Modelling of temperature profiles in Nd:YAG laser annealed GaAs/AlGaAs quantum well microstructures

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1 Modelling of temperature profiles in Nd:YG laser annealed Gas/lGas quantum well microstructures Radoslaw Stanowski Ph.D. O. Voznyy prof. J J. Dubowski 1

2 Outline 1. Motivation 2. Transient temperature analysis 3. Experiment 4. Calculated temperature profiles 5. Summary 2

3 Motivation Manufacturing of Photonics Integrated Circuits requires spatialy-selective areas of dedicated QW s energy bandgap width. Regrowth with simultaneous etching using masks is an expensive approach. Post-growth selective-area bandgap tuning by direct Nd:YG (1064nm) laser irradiation (LRT-laser rapid thermal annealing) is an attractive and cost-efective approach to fabricate monolithically integrated photonic devices. Schematic diagam illustating the effect of well/barrier interdiffusion on the shape and bandgap energy of quantum wells. from: Semiconductor Quantum Wells Intermixing, edited by E. Herbert Li 3

4 QWI technique Laser induced QWI techniques 1. PID photoabsorption disordering 2. Impurity free vacancy disordering 3. Melting - complete intermixing 4. LRT Laser Rapid Thermal nnealing lgas/gas Room temperature emission spectra of as-grown and bandgap shifted broad area Fabry-Perot laser diodes. from: Semiconductor Quantum Wells Intermixing, edited by E. Herbert Li Picture of conduction and valance band shows the confined states change with annealing 4

0a (multiphysics problems solver) Heat transfer module

5 FEM Finite Element Method FEM general idea description: Geometry For calculations we have used FEMLB 3.0a (multiphysics problems solver) Heat transfer module Geometry PDE - Partial Differential Equation Material parameters Center Radius length 5

6 Heat Transfer PDE : Subdomain equation: Q - (k T) = ρc p ( T/ T/ t) k thermal conductivity tensor [W/(m K)] T temperature [K] ρ - density [kg/m 3 ] C p heat capacity [J/(kg K)] Boundary equation: square k T T = q 0 + h (T inf T) + Const (T 4 amb T 4 ) k heat transfer T T inf Temperature close to the surface (heat convection) [K] T amb mbient Temperature (heat radiation) [K] q Invard flux [W/m 2 ] h convection coefficient [W/(m K)] Const emissivity*sigma(stefan Boltzman s heat radiation constant) Q heat source (or sink) [W] = (1-R) R) Imax_square beam_shape_ Center square absorption exp( exp(-absorption z) Boundary Subdomain Radius length Incident LSER beam 6

7 Material parameters: ssumed temperature independent: k thermal conductivity = 16280/T [W/(m K)] α optical absorption = T [cm-1], ssumed temperature dependent: ε = 0.4 Cp= 325 [J/kg K] ρ = 5317 [kg/m3] h = 20 [W/(m K)] Diameter = φ = [m] Thickness = [m] Center Radius length 7

8 Thermal conductivity - k k = 16280/T [W/m K], for T = 300 [K], k = 56 [W /m K], for T = [K], k = 20 [W /m K], for T = [K], k = 15 [W /m K] T k k=16280/t W/(mK) k=56 W/(mK) time [s] Center Radius length Transient temperature in the middle of laser irradiated spot 8

9 Optical absorption - α α = T [cm -1 ], for T= 300 [K], α = 3 [cm -1 ], for T= [K], α = 12,495 [cm -1 ], for T= [K], α = 19,991 [cm -1 ] T α α=20000 cm -1 or α= *t α= cm -1 α=100 cm -1 α=10 cm -1 α=3 cm -1 Over K the laser delivered energy is absorbed by the very first layers of the irradiated wafer time [s] Transient temperature in the middle of laser irradiated spot 9

10 Emissivity - ε ssumption of the ideal case of the black body radiation (ε = 1) results in the underestimation of the temperature. difference of 166 [K] in the saturation temperature is expected, if the surface of Gas capped with SiO 2 has its emissivity reduced to (ε = 0.4). emissivity=0.4 emissivity=0.6 emissivity=0.8 emissivity= Time [s] Transient temperature in the middle of laser irradiated spot 10

11 Experimental setup description 1. Gas wafer was coated on both sides with 270nm SiO 2 layers deposited in PVCVD reactor for both to act as an antirefractive coating and prevent from s decomposition from the annealed microstructure. 2. Sample was placed on three silica point shape ended rods to avoid big contacts with surround 3. t room ambient conditions without additional cooling or heatting 4. Convection and radiation was assumed constant during experiment 5. The Nd:YG laser delivered power density of 1W/mm 2 at the spot of 3mm diameter. 6. Temperature has been collected within 0.1s interval steps from area of about 7mm 2 (approx. 1.5mm diameter) 11

12 Modelling vs. Measurement Parameter / Material Laser beam power Laser beam diameter Reflected power Optical absorption Emissivity Convection Specific heat Thermal conductivity Density mbient temperature Wafer dimensions Wafer thickness Calculations φ = 9*10-3 [m] 7 [W] 3*10-3 [m] 10 % [W/m 2 ] 325 [J/kg K] 56 [W/m 296 [K] 16280/T [W/m K] 5317 [kg/m 3 ] 296 [K] (6*10-3 x 11*10-3 ) [m] 300µm Gas (capped with SiO 2 ) T [cm-1], for 300 [K] < T < [K] [cm-1], for T > [K] Center Temperature vs time in the middle of the laser irradiated zone Experiment Calculations Temperature measurement threshold = 1 [W/mm 2 ] Laser beam diameter = 3mm time [s] 12 Radius length

13 Calculated temperature profiles lateral resolution without background heating d=µm d=100µm Temperature vs Radius ( µm laser beam) vacuum room ambient wind cooling =5.9[W/mm 2 ] =7.9[W/mm 2 ] =13.3[W/mm 2 ] h=0 P=2.30W h=20 P=3.05W h=100 P=5.11W Temperature vs Radius (100 µm laser beam) h=0 P=0.79W h=20 P=1.08W h=100 P=1.52W =100[W/mm 2 ] =136[W/mm 2 ] Radius [µm] Radius [µm] =193[W/mm 2 ] Radius [µm] 13

14 Calculated temperature profiles lateral resolution with background heating d=µm d=100µm Temperature vs Radius ( µm laser beam) Temperature vs Radius (100 µm laser beam) =2.4[W/mm 2 ] =4.7[W/mm 2 ] =7.9[W/mm 2 ] Tsink=973K P=0.94W Tsink=773K P=1.83W Tsink=300K P=3.04W Tsink=973K P=0.22W Tsink=773K P=0.49W Tsink=300K P=1.08W =27[W/mm 2 ] =61[W/mm 2 ] =136[W/mm 2 ] Radius [µm] Radius [µm] Radius [µm] 14

15 Calculated temperature profiles in-depth resolution without background heating d=µm d=100µm Temperature in-depth of the sample ( µm laser beam) Temperature in-depth of the sample (100 µm laser beam) =5.9[W/mm 2 ] =7.9[W/mm 2 ] =13.3[W/mm 2 ] h=0 P=0.79W h=20 P=1.08W h=100 P=1.52W =100[W/mm 2 ] =136[W/mm 2 ] h=0 P=2.30W h=20 P=3.05W h=100 P=5.11W =193[W/mm 2 ] z-axis [µm] z-axis [µm] 15

16 Calculated temperature profiles in-depth resolution with background heating d=µm d=100µm Temperature in-depth of the sample ( µm laser beam) Temperature in-depth of the sample (100 µm laser beam) =2.4[W/mm 2 ] =4.7[W/mm 2 ] =7.9[W/mm 2 ] Tsink=973K P=0.22W Tsink=773K P=0.49W Tsink=300K P=1.08W =27[W/mm 2 ] =61[W/mm 2 ] Tsink=973K P=0.94W Tsink=773K P=1.83W Tsink=300K P=3.04W =136[W/mm 2 ] z-axis [µm] z-axis [µm] 16

17 Summary Finite Element Method calculations have been carried out to determine temperature profiles in Nd:YG (1064nm) laser irradiated Si and Gas wafers. Increasing thermal convection of the laser heated wafer leads to narrower temperature profiles, but higher power densities have to be used. Processing with decreasing laser beam diameter can lead to sharper temperature profiles. To maintain the incident laser beam intensity below the threshold of surface damage, background heating has to be introduced. Shallow temperature propagation has been observed for small laser beam diameters, thus depth at which Quantum Well is located is an important parameter to achieve high spatial resolution Quantum Well Intermixing Calculations describe reasonably well the measured transient temperature in the middle of irradiated zone on the wafer s surface. 17

18 Thank You for atten ua tion!!! Radoslaw Stanowski 18

Numerical Simulation of Si Nanosecond Laser Annealing by COMSOL Multiphysics

Excerpt from the Proceedings of the COMSOL Conference 28 Hannover Numerical Simulation of Si Nanosecond Laser Annealing by COMSOL Multiphysics M. Darif*, N. Semmar GREMI-UMR666, CNRS-Université d Orléans,