Multiphoton Absorption Simulation of Sapphire Substrate under the Action of Femtosecond Laser for Larger Density of Pattern-Related Process Windows

It is essential to develop pattern-related process windows on substrate surface for reducing the dislocation density of wide bandgap semiconductor film growth. For extremely high instantaneous intensity and excellent photon absorption rate, femtosecond lasers are currently being increasingly adopted. However, the mechanism of the femtosecond laser developing pattern-related process windows on the substrate remains to be further revealed. In this paper, a model is established based on the Fokker–Planck equation and the two-temperature model (TTM) equation to simulate the ablation of a sapphire substrate under the action of a femtosecond laser. The transient nonlinear evolutions such as free electron density, absorption coefficient, and electron–lattice temperature are obtained. This paper focuses on simulating the multiphoton absorption of sapphire under femtosecond lasers of different wavelengths. The results show that within the range of 400 to 1030 nm, when the wavelength is large, the number of multiphoton required for ionization is larger, and wider and shallower ablation pits can be obtained. When the wavelength is smaller, the number of multiphoton is smaller, narrower and deeper ablation pits can be obtained. Under the simulation conditions presented in this paper, the minimum ablation pit depth can reach 0.11 μm and the minimum radius can reach 0.6 μm. In the range of 400 to 1030 nm, selecting a laser with a shorter wavelength can achieve pattern-related process windows with a smaller diameter, which is beneficial to increase the density of pattern-related process windows on the substrate surface. The simulation is consistent with existing theories and experimental results, and further reveals the transient nonlinear mechanism of the femtosecond laser developing the pattern-related process windows on the sapphire substrate.