper valence ($v$)\char22{}lower conduction ($c$) band transitions at the expense of that of the lower spin-orbit split valence bands and $c$. Using reasonable values of parameters, we show that the ${E}_{1}+{\ensuremath{\Delta}}_{1}$ transition in ER is weakened to the point where it appears only as a subsidiary oscillation, qualitatively in agreement with experiment. Other experimental evidence for the $k$-linear term includes the absence of a low-field limit for the ${E}_{1}$ structure, which is believed to arise from the strong nonparabolicity of the valence bands near the $〈111〉$ axes. All ${E}_{1}$ data, including in addition ER polarization anisotropies and a comparison between ER and numerically differentiated third-derivative spectra, are consistent with a three-dimensional ${M}_{1}$ critical point (or point set) at or near $L$ and a three-dimensional ${M}_{0}$ critical point at $\ensuremath{\Gamma}$. A third, non-$\ensuremath{\Lambda}$ critical-point structure is observed slightly above the ${M}_{1}$ structure, too close to be resolved. Both theory and experiment yield no evidence for the anomalously small transverse reduced mass reported by Grover and Handler: the ${E}_{1}$, not the ${E}_{1}+{\ensuremath{\Delta}}_{1}$, transition dominates, and as may be expected from the nonparabolicity the apparent mass obtained from the ratio of the magnitudes of the ER and third-derivative spectra, both theoretical and experimental, is larger than that calculated without intravalence coupling. Threshold energies are obtained for all observed critical points. For the ${E}_{2}$ region, a numerically differentiated second-derivative line shape gives the best fit to the ER spectrum for reasons which are not clear.

Study of theE 1 andE 1+Δ 1 edges of GaSb by electroreflectance with Frans-Keldysh oscillations and low-field electroreflectance in high magnetic fieldsedges of GaSb by electroreflectance with Frans-Keldysh oscillations and low-field electroreflectance in high magnetic fields

We have observed Franz-Keldysh oscillations in the electroreflectance (ER) spectra of GaSb above theE0+Δ0,E1 andE1+Δ1 edges. The theory of Aspnes allows us to extract band parameters of theE1 andE1+Δ1 edges from the values of theE0+Δ0 parameters known from previous magneto-optical measurements. We have also performed low-field ER of this compound in magnetic fields up to 180 kG in order to complete these results. The data were taken in the Faraday configuration by extracting σ+ and σ- spectra with the magnetic field in several crystallographic directions. We have considered lineark terms and nonparabolicity in order to interpret the experimental results. The data obtained with the magnetic field (MER) are compared with those obtained by intermediate-field ER.

Optical critical-point structures of Si: Symmetry analysis by low-field electroreflectance

The critical-point locations in the Brillouin zone and the relations among the interband reduced masses at these points are determined for theE’0,E1 andE2 optical structures in Si. As a synthesis, theE4–5(k) energy contours are constructed from the experimental results.

Symmetry analysis and uniaxial-stress effect on the low-field electroreflectance of Si from 3.0 to 4.0 eV

The low-field electroreflectance (ER) spectra of Si in the energy range from 3.0 to 4.0 eV have been measured and analyzed in the absence and in the presence of strain. In the absence of strain, the symmetry location ${\stackrel{\ensuremath{\rightarrow}}{K}}_{0}$ of a critical point can be deduced from both the polarization anisotropies and the line shape of a low-field ER spectrum. Uniaxial-stress effects on a low-field ER spectrum are also described in the low-strain limit. These results are used to reveal the 3.4-eV complexities. The structures of the low-field ER spectrum of Si from 3.0 to 4.0 eV may arise from two critical points with different symmetries. First, the main structure in the higher-energy side is attributed conclusively to a high-symmetry critical point along the $\ensuremath{\Lambda}$ axis (or at the $L$ point) in the Brillouin zone [${\ensuremath{\Lambda}}_{3}^{v}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{1}^{c}$ (or ${L}_{{3}^{\ensuremath{'}}}^{v}\ensuremath{\rightarrow}{L}_{1}^{c}$) in Si]. The experimentally determined band-edge parameters are as follows: the critical-point energy ${E}_{g}=3.412\ifmmode\pm\else\textpm\fi{}0.005$ eV (300 K); the phenomenological broadening energy $\ensuremath{\Gamma}=0.060\ifmmode\pm\else\textpm\fi{}0.005$ eV (300 K); and the pair band deformation-potential parameters ${D}_{1}^{1}=\ensuremath{-}9.8\ifmmode\pm\else\textpm\fi{}1.3$ eV, ${D}_{1}^{5}=6.5\ifmmode\pm\else\textpm\fi{}1.4$ eV, ${\mathfrak{D}}_{3}^{3}=4.7\ifmmode\pm\else\textpm\fi{}0.5$ eV, and ${\mathfrak{D}}_{3}^{5}=3.0\ifmmode\pm\else\textpm\fi{}1.7$ eV (77 K). In addition, this critical point is three-dimensional ${M}_{1}$ type and the relations between the assumed reduced masses ${\ensuremath{\mu}}_{T}$ and ${\ensuremath{\mu}}_{L}$ are ${\ensuremath{\mu}}_{T}\ensuremath{\ll}|{\ensuremath{\mu}}_{L}|$, ${\ensuremath{\mu}}_{T}g0$, and ${\ensuremath{\mu}}_{L}l0$. From the mass relation, ${\ensuremath{\mu}}_{T}\ensuremath{\ll}|{\ensuremath{\mu}}_{L}|$, the critical point may be nearly two-dimensional (${M}_{0}$ type). Second, for the weak structure in the lower-energy side the experimental results under uniaxial stress can not be explained by any high-symmetry critical point except the degenerate critical point in the $\ensuremath{\Delta}$ direction (${\ensuremath{\Delta}}_{5}^{v}\ensuremath{\rightarrow}{\ensuremath{\Delta}}_{1}^{c}$ near $\ensuremath{\Gamma}$ in Si). If we assume that this structure is attributed to the $\ensuremath{\Delta}$ critical point, the experimentally determined parameters are as follows: ${E}_{g}=3.294\ifmmode\pm\else\textpm\fi{}0.005$ eV (300 K); $\ensuremath{\Gamma}=0.060\ifmmode\pm\else\textpm\fi{}0.005$ eV (300 K); and this critical point is three-dimensional ${M}_{0}$ type ($\frac{{\ensuremath{\mu}}_{T}}{{\ensuremath{\mu}}_{L}}=1\ensuremath{-}3$).

Electroreflectance of Si-MOS

This paper describes the applicability of low-field electroreflectance (ER) to MOS capacitors to determine the surface properties of thermally oxidized silicon. The ER signal amplitude versus the dc gate voltage is calculated, including interface states. The flat-band voltage of the MOS structure is estimated from the ER method. This value is almost the same as that obtained from the conductance method within the experimental errors. It is shown that the relative change in reflectivity in the Si-MOS system includes not only the ER signal but also a signal possibly due to piezoreflectance ascribed to piezoelectrically active regions of the thermally grown Sio2. layer. This explanation is based on our observations of piezoelectric phenomena in Si MOS capacitors fabricated by thermal oxidation technique.

Electroreflectance measurements on indium sulfide grown from indium melt

Electroreflectance spectra of InS grown from In melt have been measured in the photon energy range from 2.0 to 4.0 eV. The spectra reveal structures associated with the E 0 fundamental edge due to direct transitions and some higher interband transition edges. The analysis of the E 0 structure which indicates characteristic features of low-field electroreflectance spectra has enabled us to determine for the first time the direct band gap of this material.

Third-derivative modulation spectroscopy with low-field electroreflectance

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.

Interband critical-point symmetry from electroreflectance spectra

The theoretical basis for electroreflectance symmetry analysis is reviewed, with emphasis on its application to common diamond, zinc blende, rock salt, and wurtzite type materials. Both longitudinal and transverse geometries are considered. The use of atomic-state selection rules in determining electroreflectance polarization dependences is reviewed. Symmetry analysis of excitonic transitions and transitions involving degenerate states is discussed, along with the importance of low-field spectra, and the roles of thermal and lifetime broadening. The phenomenological theory of linear and quadratic low-field electroreflectance is presented for both longitudinal and transverse geometries, and the expected polarization dependences of these are analyzed in detail. The relationship of tensorial polarization dependence to symmetry analysis is also examined along with the measurement of individual tensor components. Experimental considerations such as photocarriers and surface barriers are reviewed, as are techniques for separately observing linear and quadratic low-field spectra. The utility of linear low-field spectra in symmetry analysis of wurtzite type materials is pointed out.

Linearized Third-Derivative Spectroscopy with Depletion-Barrier Modulation

Low-field (third-derivative) electroreflectance spectra taken on fully depleted space-charge regions are shown to be linear in the modulation potential and free from experimentally induced line-shape distortions due to modulation wave-form, dc bias, or barrier-potential effects. Using a metal-semiconductor (Schottky diode) configuration, accurate threshold energies of the ${{E}_{0}}^{\ensuremath{'}}$ triplet of Ge are obtained. The observed spin-orbit-splitting energy of the valence band confirms that the highest transition also occurs at $\ensuremath{\Gamma}$.

Direct Verification of the Third-Derivative Nature of Electroreflectance Spectra

The electric-field-induced change in the linear dielectric function for the ${E}_{1}$ and ${E}_{1}+{\ensuremath{\Delta}}_{1}$ transitions of Ge, determined from low-field electroreflectance measurements, is shown to be in quantitative agreement with the third derivative of the linear dielectric function measured by high-resolution ellipsometry techniques. This result relates electroreflectance spectra to other types of modulation spectra and provides the first direct verification of the nonlinear optical interpretation of electroreflectance.