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Surface processing of silicon using a 400-fs ytterbium fiber laser has been experimentally investigated. Processing was conducted using an average power of 20 W at laser repetition rates from 500 kHz – 2 MHz and scanning speeds up to 2.8 mm/s. Samples showed both effective material removal and detrimental surface artifacts resulting from high surface temperatures during the ablation process. A numerical model has been constructed to simulate the macroscopic surface heating mechanism in femtosecond laser processing. The model validates the experimental results, predicting the observed occurrence of oxidation and melting for un-optimized laser parameters. The surface-heating sensitivity to laser repetition rate, laser fluence, and scanning speed has been comprehensively analyzed, allowing for the first identification of optimized processing conditions to control surface heating and mitigate thermal artifacts in femtosecond laser processing. This work demonstrates a path for predicting deterministic femtosecond laser processing of silicon and other materials.
© 2016 Optical Society of America
1. Introduction
Pulsed-laser processing is performed by scanning a focused laser along a material, whereby incident pulses cause permanent changes in its structural, mechanical, and/or optical properties. Reducing the temporal width of the incident laser pulses from the millisecond to the ultrafast regime causes the primary breakdown mechanism to change from melting to vaporization and shockwave propagation [1]. Processing in the femtosecond pulse regime enables increased precision and deterministic breakdown [2]. The confinement of energy absorption within the focal volume of the laser in the gentle ablation regime allows the location and physical extent of the material breakdown to be controlled [3]. The short timescale and lower energy of femtosecond laser pulses can enable a minimized heat-affected zone in comparison to processing with longer pulses [4]. The high pulse energies and repetition rates of commercially available femtosecond lasers also enable increased ablation efficiency and processing rates [5,6].
Femtosecond laser processing has been tested on various materials, including glasses and semiconductors, for a variety of different optics-related applications. It can be used to fabricate optical structures on silicon, including micro-lens arrays and diffractive optical elements [7,8], or to write waveguides and gratings in dielectric materials to suit applications like monolithic lasers [9–11]. Self-assembly of nanoparticles and nanostructures can be initiated by femtosecond lasers to achieve birefringence and dichroism in both glass and silicon or to enhance the absorption capability of photovoltaics materials [12–14]. Surface processing of silicon substrates using femtosecond laser radiation can further cater to photonics and photovoltaics applications by enabling damage-free delamination and patterning of silicon oxide [15,16]. Femtosecond lasers can also be used to weld glasses and glass to silicon for microelectronic applications or to cut glass for consumer electronics [17–19]. In the aforementioned processes, materials are subjected to high temperatures and pressures which change the material density, structure, and/or refractive index [3,20]. In surface processing experiments, over-exposure to femtosecond laser radiation via un-optimized laser parameters leads to blistering, oxidation, melting, and cracking [21–24]. Simulations of femtosecond-laser-material-interaction have shown that these phenomena result from high temperatures generated during processing [24–26]. Inert gas, liquid, and vacuum environments can enhance the quality of surface processing [27,28], but reduce the utility of femtosecond lasers for batch processing, short lead-time products, and large-scale element applications. A method for controlling the surface quality for processing in air must be achieved to maintain the utility of ultrafast laser processing for various applications.
We have investigated the effectiveness of femtosecond laser surface processing of monocrystalline silicon. Section 2 shows that experimental femtosecond processing effectively removed surface material, but caused pileup adjacent to the ablated track as a result of high surface temperatures. Surface oxidation at the pileup location was confirmed, showing that optimized processing conditions are required to control the surface temperature to mitigate detrimental processing artifacts. Section 3 presents a classical thermal model, to serve as a first approximation of heating during femtosecond laser processing, which confirms high surface temperatures for the experimental conditions. This model can be easily adapted for different materials and offers a means to predict deterministic, optimal femtosecond laser processing parameters. Section 4 describes the heat accumulation mechanism in femtosecond laser processing. Section 5 presents the first (to the best of our knowledge) comprehensive analysis of the sensitivity of heat accumulation to laser processing parameters including repetition rate, scanning speed, laser pulse energy, and focal spot size. Using the results of the sensitivity studies, we predict optimized conditions for experimental femtosecond laser processing of silicon which mitigate heat accumulation to eliminate thermal artifacts.
2. Experimental femtosecond laser ablation of silicon
An experimental laser processing system consisting of a femtosecond laser, a focusing optic, and a three-axis translation stage for sample mounting was constructed to investigate the effectiveness of femtosecond laser processing of thick (0.5 cm), rough silicon substrates. The laser source was an Ytterbium fiber laser from Amplitude Systèmes (Satsuma) producing 400 fs pulses at 1030 nm. The laser beam was focused to a diameter of 70 µm on the silicon surface. An average power of 20 W was maintained in all processing experiments for laser repetition rates of 500 kHz, 1 MHz, and 2 MHz. The three-axis motorized sample-mounting stage enabled line and area ablations at speeds between 0.1 mm/s and 2.8 mm/s.
Surface topographies of processed samples were measured using laser scanning confocal microscopy (Keyence VK-X210). Figures 1(a) and 1(b) respectively show the surface profile and the corresponding average line profile of femtosecond-laser-processed silicon using 10 µJ pulses, a repetition rate of 2 MHz, and a scanning speed of 1.5 mm/s.
Fig. 1 (a) Surface topography of a femtosecond line ablation on silicon (b) Average line profile of the processed surface, showing ablation and material pileup.
An ablation depth larger than 10 µm and width of 19 µm was achieved for silicon, showing the effectiveness of femtosecond laser ablation in removing surface material. The surface topography shows two regions of material pileup adjacent to the ablated trench, with respective heights of 8 µm and 20 µm on the left and right sides. The uneven pileup height is attributed to an asymmetric intensity distribution at the focal plane resulting from alignment-induced aberrations. The greater area of the pileup in comparison to the ablated material suggests that the true ablation depth is larger than is seen via surface profilometry. A recent cross-section analysis has revealed that the surface voids are approximately 50 μm in depth and the laser-affected region, which includes additional sub-surface voids, extends to a depth on the order of 100 μm. Material ejected from both surface and sub-surface voids likely contributed to the height of the pileup.
Energy-dispersive X-ray spectroscopy (EDS) was used to determine the elemental compositions of laser-processed and unprocessed silicon surface regions. Figure 2 shows normalized spectra for both conditions.
Fig. 2 Normalized silicon EDS spectra collected for material pileup and unprocessed surface regions. The region of material pileup shows increased oxygen and carbon content.
Figure 2 shows a significant increase of both oxygen (8.4:1) and carbon (6.5:1) when comparing the elemental composition of the pileup to the unprocessed region. Increased oxygen content indicates oxide growth at the location of material pileup. Oxidation in silicon occurs over the temperature range of 973 – 1573 K [29], indicating that high surface temperatures were reached during femtosecond laser processing. Ablation of material is evidence that vaporization occurred during material processing. The interaction of vaporized material with hydrocarbon pollutants and carbon dioxide in the surrounding air resulted in carbon-doping of the laser-affected region [30]. Re-condensation of ablated surface material and melting may also play a role in pileup formation.
3. Investigation of surface heating via numerical thermal modeling
3.1 Heat generation and thermal modeling
3.1.1 Overview
A femtosecond laser pulse causes a large density of photons to strike the surface of a material on a nearly instantaneous timescale. Photon energy is linearly absorbed to excite electrons if it is higher than the bandgap of the material, or is nonlinearly absorbed via multiphoton processes enabled by the high photon density [25]. A large density of excited electrons can induce vaporization-based material removal if the total energy is high enough, i.e., when the laser fluence is above the ablation threshold [31]. During and immediately after the pulse, energy is transferred to the material lattice to cause melting and/or heating [2]. The induced surface temperature decays over time as heat diffuses through the bulk of the material. In multi-pulse processing, heat can accumulate if the diffusion time between pulses is restricted, enabling the occurrence of thermal phenomena such as melting and oxide growth.
Models based on classical definitions of heat sources and energy transfer have been developed to simulate heating in ultrafast laser processing [23,24,26]. These models approximate the magnitude of the pulse-induced temperature rise without the need for subatomic simulation of energy absorption, electron plasma density, and electron/lattice heat exchange as in two-temperature models [32–34] and without the requirement of high-capacity computation platforms [35]. Based upon the modeling theory presented by Bauer et al. [24], we have constructed a numerical model to predict the surface temperature evolution during femtosecond laser processing of silicon. In this model, we assume that the femtosecond laser pulse acts as an instantaneous heat source because the pulse width does not exceed the time required for normal heat diffusion [24]. The model acts as a first approximation of ultrafast laser heating; it does not consider electronic-level phenomena occurring within the timescale of the pulse or melt/vapor phase transitions. Additional phenomena which impact heat generation and ablation, but are out of the scope of this first-approximation model of heating during ultrafast laser processing, include free-carrier absorption of photons [36], the effect of the generated plasma temperature on surface-heating [37], decreased absorption of laser light in multi-pulse ablation caused by the plasma and ablated particles [14], change in surface roughness [38], and volume changes in material resulting from ablation/melting which affect heat transfer [39]. The consideration of these phenomena is underway in the following phase of the modeling work. The ultimate objective of this modeling is to predict deterministic, optimal laser processing conditions to minimize heat accumulation and mitigate the onset of detrimental thermal effects.
3.1.2 Deposition of femtosecond laser pulse energy and temperature rise
The amount of deposited laser pulse energy directly increases the energy of the surface according to the fluence distribution of the incident pulse [24]. The heat-inducing surface energy density, Ω, deposited by the nth laser pulse centered at (xn,yn) is described by Eq. (1):
Here, A is the fraction of incident energy remaining in the surface after ablation, Epulse is the energy of the incident Gaussian pulse with waist, wo, and the Dirac delta function, δ(z), with units of inverse meters, ensures that energy is only deposited within the defined surface layer, z = 0. The factor of 2 in the numerator accounts for heat being deposited into a half-space, rather than into the infinite space required for classical, analytical temperature distribution calculations [40]. A reference value of 0.8 [41] was used for A to accommodate the ground finish of samples and the steep rise in energy absorption seen in experimental, above-fluence-threshold multi-pulse femtosecond laser processing of silicon. It is possible that the energy density predicted in Eq. (1) may be higher than in experimental implementation. Multiplying Ω by the discrete volume of a surface element gives the element-specific increase in surface energy. The instantaneous rise in temperature associated with this surface energy increase is calculated using Eq. (2) [24]:
The surface temperature is directly proportional to its energy, E, and inversely proportional to the material density, ρ, the temperature-dependent specific heat capacity, c, and the discrete volume of a matrix element, ΔV.
3.1.3. Heat diffusion
The induced surface temperature decreases over time as heat diffuses through the material bulk. The analytical heat conduction equation in Eq. (3) links the temporal and spatial rates of temperature change:
This relation depends upon three material properties: density, specific heat capacity, and thermal conductivity (k). The temperature dependencies of thermal conductivity and specific heat capacity were taken into account using an explicit central finite difference solution to the heat conduction equation for a 5-ns time step.
3.1.4. Temperature dependence of silicon properties
The thermal conductivity and specific heat capacity of silicon change with temperature [42,43]. Figure 3 shows that the specific heat capacity increases and thermal conductivity decreases as temperature rises. A higher specific heat capacity requires increasingly more heat to change the temperature of silicon by a unit Kelvin. Therefore, the instantaneous temperature rise caused by a femtosecond laser pulse will decrease in magnitude as the surface temperature rises. A decrease in thermal conductivity with higher surface temperature causes silicon to act as a worse heat conductor. This reduces the rate of heat diffusion, limiting the amount of surface temperature decay between incident pulses.
Fig. 3 As temperature is increased from 273 to 1685 K (silicon melting point), thermal conductivity decreases by approximately 150 W/(m·K) [42], while specific heat capacity increases by approximately 350 J/(kg·K) [43].
3.2. Thermal modeling of experimental processing conditions
The temperature evolution in silicon was simulated using the mathematical methods described in Sections 3.1.2 – 3.1.3 for the experimental laser processing conditions presented in Section 2: 10 µJ pulse energy, 2 MHz repetition rate, and 1.5 mm/s scanning speed. (Because energy deposition by a femtosecond pulse is considered instantaneous in comparison to heat diffusion, pulse duration is not a parameter in the numerical model.) Fig. 4 shows that the predicted maximum surface temperatures for the experimental processing conditions are consistently higher than the oxidation threshold of silicon after four pulses and fully exceed the melting temperature after ten pulses. The maximum temperatures achieved during laser processing will occur at the surface of silicon at spatial locations corresponding to peak energy deposition by the most recently incident pulse. The maximum temperature continues to increase past the melting point with the incidence of more pulses. The predicted temperatures infer the onset of thermal phenomena for the experimental processing conditions, in agreement with the material analysis presented in Section 2.
Fig. 4 Evolution of the maximum temperature of silicon over time due to an incident femtosecond laser pulse train. The initial temperature is 293 K. Local temperature maxima arise due to pulse energy deposition and local temperature minima result from heat diffusion after the pulse. To denotes the oxidation temperature threshold for silicon (973 K [29]) and Tm corresponds to the melting temperature (1685 K).
4. Discussion of the heat accumulation mechanism and thermal equilibrium
4.1. Heat accumulation mechanism
A repetitive-pulse femtosecond laser deposits multiple pulses onto the surface of a material at times and locations dictated by the laser repetition rate and sample scanning speed. The amount of energy absorbed at a given surface location over the course of processing is related to the scanning speed of the sample. The laser repetition rate restricts the amount of heat diffusion occurring between incident pulses, where low repetition rates are required for the surface to cool to its initial temperature following the incidence of a pulse. Figure 5 shows how multi-pulse processing at a repetition rate of 500 kHz (10 μJ pulse energy, 1 m/s scanning speed, 70 μm focal spot) leads to heat accumulation.
Fig. 5 Surface temperature monitored at a location 50 μm along the scan path (100 μm total length). The dotted line marks the time when the peak of an incident pulse is centered at this location. Pulses arriving prior to and after this time impact the temperature via energy deposition and heat exchange.
Each incident laser pulse radially heats a region of the surface, including locations along the processing path. Figure 5 shows that each incident pulse plays a role in preparing the initial surface temperature at locations farther along the scan path in the time leading up to maximum energy deposition at those locations. Heating along the processing path drives the rise in maximum temperature over time, as seen in the simulation of experimental processing conditions in Section 3.2. Pulses incident after maximum energy deposition continue to heat previously processed locations in accordance with the Gaussian pulse energy distribution and through heat exchange, increasing the likelihood for the onset of thermal phenomena. As time increases and the beam moves farther along the scan path, the energy deposited by an incident laser pulse becomes insignificant and the surface temperature relaxes back towards the initial material temperature.
4.2. Temperature equilibration
The change in the thermal behavior of silicon during femtosecond laser processing enables equilibration of the magnitude of the temperature rise due to an incident pulse and the magnitude of the surface temperature decay due to heat diffusion. Figure 6 shows that the magnitude of the temperature rise due to an incident pulse decreases with increasing number of pulses. This is due to the rise in silicon specific heat capacity with increasing surface temperature. The magnitude of the temperature decay between pulses due to heat diffusion rises with the incidence of a few pulses because the temperature gradient along the processing path is still steep and silicon acts as a better heat conductor. As more pulses are deposited, the magnitude of the temperature decay then begins to decrease because the temperature gradient broadens and degrades the conduction performance as the surface temperature of silicon continues to rise. As shown in Fig. 6, the magnitude of the temperature rise and the magnitude of the temperature decay equilibrate over time and the surface reaches a constant relaxation temperature after each pulse, defined as the “equilibrium temperature.”
Fig. 6 The magnitude of the temperature rise due to an incident pulse, the magnitude of temperature decay due to diffusion, and the surface temperature immediately prior to pulse incidence are shown for 50 incident pulses, using a 500-kHz repetition rate, a 10-μJ pulse energy, a 70-μm focal spot, and a 4-m/s scanning speed. The temperature changes equilibrate after approximately 30 pulses, causing the surface temperature to reach a constant value.
5. Optimizing laser parameters via thermal modeling
The heat accumulation process is affected by both spatial and temporal surface exposure to femtosecond laser pulses. The magnitude of the local temperature maxima resulting from incident pulses is proportional to the beam fluence. The amount of heat diffusion is limited by the temporal spacing of the laser pulses. The pulse overlap, or percentage of the incident pulse overlapping the surface area affected by the previous pulse, can be controlled by changing either the scanning speed of the sample or the focal spot size. The thermal model presented in Section 3 can be used to control the heat accumulation process by determining optimal laser pulse energy, focal spot diameter, repetition rate, and sample scanning speed.
The sensitivity of heat accumulation to the aforementioned laser processing parameters was studied. Parameters enabling an equilibrium temperature below the oxidation threshold and local temperature maxima below the melting temperature were considered optimal.
5.1. Repetition rate
The sensitivity of heat accumulation to repetition rate was investigated first, as it affects both the temporal exposure to pulses and the pulse overlap. The focal spot diameter, sample scanning speed, and incident laser pulse energy were respectively fixed at 70 µm, 1.0 m/s, and 10 µJ, which can be achieved by commercial laser and scanning systems. The maximum temperature evolutions predicted for repetition rates of 1MHz, 500 kHz, and 100 kHz are shown in Fig. 7. The key simulation results are summarized in Table 1.
Table 1. Simulation Results for Repetition Rate Sensitivity
Figure 7(a) shows that a 1 MHz repetition rate leads to processing within the oxidation regime with the potential for melting. Figure 7(b) shows that, for a repetition rate of 500 kHz, a 2 × increase in diffusion time is achieved, allowing mitigated heat accumulation and processing below the oxide regime. Decreasing the repetition rate to 100 kHz indicates that an additional 5 × increase in diffusion time allows minimal heat accumulation in the silicon surface, as shown in Fig. 7(c). Reducing the repetition rate from 1 MHz to 500 or 100 kHz also causes a 2% or 16% respective reduction of pulse overlap, minimizing the exposure of a specific surface region to incident laser pulses.
The repetition rate drives the overall rise in temperature during femtosecond laser processing. Although the 100 kHz repetition rate offers minimal heat accumulation, the 500 kHz repetition rate is adopted as the optimal fixed parameter in the following simulations so that the sensitivity of heat accumulation to parameter variation can be readily seen.
5.2. Scanning speed
The scanning speed impacts the exposure of a surface region to incident femtosecond laser pulses by changing their overlap. Heat accumulation can be mitigated by decreasing the pulse overlap. Figure 8 shows the temperature evolutions at the spatial location corresponding to the center of the 26th incident laser pulse for different scanning speeds. The repetition rate, pulse energy, and focal spot diameter were respectively fixed at 500 kHz, 10 µJ, and 70 µm. Figure 8(a) shows that, for a scanning speed of 1 m/s, the temperature evolution at the fixed location is affected by every pulse incident within 100 µs. Figure 8(b) shows that, when increasing the scanning speed to 4 m/s, the heating contribution from non-local pulses is negligible, reducing the time over which that location is heated. This is because increasing the scanning speed by a factor of 4 results in an 11% decrease in pulse overlap.
Fig. 8 Surface temperature evolution over time at the spatial location of incidence of the 26th incident laser pulse along the scan direction for (a) 1 m/s and (b) 4 m/s.
The maximum temperature evolutions for the scanning speeds in Fig. 8 are shown in Fig. 9. Increasing the scanning speed enables faster equilibration of the maximum surface temperature. After 40 µs, the 1 m/s case achieves a local minimum temperature of 496 K without reaching equilibrium, while the 4 m/s case achieves an equilibrium temperature of 450 K after 30 µs. The total reduction in heat accumulation for this 4 × speed increase is 46 K. The 4 m/s scanning speed allows the silicon surface to maintain uniform thermal conditions throughout processing which will control the onset of thermal phenomena. Therefore, a 4 m/s scanning speed is considered optimal.
Fig. 9 Temperature evolutions for a repetition rate of 500 kHz and a scanning speed of (a) 1 m/s or (b) 4 m/s.
5.3. Laser fluence
Because the laser fluence is directly proportional to the laser pulse energy and inversely proportional to the laser spot size, it impacts both the magnitude of peak energy deposition and the surface area affected by an incident pulse. The fluence also determines whether ablation can occur and the corresponding material removal rate [5,6]. Although heat accumulation must be mitigated in processing, the fluence must be above the ablation threshold (~0.2 J/cm2 for silicon [31,44]) to remove material. To maintain fluence above this threshold, we investigate the sensitivity of heat accumulation to fluence by increasing its value. Specifically, a 2 × increase in fluence from 0.26 J/cm2 (assuming a 10 µJ pulse energy and 70 µm focal spot) to 0.52 J/cm2, as shown in Fig. 10, was tested for changing either the pulse energy or the focal spot diameter. Scanning speed and repetition rate were respectively fixed at 1 m/s and 500 kHz. Table 2 summarizes the processing parameter combinations used to achieve the simulation results in Fig. 10.
Fig. 10 Maximum temperature evolutions showing the effect of a 2 × increase in fluence achieved by changing either the focal spot size or pulse energy. (a) Reference temperature evolution with 0.26 J/cm2 fluence. (b) Temperature evolution for 0.52 J/cm2 fluence attained by reducing the focal spot from 70 µm to 49.5 µm. (c) Temperature evolution for 0.52 J/cm2 fluence attained by increasing the pulse energy from 10 µJ to 20 µJ, showing increased heat accumulation.
Table 2. Simulation Parameters and Results for Testing Fluence Sensitivity
Figure 10 shows that increasing the fluence by changing either the focal spot size or the pulse energy leads to different amounts of heat accumulation. When increasing the pulse fluence from 0.26 J/cm2 to 0.52 J/cm2 via focal spot reduction, respectively shown in Figs. 10(a) and 10(b), the rise in the local minimum after 30 µs is 134 K, while increasing the fluence by doubling the pulse energy, as shown in Fig. 10(c), leads to a rise of 570 K. The smaller focal spot size reduces the extent of the pulse-affected surface region and decreases the pulse overlap by 1.5%. The control over spatial energy deposition via reduction of focal spot size mitigates the heat accumulation by allowing the entire silicon surface to remain a better heat conductor.
Increasing the laser fluence to achieve effective ablation can be performed with a minimal rise in heat accumulation by reducing the focal spot size of the beam. Decreasing the fluence to minimize heat accumulation is most effective when reducing the pulse energy, assuming that the ablation threshold is still exceeded. Because a fluence of 0.26 J/cm2 offers cooler thermal conditions and exceeds the ablation threshold for silicon, a focal spot size of 70 µm and pulse energy of 10 µJ are considered optimal.
5.4. Discussion of optimized processing conditions
Sensitivity tests showed that the repetition rate plays the most significant role in heat accumulation in femtosecond laser processing of silicon. Changing the repetition rate from 1 MHz to 500 kHz doubled the heat diffusion time and reduced the pulse overlap by 2%, causing the local temperature minimum after 30 µs to be reduced by ~700 K. Further reduction of the repetition rate to 100 kHz allowed the surface temperature to decay to its initial temperature between pulses. The repetition rate dictates the extent of heat accumulation in processing and plays the largest role in eliminating the onset of thermal artifacts.
The scanning speed can be increased to reduce the heat accumulation effect in femtosecond laser processing by reducing the overlap of incident pulses. Comparing the minimization of heat accumulation for a 4 × increase in scanning speed (46 K temperature difference after 30 µs) and the 5 × reduction in repetition rate (180 K temperature difference after 30 µs for 500 kHz → 100 kHz) showed that increased diffusion time is the main contributor to temperature reduction. Significant minimization of heat accumulation via increased scanning speed is restricted by the physical limit of mechanical translation and optical scanning speeds and by the pulse overlap required to achieve uniform material removal. Nevertheless, the scanning speed plays the largest role in attaining uniform thermal conditions during processing: a scanning speed of 4 m/s enabled temperature equilibration after 30 µs, whereas equilibrium was not predicted for 1 m/s.
The laser pulse fluence must be high enough to enable material removal, but low enough to eliminate unnecessary heat accumulation in processing. When increasing the laser fluence by a factor of 2, it was found that the reduced spatial energy increase and pulse overlap via focal spot reduction enabled minimized heat accumulation in comparison to doubling the laser pulse energy. This indicates that a marked reduction of heating in processing can be achieved by reducing the pulse energy, assuming that the fluence remains above the ablation threshold. Additionally, increasing the fluence to achieve effective ablation with minimal heat accumulation can be attained by reducing the focal spot size.
The predicted set of optimized processing conditions determined by heat accumulation sensitivity studies includes a 500 kHz repetition rate, a 4 m/s scanning speed, a 10 µJ pulse energy, and a 70 µm focal spot diameter. This combination allows equilibrium to be reached below the oxide threshold and for the local temperature maxima to remain below the melting temperature of silicon. With these optimized laser parameters, effective, uniform ablation is expected with mitigated thermal artifacts. Predictions of optimized processing conditions will enable high-quality surface processing of silicon using femtosecond lasers. These conditions are being tested to verify predictions and assess thermal artifact mitigation and processing quality.
In our current model, to accommodate planned experiments at three different wavelengths (343, 515, and 1030 nm) while maintaining a reasonable computational load, we have assumed that all heat-inducing energy is absorbed into a surface layer with 1.5-μm thickness. For 515 nm and 343 nm wavelengths, the absorption depth is less than this thickness. For 1030 nm wavelength light at low surface temperatures, nonlinear absorption dominates and the absorption depth may exceed the layer thickness [44], resulting in overestimation of pulse-induced temperature rises. However, because a steep surface temperature gradient diffuses heat faster than a more gradual, dispersed gradient, the predicted decay temperatures following the incidence of a pulse quickly become consistent for both gradient types, leading to a consistent equilibrium temperature.
6. Conclusion
We have experimentally demonstrated the effectiveness of femtosecond laser surface processing of silicon, showing effective material removal and detrimental surface artifacts along the ablated track as a result of high surface temperatures. The heating mechanism in femtosecond laser processing of silicon has been studied and a numerical model has been constructed to predict the surface temperatures achieved during laser processing. This model can be expanded to accommodate nonlinear beam propagation and adapted to a variety of materials. The simulated surface temperature for experimental processing conditions confirmed the onset of oxidation and the potential for material melting. The sensitivity of heat accumulation to femtosecond laser and scanning parameters was studied to mitigate detrimental thermal artifacts. The repetition rate was found to drive the overall magnitude of heat accumulation in processing and the scanning speed was found to enable uniform thermal processing conditions. A reduction in laser pulse energy was found to enable better mitigation of heat accumulation than an increase of the focal spot size. A set of optimized processing parameters was predicted using the results of the sensitivity study to mitigate heating and the onset of thermal effects in processing. Validation of predicted temperatures and processing results is underway for processing at 1030 and 515 nm wavelengths. Modeling of complex, electron-level physical phenomena during the laser pulse and phase transitions is being carried out to confirm the approximations made in the current model. The presented method can be readily used to predict deterministic, optimal processing parameters for non-thermal femtosecond laser processing of other materials.
Acknowledgments
We thank OptiPro Systems for supplying the silicon sample and the three-axis sample translation system. We acknowledge Dr. David Ross and Dr. Aaron Schweinsberg for insightful discussions regarding thermal modeling and Dr. Richard Hailstone for assistance with EDS measurements. This work was supported by the corresponding author's new-faculty startup fund provided by the Rochester Institute of Technology, by OptiPro Systems and by the Center for Emerging and Innovative Sciences.
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