Danielson, D. T.; Sparacin, D. K.; Michel, J.; Kimerling, L. C., Surface-energy- ... Singer, J. P.; Lin, P. T.; Kooi, S. E.; Kimerling, L. C.; Michel, J.; Thomas, E. L., ...
Supplementing Information Directed Dewetting of Amorphous Silicon Film by a Donut-Shaped Laser Pulse Jae-Hyuck Yoo, Jung Bin In, Cheng Zheng, Ioanna Sakellari, Rajesh N. Raman, Manyalibo J. Matthews, Selim Elhadj, and Costas P. Grigoropoulos
Figure S1. (a) Schematics of morphology transformation of silicon film upon Gaussian laser beam irradiation. (b) bright-field and (c) dark-field microscopic pictures of 20 nm thick amorphous silicon film after nanosecond single laser pulse irradiation. Scale bars are 10 µm. As illustrated in Figure S1(a), upon irradiation of a Gaussian laser beam (a TEM00 mode) on a silicon film on a glass substrate, the highest temperature is achieved in the beam center. From the center, laser ablation is initiated, resulting in material removal at the center of the spot. Consequently, the silicon nanodome structure is not produced. Figures S1(b, c) show bright- and dark-field microscopic pictures of a 20 nm thick amorphous silicon film on a glass substrate after nanosecond single laser pulse irradiation. The same method described in the paper was used to produce a train of spatially distributed laser pulses, and the phase plate for the donut-beam shaping was removed in the beam path to maintain the Gaussian laser beam profile. Due to the ablative material removal at the beam center, the silicon nanodome structure was not observed.
Figure S2. FEM simulation and schematics of ultrathin amorphous silicon film on fused silica substrate upon single pulse irradiation of donut-shaped laser beam at laser power of 0.34 mW (= 0.74 J/cm2). The molten silicon (red) under the complete melting regime is transported radially (the direction is indicated by the white dashed arrows) due to the thermocapillary-induced dewetting. The resulting morphology is highlighted with red dashed outlines. Figure S2 shows the temperature profile obtained by the finite element method (FEM) simulation. The simulation was conducted based on the diffusive heat transfer equation,
ρ C p (T )
∂T = ∇ ⋅(K(T )∇T ) + Qab (r, z,t) , ∂t
(S1)
where ρ, Cp, K, T, and Qab represent the density [kg/m3], the specific heat at constant pressure [J/kgK], the thermal conductivity [W/mK], the temperature [K], and the volumetric power absorption or the heat source [W/m3], respectively.1 Since the amorphous silicon film was thinner than the absorption depth of the laser light, the finite difference time domain (FDTD) simulation was also performed to estimate the absorbed laser energy. The simulated temperature profile of the 20 nm thick amorphous silicon film deviated from the donut-shaped heat source due to lateral heat conduction. At elevated laser powers, the irradiated zone experiences melting and vaporization. The melting temperature of amorphous silicon (Tm = 1,420 K) and the temperature plateau at the boiling temperature of silicon (Tb = 2,654K) serve as indicators of these phase transitions.2, 3 The present modeling does not include convective effects and is used only for demonstration purposes, since the rapid phase change induced by the nanosecond laser pulse may depart from the equilibrium thermodynamic trajectory. It is recalled that the boiling point is meaningful under ambient atmospheric pressure conditions and is herein used solely as an indicator. In the schematic of Figure S2, the complete-melting region at the temperature over Tm is presented in red, and the material removal region by laser ablation is illustrated in black. We
experimentally quantified the material removal by comparing the volume of the initial silicon film (0.598 µm3) and the volume of the resulting structure (0.465 µm3), consisting of the silicon nanodome (0.076 µm3) and the rim (0.389 µm3). The initial silicon film volume was estimated by πRout2tfilm, where Rout is the radius of the outer rim (3.088 µm), and tfilm is the film thickness (0.020 µm). The volume of the silicon nanodome was estimated assuming a hemi-ellipsoid geometry by 2/3πRbottom2Rheight, where Rbottom is the radius of the base (0.2895 µm), and the Rheight is the height (0.434 µm). The volume of the rim was estimated by π(Rout2-Rin2)trim, where Rout is the radius of the outer rim (3.088 µm), Rin is the radius of the inner rim (2.5045 µm), and the trim is the height of the rim (0.038 µm). The dewetting of the ultrathin film was initiated at the inner free edge produced by the laser ablation.4 The temperature gradient developed in the complete-melting region induced thermocapillary force by the Marangoni effect. The thermocapillary shear stress can be expressed as,
dγ τ! = ∇γ = ∇T , dT where τ! the shear stress, γ the surface tension, and
(S2)
dγ is the surface tension temperature dT
coefficient.5 The surface tension temperature coefficient of liquid silicon is negative.6 The thermocapillary force drove the completely molten silicon to the direction presented as white dashed arrows. Considering that the silicon melt lasts less than 100 ns,7 due to the heat loss to the substrate, the radial transport velocity of the molten silicon can be estimated as at least 18 m/s (wp/100 ns).
Figure S3. (a) Schematics of FDTD simulations. (b) Reflectivity (R, blue line), transmissivity (T, green line), and absorptivity (A, red line) under varied film thickness. Figure S3(a) shows the sample schematic for the FDTD simulations. A plane light wave at the wavelength of 532 nm was normally incident on an amorphous silicon film on a 500 µm thick glass substrate. The refractive index of amorphous silicon (n = 4.85943, k = 6.5347e-1) at the wavelength was assigned to the film. The reflectivity (R) from the film and the transmissivity (T) throughout the sample were simulated over varied film thickness in Figure S3(b). The absorptivity (A) of the film was calculated by 1 – (R + T), assuming that the absorption in the glass substrate is negligible. For a 20 nm thick amorphous silicon film, the absorptivity was calculated as 0.127 from the reflectivity (0.266) and the transmissivity (0.607). 1. Grigoropoulos, C. P., Transport in Laser Microfabrication - Fundamentals and Applications. Cambridge University Press: 2009. 2. Bauerle, D., Laser Processing and Chemistry. 4th ed.; SpringerLink: 2011. 3. Hatano, M.; Moon, S.; Lee, M.; Suzuki, K.; Grigoropoulos, C. P., Excimer laser-induced temperature field in melting and resolidification of silicon thin films. J Appl Phys 2000, 87 (1), 36-43. 4. Danielson, D. T.; Sparacin, D. K.; Michel, J.; Kimerling, L. C., Surface-energy-driven dewetting theory of silicon-on-insulator agglomeration. J Appl Phys 2006, 100 (8). 5. Singer, J. P.; Lin, P. T.; Kooi, S. E.; Kimerling, L. C.; Michel, J.; Thomas, E. L., DirectWrite Thermocapillary Dewetting of Polymer Thin Films by a Laser-Induced Thermal Gradient. Adv Mater 2013, 25 (42), 6100-6105. 6. Hardy, S. C., The Surface-Tension of Liquid Silicon. J Cryst Growth 1984, 69 (2-3), 456460. 7. Grigoropoulos, C. P.; Moon, S.; Lee, M.; Hatano, M.; Suzuki, K., Thermal transport in melting and recrystallization of amorphous and polycrystalline Si thin films. Appl Phys a-Mater 1999, 69, S295-S298.
