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Gábor Varga |
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Curriculum vitae |
I was born on 30 November
in 1959 in
2. Education
Final exam. János Bolyai secondary school of Salgótarján
(mathematics division) 1978.
M.Sc. Technical University of Budapest, mechanical engineer (mathematician-engineer) 1984.
Dr. UNIV. in physics 1996.
Ph.D. in physics 1997.
Lectures on:
I have dealt with Thermal Energy Atomic Scattering from solid surfaces
(TEAS) and surface physics since 1983 when I started my diploma
work at the Physics Department, Technical University of Budapest. I
graduated at the Technical University of Budapest in 1984 and I got the diploma
(M.Sc.) as a mathematician-engineer. My diploma work
written on TEAS is entitled "Investigation of He-Ni scattering by
normalised distorted wave Born approximation" (1984). On the
basis of the results of exams and diploma work I received a position at the
Physics Department at the Technical University of Budapest. I have worked at
the Physics Department since 1984. I am a senior lecturer at present. During
this time I have continuously given lectures on experimental physics, solid
state physics, surface physics, quantum physics and computers. I continued my
researches in TEAS and I participated at conferences on vacuum and surface
science, too. I took part in Trieste on a Spring College on condensed matter in
1988. I won a financial support from the Hungarian Academy of Sciences in the
period 1990-1994 for the theoretical investigation of TEAS. I completed this
project successfully, and among others I wrote - in 1993 - my Ph.D. thesis with the title
"Computations of thermal energy atomic scattering from solid surfaces by
hard corrugated wall model". I took my doctoral exams with results
"summa cum laude" and I successfully defended my dissertation in
1996. I obtained maximal points from the opponents and the doctoral committee.
These facts led to be awarded by the degrees of "dr. Univ." and of
"doctor (Ph.D.)" in 1996 and 1997,
respectively.
Firstly I interpreted the Normalised Distorted Wave Born Approximation (NDWBA) and after that I improved a method to solve the inverse scattering problem [A1][S1][P2]. Since NDWBA is applicable only for very smooth surfaces I focused on the Hard Corrugated Wall Model (HCW) because it describes TEAS in first order also in the case of adsorbed layers. I improved the stability of the so called GR method [A2]A3][A4][P1][P3][P5]. (GR method uses Rayleigh Ansatz of wave function and chooses appropriate set of points in the reciprocal space (G) and in the direct space (R). Considering the boundary condition at the surface, the solution of a linear system of equations of amplitudes with complex coefficient matrix is required.) In addition I developed a procedure to solve HCW model by GR method for symmetrical experimental arrangement [A5] which led to the decrease of computational efforts for 2% of the original case. This abrupt decrease opened the possibility to work out an inverse scattering method. This method fits the corrugation parameters of the surface to the experimental results. I introduced a refined version of the inverse problem [A7][A13][S3][S4][P4][P7]. In that case I fit the unknown corrugation parameters and the unknown parameters of the Debye-Waller factors at the same time. I worked out this model using HCW model and kinematic theory of Debye-Waller factors. The numerical results support the choice of this model. For more realistic cases its further implementation is required. I think my results provide good initial values to a more complicated model calculation, for example to that which exploits the time dependent Schrödinger equation. As I described above my published results mainly join the surface structure investigation by TEAS. I prepared not only papers and conference presentations but some global reviews for TEAS [S1-S4].
In my Ph.D. thesis I reviewed the experimental
set-up of TEAS focusing on the resolution and the transfer width in chapter 1.
In the next chapter I showed the main classical, quantum mechanical and
semi-classical models. The HCW model was compared with more sophisticated model
computations and the results proved the HCW model as appropriate for analysing
surface structure. In addition I scanned the effect of the thermal attenuation.
The Debye-Waller factor was investigated in the case of X-ray, electron,
neutron and atom scattering. In chapter 3 my new results in HCW model
computations were discussed. First the stability and the convergence of the HCW
model were improved. After that the symmetrical experimental arrangements were
investigated, which led to an abrupt decrease of the computation efforts. This
result provided an efficient basis for the solution of the inverse atomic
scattering problem. Last chapter outlined the solution of the inverse
scattering problem in the case of a more realistic physical model.
My newer results are in connection with wave-packet model, surface disorders
and chaotic scattering. I published - first in my Ph.D.
thesis - my computations considering the TEAS in a time dependent picture when
solving time dependent Schrödinger equation. I modeled the atomic supersonic
beam by wave-packet as an ensemble of non-interacting particles. Additionally I
have already published a part of my new results at the international 7th Joint
Vacuum Conference (JVC-7) [A6-A9] [P6-P7], at the 10th International Conference
on Solid Surfaces (ICSS-10) [A10-A12] [P10-P12] and at the 18th European
Conference on Surface Science (ECOSS-18) [A15][A16] [P13][P14]. I do research
on description of TEAS when the supersonic He beam is
modeled by its realistic velocity distribution quantum mechanically. I have
been looking for its relation to the simple plane wave model and the validity
of two-dimensional Bragg condition. An another subject is also very
interesting. I try to find the quantum mechanical counterpart of the
classically chaotic He-Cu(117) scattering using not
the semiclassical trajectory method, but a pure stochastic one, the Heidelberg
method.
My very recent researches relate to nanometer scale science, nano-technology,
nanoelectronic.
Theoretical Investigation of Thermal Energy Atomic Scattering from solid surfaces (TEAS)
Below I give some fields of surface physics, which I have been investigating recently. I have published and unpublished results in connection with these problems.
1 Background
The Thermal Energy Atomic Scattering from solid
Surfaces (TEAS) is related to the subject of surface physics. The TEAS is an
especially useful tool for surface investigations, because it is extremely
sensitive to the top layer of the solid surface and it does not damage the
structure. The explanation for this fact can be found in the low average energy
of probe particles. 10 - 100 meV energy is typical of neutral atomic beams
providing narrow relative velocity spread. The probe particles, the quasi monochromatic
beams ensure the high resolution of intensity distribution. There are three
main areas where the TEAS has achieved successes. First one is the surface
structure determination based on diffraction peaks, second one is the
determination of phonon spectra using time-of-flight measurement and the third
one is the investigation of surface impurities exploiting the surprisingly
large cross section of individual disorders.
2 Problems, ideas and methods
(A) Inverse scattering from adsorbed layers on solid surfaces
Problem: The topology of solid surfaces with adsorbed layer should be
determined by a refined method [A7] [A13] P7].
Ideas: The corrugation parameters and the unknown parameters of Debye-Waller
factors should be fitted to diffraction peak intensities simultaneously in
contrary to the standard methods when only the corrugation parameters are
fitted.
Methods: In general this is a semi-empirical procedure. In the specific case
one particle scattering model should be chosen and the task looking for minimum
has to be formulated and solved.
Difficulties: The solution may consume too much computer effort and it may lead
to unstable numerical procedure.
Results to be expected: The research may provide a more correct topology of
adsorbed layers and a more realistic picture of the dynamic of coverage as a
function of adsorbate exposure.
(B) Beam velocity distribution shape effect
Problem: Theatomic beam is non-monoenergetic [A9] [A12][A17] [P8][P10].
Ideas: The wave-packet approximation is needed instead of ideally monoenergetic
plane wave discussion of TEAS. The atomic beam velocity distribution profile is
known using supersonic jet when the continuum stream turns into free atomic
stream. This distribution can be described by a quantum mechanical wave-packet.
Methods: This more realistic TEAS is analysed by the solution of time dependent
Schrödinger equation.
Difficulties: The problem may consume too much computer effort. The inverse
scattering problem may lead to unsolvable numerical procedure.
Results to be expected: Validity range of the plane wave model and of the
two-dimensional Bragg condition, in addition answer the question "What is
the model reliability".
(C) Chaotic scattering (physical processes)
Problem: In certain cases TEAS is chaotic. It is discussed classically and
semi-classically. Does its purely quantum (stochastic) counterpart exist [A9]
[A11][A15][A16][P9][P12][P13][P14].
Ideas: The scattering matrix of a given TEAS set-up should be determined by
numerically since there is no analytical solution.
Methods: Analysis of the scattering matrix by energy and time delay
investigation.
Difficulties: There may not be quantum counterpart.
Results to be expected: The quantum pair will be found. New physical effects in
the scattering processes and in the patterns of scattered beam.
(D) Disordered systems
Problem: TEAS provides extremely large cross-section of individual
impurities on surfaces. The disordered surface is not ideally periodic. This
underlines that simple diffraction theory (Bragg condition) is unable to
describe the scattering process. Wave-packet method is necessary to be applied
[A8][A12] [A17][P8][P10].
Ideas: One particle model is needed to describe TEAS. One particle ensemble as
a wave-packet is handled.
Methods: Solution of the time dependent Schrödinger equation with wave-packet
initial wave function and with appropriate interaction potential that describes
atom-surface interaction.
Difficulties: Numerical efforts and quantum mechanical implementation of the
physical processes.
Results to be expected: A surface tool to explore a more complex structure on
surfaces.
(E) Validity range of Bragg condition in the case of TEAS and LEED
Problem: Does the scattering probe particle feel a two-dimensional surface
lattice [AC1].
Ideas: The wave-packet has to be scattered on the solid surface and the
directions of the diffraction peaks have to be compared with the results of
Bragg condition.
Methods: The solution of time dependent Schrödinger equation is required.
Difficulties: Numerical efforts.
Results to expected: Refined models of TEAS and LEED.
(F) Condensation seeds on solid surfaces
Problem: Construction of an appropriate model of condensation seeds on
surfaces.
Ideas: Surface is described as a set of contours of the time dependent
interaction potential. The seeds are the special places which attract the
atoms. The places and the existence of the seeds are determined by the usage of
the wave-packet on the fluctuating potential surface. Time dependent
Schrödinger equation solution is required.
Difficulties: Uncertainty of physical model and numerical efforts.
Results to be expected: A realistic dynamic model of seed evolution on solid
surfaces.