April 2015
Spotlight Summary by Taek Yong Hwang
Modeling and experiments of self-reflectivity under femtosecond ablation conditions
Femtosecond (fs) laser material processing has attracted a great deal of attention due to unique advantages over conventional laser processing techniques that employ nanosecond and longer pulsed lasers. One of the most special advantages of using fs lasers for material processing is the ability of achieving a higher spatial resolution. In many cases, the spatial resolution of laser processing is determined by the spatial distribution of excited carriers and lattice temperature resulting from energy deposition by laser pulse irradiation. With fs laser pulses, the excitation of electrons and subsequent heat transport from electrons to lattice can be confined within the focal volume during laser pulse irradiation, due to the extremely short timescale of excitation. Therefore, the spatial resolution is comparable to the focal volume, whereas a large amount of thermal diffusion comes into play during laser irradiation and induces various photophysical and photochemical processes outside of the focal volume, significantly reducing the resolution of laser processing with nanosecond and longer pulsed lasers. Therefore, if a spatial resolution of the nanoscale without any special techniques is needed, employing femtosecond lasers is the only option.
In this paper, to get a deeper insight on the fs laser nanostructuring of materials, the authors suggest a numerical model describing the propagation and energy deposition of a single fs laser pulse in bulk silicon, silicon on insulator, and gold thin film under laser ablation conditions. A brief description of the authors’ strategy is as follows: their numerical modeling starts by using a finite difference time domain (FDTD) method to solve Maxwell’s equations. For the first optical half-cycle, they assume the laser pulse propagates in an unexcited material. From the next optical half-cycle until the end of the pulse, at every optical half-cycle the authors keep the optical susceptibilities of materials updated by calculating the carrier and/or heat diffusion equations with various source terms depending on the intensity of light. For silicon samples, the optical susceptibility changes with the number of carriers in the conduction band, increased by various routes during optical excitation. Therefore, the authors calculate the carrier diffusion equation by considering the source terms including one-photon absorption, two-photon absorption, and impact ionization, and also solve the heat equation to take into account the effective mass and diffusivity, both as functions of carrier temperature, to estimate the susceptibility. In the case of gold, the authors only consider the heat equation to use the electron-electron collision frequency as a function of electron temperature retrieved from experiments, and then update the susceptibility of gold at every optical half-cycle. Using this strategy, the authors successfully show that the self-reflectivity of silicon and gold samples under ablation conditions is consistent with experiments. Moreover, they are also able to pick out the dominant mechanisms causing the change in the self-reflectivity of samples with the fluence of laser. Therefore, not only can this method be extended to further understand the heat and charge transport after the excitation as the authors note, but it can also be a very useful tool to find a better condition for advanced laser processing.
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In this paper, to get a deeper insight on the fs laser nanostructuring of materials, the authors suggest a numerical model describing the propagation and energy deposition of a single fs laser pulse in bulk silicon, silicon on insulator, and gold thin film under laser ablation conditions. A brief description of the authors’ strategy is as follows: their numerical modeling starts by using a finite difference time domain (FDTD) method to solve Maxwell’s equations. For the first optical half-cycle, they assume the laser pulse propagates in an unexcited material. From the next optical half-cycle until the end of the pulse, at every optical half-cycle the authors keep the optical susceptibilities of materials updated by calculating the carrier and/or heat diffusion equations with various source terms depending on the intensity of light. For silicon samples, the optical susceptibility changes with the number of carriers in the conduction band, increased by various routes during optical excitation. Therefore, the authors calculate the carrier diffusion equation by considering the source terms including one-photon absorption, two-photon absorption, and impact ionization, and also solve the heat equation to take into account the effective mass and diffusivity, both as functions of carrier temperature, to estimate the susceptibility. In the case of gold, the authors only consider the heat equation to use the electron-electron collision frequency as a function of electron temperature retrieved from experiments, and then update the susceptibility of gold at every optical half-cycle. Using this strategy, the authors successfully show that the self-reflectivity of silicon and gold samples under ablation conditions is consistent with experiments. Moreover, they are also able to pick out the dominant mechanisms causing the change in the self-reflectivity of samples with the fluence of laser. Therefore, not only can this method be extended to further understand the heat and charge transport after the excitation as the authors note, but it can also be a very useful tool to find a better condition for advanced laser processing.
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Article Information
Modeling and experiments of self-reflectivity under femtosecond ablation conditions
Hao Zhang, S. A. Wolbers, D. M. Krol, J. I. Dijkhuis, and D. van Oosten
J. Opt. Soc. Am. B 32(4) 606-616 (2015) View: Abstract | HTML | PDF