Andrea Benassi's Thesis

204 Pages·2009·9.35 MB·English

Universita` degli Studi di Modena e Reggio Emilia
Facolta` di Scienze Matematiche Fisiche e Naturali
Ph.D. School in Physics and Nanoscience
Role of the vacuum fluctuation forces in
microscopic systems
Author Supervisor
Andrea Benassi Prof. Carlo Calandra
Buonaura
Colloquia Doctoralia XXI ciclo. Modena, November 2008
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To my parents
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Introduction
In the last few years an increasing attention has been addressed to the nature and inten-
sity of the forces arising from the electromagnetic vacuum fluctuations (Casimir and van
der Waals or dispersion forces) [1, 2]. The interest in this subject comes from some basic
developments: (i) the increased experimental effort, that has led to accurate measurements
of the force intensity for specific configurations [3, 4, 5, 6, 7, 8, 9, 10], (ii) the understanding
of the relationship between the force and the elementary excitations of the interacting bod-
ies, that has allowed to generalization to real materials of results originally obtained using
idealized boundary conditions [11, 12, 13, 14, 15, 16, 17, 18], (iii) the role played by these
forcesinnano-andmicrodevices[19,20,21,22,23],(iv)thepossibilityofexploitingdifferent
geometrical configurations to achieve the desired properties of the forces [24, 25].
Thepurposeofthepresentthesisistostudytherolethatelectromagneticvacuumfluctu-
ation forces may play in a number of issues that are relevant at the nano- microscopic scale.
The study is devoted to the following problems:
i) Stability of deposited metal films: investigation of the importance of vacuum
fluctuation force in determining the critical thickness of metal overlayer with respect to the
transition between a uniform two-dimensional phase and a corrugated one [26, 27, 28]. The
attention is focused first on the force acting on the film boundaries in the case of a free
standing film and then on the modifications of this force when the film is deposited on a
metal substrate. It is shownthat, while the force does notcontribute to the surfacestability
in the case of an isolated film, being too weak in comparison with the surface stress, it can
be crucially important in the case of deposition, where vacuum electromagnetic energy may
be of the same orderof magnitude ofthe difference between the elastic energycausedby the
lattice mismatch, which favours the surface corrugation to release the excess elastic energy,
andthesurfaceenergy,whichtendstofavourtheplanarconfiguration. Thestudyprovidethe
conditions under which the force on the film can sustain the stability of the planar configu-
ration,givenintermsoftheparametersenteringintotheexpressionofthedielectricfunction.
ii)Size effectsintheCasimirinteractionbetweenultrathinfilms: studyoftheef-
fectsofthequantizationoftheenergylevelscausedbyquantumconfinementontheintensity
of the force between metal films. The use of bulk dielectric functions in the force calculation
within the framework of the Lifshitz theory, while appropriate for thick enough films [29], is
expectedtogiveunrealisticresultswhenthefilm thicknessisofthe orderoffewnanometers.
The study has been carried out by determining the dielectric function of a confined system
of free electrons using the RPA approximationto calculate the dielectric function [30]. This
turns out to have a tensorialcharacter,consistent with the strong anisotropy of the electron
distribution, and to depend upon the film thickness through the electron energies and the
dipole matrix elements. In view of the importance of the confinement potential different
models have been considered: the particle in a box model [31] and models where the later-
ally averaged one electron potential is represented by a finite well. The modifications with
respect to calculations with the bulk dielectric function have been analyzed as a function of
the potential depth and of the electron density.
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iii) First principles calculation of the force between ultrathin silicon films: a
study aiming at understanding how modifications in the dielectric function induced by the
reduced film size and by the occurrence of surface states may cause changes in the vacuum
fluctuationforcebetweensiliconslabs. Densityfunctionaltheoryhasbeenusedtodetermine
the film dielectric tensor starting from the one electron energies and wavefunctions calcu-
lated self-consistently for the film, using both simple RPA [30] and the RPA corrected by
localfieldeffectstodeterminethemacroscopicdielectrictensoratvanishingwavevectorfrom
the inverse dielectric matrix [32, 33]. The force calculated using the film dielectric tensor is
compared with the calculation starting from the bulk dielectric function obtained with the
sametheory. Evidenceisprovidedthatthepresenceofsurfacestatescanaffecttheforceover
a large range of film separation distances. The macroscopic dielectric tensor turns out to be
very sensitive to local field effects. As a consequence the force can be significantly modified
by their inclusion.
iv) Influence of metal insulator transition in device actuated by the electro-
magnetic vacuum force: the proposal of a device that exploits the phase transition to
extendthe distance and energyrangesoverwhichit canbe operated. The basic device com-
ponentsarefilmsofGeTe[34,35,36](orothercompoundswithsimilarbehaviour[37,38,39])
, a material that undergoes a rapid transitions between polycristalline phases, which show a
metallicbehaviourwithap-type conductivitydueto vacantGe sites,andamorphousphases
withtypicalsemiconductorproperties[40]. Startingfromempiricallyderiveddielectricfunc-
tion one can obtain device potential profile and bifurcation diagrams illustrating how the
device proprties can be tuned optically.
The plan of the thesis is the following. The first two chapters are devoted to the pre-
sentation of the basic theory. In particular the first one summarize basic concepts of elec-
trodynamics of linear media and presents a discussion of model dielectric functions to be
used in the applications. The second chapter is a presentation of the Lifshitz theory of the
electromagnetic vacuum fluctuation forces and shortly review recent developments. Each of
the following chapters is devoted to one of the above outlined issues and presents a detailed
discussion of the subject under consideration, a complete illustration of the results and the
appropriate conclusions.
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Acknowledgments
I would like to express my special thanks to professor Carlo Calandra Buonaura for his in-
valuable guidance, help and support over these years.
Another special thanks to professor Elisa Molinari who hosted me in S3 national research
center giving me the opportunity to attend schools, workshop and seminars all over the
world.
I want to acknowledge CINECA consorzio interuniversitario for funding my Ph.D. fellow-
ship. I am grateful to Carlo Cavazzonifrom the High Performance Computing Department,
for the huge amount of computational time and for the precious technical help he provided
me with.
I am grateful to Dr. Andrea Ferretti, Dr. Daniele Varsano and Dr. Stefano Corni for their
interest in my activity and for their important contributions.
Many thanks to Dr. Layla Martin-Samos, Dr. Agostino Migliore, Dr. Gianmarco Bra-
manti, Dr. Massimo Rontani for the helpful material they address me to and for the useful
discussions about the theoretical concepts reviewed in the first part of this thesis.
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