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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 [email protected], [email protected], [email protected] 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. References:1. J.S. Im, R.S. Sposili, M.A. Crowder: Appl. Phys. Lett. 70, 3434 (1997) 2. D Bauerle. Laser processing and Chemistry,second edition, Springer, p. 581. 3. C.P. Grigoropoulos, S. Moon, M. Lee, M.Hatano, K. Suzuki, Appl. Phys A 69 S295- S298 (1999) 4. Jiri Martan, Ph. D. THESIS, Universite of Orleans.. (2005). 5. G. Groos, M. Stutzmann: J. Non-Cryst. Solids 227, 938 (1998) 6. V.V. Gupta, H.J. Song, J.S. Im: Appl. Phys.Lett. 71, 99 (1997) 7. J. Tesar, N. 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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