The used solver settings for Fluent v. 6.3 are given for those different from the standard settings. These settings are also used for the coupled code.
description setting remarks fixed time step size 0.2−0.3ns
volume fraction discretization scheme
geometric reconstruction
to ensure the free surface to be one element sharp
water UDS discretization scheme third order muscle
lower order discretization gives bad results for free surface heat transfer all other discretization schemes second order
UDS under relaxation factor 0.9
UDS convergence residual 5e−7 similar to the energy residual
silicon viscosity for silicon below
melting temperature ms
kg 07 . 0
higher values causes divergence of pressure; lower values increase numerical movement of solid silicon
149
symbol unit description
a volume fraction
A m 2 area
b beam direction vector with unit length
c coefficients of the temperature – enthalpy relation
l
c m s speed of light
p
c J (kgK) specific heat capacity C m −3 species concentration
H
C J m2 constant for semi analytic surface enthalpy distribution U
C ,C V constants for ADE expressions
d m thickness or diameter
D m2 s diffusion coefficient
E unit tensor
E J energy
f s −1 frequency or repetition rate
F J m2 laser fluence
G gray value of CCD image
h J s Planck constant
ht W (m2K) heat transfer coefficient
H J m3 enthalpy
i imaginary unit
symbol unit description
I W m2 spatial averaged laser light intensity
J W m2 heat flux
k negative imaginary part of refraction index, extinction coefficient
r
k m3 (mols) kinetic rate constant
B k J K Boltzmann constant K W (mK) heat conductivity l m length L J m3 latent heat mol
L J mol molar latent heat
a
m kg atom mass
M kg mol molar mass
n real part of refraction index
*
n complex refraction index
n surface normal vector with unit length
n& s −1 removal rate
np multiphase phase count
nx element count in x coordinate
ny element count in y coordinate
nz element count in z coordinate
A
N mol −1 Avogadro constant
p N m2 static pressure
P W laser power
r m radial coordinate, distance from centre of axial symmetry
*
symbol unit description
R reflectivity
m
R J (Kmol) molar gas constant
S source term, unit with respect to the corresponding equation
t s time
T K temperature
U
(
J m3)
forward part in ADE algorithm, unit of enthalpy for heat transportequation
v m s velocity vector
V m ;3
(
J m3)
volume; backward part in ADE algorithm, unit of enthalpy forheat transport equation
α m −1 absorption coefficient
β liquid fraction
δ relative path enlargement
f
δ optical path difference
r
H
Δ J mol reaction enthalpy
t
Δ s time step size
x
Δ m element size in x coordinate
y
Δ m element size in y coordinate
z
Δ m element size in z coordinate
ε relative permittivity
*
ε complex relative permittivity
0 ε As (Vm) dielectric constant T ε relative emissivity Φ m s general flux d Φ quantum efficiency
symbol unit description
ϕ ° angle
Γ m2 s general diffusivity
γ s −1 collision rate
Κ m s kinetic rate constant
λ m wavelength
μ Ns m2 molecular viscosity
ρ kg m3 density
σ W (m2 K4) Stefan-Boltzmann constant
c
σ m 2 collision cross section gauss
σ m Gaussian standard deviation
Θ m −2 dopant loading
τ N m2 stress tensor
0
τ s smooth pulse time constant
p
τ s pulse duration
Ψ general scalar
ω s −1 angular frequency
ξ arbitrary fluid property
index description
+ shifted element value in positive coordinate direction
++ two times shifted element value in positive coordinate direction
5 . 0
+ face value in positive coordinate direction
– shifted element value in negative coordinate direction
index description
5 . 0
− face value in negative coordinate direction
b boiling
bc boundary condition
beam light beam
crit critical
eff effective
expl explicit
f film
h heat
i element number in x coordinate
in inlet
inc incident
ins intersection
imag imaginary part
impl implicit
j element number in y coordinate
jet liquid jet
k element number in z coordinate
kn Knudsen evaporation
l liquid phase
lv liquid – vapour interface
m melting
mass mass
mixt mixture phase
mom momentum
n time step number
index description
p laser pulse
pl plasma
q multiphase phase number
real real part
refl reflection
refr refraction
s solid phase
sp species
sat saturation
sl solid – liquid interface
solv solvent
surf surface
v vaporization
abbreviation description ADE alternating direction explicit
CCD charge-coupled device
CW continuous wave
EEG Erneuerbare Energien Gesetz
FWHM full width half maximum
ISE Institute for Solar Energy Systems
LBSF local back surface field
LCP laser chemical processing
LMJ LaserMicroJet™
MWSS multi wire slurry saw
abbreviation description
ODE ordinary differential equation
PDE partial differential equation PERC passivated emitter and rear cell
PSG phosphorous silicate glass
PV photovoltaic
SEM scanning electron microscope
SIMS secondary ion mass spectroscopy
UDF user defined functions
UDS user defined scalar
UV ultra violet
156
Journal articles:
• Fell, A. and G.P. Willeke, Fast simulation code for heating, phase changes and dopant diffusion in silicon laser processing using the alternating direction explicit (ADE) method. Applied Physics A, 2009. 98(2): p. 435-440.
• Fell, A., K. Mayer, S. Hopman, and D. Kray, Potential and limits of chemical enhanced deep cutting of silicon with a coupled laser-liquid jet. Journal of Laser Applications, 2009. 21(1): p. 27-31.
• Fell, A., D. Kray, and G.P. Willeke, Transient 3D/2D simulation of laser-induced ablation of silicon. Applied Physics A, 2008. 92(4): p. 987-91.
• Hopman, S., A. Fell, K. Mayer, M. Mesec, A. Rodofili, and D. Kray, Comparison of Laser Chemical Processing and LaserMicroJet for structuring and cutting silicon substrates. Applied Physics A, 2009. 95: p. 857-866.
• Kray, D., A. Fell, S. Hopman, K. Mayer, S.W. Glunz, and G.P. Willeke, Laser Chemical Processing (LCP) – A versatile tool for microstructuring applications. Applied Physics A, 2008. 93(1): p. 99-103.
Conference contributions:
• Fell, A., F. Granek, and G.P. Willeke. Simulation of Laser Melting of Silicon and Silicon Melt Expelling by Liquid Jet using Transient Coupling of Fluent with a Finite Differences Code in Matlab. in 10th Conference on Laser Ablation. 2009. Singapore.
• Fell, A., D. Kray, T. Wütherich, M. R., G.P. Willeke, and S.W. Glunz. Simulation of phase changes and dopant diffusion in silicon for the manufacturing of selective phosphorous emitters via laser chemical processing. in Proceedings of the 23rd European Photovoltaic Solar Energy Conference. 2008. Valencia, Spain.
• Fell, A., S. Hopman, D. Kray, and G.P. Willeke. Transient 3d-simulation of laser- induced ablation of silicon. in Proceedings of the 22nd European Photovoltaic Solar Energy Conference 2007. Milan, Italy.
Laser Parameters for Silicon Solar Cells with LCP Selective Emitters. in Proceedings of the 24th European Photovoltaic Solar Energy Conference. 2009. Hamburg.
• Rodofili, A., S. Hopman, A. Fell, K. Mayer, M. Mesec, F. Granek, and S.W. Glunz. Characterization of doping via laser chemical processing (LCP). in Proceedings of the 24th European Photovoltaic Solar Energy Conference. 2009. Hamburg, Germany.
• Kray, D., M. Alemán, A. Fell, S. Hopman, K. Mayer, M. Mesec, R. Müller, G.P. Willeke, S.W. Glunz, B. Bitnar, D.-H. Neuhaus, R. Lüdemann, T. Schlenker, D. Manz, A. Bentzen, E. Sauar, A. Pauchard, and B. Richerzhagen. Laser-doped silicon solar cells by laser chemical processing (LCP) exceeding 20% efficiency. in Proceedings of the 33rd IEEE Photovoltaic Specialists Conference. 2008. San Diego, USA.
• Hopman, S., A. Fell, K. Mayer, M. Mesec, G.P. Willeke, and D. Kray. First results of wafering with laser chemical processing. in Proceedings of the 23rd European Photovoltaic Solar Energy Conference. 2008. Valencia, Spain.
• Rodofili, A., A. Fell, S. Hopman, K. Mayer, G.P. Willeke, D. Kray, and S.W. Glunz. Local p-type back surface fields via laser chemical processing (LCP): first experiments. in Proceedings of the 23rd European Photovoltaic Solar Energy Conference. 2008. Valencia, Spain.
• Kray, D., A. Fell, S. Hopman, K. Mayer, M. Mesec, S.W. Glunz, and G.P. Willeke. Progress in laser chemical processing (LCP) for innovative solar cell microstructuring and wafering applications. in Proceedings of the 22nd European Photovoltaic Solar Energy Conference 2007. Milan, Italy.
• Hopman, S., A. Fell, K. Mayer, M. Aleman, M. Mesec, R. Müller, D. Kray, and G.P. Willeke. Characterization of laser doped silicon wafers with laser chemical processing. in Proceedings of the 22nd European Photovoltaic Solar Energy Conference 2007. Milan, Italy.
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161 beigetragen haben und mit denen ich in den letzten Jahren sehr gut zusammengearbeitet habe, insbesondere
Herrn Prof. Dr. Gerhard Willeke für die Vergabe und Betreuung dieser Arbeit,
Herrn Prof. Dr. Peter Nielaba für die Übernahme des Koreferrats und zusammen mit Herrn
Prof. Dr. Alfred Leitenstorfer für die Bereitschaft meine Prüfer zu sein,
meinen Mit-Doktoranden Sybille Hopman und Dr. Kuno Mayer für zahlreiche wertvolle Diskussionen, eine sehr gute Zusammenarbeit auf engem Raum und vor allem für die Verwendung eurer experimentellen Ergebnisse,
Andreas Rodofili für das ausführliche Testen der Simulationsprogramme und der
(unfreiwilligen) Fehlersuche,
Matthias Mesec und Christoph Fleischmann für das Durchführen von Experimenten und
Messungen,
meinen Gruppenleitern Dr. Daniel Kray und Dr. Filip Granek sowie meinem Abteilungsleiter Dr. Stefan Glunz für den guten organisatorischen Rahmen und die weitgehende wissenschaftliche Freiheit dieser Arbeit,
Annerose Knorz, Tobias Wütherich und Jan Nekarda für wertvolle Zusammenarbeit und
experimentelle Ergebnisse auf dem Gebiet der trockenen Laserprozessierung,
Markus Fratz für die umfangreichen und sehr hilfreichen Korrekturen der Dissertation,
Meiner Familie, insbesondere meinen Eltern Annemarie und Hans-Josef und Großeltern
Anna und Karl für die Sicherheit, mich auf Eure uneingeschränkten Unterstützung jeder Art
und während meiner gesamten Ausbildung verlassen zu können,
und nicht zuletzt meiner kleinen Familie Sarah und Frieda, für ein liebevolles Zuhause und die Geduld besonders während der intensiven Endphase.