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Modulation techniques such as electroreflectance, photoreflectance and piezomodulation have become
popular room temperature probes of the optical and electronic properties of two dimensional systems
such as quantum wells and superlattices. Because of their derivative nature, they allow us to obtain
sharp optical features related to interband transitions in the material under study. From this one can obtam
transition energies of the microstructure of interest, from which quantum well widths, barrier
heights and thicknesses (superlattice case) can be determined. As a direct consequence of the derivative
nature of modulation spectroscopy (MS), information can be obtained about the response of the sample to
the applied perturbation (used for the modulation), i.e. the electric field or optically induced free carriers.
In this paper, we will review the application of MS to the study of optical and electronic
properties of microstructures. We will consider not only the experimental implementation of the various
techniques, but also discuss the nature of the electromodulation line shapes. From this it will be seen
how these techniques can be applied to device structures. Examples from recent work will be presented.
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We describe both reflectance anisotropy and electroreflectance measurements carried out to
determine the physical origin of the anisotropies observed in the reflectance spectrum of (001) and
(110) GaAs. We find an anisotropy component which depends on impurity concentration for both
(001) and (110) surfaces [and on conductivity type for (001) GaAs]. This component is actually a
bulk-related electro-optic effect produced by the electric field present at the semiconductor surface.
This electric field is due to the pinning of the Fermi level at surface states. We find that a linear
electro-optic effect is responsible for the impurity-dependent aniso tropies observed in GaAs (001),
while a quadratic electro- optic effect is responsible for those observed in GaAs (110). We give an
estimate for the linear electro-optic coefficients of GaAs at energies around the E1 and E1 + z
transitions.
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Electron Beam Electroreflectance (EBER), a low power-density form of cathodoreflectance, has been
investigated for use in a wide variety of potential applications. Herein, we describe a phenomenological theory of
EBER and provide experimental support for the inherent electroreflectance and thermoreflectance mechanisms.
In addition to pair generation and heating proposed earlier, a new mechanism, electron charging of the surface, is
identified from the 2f EBER signal of P-type semiconductors. Finally, we compare the potential advantages of
EBER to those of photoreflectance.
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Using both photoreflectance (PR) at 80 and 300 K and photoluminescence (PL) at 77 K, we have investigated the
passivation by H-gun treatment of the surface, interface and volume defects in Ga83Al017As/GaAs/GaAs MBE-grown
heterostructure on LEC substrate. Both amplitude of PR and phase delay angle between laser excitation and response were
measured. After H-treatment, substantial changes were observed in all properties. Room temperature PR is indicative of the
ready disappearance of surface and interface defects at early stages of hydrogenation. Deep trap passivation in the bulk gives
rise to increased PL emission in both GaA1As and GaAs, the effect being large only for the latter. A concomitant low in the
phase delay angle is detected. The optimum occurs when the total dose of H ions reaching the surface is 1017 cm2. When
the largest doses of H are attained, a high density of new bulk defects develops in GaAs, which virtually wipe-out
luminescence and reinstate a large phase delay.
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Photoreflectance (PR) spectroscopy has been used to study the built-in surface
potential in GaAs epitaxial film grown by molecular beam epitaxy (MBE). The PR
signal amplitude ILIR/RI sensitively depends on modulation light power, built-in
surface potential and temperature. From the analysis of the modulation light power
dependence of IzlR/RI, the built-in surface potential of 0.47±0.09eV was determined
for a MBE-grown GaAs(lOO) epitaxial film, and the increase of the surface potential
by gold deposition was observed.
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We report the use of rooni-Lemperature photorefleetance measuremenLs to
deLenitine radial arid axial nonuniformity of low levels of indium in 3-inch
diameter semi-insulaLing GaAs bulk materials grown by the liquid-encapsulaLed
Cochralski method. These resulLs were compared with umc. Types
of inhomogeneities are discussed in Lerms of indium segregation and the shape of
the solid and liquid interface during crystal growth.
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A1GaInP alloy grown by organometallic vapor phase epitaxy (OW/FE) was
examined with various optical spectroscopic techniques; photoluminescence,
electroref'lectance, Raman scattering, extended X-ray absorption fine
structure, and with electron microscopy. It turns out that the band gap
shrinkage observed in AlGaInP is caused by deviation of atomic position from
the lattice sites of the normal zinc-blende lattice which is effected by the
interaction of random distribution structure and long-range ordering. The
long-range ordering is found to be specific to the (100) substrate plane.
Anomally in low temperature photoluminescence which may be related to long-
range ordering is also reported.
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Reflectance Difference Spectroscopy and Scanning Ellipsometry
We discuss the application of thermorefiectance to two interesting physical systems: ferromagnetic CrBr3 and
heavily doped silicon. This technique allows us to identify the physical mechanisms affecting the optical response
below the transition phase of CrBr3 . In the case of heavily doped silicon we analyse the many-body effects of high
doping on the E1 and E2 edges; the variation of some interesting related parameters is evaluated as a function of
the dopant concentration (up to 6x 1021 cm3).
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Reflectance difference spectroscopy (RDS) is a surface analysis technique that was invented in 1985 by
Aspnes. Here, we give a summary of its application to crystal growth techniques which gave new and
valuable real tinw information about the growth process. Also, this information was obtained in-situ, in
molecular beam epitaxy (MBE) and organometallic chemical vapor deposition (OMCVD) crystal growing
setups which are routinely used to produce high quality device structures. The application of RDS to
OMCVD allowed us to develop a "textbook" like model of growth kinetics, which includes two independent
microscopic mechanisms, i.e. adsorption (at -26 kcal I mole) of the reacting molecule (trimethylgallium
(TMG) in the case of GaAs), followed by its decomposition (at 39 kcal/mole) on the growing GaAs surface.
Our model includes an effect called steric hindrance, associated with the large size of the TMG molecule.
This study represents the first direct quantitative evaluation of the catalytic effect of the GaAs surface for the
decomposition of TMG. We discuss implications of the model both for growth in the ALE mode as well as
for conventional OMCVD growth and comment on the relative importance of surface and gas phase
reactions. The application of RDS to MBE revealed remarkable details about the complex intermediate
steps that surfaces undergo during growth and enabled to extract directly surface dielectric functions. Finally,
applications of the technique as well as results obtained in a number of laboratories where RDS is currently
being developed are discussed.
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Spectral ellipsornetry has been proven to be a very powerful tool to study the band
structure and electronic properties of semiconductors. Line-shape analysis of the
derivative spectra of the pseudo-dielectric function allows a precise determination of
critical point parameters, such as amplitudes, energies, broadening and excitonic phase
angles. Here we will review the application of the technique, showing examples of the
effects of temperature, alloy and doping in the band structure of semiconductors and the
effects of a new periodicity along the growth direction in semiconductor structures.
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Using the contactiess modulation spectroscopy technique of photoreflectance, the
temperature variations of the direct gap E0 of GaAs, InP, GaA1As, InGaAs have
been measured at elevated temperatures up to 600°C. The parameters which describe
the temperature dependence of the band gap energies have been evaluated.
The ability to measure the band gap at elevated temperatures opens up many new
possibilities for in-situ monitoring of MBE and MOCVD processes. In this paper,
we review some of the recent developments in the use of photoreflectance at
elevated temperatures.
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Differential reflectance (DR) spectroscopy, applied to semiconductors, is shown to be
equivalent in some cases to a contactless electro-reflectance technique. DR spectra are achieved by
modifying one half of the sample surface or, in the case of semiconductor alloys, just relying on the
inhomogeneities present. Our DR spectra of GaAs reveal sharp critical point structures and are
comparable to the known electro-reflectance data. The DR spectra show a marked improvement in
signal to noise ratio over photoreflectance spectra of the same samples. This new technique has also
been used to characterize 111-V quantum well structures.
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Differential Reflection Spectrometry utilizes two almost identical samples which are mounted stationary, side by
side. The samples differe slightly in their surface properties, for example, in composition, crystal structure, etc.
Unpolarized light is alternately deflected to one or the other specimen by means of a vibrating mirror. Electronic
processing yields the difference in the reflectivities, that is, a first derivative-like spectrum. Examples for applications are
given, such as in situ studies of corrosion and passivation in aqueous solutions, investigations of alloys, and studies of the
fmer details of implantation damage in semiconducting materials.
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Photoreflectance spectra from superlattices and quantum wells exhibit a
variety of pecularities which may be used in order to derive electronic
structure data, provided experimental lines shapes are properly understood.
This problem is addressed in the present paper. The electric field effect on
optical constants is expressed in terms of the Franz-Keldysh as well as Stark
effect of mini- and subbands. Theoretical line shapes are given and compared
with experiment.
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The excitonic photoreflectance (PR) spectra of GaAs/A1GaAs multiple quantum wells, grown by the molecular beam
epitaxial (MBE) technique, were investigated at oblique and near-normal incident angle with different polarized probe lights.
The PR spectra have been measured at room temperature using He-Ne laser as a pumping beam in order to study the
variations of the spectral line shapes. The experimental results show that the usefulness of the electromodulation to
characterize the microstructure of the substrate may be enhanced if we take in account the polarization state of the probe light
which is incident at larger oblique angle. The PR spectra were fitted by a third order derivative functional line shape, thus
making it possible to determine the energy band gap, broadening parameters, amplitudes, and the phases of the spectral
features precisely.
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Superlattices of alternating layers of semiconductors were first proposed1 in 1970, and since then a variety
of structures have been grown. Their technological importance has spurred considerable experimental and
theoretical work. The unique feature of quantum confinement of carriers has made possible unusual
devices. By combining various semiconductors and alloys of ffl-V, 11-TV and group IV materials, unusual
band lineups between neighboring layers have been obtained. Both lattice matched and strained layer
structures have been grown.
In this article we will focus on the electronic structure of the quantum well heterostructures under the
external perturbation of hydrostatic pressure. Pressure has been used extensively to investigate materials
in regions of phase space not otherwise accessib1. lu the study of quantum well structures, it has also
been used to move band edges in a controlled fashion, and alter band lineups, allowing the determination
of band offsets with an accuracy that was not possible without the use of pressure. As in bulk
semiconductors, optical techniques provide powerful tools in studying the electronic states in quantum
well heterostructures (QWH). Photoluminescence (PL) spectroscopy is only sensitive to spectral features
associated with energy states close to the bottom of the well due to rapid thermalization of carriers.
Photoluminescence excitation (PLE) is often limited by the availability of tunable lasers. Photoreflectance
(PR), on the other hand, can provide a rich structure due to both symmetry allowed and forbidden
transitions encompassing the entire quantum well. This sensitivity is due to the derivative nature of the
spectroscopy. Experiments can be carried out easily at different temperatures and over wide spectral
regions.
This article is organized as follows. In section 2 we will review some of the theoretical calculations of
electronic bands in quantum wells and discuss the changes expected under pressure. In Sec. 3, we
discuss the experimental details, including descriptions of the optical techniques used. Section 4 will deal
with studies of the quantized transitions in GaAs/GaixAlxAs and GaSb/A1Sb QWH under pressure,using
PR and PL. The examples are illustrative of the comparative merits of the two techniques.
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The dependence of intersubband transitions on
temperature and pressure in strained InGa1As/GaAs multiple
quantum wells with different x and well widths has been
investigated by use of the modulated reflection and absorption
spectroscopies. The identifications for dislocation free at the
interface will be discussed.
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Photoreflectance measurements of InGaAs/InP superlattices grown by solid source molecular beam epitaxy show
a well resolved ground state exciton and some of the higher confined transitions in the quantum wells. Ground
state splitting possibly due to one monolayer variations in the layer thicknesses is observed. Strong unconfined
transitions below the InP band gap are due to arsenic doping of the barriers caused by small amounts of arsenic
leakage from the evaporation sources during the epitaxy.
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Photoreflectance and photoluminescence experiments are carrIed out in (GaAs)/(AlAs) (n = 1-15)
in the temperature range from 25 to 275 K. Weak signals of photoreflectance associated with the critical
point of the pseudodirect transition, weakly allowed direct transition arising from the zone-folding effect,
have been found as well as main signals associated with the direct allowed transitions. This assignment is
supported by the temperature dependence of the photoluminescence intensity, which gives the transition
probability ratio of the direct allowed to pseudodirect transition about 102. Temperature dependence of
the critical point energies and luminescence peak energies shows a similar behavior to bulk semiconductors.
These observations show also that the monolayer number n for which the crossover of direct and
pseudodirect transitions occurs depends on temperature. In addition the broadening parameters determined
from photoreflectance spectra are found to be almost independent of temperature and depend on
the monolayer number n, which may be explained in terms of broadening induced by the layer number
fluctuation.
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InGaAs/InAlAs quantum wells provide large barrier height for electrons accommodating numerous
confined states. Absorption and electroabsorption spectra of samples with 50 - 100 wells are
compared. Heavy hole excitons respond strongly to the electric field which for the lowest state is
in good agreement with the predicted red shift due to the quantum confined Stark effect. Higher
confined excitons show spectra of similar strength and lineshape but not because of a red shift of
the transitions but due to redistribution of oscillator strength. Superlattices with thin barriers
develop minibands whose spectra are very different from those of uncoupled wells. Features arising
from M0 and M1 singularities enable direct determination of the width of the minibands and
determination of the conduction band disontinuity. Large electric fields destroy the minibands
and quantum confined excitons reappear.
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Resonance Raman Scattering is a unique form of modulation spectroscopy that uses the
material's phonons rather than externally supplied agents to modulate the electronic structure.
We review the applications of this technique to semiconducting materials. Special emphasis is
given to research on quantum well and superlattice systems, particularly to phonon localization
effects and to analysis of resonant profiles.
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Photoreflectance and photoluminescence measurements are carried out to clarify optical properties
of (GaAs)/(AlAs) (n = 1-15) short-period superlattices, placing main interest in the crossover of
direct-indirect transition and zone-folded weak transition. Photoreflectance spectra of (GaAs)/(A1As)
with n < 10 exhibit a weak structure below the main (strong) structure. Photoluminescence peaks
appear at the photon energies corresponding to the critical points of these weak and strong structures.
Energy band calculations are performed by using the empirical tight-binding method. Calculations of
momentum matrix elements between the top valence band and lowest three conduction bands at the I'
point show an existence of weakly allowed direct transition below the strongly allowed direct transition
edge in (GaAs)/(AlAs)with n < 5. These results strongly suggest that the observed weak structures
in the photoreflectance arise from the weakly allowed direct transition, indicating that the conduction
band reflects the nature of the zone-folding effect (Xi).
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We report investigations of layered structures whose modulated reflectance spectra not only have features that
suggest the occurrence of spatially indirect transitions but also display anomalous electric field effects. The spatially
indirect transitions can occur from either the GaAs conduction or valence band to quantum levels of carriers confined
between narrow potential barriers. In addition to the usual band-to-band excitonic transitions, we discuss spatially
direct transitions between the conduction band and the two-dimensional hole states that exist in a spacer layer
separating heavily-doped GaAs regions from AlGa1_As barriers. Finally, we comment on spectral lineshapes
asssociated with built-in electric fields that differ from those predicted using Franz-Keldysh theory. The energies
of all transitions are compared with those calculated using potential profiles based upon the growth parameters.
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We have employed the transverse electroreflectance technique to characterize multiple quantum well structures. A weak
modulating electric field (1-100 V/cm) was applied transversally to the probe light beam, i.e., parallel to the quantum well
layers. Photoreflectance and in-plane photoconductivity spectra can also be measured with this configuration. The transition
energies measured were closely the same as those obtained from the photoreflectance and Schottky barrier electroreflectance
spectra. The method can be applied for relatively highly resistive undoped layers grown on semi-insulating substrates. The
modulation mechanism in transverse electroreflectance is not well understood.
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Using photoreflectance spectroscopy, fifteen electronic transitions have been measured from a 60 period Si8Ge32
superlattice grown on a Si02Ge0•8 buffer layer on < 100 > Si. The superlattice transitions fit well to a third derivative
functional form and most of their energies were determined using a one band envelope-function model, including strain
effects. The temperature dependences of the E0 transition in bulk Ge and in the Si8Ge32 superlattice were also fit
to a nonlinear functional form.
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An electroreflectance study of several short-period Si/Ge
superlattices and SiGe alloy layers grown by molecular beam
epitaxy has been performed. Contactless Electron Beam
Electroreflectance (EBER) measurements taken at 120K provide
clear evidence of superlattice transitions. Comparisons between
EBER spectra from sequentially stripped samples reveal
superlattice transitions accompanied by those related to the
substrate material and buffer layers. Results from the EBER
measurements are compared with predictions from empirical
pseudopotential calculations. The experimental features support
the theoretical predictions.
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Low field electroabsorption spectra are compared with absorption spectra and are used to determine
accurately the band gap. The spectra show for larger fields F numerous Franz-Keldysh
oscillations above the absorption edge which shift in perfect agreement with theory. This shift
allows determination of built-in fields and the actual field-strength in the sample. Lattice mismatch
removes the valence band degeneracy and causes for fractional change of the lattice constant
za/a < 0 splitting into a doublet of the electroabsorption spectrum at small fields. The
splitting disappears at higher fields and is never observed for La/a > 0. This different behaviour
probably results from differences of the band structure in field direction.
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We report results of photoreflectance (PR) investigations of GaAs/Alo.3Gao.7As hetero-n-i-p-i crystals with either
GaAs-QWs ("type II") in the intrinsic region or GaAs-QWs interspersed in the n-region ("type I"). To understand
the complex PR-spectra of these samples we changed several measurement parameters such as ac-pump-intensity,
dc-pump-intensity, pump frequency and temperature. Especially the spectra of type II showed a strong temperature
dependence. We compare these spectra to spectra calculated with the model of an infinite quantum well in an electric
field. Because of the dielectric function being periodic in space the z-dependence of the dielectric function is taken
into account.
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Silicon S-doped GaAs samples grown by molecular-beam epitaxy
with different dopant concentration and cap layer thickness were
investigated by photoreflectance spectroscopy. The features observed
above the GaAs fundamental energy gap are temptatively attributed to
transitions involving continuous valence band states and quantum-
confined states at the conduction band. These interband transition
energies are in qualitative agreement with the self -consistent ones
calculated taking into account the spreading of dopants.
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We performed room temperature photo- and electro-modulation measurements on MBE-grown GaAs pnp and
pin structures with large layer thicknesses. In these crystals the optical properties are expected to be dominated
by the local field-induced changes of the dielectric function rather than by subband-transitions. The dominating
effect in the pnp-structure turns out to be the spatial dependence of the varying refractive index, resulting in a
characteristic interference pattern. For the case of the pin structure we clearly observe Franz-Keldysh oscillations
changing in amplitude and width with the internal field. Theoretical calculations using effective mass theory are in
very good quantitative agreement with the experimental results. This agreement can be achieved only by the inclusion
of excitonic effects in the calculation of the field-dependent absorption.
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The technique of photoreflectance (PR) spectroscopy has been
applied to study the two-dimensional electron gas (2DEG) in a
modulation-doped GaAlAs/GaAs heterojunction. We investigate the
dependence on temperature of the PR results. At room temperature
Franz-Keldysh oscillations-like features are observed. The energy
spacing of this oscillations decreases with temperature. Theoretical
self-consistent calculations have been carried out to determine the
potential profile and sub-band energies in this system. The comparison
of the values for the electric field estimated from the calculations
and those extracted from the experiment suggests that the observed
features are due to the electric field in the space charge region.
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We report photoreflectance studies ofMOCVD grown doped GaAs at the higher energy
transition E1( 2.9 eV). We are especially interested in the variation ofboth the energy position
and the broadening parameter F of the E1 transition with doping concentration. Above 1 x
10'8cin3 for Si:GaAs and ' 7 X 1018 for Zn:GaAs, we observe an increasing overlap of B1 and
E1 + Li structures. Evaluation of r based on curve fitting of the KramersKronig analysed
data shows a nearly linear relation between F and the logarithm of carrier concentration. This
observation has potential application in the determination of carrier concentration for heavily
doped films.
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Laser excitation above the bandgap of semiconductor materials like GaAs creates a high density of
electrons and holes. These quasi particles form a quantum mechanical system in which optical
nonlinearities arise as a result of many-body effects such as screening of the Coulomb potential,
reduction of the bandgap, and filling of the band and of the states.'
The refractive index change resulting from such processes may be employed to demonstrate a
variety of devices such as nonlinear switches, modulators, and logic gates. These optical nonlinearities
may be measured using various techniques such as four-wave mixing, interferometry, and modulation
spectroscopy. In the latter technique, an analogy is established to the electroreflectance effect2'3 in
which the optical properties of a semiconductor are modulated by the application of a low-frequency
electric field. In the experiment reported here, the modulating element is the E-field of the pump
beam. At a much higher frequency than in electroreflectance spectroscopy, the pump beam thus
produces field-induced reflectance and transmittance changes from which the refractive index change is
obtained.
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Electric fields alter the optical properties of the various layers in a quantum well laser by the
Franz-Keldysh effect or by the quantum confined Stark effect. The resulting features of an electroabsorption
spectrum obtained by combination of dc and ac fields are characteristic for confined
and unconfined states and allow the determination of transition energies, band gaps of bulk layers,
internal fields and homogeneity of the sample. The results of two structures of different barrier
height are compared with luminescence and photocurrent data and with model calculations.
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We have studied the photoreflectance spectra at 300 K from a number of
GaAs/Ga1AlAs heterojunction bipolar transistor (HBT) structures grown by molecular
beam epitaxy and metal-organic chemical vapor deposition. From the observed
Franz-Keldysh oscillations we have been able to evaluate the built-in dc electric
fields, F , in the Ga Al As emitter as well as the n GaAs collector region. In
dc 1-x x
addition, the Ga1AlAs band gap (and hence Al composition) has been determined.
The obtained values of Fd are in good agreement with numerically-computed values
for the analyzed HBT structures, thus making it possible to deduce doping levels in
these structures. The GaAlAs FKO have been correlated with device performance.
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Photoreflectance (PR) was used to determine the surface damage caused by polishing on
semi-insulating lnP:Fe substrates. PR measurements were performed between subsequent
etching steps. The PR results on substrates, obtained from various vendors and laboratories,
indicate that the exciton structure near the fundamental absorption edge transition is very
sensitive to surface imperfections and the bulk resistivity of the substrates.
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Extensive measurements and theoretical calculations have provided strong evidence
for the creation of direct bandgap superlattice structures from indirect bandgap Ge and Si.
Much of the experimental evidence for this conclusion is drawn from electroreflectance
measurements. Interpretation of this experiment begins with the standard lineshape fitting
analysis, but it is complicated by local electric fields and interference effects. We will discuss
these effects and how they can be separated from properties intrinsic to the electronic
structure.
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Reflectance Difference Spectroscopy and Scanning Ellipsometry
Optical transitions in the range I .9—4.3eV have been observed in Si:Ge superlattices by spectroscopic ellipsometry (SE) and electron—beam electroreflectance (EBER). Interference is shown to play an important role in both techniques, leading to complications in • interpretation. Strong features may be produced both by multiple reflections from capping layers and from buried growth imperfections.
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The electroreflectance lineshapes of 111/V semiconductors are modelled using the intermediate
field theory and a multilayer reflection routine to include electric field variation. This
introduces additional structure into the lineshape, which has previously been assumed to be from
impurity or exciton effects. By using a thermal broadening parameter of F0=O.OO9eV we show that
spectrum size as well as shape can be fitted successfully to experimental data so that depletion
layer voltages can be measured.
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