Deep drilling on a silicon plate with a femtosecond laser: experiment and model analysis

The ablation rate when drilling fine holes having large aspect ratios in silicon substrates with femtosecond laser pulses was estimated from mechanically ground cross sections of the ablated holes. The ablation rate shows a dramatic change at the depth at which the laser pulse reaches a certain fluence, which is nearly constant when the initial laser fluence was varied from 14.5 to 59.4 J/cm(2). The ablation rate, threshold fluence, in three fluence domains, and the transition fluences at which the ablation rate shows a dramatic change, were derived. However, when a pulse energy of 200 mu J was used a much greater ablation rate was obtained, suggesting that another fluence domain for larger ablation rates exists. The experimentally obtained hole depths as a function of shot numbers were reproduced by a theoretical model, which incorporates laser pulse attenuation in the holes that is the same as that in waveguides for some attenuation coefficient and ablation rates for three fluence domains.