Two-temperature model for pulsed-laser-induced subsurface modifications in Si

Abstract

We investigated the laser-material interaction during the production of laser-induced subsurface modifications in silicon with a numerical model. Such modifications are of interest for subsurface wafer dicing. To predict the shape of these modifications, a two-temperature model and an optical model were combined. We compared the model results with experimental data obtained by focusing laser pulses in the bulk of silicon wafers using a microscope objective. This comparison revealed a good agreement between the simulations and the experimental results. A parameter study was performed to investigate the effect of the laser wavelength, pulse duration and pulse energy on the formation of subsurface modifications. We found that both single-and multi-photon absorption may be used to produce subsurface modifications in silicon. P.C. Verburg ( ) •

Transient EUV Reflectivity Measurements of Carbon upon Ultrafast Laser Heating

“…A comparison of the present results with those achieved by using an optical probe [11] underlines how the optical probe is sensitive to both carrier and lattice dynamics, even when the hydrodynamic expansion of the lattice becomes the dominant parameter to define the thermodynamic state of the system. Such sensitivity to both dynamical processes ineluctably complicates the data interpretation, in particular in cases similar to the present one, i.e., when the hydrodynamic expansion occurs on time scales similar to that typical of carrier dynamics [12,13,34]. However, since the EUV probing is more sensitive to the lattice dynamics, one can speculate on the possibility to perform a combined campaign of an optical/EUV transient reflectivity measurements, able to disentangle electron and lattice dynamics.…”

Two-photon–induced internal modification of silicon by erbium-doped fiber laser

“…Requirement (2) is also unlikely to be violated. For a pulse energy of 90 µJ, no subsurface damage could be found [17], even though this energy value is two orders of magnitude beyond the required energy to form a subsurface modification [12,13,19].…”

“…The volume that is heated by the laser may be larger than the focal volume, due to the diffusion of carriers, electronic heat conduction and lattice heat conduction. Since numerical simulations showed that diffusion effects have little effect during subsurface processing of silicon on a short nanosecond timescale [20], the extension of the laser-heated volume by diffusion has been neglected. A study of nanosecond surface heating of silicon also reported limited effects of carrier diffusion and electronic heat conduction [28].…”

“…Since multiphoton absorption depends on the square or higher powers of the intensity of the light, it allows for better confinement of the absorption of laser energy than can be achieved by merely focusing the beam. Recently, several authors studied the formation of subsurface modification in silicon using two-photon and three-photon absorption [9,10,17,18], in addition to studies that employed a photon energy near the band-gap of silicon [12,13,19]. The experimental conditions that were applied during these studies are listed in table 1.…”

“…The success of the 1064 nm process, corresponding to a photon energy near the band-gap of silicon, is based on a thermal runaway [12,20]. Because the linear absorption coefficient of silicon strongly increases with temperature for photon energies near the band-gap [21], an initial temperature rise results in a higher absorptivity, creating an even faster increase in temperature.…”