Modelado del cambio de la reflectancia, bajo la acción de un pulso láser, de una lámina delgada de alúmina con nanopartículas de bismuto

Facultad de Ciencias Trabajo Fin de Grado Grado en Física Modelado del cambio de la reflectancia, bajo la acción de un pulso láser, de una lámina delgada de alúmina con nanopartículas de bismuto Autor: Miguel Álvarez Sánchez Tutor: Marco Antonio Gigosos Pérez 8 ns 800 nm s 1 KHz 590 mW λ/2 52° 30−150 mJ/cm290− 700 mJ/cm2 532 nm 25 μs λ/4 ×20 λ/4 532 nm BiNPs 460 nm Bi150(Si) 50 μm 482.5 mJ/cm2 242.8 mJ/cm220 μm Bi150 BiNPs BiNPs 2 μs 135 mJ/cm2 0 1 2 3 4 5 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 Bi150(FS) Relative Reflectivity Change Time (s) 29 mJ/cm2 41 mJ/cm2 59 mJ/cm2 90 mJ/cm2 116 mJ/cm2 135 mJ/cm2 151 mJ/cm2 177 mJ/cm2 Bi150(FS) 0 1 2 3 4 5 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Bi150(FS) Relative Reflectivity Change Time (s) 29.03 mJ/cm2 90.08 mJ/cm2 41.48 mJ/cm2 116.15 mJ/cm2 59.26 mJ/cm2 135.12 mJ/cm2 BiNPs Bi150 020 40 60 80 100 120 0 200 400 600 800 1000 1200 1400 1600 Solidification time of Bi_NPs Time (ns) Fluence (mJ/cm2) 0 1 2 3 4 5 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 Bi150(FS) Relative Reflectivity Change Time (s) 107 mJ/cm2 88 mJ/cm2 79 mJ/cm2 70 mJ/cm2 58 mJ/cm2 49 mJ/cm2 39 mJ/cm2 BiNPs 0 1 2 3 4 5 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Bi150(Si) Relative Reflectivity Change Time (s) 242.8 mJ/cm2 285.8 mJ/cm2 316.5 mJ/cm2 347.3 mJ/cm2 367.78 mJ/cm2 400.6 mJ/cm2 441.6 mJ/cm2 470.2 mJ/cm2 482.5 mJ/cm2 507.1 mJ/cm2 0100 200 300 400 500 0 100 200 300 400 500 600 700 Time of Solidification Time (ns) Fluence (mJ/cm2) 0 1 2 3 4 5 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 Bi150(Si) Relative Reflectivity Change Time (s) 470.2 mJ/cm2 20 nm 10 nm 20 nm 2∶1 Z 𝑧=0 X Y Z BiNPs Δ𝑡 Z BiNPs 10 nm 1 μm X Y 1 μm 𝑡=4 ns 8 ns W/m2 𝐼(𝑡)=𝐼𝑚𝑎𝑥exp[−( 𝑡−𝑡𝑝 𝑡𝑝 )2 ] 𝑡𝑝=4 ns 𝐼(𝑥)=𝐼(𝑥0)exp[−𝜎(𝑥−𝑥0) ] 𝜎 𝑥 𝐼𝑎𝑏𝑠(𝑥)= 𝐼(𝑥0) ( 1 − exp[−𝜎(𝑥−𝑥0) ]) Δ𝑥 𝜎𝑛 𝐼𝑛𝑛 𝑡 𝐼𝑛(𝑡)=𝐼𝑚𝑎𝑥exp[− Δ𝑥 ∑ 𝜎𝑖 𝑛−1 𝑖=1 ]exp[−( 𝑡−𝑡𝑝 𝑡𝑝 )2 ] 𝑛 Δ𝑡 𝑡 Δε𝑎,𝑛(𝑡,Δ𝑡)=𝐼𝑎𝑏𝑠 ,𝑛(𝑡)(Δ𝑥)2Δ𝑡=𝐼𝑛(𝑡) (Δ𝑥)2Δ𝑡 ( 1 − exp[−𝜎𝑛Δ𝑥]) Δ𝑡 𝜕𝑇 𝜕𝑡=𝛼𝜕2𝑇 𝜕𝑥2+𝐸𝑚𝑎𝑥 𝜌𝐶 exp[−( 𝑡−𝑡𝑝 𝑡𝑝 )2 ]exp[−𝜎𝑥] 𝐸𝑚𝑎𝑥 𝑡𝑝=4 ns o o o o o o o o o o o o o ▪ ▪ ▪ ▪ 0.2 nm 100 50 100 2.5·1011 W/m2 300 K 𝑍 𝑓 𝑓2𝑛 𝑓𝑛Δ𝑥 100 𝑓=1.145 1.2 mm 300 K 𝑛 𝑓𝑛𝑓𝑐 𝑘𝑛→𝑐 =(𝑓𝑛+𝑓𝑐)𝑘𝑛𝑘𝑐 𝑓𝑐𝑘𝑛+𝑓𝑛𝑘𝑐 𝜎 𝜎=4𝜋𝑘  𝜆 𝑘 𝜆800 nm 0.2 nm 100 50 100 5·1011 W/m2 300 K 2.5·1011 W/m2 0100 100 150 150 250 250 350 t=12 ns t=12 ns 0250 50 nm 250 350 𝑓=1.145 1.2 mm t=12 ns X 50 nm (~1.2 mm) 544 K 4 ns 4 ns BiNPs 5·1011 W/m2 lim Δ𝑡→∞𝑇1(𝑡+Δ𝑡)= 𝑇1(𝑡)+𝑇2(𝑡) 2 lim Δ𝑡→∞𝑇2(𝑡+Δ𝑡)=𝑇1(𝑡)+𝑇2(𝑡) 2 Δ𝐸𝑖(𝑡,Δ𝑡)=𝜌𝑖𝐶𝑖(Δ𝑥)3 (𝑇𝑖(𝑡+Δ𝑡)−𝑇𝑖(𝑡)) Δ𝐸1(𝑡,Δ𝑡)=−Δ𝐸2(𝑡,Δ𝑡) ⇔ 𝜌1𝐶1 1+𝛽2/𝛽1 =𝜌2𝐶2 1+𝛽1/𝛽2 𝛽𝑖=𝑘1→2/𝜌𝑖𝐶𝑖(Δ𝑥)2𝑘1→2 =𝑘2→1 Δ𝑡 𝑇𝑛(𝑡+Δ𝑡)=𝑇𝑛(𝑡)+ ∑[ 1−exp[−(𝛽𝑐+𝛽𝑛)Δ𝑡] 1+𝛽𝑐/𝛽𝑛 (𝑇𝑐(𝑡)−𝑇𝑛(𝑡))] 𝑐 +Δ𝑡 Δ𝑥 1 − exp[−𝜎𝑛Δ𝑥] 𝜌𝑛𝐶𝑛𝐼𝑛(𝑡) 2×2 2𝑁×2𝑁 𝑁 𝑇1𝑇2 𝑦 𝑇3𝑇1 𝛽𝑖=𝑘1→2/𝜌𝑖𝐶𝑖(Δ𝑥)2 𝜌(kg/m3) [10] 𝜌𝑠ó𝑙𝑖𝑑𝑜(𝑇)=9910.3−0.3599· 𝑇 𝜌𝑙í𝑞𝑢𝑖𝑑𝑜(𝑇)=10695.8−1.1868·𝑇 544 K [11] 3980 kg/m3 [12] 2200 kg/m32310 kg/m3 300 K 1.2 kg/m3 𝑘( W / m · K ) [13] 𝑘(𝑇)=7.34+9.5·10−3·𝑇 8.2 W/m K [11] 𝑘(𝑇)=2.045·104·𝑇−1.135 1.4 W/m K 300 K 119 W/m K 300 K [12] 0.0262 W/m K 300 K 𝐶( J / kg· K ) [14] 𝜆 ~ 54 kJ/kg [11] (1.08·104+1.808·𝑇−3.143·108·𝑇−2) 704 J/kg·K 300 K 839 J/kg·K 300 K [12] 1.012·10−3 J/kg·K 300 K 𝜎( m−1 ) 𝜆=800 nm 3.7883 800 nm [15] 6·107 m−1 0.00654 800 nm [15]105 m−1 [1] [2] [3] [4] [5] [6] Al2O3 [7] [8] [9] [10] [11] [12] [13] [14] [15]