Light Scattering in Solids V: Superlattices and Other Microstructures

333 Pages·1989·19.369 MB·English

by  Manuel Cardona, Gernot Güntherodt (auth.), Professor Dr., Dres. h.c. Manuel Cardona, Profssor Dr. Gernot Güntherodt (eds.)

1. Introduction
Manuel Cardona and Gernot Giintherodt
With 2 Figures
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majestat del senyor Emperador.
J. Martorell, M. J. de Galba: Tirant o1 Blanch .4'1( Spindeler,
Val6ncia, )0941
This is the fifth volume of the Series "Light Scattering in Solids" which appears
in the collection "Topics in Applied Physics". The first volume of the series
(1975) was reissued in 1982 as a second corrected and annotated edition, with
cross references to other volumes of the series ]. [1.1 It includes the list of contents
of Volumes I-IV. Volumes II [1.2] andIII [1.3] also appeared in 1982 while
Volume IV was published in 1984 [1.4]. Volume VI, including work on organic
polymers (polyacetylene), semimagnetic semiconductors, silver halides, heavy
fermion systems, high-Tc superconductors, and a chapter on the formal theory of
light scattering in solids is in the planning stage.
We should mention that the preparation of the present volume coincides with
the 100th birthday of Prof. Chandrasekhara Venkata Raman and the 60th
anniversary of the discovery in Calcutta of the effect which bears his name and
which earned him the Nobel Prize (awarded two years after the discovery, in
1930). We would like to dedicate this volume to his memory.
1.1 Contents of Previous Volumes
dna Related Recent Developments
Volume I of this series was written at a time when the power of light scattering for
studying elementary excitatons in solids had been amply established. This power
had been greatly expanded by the capability to perform backscattering
experiments in opaque materials (semiconductors, metals) using lasers as
sources of incident light. However, a large data base was not yet available.
Chapter 1 of that volume contains a historical introduction by M. Cardona.
Sir C. V. RAMAN 0791t--8881*
(Nobel laureate )0391
Introduction 3
Chapter 2, by A. Pinczuk and E. Burstein, discusses general macro- and
microscopic aspects of the theory of the scattering efficiency of phonons and
electronic excitations. Emphasis is given to so-called quasistatic or adiabatic
formulations in which it si assumed that the frequency of the created (or
annihilated) excitations si small compared to the relevant electronic frequencies.
Such formulations break down for laser (or scattered) frequencies close to sharp
electronic interband excitations. In that article, however, prescriptions are given
to transform quasistatic expressions (usually given in terms of electronic
susceptibilities and their derivatives with respect to the amplitude of the Raman
excitations) into generalized expressions in which the adiabatic restriction has
been lifted.
Chapter ,3 by R. M. Martin and L. M. Falicov, dwells on more detailed
aspects of resonant Raman scattering including its time dependence and the
phenomenon of double resonance. At that time, the latter had been observed
only in second order scattering. Very recently, several doubly resonant spectra,
in which not only the incident but also the scattered photon is resonant with
interband transitions, have been obtained in superlattices 1.5 and in bulk
semiconductors under stress 1.6. More recently, even triple resonances have
been observed for superlattices 1.7 and for bulk GaAs under stress 1.8.
Chapter 4, by M. .V Klein, was devoted to electronic Raman scattering, a
subject which up to then had received relatively little experimental (but a lot of
theoretical) attention. The author treats the theory of scattering by single-
particle excitations, plasmons, plasmon-L0-phonon coupled modes, acoustic
plasmons, electron intervalley fluctuations, and excitations involving impurity
levels. Subsequent rapid experimental developments in these fields and in related
areas involving two-dimensional samples (heterojunctions, multiple quantum
wells, superlattices, surfaces) were later collected in Volume IV. Today, many of
these spectra are used as standard techniques for the characterization of
semiconductors 1.9.
Chapter ,5 by M. H. Brodsky, is devoted to vibrational spectra of amorphous
semiconductors. It was brought up to date in Chap. 2 of 1.2 and complemented
in 1.10, 12. Raman spectroscopy has, in the meantime, become a standard tool
for the scientific and industrial characterization of amorphous semiconductors
.2(cid:127)-9.(cid:127)
Chapter ,6 by A, .S Pine, contains a discussion of Brillouin scattering as
applied to semiconductors. It was written prior to the discovery of polariton-
mediated resonant Brillouin scattering (Chap. 7 of 1.3) and to the introduction
of multipass and tandem Fabry-P6rot spectrometers by J. R. Sandercock
(Chap. 6 of 1.3), at a time when a rather reduced data base was available (in
particular, no data on opaque materials).
Chapter ,7 by Y. R. Shen, covers stimulated Raman scattering and some
related coherent nonlinear phenomena. Subsequent developments in the non-
linear optics field, including the incoherent Hyper-Raman effect, can be found in
Chap. 4 of 1.2. We have tried to keep the format of subsequent volumes similar
to that of Volume I.
4 M. Cardona dna G. Giintherodt
Volume H 1.2 contains an extensive article by M. Cardona on the theory of
Raman scattering, mainly by phonons in semiconductors, and a discussion of
extant experimental data (Chap. 2). At the time of its writing, the available data
base had grown considerably. It included scattering efficiencies in absolute units
and a large number of resonant and nonresonant data for phonons in many
semiconductors. As shown in Chap. 2 of 1.2, microscopic theory based on
electronic band structures was able to account for the absolute cross sections.
Most of the observed resonances did not, at that time, give separate incoming
(laser frequency equal to electronic gap) and outgoing (scattering frequency
equal to electronic gap) components because of the lack of resolution, related
either to instrumentation or to lifetime broadening of electronic states. Hence,
the theory in Chap. 2 of 1.2 implied the quasistatic approximation. It can,
however, be easily generalized, following the prescriptions given in Chap. 2 of
I.1, to describe separate incoming and outgoing resonances. Such separate
resonances have become standard at low temperatures for the lowest absorption
edges of bulk semiconductors 1.11 and semiconductor superlattices 1.13 (see
also Chap. 3 of this volume). In Chap. 2 of 1.2 the dipole-forbidden, Fr6hlich-
interaction-induced scattering by L0-phonons in polar materials was discussed
to have three contributions: q-induced (quadrupole), E-(electric field)-induced,
and ionized-impurity-induced. The existence of a q-induced component has been
widely documented in the meantime through coherent interference with allowed
components 1.11, 14. The E-induced components, also observed, are discussed
at length in Chap. 2 of 1.4. Impurity-induced components are also documented
in 1.11, 13.
Chapter 3 of 1.2, by R. K. Chang and M. B. Long, is devoted to the
experimentally important topic of multichannel detection. While early work
(Raman) was performed using "multichannel" photographic plates which
enable simultaneous detection of the whole scattered spectrum, developments in
photoemissive electron multipliers, permitting single photon counting, displaced
photographic detection. Single channel photomultipliers, however, imposed the
constraint of single frequency channel detection, and rejection, at one given time,
of most of the scattered fequencies. Chapter 3 of 1.2 discusses early methods of
multichannel detectors (optical multichannel analyzers, OMA). The most
popular of such devices at the time consisted of a photocathode and a
microchannel plate electron multiplier followed by a Si diode array. Since then,
other systems have appeared on the market, including position-dependent
detectors (MEPSICRON) and charge coupled devices (CCD). They are
discussed in Chap. 6 of the present volume.
Chapter 4 of 1.2, by H. Vogt, is devoted to non-linear Raman and related
techniques. Such techniques, especially the Coherent anti-Stokes Raman
spectroscopy (CARS) and the incoherent hyper-Raman spectroscopy (HRS)
have mushroomed (for a list of ubiquitous acronyms see Table 4.1 of 1.2) due,
in particular, to the development of high power lasers and multichannel
detectors. CARS spectroscopy has also been reviewed in 1.1 5. A list of recent
references to Hyper-Raman work can be found in 1.16.
Introduction 5
Volume III discusses light scattering spectra of typical families of materials and
for several classes of phenomena. Chapter ,2 by M. .S Dresselhaus and G.
Dresselhaus, a husband-and-wife team, discussed graphite intercalation com-
pounds. These quasi-two-dimensional structures have many features in common
with the superlattices discussed in the present volume (Chap. 2). In particular,
the lowering in the number of translational symmetry operations induces additio-
nal Raman lines. Chapter ,3 by D.J. Lockwood, discusses electronic and magnetic
excitations (magnons) in the large family of transition metal halides which in-
cludes perovskite, rutile, and layered CdC12-type structures. It was complemented
by two articles in 1.4: a theoretical (Chap. 4) and an experimental (Chap. 5)
dealing with phonons, electron-phonon interactions, spin-phonon excitations and
localized electronic excitations in in the rare earth chalcogenides. Chapter 4, by W.
Hayes, treats the problem of light scattering by superionic conductors, a family of
materials of great technological interest (solid electrolytes, solid state batteries).
They possess partly disordered structures which lead to broad vibrational spectra,
somewhat similar to those found in amorphous materials.
Chapter 5 discusses Raman spectra of phonons and related anomalies in
metallic transition metal compounds, some of which (V3Si and NbC) are
superconductors. These were probably the metals (and the highest T c materials)
most investigated by Raman spectroscopy until the recent advent of hight-To
superconductors. The article contains very detailed and rigorous theoretical
considerations whose unifying idea si that the same electron-phonon processes
which produce Raman scattering and phonon anomalies (e. g., Fano line shapes,
see Chap. 2 of 1.4) may also be responsible for superconductivity and charge
density wave (CDW) transitions. The theory in this article should be useful for
the interpretation ofphonon anomalies recently observed in hight-T c supercon-
ductors 1.17 and also for phonon anomalies encountered in heavily doped
semiconductors (Chap. 2 of 1.4).
Chapter ,6 by J. R. Sandercock, describes the high resolution, high contrast
Fabry-Prrot spectrometers developed by the author and based on the multiple
pass and tandem principle. They are the clue to Brillouin scattering measure-
ments in opaque materials using the backscattering configuration. In this way,
metals, opaque semiconductors, and thin films have been investigated. This
work includes acoustic surface waves (Rayleigh modes) and surface spin waves
(Darnon-Eshbach modes).
Chapter ,7 by C. Weisbuch and R. G. Ulbrich, is devoted to Brillouin
scattering (i.e., scattering by acoustic phonons) in strong resonance with very
sharp excitons in semiconductors (discovered first by the authors in 1977 for
GaAs). In this "strong coupling" case the photon cannot be treated in
perturbation theory: one must first solve exactly the coupled exciton-phonon
problem in terms of exact mixed eigenstates called polaritons. The scattered
particles (phonons) couple different polariton branches and can have large
values for the wavevectors perpendicular to the crystal surface. Hence, large
frequency shifts result which can be easily observed with conventional Raman
spectrometers (a Fabry-Prrot interferometer is not needed). The phenomenon
6 M. Cardona dna .G tdorehtniiG
was predicted in 1972 by Brenig, Zeyher, and Birman and it took five years to
observe it. This represents one of the rare and most beautiful recent examples of
predictive solid state theory.
Volume IV has a structure similar to Volume III, in fact it resulted as a spill-
over of the articles requested for that volume. Thus, it also contains ease studies
for families of materials and classes of scattering phenomena.
Chapter 2, by G. Abstreiter, M. Cardona, and A. Pinczuk, is devoted to
electronic excitations in bulk semiconductors and in two-dimensional electron
gases (at heterojunctions, Schottky barriers, quantum wells, and some super-
lattices). At the time of writing, the work on two-dimensional systems was at its
beginning. It had been recognized by Burstein et al. 1.18 that light scattering is
an ideal tool for the investigation of such two-dimensional systems. In the
meantime, so much progress has taken place that the writing of a new article in
the present volume (Chap. 4), completely devoted to scattering by electronic
excitations in superlattices, has become necessary. Much of the required
background can still be found in Chap. 2 of 1.4.
Chapter 3, by S. Geschwind and R. Romestain, is devoted to spin-flip
resonant Raman scattering, as illustrated by the great wealth of observations
performed by the authors for CdS. The method can be applied to study
phenomena as varied as the metal-insulator transition in impurity bands, spin
relaxation times and terms linear in k in the energy bands.
Chapter 4, by G. Giintherodt and R. Zeyher, is concerned with the effects of
magnetic order and also spin disorder on the scattering by phonons in magnetic
semiconductors, as evidenced mainly by the rare earth monochalcogenides,
cadmium chromium spinels and vanadium dihalides. Both phenomenological
and microscopic theories are presented and illustrated with experimental data
for the various magnetic phases of those materials.
Chapter ,5 by G. Gfintherodt and R. Merlin, reviews the very prolific
research area of Raman scattering in rare earth chalcogenides, a family
consisting of magnetic semiconductors, magnetic or superconducting metals,
and mixed valence compounds. In all these materials the electron-lattice .i( e.,
phonon) coupling can be consistently described by the concept of phonon-
induced local charge deformabilities.
Chapter 6 by A. Otto, treats the important topic of surface enhanced Raman
scattering (SERS), a subject which was then at the peak of its activity. Basic
research in this field has more recently subsided as the technique has achieved the
stage of a standard analytical tool. The emphasis in Otto's review is to
disentangle experimentally the various mechanisms which contribute to the
striking SERS phenomenon (enhancement by a factor of up to 10 6 of the
scattering cross section of molecules adsorbed on certain metal surfaces),
including electromagnetic resonances produced by "macroscopic roughness"
and "chemical effects" of roughness present on a microscopic scale. In many
cases, both mechanisms seem to lead to the same enhancement factor, probably
on the order of 10 3 each.
Introduction 7
Chapter 7, by R. Zeyher and K. Arya, presents a theoretical formulation of
the SERS problem based, in part, on classical electromagnetic resonances and on
the quantum-mechanical theory of chemisorption.
Finally, Chap. 8 by B. A. Weinstein and R. Zallen discusses the most widely
investigated class of so-called morphic effects, namely the effect of hydrostatic
pressure on Raman spectra ofphonons. The field had reached maturity after the
development of the ruby manometer for the diamond anvil cell in the early 1970s.
While the effect of uniaxial stress on phonon frequencies is not explicitly
discussed, a comprehensive bibliography covering work in this field done before
1984 completes the chapter. We should close by remarking that the dependence
of phonons on strain (or stress), both uniaxial and hydrostatic, has recently
regained interest 1.19, with the development of lattice mismatched, strained
semiconductor superlattices (see Sect. 3.4.4 of the present volume).
1.2 Contents of This Volume
The original call of J. W. Goethe in his death bed for more light (mehr Licht ,)!
repeated on p. I of 1.1 , has partially lost its anguish. Powerful gas and solid
state cw lasers, covering the region from the near IR to the near UV are now
commercially available. Tunable lasers of the dye and color center varieties have
become standard tools in light scattering. Excellent double and triple mono-
chromators can be purchased at modest prices. Photomultipliers with InGaAsP
photocathodes, and also cooled germanium detectors, have extended the range
of photon counting to the near infrared (~0.7 eVil.8 Ixm). And finally,
multichannel detectors are cutting down measuring times by about two orders of
magnitude, with possible improvement in the quantum efficiency/dark signal
ratio in the case of CCDs. These advances in instrumentation make light
scattering an ideal standard tool to tackle problems of new materials, such as
recently demonstrated in the case of the new high-T c superconductors 1.17.
More than 60 papers (necessarily of variable quality) on Raman spectroscopy of
these materials have appeared in the past year, a fact which will be fully
documented in the forthcoming book of the series.
The present volume is largely devoted to light scattering by two-dimensional
systems (surfaces and adsorbed layers, heterojunctions, multiple and single
quantum wells, superlattices, thin films). Some of this work would not have been
possible only a few years ago without the developments in instrumentation just
mentioned.
Maybe the development most relevant to the present work is that concerning
multichannel detectors. Thus, we have devoted a whole chapter (Chap. 6) to a
COmparative discussion of the commercially available multichannel detection
systems (without explicitly naming the manufacturers). The capabilities of these
detectors are illustrated by studies ofmonolayer-like systems deposited on bulk
substrates. Last, but not least, we should mention that much of the work
8 M. Cardona and .G Giintherodt
reported here would not have been possible without the know-how accumulated
during the past 20 years in the growth of superlattices, both semiconducting and
metallic. While some of the samples discussed here were grown by metal-organic
chemical vapor deposition (MOCVD), the large majority of the semiconductor
superlattices were grown by molecular beam epitaxy (MBE). The principles of
this technique were incipient in the early work of Giinther 1.20 but the method
was mainly developed by Arthur 1.21 and Cho 1.22 nearly 20 years ago. The
development of the technique closely paralleled advances in ultrahigh-vacuum
technology. Commercial M BE equipment, supplied by several manufacturers of
UHV components, has been available for the past l0 years. Pioneering work on
metallic superlattices by .I K. Schuller and C. M. Falco started out at Argonne
National Laboratory in the late ! 970s by using sputtering techniques, and will be
discussed in Chap. .7 Presently, the topic has been taken up by many other
groups in the US, Japan, and Europe, with the emphasis on metal-MBE.
As an example of the high quality of present day superlattices, we show in
Fig. 1.1 a transmission electron micrograph of a GaAs-AIAs superlattice and,
in Fig. 1.2, a lattice image of the same superlattice which corresponds to a
resolution of better than 3/~.
Chapter 2 by D. L. Mills presents the theoretical underpinning of many of the
elementary excitations discussed in this volume. They can be brought under a
common denominator on the basis of a macroscopic response function and
appropriate boundary conditions. In the case of electrical excitations, the
response function is the dielectric function. At frequencies at which the dielectric
constant of one of the media forming the interface is negative, excitations
localized near the interface, i.e., decaying exponentially away from it, and
propagating along it, result. They give rise to interface excitations which
propagate along and perpendicular to the interfaces for an infinite superlattice,
surface interface excitations for a semi-infinite superlattice, and standing wave
excitations for a finite superlattice. The case of magnetic excitations (spin waves)
is also treated. It gives rise to similar types of excitations, except for some
phenomena typical of the interface between magnetic and nonmagnetic layers,
and of the symmetry properties of the magnetic field and magnetization with
respect to spatial inversion and time reversal.
Chapter 3, by .B Jusserand and M. Cardona, is entirely devoted to scattering
by phonons in semiconductor superlattices and quantum wells. Emphasis is
placed on the concepts of zone folding and dispersion relation averaging,
applicable to acoustic phonons, and mode confinement, ususally applicable to
optic phonons. The formation of a superlattice induces scattering by bulk-like
phonons but with wavevectors throughout the whole bulk Brillouin zone (i.e.
forbidden in bulk samples). A macroscopic treatment of the electrostatic fields
which accompany optical phonons in polar materials yields the interface modes
already discussed in Chap. 2. Theoretical dispersion relations so obtained are
compared with experimental data and with the results of full microscopic
calculations. The various electron-phonon coupling mechanisms responsible for
the scattering and related resonance phenomena, are also treated. The effects of
Introduction 9
Fig. I.I. Dark-field transmission electron micrograph of a GaAs/AIAs superlattice taken
with beam [110] Courtesy incidence. of H. Oppholzer (Siemens AG)
, • II 11 9 • s i. • * "~ W it !1 I W ~' ,t II ~, qr"u t 'l['m'~ ~ q l W n qe
GaAs
AlAs
.1# ~ 41,.Ip II, ~ • ~ p. ~ ~ 111-.• ,lk. 41.q~.0+.11++41., o. PI • • 14 II. ~ '1+-.1~ 'il' ql+:.i~
+ll tl, lib ,11~.•.- . ~,ll. -,1' ,14 '14 q' ~ O 4k~" II~ tl+ • 111 'ip-,4il, ,14 +,I ~l' 41'.tt~+q.. ,!1
GaAs
~ I v¢ i ii I l~ kq, ,k ,,~ • ~. ~ lk. i " "~ ,~ • - 5, I~ I t + I Ill ~ 1 ~ • .~I 11 t I
+ + -+ m ,i~ T * • m • l~ +" ,< 14. I + • + .'+` +'t 6 k 41 ~ ~ I It ~ • I~ 11
',;ty1''~ ',~'~'+" I ~ ~. t .I 'z+~'~4",~'I":,," ~.'"+Q'~,-.. I ~ ,t, • :. +# I + 't • ". ~ , + ", k ",~'.~"I ~ I IIIt ~,I"!, '~-Ik'~"~-~ +,i ~ t + l ~"l ,1 nm
t
Fig. 1.2. Transmission electron lattice image of GaAs/AIAs superlattice at [110] beam
indicating the atomic perfect arrangement incidence, at Courtesy the interfaces, of K. Ploog
(Max-Planck Institut, Stuttgart)
built-in strain on the vibrational frequencies of superlattices composed of
materials with different lattice parameters are discussed.
Chapter 4, by G. Abstreiter and A. Pinczuk, considers the spectroscopy of
excitations of free carriers in semiconductor quantum wells. These electron
systems of reduced dimensionality exist in heterojunctions and superlattices and
in metal-insulator-semiconductor structures. In 1978, the inelastic light scatter-
01 M. Cardona and G. Giintherodt
ing method was proposed for studies of two-dimensional electron systems, and
the first observations, by the authors of Chap. 4, were reported in 1979. Since
then, inelastic light scattering has become a very versatile experimental probe of
the excitations of free carriers in semiconductor systems of reduced dimen-
sionality. Abstreiter, Cardona, and Pinczuk reviewed the early work in 1.4.
Chapter 4 of the present volume considers the recent developments in inter-
subband spectroscopy, collective excitations in multilayers, and excitations of
the two-dimensional electron gas in high magnetic fields. It highlights the
applications of the method to several areas of current research of quantum wells
and superlattices. This includes topics like the complex structure of the valence
states of semiconductor quantum wells and space-charge layers, the spectros-
copy and lifetimes of electron states, and the single particle and collective
excitations in high magnetic fields. The collective intra-subband excitations can
be treated with a formalism similar to that of Chap. 2: plasmon-like interface
modes result. Because of the strong dispersion of these modes for in-plane
wavevectors tending to zero, it is possible to observe such dispersion by rotating
the sample with respect to the incident and scattered light beams. Copious
experimental data are available involving standing waves and surface modes for
finite thickness superlattices. Inter-subband excitations can also have single
particle and collective character, discrimination being possible by the use of
different polarizations. A number of additional phenomena can be observed in
taylor-made wells with particular (asymmetric) shapes. The chapter also
discusses space-charge-induced potential wells, such as 6-function doped and
"nipi" structures.
During the past three years, considerable interest has been devoted to the
possible existence of quasiperiodic crystals which require a number of trans-
lational basis vectors for their description higher than their dimensionality
!.23. This interest was triggered by the discovery of materials with quasicrystal
X-ray scattering patterns (e.g., A1+14% Mn 1.24). Computer controlled
molecular beam epitaxy can be used to grow one-dimensional quasicrystals, the
most interesting of which are based on the principle of the Fibonacci sequence
(1, ,2 ,3 ,5 ,8 13...). Such crystals were first grown and investigated by
Bhattacharya, Merlin and coworkers. They probably represent the simplest
possible type of quasicrystals.
Chapter ,5 by R. Merlin, discusses light scattering by phonons, plasmons,
and other elementary excitations in Fibonacci superlattices. It also presents
theoretical and experimental results for a certain type of deterministic, non-
periodic superlattices (Thue-Morse superlattices) and for random superlattices.
The contents of Chap. 6 by J. C. Tsang, multichannel detectors and
applications, have been discussed at the beginning of this section.
Chapter7, by M. H. Grimsditch, is devoted to elastic and magnetic
properties of metallic superlattices as observed in Brillouin scattering. The first
part of this chapter treats anomalies in the composite elastic constants of metallic
superlattices (e. g. alternating layers of metal A and B) which have been observed
by means of Brillouin scattering using tandem Fabry-P6rot interferometers. The