Experimental and theoretical study of the laser micromachining of glass using a high-repetition-rate ultrafast laser

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1 Experimental and theoretical study of the laser micromachining of glass using a high-repetition-rate ultrafast laser Yuri Yashkir a*, Qiang Liu a a Institute for Optical Sciences, 60 St. George Street, Toronto, ON, CANADA L6H 5T6 ABSTRACT We present a systematic study of the ultrafast laser micro-machining of glass using a Ti:Spp laser with moderate pulse energy (<5 µj) at a high repetition rate (50 khz). Optimal conditions were identified for high resolution surface laser etching, and via drilling. Several practical applications were developed: glass templates for micro fluid diffraction devices, phase gratings for excimer laser projection techniques, micro fluid vertical channel-connectors, etc.. It is demonstrated that the interaction of ultrafast laser pulses with glass combines several different processes (direct ablation, explosive material ejection, and thermal material modification). A dynamic numerical model was developed for this process. It was successfully used for modelling of laser micro-machining with arbitrary 3D translations of the target. Keywords: Laser, micro-machining, femtosecond, laser etching, numerical model, simulation. 1. ULTRAFAST LASER MICRO-MACHINING SYSTEM An experimental laser micro-machining system was based on a high-repetition-rate ultrafast laser developed in the University of Toronto (Prof. Dwayne Miller s group). Major components of the laser are: a femtosecond ultrafast fiber laser (1560 nm) with a frequency doubler in a PPLN crystal for seeding the regenerative amplifier, and a Ti:Spp regenerative amplifier pumped with a 532 nm DPSS laser (3.5W average power at the 50 khz repetition rate). Laser parameters used for the experiments were: wavelength λ= 800nm, pulse width τ= 500 fs, and pulse energy E=4 µj. The laser beam was focused with various microscope lenses. Laser beam path and focusing depth were controlled by a threedimensional micro-positioning stage. 2. LASER MICRO-MACHINING OF GLASS: PARAMETERS To provide a reliable tool for controlled laser micro-machining of glass materials we used the following milling technique: the milled area was covered by lines, spirals, circles, etc. with gradual vertical phone ; fax ; Solid State Lasers and Amplifiers II, edited by Alphan Sennaroglu, Proc. of SPIE Vol. 6190, 61900V, (2006) X/06/$15 doi: / Proc. of SPIE Vol V-1

2 translation of the focusing objective as the milling area deepens. Typical milling parameters were: pulse energy E= 0.1 to 5 µj, feed rate v= 1 to 100 mm/min, number of pattern repeats N= 1 to 50. For laser beam focusing, a set of microscope objectives was used (numerical apertures NA= 0.1 to 0.25). Gaussian diameter of the focused beam was 5 to 6 µm. The range of laser fluence was 0.5 to 20 J/cm 2, dwelling time of the laser spot was 30 to 60 ms, number of laser pulses interacting with the target during dwelling time was 10 3 pulses. 3. LASER MICRO-MACHINING OF GLASS: RESULTS 3.1. Milling a via hole: dependence on the number of passes A glass plate, 175 µm thick, was used in this experiment. The milling pattern consisted of a set of concentric circles with a 3 µm pitch (starting from the centre). Circular translation of the target was performed at a feed rate v= 20 mm/min. For each sample a different number N of milling pattern repeats was used. Every repeat of machining pattern was done at a deeper focal plane (step -3 µm), starting from the surface. Laser parameters were: beam diameter at the focusing lens d= 6 mm, pulse energy E= 3 µj, pulse width τ= 800 fs, repetition rate f= 50 khz. Focusing was done by a microscopic objective (numerical aperture NA= 0.14). The focal spot diameter was about 6 µm. These parameters correspond to the peak laser fluence of 10 J/cm 2 and the peak intensity of W cm 2. The damage threshold corresponds to a pulse energy ~0.6 µj or a fluence of ~2 J/cm 2. These data is in good agreement with the results 1. The milling process is illustrated with the following sequence of images, as the number of repeats N increases from 1 to 60 (fig.1). The glass surface outside the milling area has no indication of damage. The milled area demonstrates irregular surface ablation with obvious thermal effects. In another experiment, the real-time dynamics of the laser drilling of a 6 µm hole were captured by a video (three typical frames are demonstrated in fig.2). It is seen that ablation is not limited to the surface of the target only fragments of glass are blown away by plasma created under the surface due to the fact that glass is a non-homogeneous material with its multi-photon ionization threshold varying from point to point. The size of ejected fragments varies from sub-microns to about 1 µm Laser micro-machining of a grating structure A similar technique was used for the manufacturing of a grating in a quartz plate (fig.3). Narrow (15 µm) strips are transparent, and milled channels provide light scattering. This grating was designed to be used as a mask in excimer laser micro-machining experiments where the image of the mask is projected with demagnification onto the target. With 10x demagnification, this mask can provide 1.5 µm machining channels. Laser parameters were: pulse energy of 2 µj, repetition rate of 50 khz, feed rate of 100 mm/min. Milled stripes were etched in one pass by parallel lines with a pitch of 2 µm and with a focusing lens NA=0.25. Proc. of SPIE Vol V-2

3 N=1 N=4 N=10 N=20 N=40 N=60 Figure 1: Ultrafast laser milling of a glass sample (progress).4 Figure 2: Images of a real micro-machining (a 6 µm hole being milled) Proc. of SPIE Vol V-3

4 H 1, \ GU '3Kv :;4ôo Figure 3: Femtosecond laser etching of a grating structure in a quartz plate 3.3. Refractive index modification inside glass When the laser beam is focused deeper under the glass surface then the local multi-photon interaction of the laser pulses modifies the refractive properties of the glass, forming the well known waveguide structures (fig.4). Laser parameters: pulse energy 0.2 µj, feed rate 50 mm/min, focusing lens NA= 0.65, spot size 1.5 µm. Corresponding laser fluence was ~ 6 J/ cm 2. I.1 S H1PI Figure 4: Writing waveguide structures in glass It is important to note that the laser fluence is well over the surface damage threshold. This observation illustrates a significant difference in surface and internal laser/material interaction. In the vicinity of the material surface, the ionization stimulates avalanche processes and the resulting plasma plume either takes away material or causes a local breakdown with a following ejection of a piece of material. Internal multi photon ionization most likely causes local photochemical reactions with a Proc. of SPIE Vol V-4

5 modified refractive index as a result Micro fluid device sample An example of a micro fluid device (three via holes of 115 µm are connected with a 25 µm channel) is presented in fig.5. '3I KV Figure 5: Manufacturing a micro fluid device (via connectors and a micro channel) This example illustrates that a low-energy high-repetition rate ultrafast laser can be used both for deep drilling (to connect micro channels at different levels) and for shallow micro channel formation. 4. NUMERICAL MODELLING OF ULTRAFAST LASER MICRO-MACHINING 4.1. Model outline The model has been developed to predict and understand etch rates, heat flow, and general light-matter phenomena during ultrafast laser pulse interactions with a target. In this version, the general model assumptions are: Ultra short laser beam with the Gaussian spatial distribution is focused onto the target surface. Its movement (trajectory, speed, on/off switching) on the surface plane is user-defined. The laser pulse has linear absorption below etch threshold. Absorbed light energy heats the material with corresponding heat diffusion. Phase transitions of the material from condensed state to liquid and to plasma take place if heat density reaches necessary levels. Proc. of SPIE Vol V-5

6 Ablation of the material due to multi-photon ionization takes place on the surface. The ablation rate function (zero below threshold, a steep nonlinear function in the vicinity of threshold, and a constant over threshold) is defined by the user based on the calibration procedure. Ablated material (plasma) transfers some fraction (to be calibrated) of its thermal energy into adjacent material, thus causing thermal load onto the target. Thermal energy absorbed by the material due to both plasma plume contact and direct absorption of the under-the-threshold beam is then thermally diffused. Photon interaction and heat diffusion in a plasma plume are neglected (we consider material transition to plasma as material removal). In this new version of the model we implemented a laser beam scanning feature. Our general approach in modeling is based on our previous results 2,3. User can define arbitrary path of the beam and feed rates Algorithm The heat diffusion is defined by numerical integration of the partial differential equation for heat energy density Q diffusion with a heat source: 2 Q 2 Q 2 Q Q t D x 2 y 2 z Ax,y,z,t 2 with heat density Q(t,x,y,z), time t, depth z, surface coordinates [x,y], diffusion coefficient DTT C T, material density, heat capacity of the material C T, thermal conductivity T, local temperature T t,x,y,z, and the heat source rate At,z,y,x. The source At,z,y,x is a temporal rate of energy inflow due to absorption of the laser light with its peak pulse power I 0, temporal and spatial laser pulse shape pt,y,x, and attenuation factor due to due to its absorption from the crater surface zh y,x to a given depth z. It is assumed that under condition z1 the heat source rate is At,z,y,x I 0 pt,y,xe zhy,x, with laser pulse peak intensity I 0 E p r x r y, laser pulse energy E p, depth of the machined feature h y,x, laser pulse shape pt,y,xexp t 2 0 xx t pulse width, and the laser beam scan path xt, yt. r x 2 yyt r y 2, laser beam radii r x,y, The temperature T is calculated as follows: Below melting point ( T T m ) T QC T T 0, where T 0 is an initial temperature. Proc. of SPIE Vol V-6

7 During melting at T T m const (complete phase transition from solid to liquid requires additional heat contribution of Q m L f ). Heating liquid phase below boiling point ( T m T T v ): T QC T T 0 L f CT. Evaporation at T T v const (complete evaporation requires an additional heat contribution of Q v L v ). Material removal modelling: When a cell reaches sufficient energy density to vaporize, then the surface profile is corrected by hy,xhy,xz, and the cell is considered removed. If laser beam intensity at a surface point x,y is over the threshold I th then a fraction abl of the cell material is considered as ablated (removed), and surrounding material receives a fraction T of the laser pulse energy. Parameters abl and T are identified through a calibration procedure (fitting model results to available experimental data) Program module The numerical algorithm is realized in c-code with a simple interface for easy data modification and extensive output in various formats (data, images, video, etc.). The following graphs illustrate the output data. Fig.6 shows the beam trajectory (user defined). The resulting micro-machined groove surface built using output data is presented in fig.7. IW I I I I I I I C 50 ED 70 I I 90 1= Figure 6: A sample laser beam path (the scale is in micrometers) Figure 7: Output of the simulation program (a spiral channel etched in silicon) The laser beam dwelling time increases in the focal area of the spiral path (when feed rate is constant), thus causing deeper etching (typical experimental situation). Proc. of SPIE Vol V-7

8 4.4. Numerical simulation example The following is an example of the numerical simulation of ultrafast laser milling of glass ( drilling a hole). Its general features correspond to the experiments presented in fig.1 and fig.2. The laser beam path is modelled as a converging spiral (as in our experiments). y. uui M. UUI SD :! 160 I Figure 8: Spiral path of the laser beam for simulation of the milling experiment in glass A sequence of images illustrates material removal and temperature distribution versus time. Material removal process: I t 1 t 2 Proc. of SPIE Vol V-8

9 t 3 t 4 Figure 9: Laser milling of glass (four frames were taken at different time moments: t 1 <t 2 <t 3 <t 4 ) Note that model describes the tapering of the hole as in the experimental results. Temperature map: T(ny0)nno T(ny0)unt I urn urn 1 2 T(XyO)VSt 3 Figure 10: Temperature distribution on the glass surface at different time moments. 4 Proc. of SPIE Vol V-9

10 Note the temperature drop along the laser beam path. SUMMARY We demonstrate ultrafast laser micro-machining of glass using a 50 khz repetition rate femtosecond laser. The heat-affected zone was limited to less than 1 µm. No cracks were observed. The numerical model of the laser micro-machining process (laser beam translation, nonlinear ablation, heat exchange, and heat diffusion) was developed. It allows the simulation of the time-dependent process of laser milling and monitoring of temperature dynamics. REFERENCES 1. M. Lenzner, J.Krger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz. "Femtosecond Optical Breakdown in Dielectrics", Physical Review Letters, v.80, (1998) 2. Y. Yashkir, M. Nantel, B. Hockley. Numerical simulation of the laser dynamics and laser/matter interactions, and its applications for laser micro-machining, International Journal of Applied Electromagnetics and Mechanics, v.19, (2004) 3. Yuri M. Yashkir, Seongkuk Lee, Maher Harb, Yuriy Yu.Yashkir. Laser micro-machining of silicon in a sulfur hexafluoride atmosphere: the experiment and numerical simulation, CLEO/EUROPE-EQEC,12-17 June 2005, Munich, Germany. Proc. of SPIE Vol V-10

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