Computer modeling of the temperature rise and carrier concentration induced in silicon by nanosecond laser pulses

Abstract

A set of simultaneous equations for lattice temperature, carrier concentration, and carrier temperature is numerically solved for typical nanosecond laser pulses. The temperature dependences of the thermal conductivity and lattice absorption are included, as well as the free carrier absorption and reflection. Carrier diffusion and electronic heat conduction are taken into account, and Auger recombination is assumed to be the dominant recombination mechanism. The calculations show that while free carrier absorption plays a major role in annealing with 1.06-μm radiation, only lattice absorption is important at wavelengths corresponding to photon energies well above the band gap. The Auger recombination coefficient is not a sensitive parameter, and the energy relaxation time does not affect the annealing results unless it is comparable to the pulse length. The results of the calculations are consistent with the hypothesis that the observed increase in silicon reflectivity is due to surface melting of the material. When literature values are used for all relevant parameters, the model predicts melt threshold energies which are in agreement with published experimental values.

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

“…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]. An important contributing factor to these results is that the lifetime of the carriers is far shorter than the pulse duration due to Auger recombination.…”

“…For the prediction of surface damage of crystalline silicon induced by laser pulses, melting has been reported to be an accurate indicator [26][27][28][29]. Due to the fast cooling that occurs after the laser pulse, the molten silicon does not fully return to its original low-defect monocrystalline state.…”

Transient laser-induced surface deformation of silicon in relation to damage

“…Peak surface temperature can be estimated from displacement data using the simple thermomechanical relationship given in equation (7). In this case, the approximated data is plotted alongside the computer simulation as shown in figure 5.…”

“…A straight-forward thermal model based on Meyer's first order approximation will be given later in this section. Meanwhile, other investigators have also been trying to tackle the same complex problem by computer simulation [7]. A numerical model was used to compute transient surface displacement and temperature for pulsed-laser heating of silicon.…”

Thermophysical characteristics of an electron gas of silicon in the region of phase transformations

“…Лазерный нагрев полупроводников (кремния), так же как и металлов, является неравновесным и протекает с большим отрывом температур носителей тока от решетки [5] - [7]. В случае металлов энергия первоначально выделяется в электронном газе (Ферми-газ), а затем посредством электрон-фононных столкновений передается решетке.…”