Femtosecond pulse laser interactions with thin silicon films and crater formation considering optical phonons and wave interference

Abstract

The extensive numerical study is conducted to examine interaction of femtosecond pulse laser with thin silicon film structure by using the two-temperature model (2TM) and the three-temperature model (3TM), on the basis of the relaxation time approximation to Boltzmann's transport equation. The present study investigates mainly transient behaviors for carrier number density, electron temperatures, and phonon temperatures, and it compares the results of 3TM with those of 2TM for energy transfer characteristics. In particular, the one-dimensional model is extended to two-dimensional model for the direct estimation of laser-induced crater formation. In addition, the thin film optics and the electromagnetic theory are used to simulate the propagation of laser energy absorption in stratified media with variation of complex refractive index. It is found that quite different tendencies are observed for femtosecond pulse lasers between 2TM and 3TM. For the 3TM, there is clearly nonequilibrium between optical phonons and acoustic phonons when the femtosecond lasers are irradiated, whereas as the laser pulse becomes longer, two different phonons are thermally in equilibrium state. The crater depths and shapes are significantly affected by film thickness, laser fluence, and pulse duration because of the wave interference effect as well as the difference in energy relaxation times. Moreover, the optical properties are found to depend on laser absorption and laser pulses. This tendency which is successfully estimated by the two-dimensional 3TM takes place in thin film structures differently unlike the bulk silicon.

Temperature dependent ablation threshold in silicon using ultrashort laser pulses

“…One assumption of the model is that the electrons reach a thermal distribution on a time-scale which is short compared to the pulse duration. The electron thermalization time is reported to be around 10 fs, 8 meaning that this criterion is well fulfilled in our case. The two-temperature model can mathematically be written as a set of coupled differential equations.…”

“…1, the laser penetration depth is smaller than the spot radius by at least an order of magnitude, making the approximation reasonable. Following Sim et al, 8 adding diffusion of carriers, 13 we write the equations…”

“…However, several articles 16,17 make use of much longer coupling times of around 1-10 ps, based on work by van Driel 13 and measurements on GaAs, 18 which we expect to be less representative for our case. The three-temperature model described by Sim et al 8 uses values from a general statement in the book by Tien et al 19 that electron-optical phonon coupling is on the order of 100 fs, while the optical phononacoustic phonon coupling time is on the order of 10 ps for "most semiconductors. "…”

“…Nevertheless, we believe that we can extract much information about the physics of our experiments with the comparatively less elaborate two-temperature model. Sim et al 8 present a theoretical study on the two-and three-temperature models in silicon, while Mao et al 9 apply a two-temperature model with electron emission. Christensen et al 10 apply a twotemperature model for metals.…”

Elasto-Viscoplastic Response of Silicon to Femtosecond Laser Heating at Elevated Temperature

“…The model solves the spatial and temporal evolutions of the lattice temperature of the silicon along with the carrier density and its temperature. Although 2TM is widely utilized in describing the transport dynamics induced by ultrafast lasers [22,23], it only considers total energy transfer in the form of heat and disregards thermal-mechanical coupling, thus not resolving thermal-mechanical interaction at the sub-nanoseonds scale.…”