Festkörperprobleme 27: Plenary Lectures of the Divisions “Semiconductor Physics” “Thin Films” “Dynamics and Statistical Mechanics” “Megnetism” “Low Temperature Physics” of the German Physical Society (DPG) Münster, March 9 … 13, 1987

322 Pages·1987·8.432 MB·English

by  Bernd Ewen, Dieter Richter (auth.), P. Grosse (eds.)

FESTK(bRPERPROBLEME
ADVANCES IN SOLID STATE PHYSICS 27
Ill
FESTKORPER
PROBLEME
ADVANCES IN
SOLID STATE
PHYSICS 27
PlenaryLecturesof the Divisions
"Semiconductor Physics"
"Thin Films"
"Dynamics and Statistical Mechanics"
"Magnetism"
"Metal Physics"
"'LowTemperaturePhysics"
of theGermanPhysical Society (DPG)
MLinster, March9... 13, 1987
Edited by
P. Grosse, Aachen
With 208 Figures
Friedr. Vieweg & Sohn Braunschweig / Wiesbaden
ISSN 04030-3393
Allrightsreserved
© Friedr. Vieweg& Sohn VerlagsgeseUschaftmbH, Braunschweig, 1987
Nopart ofthispublication may be reproduced, storedin aretrieval
system ortransmitted,mechanicalphotocopyingor otherwise,
without priorpermission ofthecopyrightholder.
Set by Vieweg, Braunschweig
Printedby Lengericher Handelsdruckerei, Lengerich
Bound by W.Langeliiddecke, Braunschweig
Coverdesign: Barbara Seebohm, Braunschweig
ISBN 3-528-08033-7
Foreword
In 1987 the springmeetingofthe ,,Arbeitskreis Festk6rperphysik" ofthe Deutsche
Physikalische Gesellschaft (DPG) was held in MOnster. It was organized together
with the Nederlande Natuurkundige Vereniging (NNV) and the Osterreichische
Physikalische Gesellschaft (OPG).
At the conference about 900 invited andcontributedpapers have been presented
covering a wide range of topics from fundamental physics to technical application.
Volume 27 of the ,,Festk6rperprobleme" contains a selection of invited talks
hold at tile conference. In choosing the authors, the editor has avoided double
publication in case the authors in question recently published a similar review on
the same subject. In some othercases, however, the editorhas been interested to
get a manuscript, but the invited authors have not been able to write it due to
some other occupations. That's apity! The lot ofmany editors!
The first contribution of B.Ewen and D.Richter deals with the analysis of the
dynamics of macromolecules in solutions and melts. This work was honoured by
the Walter-Schottky-Prize 1987. The results are a fascinating exampleofthe power
of the highly resolving spin-echoneutron spectroscopy.
The following paper reports on demonstrations of temporal and spatial structures
in non-linear systems. H.G. Purwins gave pleasure to an audience of about 900
people with hisexcellent talk andthe well organized experiments inMtinster.
D. Vollhardt's contribution gives an introduction to the phenomenon of localization
and the related theoretical models, and E. Wassermann reports on a modern ap-
proach to explain the properties of the Invar alloys. Two papers are dedicated to
new experimental results obtained at the 2-dimensional electron gas observed in
heterostructures (U. Merkt) and in superlattices (J. K. Maan). In two otherpapers,
the structure and reactivity of metal surfaces (G.Ertl) and of silicon surfaces
(M. Henzler) are considered.
The last five contributions concern topics more or less related to applications:
P. Kocevar discusses, on the basis of theoretical models, theenergy transfer from a
highly laser excited electron gas to the phonon system leadingto "hot phonons",
and H.R. Zeller presents the actual knowledge of the electrical breakdown in
dielectrics.
The contribution ofW. Uelhoffdeals with crystal growthby meansof the Czoch-
raslki-method, one of the most important steps in microelectronics. E. Kasper and
K. Kempter show the chances of unconventional semiconductor materials for the
production of devices: silicon-germanium heterostructures and amorphous silicon.
V
The authors as well as the editor and the publisher hope that volume 27 of the
,,Festkorperprobleme" will again help interested physicists to make approaches to
some actual problems ofmodern physics of condensed matter and to learn some-
thingabout the state ofthe art.
Finally, I thank my secretary, my colleagues in Aachen and the chairmen of the
,,Fachausscht~sse" for their support in preparing the scientific programme of the
conference, and Mr W. Grol~e-Nobis and thelocal organizing committee for their
excellentwork.
As the editor of this volume, I thank all the authors and the publisher for their
efficient collaboration. In particular, I have the pleasure to thankMr. E. Gerlach
for his critical readingof the manuscripts duringthe conference and B. Gondesen
from Vieweg-Verlag for his congenial cooperation. Mostly, however, I thank
Mr. J. Brunn. As in previous years, he assisted me again as a lector and a very
personal advisor duringmy editorship.
This is the last volume of a series of six volumes 1 have edited. It has been an
interesting work, and I have enjoyed very much the interaction with my fellow-
physicists and with the publisher. The next volume will be editedby U.R6Ner,
Regensburg, who is also my successor to the chair of the ,,Fachausschut,~ Halb-
leiterphysik". I wish him all the best for his future activities and the same cordial
support of all the semiconductor physicists as I have found throughout the last
years!
,,Auf Wiedersehen !"
Aachen, May 1987 PeterGrosse
VI
Contents
BerndEwen,DieterRichter
NeutronSpin Echo Studies on theSegmental Dynamics ofMacromolecules... 1
Hans-Georg Purwins, Giinter Klempt,Jiirgen Berkemeier
Temporal and Spatial Structures of Nonlinear Dynamical Systems . . . . . . . . . 27
Dieter Vollhardt
Localization Effects in Disordered Systems . . . . . . . . . . . . . . . . . . . . . . . . 63
Eberhard F. Wassermann
Invar:ANew Approach toanOldProblemofMagnetism . . . . . . . . . . . . . . . 85
Ulrich Merkt
Spectroscopy of Inversion Electrons onIII-V Semiconductors . . . . . . . . . . . . 109
Jan-Kees Maan
Magnetic Quantization in Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Gerhard Ertl
Structureand Reactivity ofSolid Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 169
Martin Henzler
The Microstructure of Technologically ImportantSilicon Surfaces . . . . . . . . . 185
PeterKocevar
HotPhonons ............................................ 197
Hans-RudolfZeller, ThomasBaumann,Eduard Cartier, HelmutDersch,
PeterPfIuger,FrediStucki
The Physics of Electrical Breakdown and Prebreakdown inSolid Dielectrics •.223
Werner Uelhoff
ThePhysics of Czochralski Crystal Growth . . . . . . . . . . . . . . . . . . . . . . . .241
ErichKasper
Silicon Germanium-Heterostructures onSilicon Substrates . . . . . . . . . . . . . .265
KarlKempter
Large-Area Electronics Based on Amorphous Silicon . . . . . . . . . . . . . . . . . .279
VII
Festk6rperprobleme 27 (1987)
Neutron Spin Echo Studies onthe Segmental Dynamics of
Macromolecules
BerndEwen
Max-Planck-lnstitut ffir Polymerforschung, D-6500Mainz,FederalRepublicofGermany
Dieter Richter
Institut Laue-Langevin, F-38042Grenoble,France
Summary: The ultrahigh resolution neutron spin echo (NSE) technique provides theunique
opportunity to investigate internaldynamicrelaxation processes ofpolymermolecules simul-
taneously in spcae and time. In particular,information on the single chainbehaviouris not
restrictedto dilute solutions but mayalsobeobtained,ifanappropriatemixtureofprotonated
and deuterated polymersis used, from concentrated systems, the melt included. This paper
gives a review on recent NSE studies on liquid polydimethylsiloxane (PDMS) systems.Single
chainrelaxationas well as collective fluctuations areconsideredin thewholerangeofconcen-
trations. Thereby especially thecross over phenomena betweendifferentdynamic regimes are
emphasized.The results are discussed in terms of microscopic modelsand compared with the
theoretical predictions concerning universal and critical behaviour.
1 Introduction
Macromolecules are chemical compounds build-up from a large number ofcovalent
bonded repeat units (monomers)[I]. In general such chain or polymer molecules
may assume an enormousarray of spatial configurations, whichis theconsequence
of the rotational freedom around the single bonds of the backbone atoms [2]. In
solution as well as in the melt and the glassy solid state the overall shape of the
individual polymer molecules is coil like. On length scales,where the details of the
chemical structure of the monomerunits becomeofsecondaryimportanceand the
polymer molecules can be described by a sequence of freelyjointed statistical
segments, certain molecular properties exhibit universal behaviour [3]. For example,
the mean square end to end distance (R~) and the mean square radius ofgyration
(R~) scale with M2v, where M is the molar mass and v the Flory exponent [2]. In
the melt and under ®-conditions in solution, where the repulsive forces between
different segments are totally balanced by the attractive van der Waals forces and
no excludedvolume interactions occur, the numerical value ofv is 1/2. In contrast,
in solutions under good solvent conditions v increases to 3/5. Similarly the coil
diffusion coefficient D scales with D ~M-~ in dilute solutions, whereas in melts
this relation isalteredto D ~ M-2 [2, 3].
Correspondingly, universal behaviour is also predicted by the microsopic models
[4 ... 9] which were introduced in order to describe the dynamics of polymers in
solution and inthe melt ona segmental scale.
Such universal behaviour became quite obvious, when the analogy between poly-
meric and magnetic systems was pointed out [3, 10]. In the framework of this
concept it can be shown, for example, that the transition from O-to good solvent
conditions indilute solutions, whichis driven by the temperature, orthe transition
from dilute to semidulute solution at increasing concentrations exhibit the features
of critical phenomena with asmooth cross over betweenthe different phases, well
knowninsolidstate physics [11].
In order to investigate these predictions of universal behaviour and to test the
different microscopic dynamic models on appropriate length and time scales,
microscopic experimental methods are required, which can provide information
on the segmental motion in space andtime.Up to the endofthe seventies no such
methodswere available. The development oftheneutronspin echo (NSE)technique
[12 ... 14] which gives direct access to the pair correlation function in the space
and time domain of segmental diffusion markedthe breakthrough. Using labelling
methods the information on the single chain behaviour is not restricted to dilute
solutions, but may also beobtainedfor concentrated systemsincludingthemelt.
This paper will give a review on recent neutron spin echo studies on segmental
diffusion of polydimethylsiloxane [PDMS:-(Si(CH3)2-O)-n] systems [15 ... 23]
in the full concentrationrange.Aftercommentingontheprinciples ofthe method
and addressing to some details of the microscopic models for the internalchain
relaxation, segmental diffusion in dilute~9-solutionsiscomparedwiththe predictions
of the Zimm model. This model is based on the assumption that hydrodynamic
interactions between the different segments occur down to microscopic scales. In
addition, the cross over from ®- to good solvent conditions whichis initiated by
increasing the temperature is studied. In semidilute solutions, where the different
polymercoils interpenetrate eachother, the collective response is characterized by
a cross over from Zimm dynamics at short scales to collective relaxation at larger
scales, whereas the single chain relaxation is dominated by the screeningof the
hydrodynamic interactions. Finally, in polymer melts and melt-like concentrated
solutions the microscopic data of single chainrelaxationseem tofavourthe Rouse
model (Zimm model without any hydrodynamic interactions), while the macro-
scopic data require topological constraints between the different chainsto betaken
into account.
2 The Spin EchoMethod
The unique feature of neutron spin echo (NSE) is its ability to measure energy
changes of neutronswhichoccurduringa scattering process in adirect way [14].
This differentiates it from conventional scattering techniques, wherethe scattering
experiment takes place in two steps: first the monochromatization of the in-
comingand thereafter theanalysis ofthe scattered beam.Theenergy and momentum
changes during scattering then are obtained from evaluating the appropriate differ-
ence from the two initial measurements. Consequently, conventional high energy
resolution techniques requireto cut out a very small primary energy interval from
the comparatively weak spectrum of the neutron source and in general have to
fight with low neutron intensities. Other than the conventional techniques, NSE
measures the neutron velocities of the incoming and scattered neutrons utilizing
the Larmor precessions of the neutron spin in anexternalguide field. This meas-
urement is performed for each neutron individually, since the neutronspin vector
acts like the hand of an"internalclock"attachedtoeachneutronwhichstores the
result ofthe velocity measurement on theneutron itself. Therefore, the incoming
and outgoing velocities of oneandthe sameneutroncan be compared directly, and
a velocity difference measurement becomes possible. Thus, energy resolution and
monochromatization of the primary beam or the proportional neutron intensity
are decoupled and anenergy resolution in theorder of l0-s can beachievedwith
an incident neutron spectrum of 20% bandwidth. In the following we first ex-
plainbasic neutron spin manipulations by means ofexternalmagnetic fields and
thereafter discussthe NSE principles.
2.1 Neutron Spin Manipulations by Magnetic Fields
The motionofaneutronspin inamagneticfieldHis described by
d. 2171~i
dt s~- ra [ta.~,~] (a:x,y,z) (1)
whereS=(Sx, Sy, Sz)is the spin operator; 7= - 1.91, tlthenuclearmagneton,and
i=x/-s-f;[ ] denotes the commutator. The neutron polarization Pa is obtained
from the expectation values (Sa)=-sa for which the classical equations of motion
are valid
d 2171#
dt sa= ~ - ~ (fi (t) xs(t))a, (2)
(h Planck constant h divided by 2r0.
Eq. (2) is the basis for the manipulation of the neutron polarization by external
fields. We discuss two simple spin turn operations: Let us consider aneutronbeam
whichpropag~es in z-direction with a spin polarization parallel toits momentum.
AguidefieldHo parallel toz stabilizes the polarization. First weexplaina so-called
~r-coil. There, two components of the neutron spin are reversed. Its principle is
shown in Fig. la and b. A fiat long~ctangular coil, a so-called Mezeicoilisturned
slight~ out_+ofthe x-y plane. AfieldHe isproducedin such away that the resulting
fieldH,r= Ho+Heis pointing in x-direction and starts to precess aroundthis axis.
During a time t= d/v,where d is the coil thickness and v the neutron velocity, a
Fig 1 Basic spin turnoperationrelevantforNSE:
a) Mezei-coil set-upforan-turnoftheneutronspins
b) Motion oftheneutron polarization on theactionofthe~r-turn coil
c) Motionof theneutron polarization duringa~r/2turn.
2171~
phase angle qb= colt is covered. With the Larmor frequencycoL h H~r and
= - -
v =h/reXwe find
21"rlgrrt
a, = h: z---T- d- X. (3)
where m is the neutron mass and X the neutron wavelength. Thus,el,isgivenby the
path integral f Hds and is proportional to X.E.g., for a coil thickness ofd= 1cmand
X= 83-a field H,r of 8.5 0e is needed for a 180° turn. Such a spin turn is schem-
atically shown in Fig. lb. As can be seen it transforms the spin components (x, y, z)
to (x, - y, - z).
The secondimportant spin turn operationis the 7r/2 turn. There, the polarization
is turned from the z- into the x-direction or vice versa. A Mezeicoil in the x-yplane
is tuned such that the resulting field points into the direction of the bisectorof the
angle between x and z. Then, a 180° spin turn around this axis transforms the z-
component into the x-direction. At the same time the sign of the y-component is
inversed (Fig. lc).
2.2 The Principles of Neutron Spin Echo
The basicexperimental set up ofa neutron spin echo spectrometer is shown in Fig.
2. A velocity selector in the primary neutron beam selects a wavelength interval of
about 20 % full widthhalfmaximum.Thes.spectrometeroffersprimaryandsecondary
neutron flight paths, whereguide fields H and H' can be applied. At the beginning
of the first flight path a supermirror polarizer polarizes the neutronsin direction
of propagation. A first rr/2 coil turns the neutron spins into the x-direction per-
pendicular to the neutron momentum hk. Starting with this well defined initial