Three-temperature modeling of laser-induced damage process in silicon

Abstract

Laser excitation in silicon from femto- to pico-second time scales is studied. We assume the Three-Temperature Model (3TM) which describes the dynamics of the distinct quasi-temperatures for electrons, holes, and lattice. Numerical results for damage threshold reproduce the experimental results not only quantitatively, but qualitatively as well, showing dependence on laser pulse duration. Comparison with experimental data suggests that electron emission and thermal melting are both responsible for damage in silicon. We found that electron-phonon relaxation time has a significant effect on pulse duration dependence of electron emission.

Wavelength dependence of laser-induced excitation dynamics in silicon

“…Also, the effect of band structure re-normalization is taken into account while calculating the dielectric function and single-and two-photon absorption coefficients.The model is explained in detail in Ref. [11]. Tables 1 and 2 list the notation and values for various parameters and variables used.…”

“…e(h) is the Auger re-combination coefficient [13] and e(h) is the impact ionization coefficient [7]. Equation 1 also includes the effect of spatial charge distribution and the associated electric field, and J e(h) , D e(h) and ⃗ F are the charge current, diffusion coefficient and the electric field induced by the electron-hole separation, respectively [11].…”

“…n e and n h are nearly the same due to the effect of ⃗ F and can be approximated at n e . L ( ) is the innate dielectric function, E g represents the band re-normalization by carrier density, and D is the complex dielectric function calculated from Drude model [11]. The total one-photon absorption coefficient including free-carrier absorption is calculated using the complex dielectric function [11].…”

“…Also, the decreased electron-hole scattering frequency indicates that it is important to take quasi-temperatures of electrons and holes into consideration. A modified nTTM treating the evolution of quasi-temperatures in CB, VB and lattice (3TM) has been proposed in our previous work [11].…”

“…To understand and define damage in silicon, we can assume several processes that may be responsible for causing permanent structural changes. In our previous study, we have compared the calculated thresholds for possible damage mechanisms with the experimental damage thresholds to understand the nature of damage in silicon and the interaction conditions affecting it [11]. Changing the wavelength of incident pulse can lead to significant changes in the dynamics of the interaction [21].…”