Numerical Simulation of Carbon Nanosecond Laser
Annealing in MATLAB.
Chetan Barde, Nitish Barya, and Himanshu Jaiswal
Department of Electronics and communication,Truba Institute of Engineering
and Information Technology, Bhopal
chetanbarde14@gmail.com, barya1993@gmail.com,
himanshujaiswal2050@gmail.com
Abstract:
conduction for heat pattern is developed in MATLAB for the simulation
and the obtaining graph of temperature change for material, When Laser
(KrF) beam (248 nm, 27 ns) confined on the Carbon surface , the results
are obtained and verified in case of Carbon(Graphite). The heat source
is spreading with time as ‘gate’ shape. Different values of Thermal
properties where obtained, with of 'gate' shape. The returned result
concerns surface temperature versus time. Typically ,over a laser
fluence of 2000 mJ/cm², ablation process occurs on Carbon surface.
Keywords: MATLAB Simulation, Laser heating, Carbon thermal
properties.
Introduction: The importance of investigating the
laser thermal
processing (LTP) and thermal properties investigation of bulk and
complex materials is increasing. We use Lasers in material processing
(cutting, drilling, welding, marking etc.). Now we Pulsed lasers are to
heat, to melt or to ablate the upper surface part exact amount of energy
and keeping the inner part stays without any changes. The main
objective of this project is to check the heating thickness by pulsed laser
treatment, for recrystallition .For this, simulation we use MATLAB is used
to find the melting affect by pulsed lasers. For achieving this purpose,
different methodology have been developed, by using spatially slected
melting
with
lateral
temperature
change.
A
heating-mediated
transformation picture has been coined, proposing that the recrystallized
Carbon morphology is obtained by the transformation in the complex
phase. Now the happening of these phenomena of heating was not
verified by the measurement of direct change in the temperature with the
use of MATLAB.
In this paper effect of laser heating on carbon sample is
solved with affected area 2*2 mm2 . The time resolution is in order of ns
due to the pulse duration of the KrF laser which is closely 27 ns (FWHM)
(Full Width at Half Maximum). The Numerical procedure is developed
under MATLAB project The obtained result deals with surface
temperature change versus the time and ,and also with temperature
versus the depth (y).
Basic Concept
Laser:
Laser’s full form is Light Amplification by Stimulated Emission of
Radiation. It is a monochromatic, convergent, coherent and beam of
electromagnetic radiation. The wavelength of the Laser ranges from the
ultraviolet to that of wavelength of infrared
The underlying basic fundamental of laser working, was first found and
introduced by A.Einstein in the year of 1917. Later, in the year 1960, T.H.
Maiman with ruby laser first introduced us to the working model of laser.
In Laser the production of the Laser is done in the three steps they as
follows population inversion,followed by stimulated emission and then
amplification.
Population inversion: It is a essential and important phenomena
for
stimulated emission. As we are familiar the sates having the more energy
are having the least population of electron ,so the population of the
electron of the more higher energy of state get reduced i.e. decreases
with
the
increase
in
the
energy.
Inversion Process in Laser
Stimulation:- Stimulated emission occurs while the high energy incidating
photon which is having frequency v, acts upon the atom which is in the
excited state of the active medium of Laser .The population inversion
happens in the state of 1 and 2 having the E1 & E2 as the energy.
Simulated process in Laser
The incident photon activate the emission of Laser by collecting the high
energy atom to low value of energy state. The result is that the radiation
has frequency component ,the phase and the direction in which it was
travelling is same as of the acting photon ,which results in the narrow
stream of the photons.
Amplification:
The resulting photons after the stimulation are having the phase as same
and also the polarization,so there is constructive addition with the
photons which are incoming ,so the amplitude is increased.So,light is
amplified
through
the
stimulation
of
emission
of
radiation.The
Amplification is done through the resonanting cavity which contain of a
mirror which poses the property of high reflection that are well aligned to
the ends ,that placed in normal to the axis of cavity.
Heating effect:
Electromagnetic radiation always reacts with the electrons of the atoms
of a material because we know that the much heavier nuclei are unable
to travel along the huge frequencies of laser radiation. During process of
passing electromagnetic radiation over the electrons, it wield a force and
sets these electrons into motion under the electric field of the radiation.
The Incident (arriving) Beam of the laser may have different path to
travel along depending upon laser material interaction. It depends upon
different factor like reflectivity(R), extinction coefficient (k) ,wavelength
(lambda) of the LASER .
Possible way of interaction laser with Solid
Different Stages During Interaction of carbon and laser
To interpret the effects of laser irradiation on material, it is needful to
calculate temporal and spatial variation of temperature distribution.
Ruling equation of one dimensional heat transfer is given by:
Ruling equations:The heat source is circulated in time with shapes. The re-elected results
were almost simulated by the conduction/diffusion models (B. Dragnea
et al., PRL 1999) which are not well reserved to understand transport
phenomena in the Carbon. Mathematical formulation of problem is
accounted by volume equation of heat conduction,
Where ρ is the density of material, Cp specific heat capacity,Ttemperature, t - time and k - thermal conductivity.
Solution of this is given as follows
……………For Heating
For Cooling.
Putting Z=0 For Surface;
………For Heating
And
………for cooling.
Model Graph for heating and cooling
Gt is the heat source distribution in depth (Y) by using Beer-Lambert law
(Figure 4); it's accounted by following equation :
I (t)[W/cm²] is Time distribution of the laser beam intensity. The sample
can be modified into 2D rectangle, On X-axis co-ordinate for width and
On Y-axis coordinate for depth as shown in (Fig.2). The interface part
which is in between heated and unheated part only is worked out i.e. half
of the sample is irradiated due to laser and remaining half is not
irradiated. As it is the source of heat it is utilized in the energy absorbed
volume. The reflectivity for λ = 248nm; at 300 K on monocrystalline is
about 34% .The penetration depth δa under these last conditions is
about δa ≈ 11nm, it varies with respect to optical properties of Carbon,
refractive index n1 and extinction coefficient n2.
Where ω denotes circular frequency and c denotes the speed of light. α
is utilized in Beer-lambert law as below given,
Where I (y) is the depth dependent laser intensity, Io is the intensity of
the surface and y is the depth as shown.
MATLAB It is programming platform for development of the algorithm
,analysis of data can be done also the numerical analysis with
visualization can be considered in MATLAB.It is based on the C/C++ .
MATLAB can be used for signals processing ,image processing ,in the
area of communication and many more interesting applications are there
.Here we using MATLAB for writing the basic equations and obtaining
the different graphs corresponding to the equation.
Result:The Following results where obtained when the heat flow equation and
the Intensity equation was implemented in the MATLAB environment.
This Result Shows the variation of the Intensity with the depth when the
pulsed laser is focused on graphite.
Result showing variation of temperature with time at 27 nsec Laser was
turned OFF.
Conclusion:The variation of the pulsed laser energy intensity is varied exponentially
inside the graphite surface. The variation in intensity is depends upon
the negative exponential of intensity of the pulsed laser. Giving
maximum intensity at the surface of the graphite which is around the
value of 2*10^20 W/M^2.
Results on Graphite exhibit values of the melting point of
and the
melting duration under the pulsed laser treatment. Typical values of
working laser fluences (i.e. 800 to 1300 mJ/cm²) give a melting point
4100 K for the graphite during the pulsed laser treatment for 27 nsec.
The control of the melting kinetics is easier than in the gate shape one.
However, in the case of pulsed laser, the melting threshold requires
more energy. The returned results show that investigation of melting
kinetics should considered mainly in the range 800 to 1100 mJ/cm² , in
order to refine the laser threshold. Effort of computing will be focalized
on the congruence of the numerical resolution between the space and
the time steps to better control very fine melted structures as expected
from our first objective.
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MATLAB Program:
1) Program for Heat source Distribution with the Distance.
clear all;
close all;
clc;
y=-1:0.000001:0;
dela=0.109;
it=5.5*10^35;
rt=0.61;
rtt=(1-(rt));
g=exp(y/dela)/dela;
et=it*rtt;
gt=(et*g);
figure(1);
plot(y,gt);
xlabel('DEPTH Y(nm)---->');
ylabel('Gt[W/nm^3]------>');
title('Heat source distribution in depth');
grid on ;
2)Program for Temperature Vs Time .
clear all
I=5*10^7;
R=0.34;
A=0.65;
K=200;
alpha=1.1*10^-4;
t=0:0.0001:50;
H=A*I;
y=((4*alpha*t)/3.14);
c=sqrt(y);
T=(H*c)/K;
x=0.27;
H1=x*I;
r=H1*(c-sqrt(4*alpha*((t-27)/3.14)))/K;
plot(t,T);
plot(t,r);
xlabel('Time------>');
ylabel('Temperature----------->');
title('Temperature vs Time For Pulsed shape Laser');
grid on ;
grid on