A Study of Angular Dependence in the Ablation Rate of Polymers by Nanosecond Pulses

Transcription

1 A Study of Angular Dependence in the Ablation Rate of Polymers by Nanosecond Pulses James E.A. Pedder and Andrew S. Holmes Department of Electrical & Electronic Engineering, Imperial College London Exhibition Road, London SW7 2AZ, UK ABSTRACT Measurements of ablation rate have traditionally been carried out only at normal incidence. However, in real-world applications ablation is often carried out at oblique angles, and it is useful to have prior knowledge of the ablation rate in this case. Detailed information about the angular dependence is also important for the development of ablation simulation tools, and can provide additional insight into the ablation mechanism. Previously we have reported on the angular dependence of direct-write ablation at 266 nm wavelength in solgel and polymer materials. In this paper we present a systematic study of angular dependence for excimer laser ablation of two polymer materials of interest for microfabrication: polycarbonate and SU8 photoresist. The results are used to improve simulation models to aid in mask design. Keywords: laser ablation, excimer laser, solid-state laser, modelling, simulation, MEMS, microstructures 1. INTRODUCTION Laser machining of materials by ablation is an established process in advanced manufacturing. Surface marking and micro-hole drilling are among the more common applications of high power lasers due to the simplicity and speed of operation [1]. New applications in the field of micro-optical and micro-electromechanical systems (MEMS) are also emerging, where the surface features are more complex and require variable removal of material from a substrate [2]. Surface scribing of hard materials with lasers has been instrumental in the production of large solar-cell arrays. Similarly, microhole drilling by ablation is now an established method of producing interconnects for circuit-boards. These applications are usually the territory of pulsed solid-state lasers, where khz pulse repetition frequency and high beam quality allow rapid processing of substrates using a focussed spot [3]. High accuracy motion stages and/or laser beam scanners can be used, together with CAM control software to define a particular tool path for the laser spot. Other surface patterning, such as thin-film removal and processing of microlens arrays, can be performed using a maskprojection method [4]. This technique is usually reserved for excimer lasers, where the higher peak power allows simultaneous patterning over large areas. Traditional binary chrome-on-quartz masks, commonplace in photolithography, are used where high resolution is required. Features with variable surface height can be machined using mask projection methods by changing the aperture shape and/or size during machining. For example, in [5] a sequence of exposures with different static masks was used to create rotor blades for micro-turbines. For micro-optical structures, surface roughness can seriously affect the device performance. In this case, the number of static masks is increased to reduce the step height formed in the substrate between successive exposures. Furthermore, on-the-fly machining, where the substrate is moved in synchronisation with the laser firing, can drastically reduce the processing time for large substrates. These techniques form the basis of the synchronised image scanning (SIS) technique [6]. Other methods for producing varying surface relief include mask and/or workpiece dragging with a defined aperture shape [7] and static machining with a half-tone mask [8]. The photomask must be correctly designed to create the desired surface features when using mask projection ablation. This is only one of several issues that must be addressed in order to optimize a laser machining process. Both the cost of Photonics West 26 1/9

2 mask manufacture and the delay caused by iterative corrections to the mask design can be a problem for many potential users of laser ablation. We have previously reported on the development of simulation tools to aid in the design of laser tool paths and photomasks [9-11]. These tools can reduce the need for iterative corrections and reduce the overall cost of producing a prototype structure. However, they rely on having accurate information about the material ablation characteristics, both for normal and oblique incidence. The latter is particularly important when simulating the ablation of deep structures with complex surface topography. In this paper we report on a recent investigation into the angular dependence of the excimer laser ablation rate in two important polymer materials: polycarbonate (PC) and SU8 photoresist. Measurements were made for both materials at angles up to 85 from normal, using both ArF (193 nm wavelength) and KrF (248 nm) excimer lasers. The results are compared with the predictions of two simple theoretical models for angular dependence of ablation rate, one of which has been used extensively in the literature. Also, simulation results obtained using both the measured angular dependence for PC at 248 nm and one of the two theoretical models are assessed by comparison with test structures machined in polycarbonate using a half-tone projection mask. 2. MODELS FOR ANGULAR DEPENDENCE OF ABLATION RATE The majority of experimental and theoretical ablation studies carried out over the past 2 years have been concerned with normally incident radiation. Nevertheless, a small number of authors have considered the question of angular dependence of polymer ablation rates. In virtually all cases it has been assumed that the ablation rate for a given wavelength and temporal pulse profile should be a function only of the total pulse energy crossing unit area of the material surface. In this case, it is expected that the etch depth per pulse, R, normal to the surface will vary with fluence F and angle of incidence θ as: 1 R MODEL 1: ( ) θ R F, θ = f F cosθ, with f ( F cosθ ) as R In this equation R ( F, ) = f ( F ) 1 R R θ (1) is the usual ablation curve for the material at normal incidence (θ = ), and R θ represents the angle-dependent reflectivity of the surface. The limiting form shown to the right is expected to be a good approximation for low index materials, except near grazing incidence. The model in (1) has been used previously to explain specific geometrical effects such as the variation of side-wall angle with fluence and illumination conditions [12,13] and the formation of conical structures due to micro-masking [14]. In recent years it has also been included in fluence calculations for photorefractive laser surgery [15]. The basic assumption of the model seems reasonable if the ablation process is photothermal, as is generally accepted to be the case for ablation of organic materials by nanosecond pulses. However, the model is over-simplistic in assuming that only the total energy per unit area crossing the surface is important. For example, the effective optical absorption length normal to the surface varies with angle of incidence, and this may be an important factor if this absorption length is comparable to or longer than the thermal diffusion length on the timescale of the laser pulse. It is therefore not surprising that quantitative agreement between predictions made using (1) and experimental results is not usually very close. An alternative model for angular dependence is obtained if one returns to the earliest picture of laser ablation, where it is assumed that light is absorbed inside the material according to the Beer-Lambert relation, and that ablation occurs wherever the fluence is above a critical threshold level, F T. In this case, the normal incidence ablation curve is of the classic form f = α -1 ln(f/f T ), with α being an effective optical absorption coefficient. This is commonly referred to as a Beer s law ablation curve. The corresponding angle-dependent etch function is expected to be: MODEL 2: R( F, θ ) cosθ' f F ( 1 Rθ ) cos ( 1 R ) cos θ θ', with f ( F ) cosθ as R R θ (2) Photonics West 26 2/9

3 Here θ denotes the propagation direction of the refracted light inside the material. According to this model, the ablation depth along the direction of light propagation is constant apart from a correction to the fluence due to reflection/refraction. The cosine term outside the ablation curve function is simply a geometrical factor that transforms the ablation depth along the direction of propagation into the depth normal to the surface. It is important to note that, in cases where the normal incidence ablation curve is approximated well in any region by a straight line passing through the origin (i.e. f kf for some k), then the overall cosine angular dependence in the ablation depth predicted by MODEL 2 will also be predicted by MODEL 1 in that fluence regime. We have previously observed this kind of angular dependence in solgel and polymer ablation at 266 nm wavelength [16]. 3. EXPERIMENTAL METHODS AND RESULTS To test the suitability of the above models for making quantitative or semi-quantitative predictions about angular dependence, we made measurements of ablation rate at normal and oblique incidence in polycarbonate and cross-linked SU8 photoresist. The normal incidence measurements were used to derive the ablation curve, and then the model predictions based on this curve were compared with the oblique incidence data. All experiments were carried out using either an Exitech 72 series workstation (193 nm wavelength measurements) or an Exitech 81 series workstation (248 nm wavelength). In both systems, accurate control over the incident fluence was achieved using an in-line attenuator, and a 6x6 fly s eye homogenizer was used to ensure uniform exposure over the area of illumination. Projection lenses with 4X and 5X magnification were used for the 193 nm and 248 nm machining respectively. 3.1 Normal incidence measurements A method has previously been described that enables rapid measurement of the material ablation curve using a half-tone mask [17]. This method uses a mask with regions of known transmission to create a stepped-multi-level structure in the workpiece after exposure with a homogenized laser beam. The use of such a mask reduces the uncertainty in the fluence levels to a single overall scale factor, since the relative fluence levels in the different regions are defined by the half-tone pattern. The etch depths are measured using a surface profilometer. This method was used to generate the data for the ablation curves shown in Fig. 1. Least squares fitting was used to derive a cubic fit to each set of ablation curve data, indicated by the solid lines in Fig. 1. Curve fitting was based on larger data sets than those shown, except in the case of SU8 at 248 nm wavelength where all of the data used for fitting is shown. Each plot in Fig. 1 also shows the best fit of a Beer s law ablation curve to the data points lying above a certain etch depth (.5 μm for 248 nm data, and.1 μm for 193 nm data). It can be seen that, for all four combinations of material and wavelength, the Beer s law ablation curve represents a very good fit to the data at higher fluence levels, but under-estimates the ablation depth at fluences near the ablation threshold; this is quite typical for polymer ablation by nanosecond pulses. 3.2 Oblique incidence measurements To investigate the angular dependence of the ablation rate, a rotary stage was employed that could alter the angle of incidence between the laser beam and the sample surface, as shown in Fig. 2. In addition, an adjustable chuck position ensured that the centre of rotation was always lying in the top surface of the substrate. This method allowed us to accurately calibrate the angle of incidence, without the need to characterize the surface before and after exposure. Analysis of data obtained in this way eliminated the need for iterative calculations required by other methods [18]. Each sample was subjected to a series of 3-pulse exposures at constant fluence and different angles of incidence in the range to 85. The sample was translated between successive exposures to produce a staircase pattern from which the angular dependence could be directly extracted using a surface profilometer. A 2x2 μm 2 square exposure site was Photonics West 26 3/9

4 used throughout, and measurements were made at fluences in the range 5-35 mjcm -2 and mjcm -2 for the 193nm and 248nm experiments respectively..35 PC at 248nm wavelength.35 SU8 at 248nm wavelength Ablation depth per shot (microns) Ablation depth per shot (microns) Fluence (mj/sq.cm) 1 1 Fluence (mj/sq.cm).12 PC at 193nm wavelength.12 SU8 at 193nm wavelength Ablation depth per shot (microns) Ablation depth per shot (microns) Fluence (mj/sq.cm) 1 1 Fluence (mj/sq.cm) Fig. 1. Normally incident ablation curve measurements for PC and SU8 at 248nm and 193 nm wavelengths. Solid lines are cubic polynomial fits to extended data sets; dashed lines are best-fit Beer s law ablation curves. Fig. 2. Experimental set-up used for investigating angular dependence of ablation rate. Photonics West 26 4/9

5 Fig. 3 below shows the measured angular dependence of ablation rate at three different fluence levels for each combination of material and wavelength. Each plot also shows the angular dependencies predicted by MODEL 1 (dashed lines) and MODEL 2 (solid lines), assuming the polynomial ablation curves in Fig. 1. Reflection and refraction effects were ignored in all cases F=925 PC at 248 nm wavelength.35.3 SU8 at 248 nm wavelength F=175 Ablation depth (microns) F=75 F=375 Ablation depth (microns) F=25 F= Angle of incidence (degrees) Angle of incidence (degrees) Ablation depth (microns) F=5 F=15 PC at 193 nm wavelength F=35 Ablation depth (microns) F=5 F=15 SU8 at 193 nm wavelength F= Angle of incidence (degrees) Angle of incidence (degrees) Fig. 3. Measured angular variations of ablation depth for PC and SU8 at 248nm and 193 nm wavelengths. Dashed lines are predictions using MODEL 1; solid lines are predictions using MODEL 2. Fluence levels are in mjcm -2. From Fig. 3 we can see that the angular dependence at higher fluence levels is more consistent with MODEL 2 (solid line) than with MODEL 1 (dashed lines). Indeed MODEL 2 matches the experimental data at the highest fluence levels extremely well for three out of the four material/wavelength combinations, except at very high angles of incidence. The more commonly used MODEL 1 appears to over-estimate the ablation depth at oblique incidence in this fluence regime. These observations, which suggest that the ablation depth along the direction of propagation is largely independent of angle of incidence at high fluence levels, are consistent with our earlier measurements on SU8 made at 266 nm wavelength [16]. In contrast, at low fluences MODEL 1 shows close agreement with the experimental data for all four material/wavelength combinations, while MODEL 2 over-estimates the ablation depth. Also, there is an intermediate range of fluences where neither model appears to make accurate predictions, with both over-estimating the ablation depth. Currently we do not have an explanation for these observations. It is worth noting that inclusion of reflection and refraction in the models does not lead to an overall improvement in their performance. Photonics West 26 5/9

6 4.1 Multi-pulse ablation simulator 4. APPLICATION TO MULTI-PULSE ABLATION SIMULATION We have developed a multi-pulse projection ablation simulator based on a two-stage approach as illustrated in Fig. 4. The first stage involves calculating the fluence distribution in the region of the workpiece. Standard imaging theory is used to propagate the laser radiation as far as the image plane of the projection optics; the fluence distribution in the region beyond the image plane is then determined by propagating the angular spectrum of plane waves. This calculation neglects the effect of the workpiece itself, and consequently it needs to be performed only once at the start of the process. Ignoring the workpiece greatly simplifies the calculation, while at the same time limiting the range of situations to which the simulator can be applied. Details of the calculation, which takes full account of the illumination optics, can be found in earlier publications [9,11]. The second stage involves propagation of the ablated surface. This is performed on a pulse-by-pulse basis by combining the fluence distribution over the partially etched structure with a material ablation curve derived either from experimental data or from physical modeling of the ablation process. Previously, in the absence of any experimental angular dependence data, we have assumed an angular dependence of the ablation rate according to MODEL 1. The results produced have generally been in close agreement with experiment, but with some discrepancies, particularly in regions where the surface is steeply inclined. One of the motivations for the work reported in this paper was to investigate whether these discrepancies might be caused by inaccuracies in the angular dependence model. To this end, test structures were fabricated in polycarbonate by half-tone ablation and compared with simulations carried out using both MODEL 1 and the experimentally determined angular dependence. Mask pattern Fluence calculation Surface propagation Machined surface Laser params Optics params Ablation curve Angular dependence (Cumulative effects) (Surface morphology) # pulses Fig. 4. Two-stage multi-pulse ablation simulation method. 4.2 Simulation of half-tone machining in polycarbonate A range of test structures was produced in polycarbonate by projection ablation at 248 nm wavelength using a half-tone mask. These exposures were carried out on an Exitech 81 series workstation with a 5X,.18NA projection lens. The half-tone mask was designed to produce a smoothly varying convex surface so that the performance of the simulator could be assessed over a range of depths and surface gradients. Fig. 5 shows a sketch of the half-tone mask and a scanning electron micrograph of a typical test structure machined using 6 pulses at 1 J/cm 2 fluence (1% transmission value). The test structures were diced by laser machining from the reverse side of the substrate, and their cross-sectional profiles were extracted from digital photographs taken under an optical microscope. Fig. 5 shows measurements taken from structures produced with 6 and 12 pulses (circles and diamonds respectively). Also shown in this figure are the results of simulations performed both with an assumed angular dependence according to MODEL 1 (dashed lines) and with the measured angular dependence for PC at 248 nm (top-left plot of Fig. 3). In the latter case, an empirical Photonics West 26 6/9

7 n angle-dependent etch function of the form R( F θ ) f ( F cos θ ), =, with n = 1.37, was implemented in the simulator, as this was found to be a good fit to the experimental data for PC at 248 nm over a wide range of fluences. Fig. 5. Transmission profile of half-tone mask used to machine polycarbonate test structures (left), and scanning electron micrograph of a typical structure produced using 6 pulses at 1 Jcm -2 fluence (right) Depth (microns) Position (microns) Fig. 6. Comparison of cross-sectional profiles for fabricated PC test structures with (a) simulations assuming angle dependence as in MODEL 1 (dashed lines), and (b) simulations using the measured angular dependence for PC at 248 nm wavelength (solid lines). As can be seen in Fig. 6, the simulations using MODEL 1 show significant over-estimation of the ablated depth in regions of high surface gradient, particularly for the deeper structure. This is consistent with the data in Fig. 3, which shows that MODEL 1 tends to over-estimate the ablation rate under oblique incidence at high fluence levels. For the deeper structure, a significant improvement is seen in the simulation based on the measured angular dependence. Use of the measured angular dependence also improves the overall simulation accuracy for the shallower structure, although in Photonics West 26 7/9

8 this case the improvement is less pronounced. Both simulation models showed unexpectedly large discrepancies in the regions near the edges of the shallower structure, for reasons which are not yet understood. 5. CONCLUSIONS We have investigated the angular dependence of the ablation rate in polycarbonate and SU8 under excimer laser exposure at both 248 nm and 139 nm wavelengths. The results suggest that the widely adopted model for angular dependence, in which the fluence F is simply replaced by Fcosθ inside the normal incidence etch function, is applicable only at lower fluences. At higher fluence levels, a model based on the assumption of constant ablation depth along the direction of propagation appears to give better agreement with experimental data. Further work is necessary to understand the observed angular dependence behaviour and to develop a self-consistent model that will make correct predictions over a wide range of fluences. This work was motivated in part by a desire to improve the accuracy of our multi-pulse ablation simulator, and we have demonstrated that, by using the measured angular dependence during simulation, closer agreement can be achieved between simulation and experiment, at least for deep polycarbonate structures machined at 248 nm wavelength. 6. ACKNOWLEDGEMENTS This work was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) and by the European Commission. Experiments were carried out using laser facilities kindly provided by Exitech Ltd. One of the authors, J.E.A. Pedder, is supported jointly by the EPSRC and Exitech Ltd. The authors would like to thank N. Sykes of Exitech Ltd for assistance with the equipment used for this work. 7. REFERENCES 1. Hirogaki T., Aoyama E., Inoue H. et al., Laser drilling of blind via holes in aramid and glass/epoxy composites for multi-layer printed wiring boards, COMPOSITES PART A-APPL. SCI. MANUFACT., vol. 32, no. 7, pp , Lee Y.C., Chen C.M., Wu C.Y., A new excimer laser micromachining method for axially symmetric 3D microstructures with continuous surface profiles, SENS. ACT. A-PHYS., vol. 117, no. 2, pp , Compaan A.D., Matulionis I., Nakade S., Laser scribing of polycrystalline thin films, OPTICS AND LASERS IN ENGINEERING, vol. 34, no. 1, pp , Booth H.J., Recent applications of pulsed lasers in advanced materials processing, THIN SOLID FILMS, vol. 453, pp , Sp. Iss. SI APR Hong G., Holmes A.S., Heaton M.E. and Pullen K.E., Design, fabrication and characterization of an axial-flow turbine for flow sensing, Proc. Transducers Conf., Boston, MA, 8 12 June, 23, pp Boehlen K.L., Stassen Boehlen I.B., Allott R.M., Advanced laser micro-structuring of super-large-area optical films, SPIE vol. 572, pp , Braun A., Zimmer K., Bigl F., Combination of contour and half-tone masks used in laser ablation, APPL. SURF. SCI., vol. 168, nos. 1-4, pp , Quentel F., Fieret J., Holmes A.S., and Paineau S. Multilevel diffractive optical element manufacture by excimer laser ablation using halftone masks, SPIE vol. 4272, pp , Paterson C., Holmes A.S., and Smith R.W., Excimer laser ablation of microstructures: a numerical model, J. APPL. PHYS., vol. 86, no. 11, pp , Onischekno A.I., George D.S., Holmes A.S., Otte F., Efficient pocketing simulation model for solid state laser machining and its application to a sol-gel material, SPIE vol. 5339, pp , Holmes A.S., Onischenko A.I., George D.S., Pedder J.E., Modelling of solid-state and excimer laser processes for 3D micromachining, SPIE Photonics West LASE 25, San José, CA, Jan. 25. Photonics West 26 8/9

9 12. Kahlert H.-J., Sarbach U., Burghardt B. And Klimt B., Excimer laser illumination and imaging optics for controlled microstructure generation, SPIE vol. 1835, pp , Hodapp T.W., Fleming P.R., Modeling topology formation during laser ablation, J. APPL. PHYS., vol. 84, no. 1, pp , Dyer P.E., Jenkins S.D., Sidhu J., Development and origin of conical structures on XeCl laser ablated polyimide, APPL. PHYS. LETT., vol. 49, pp , Jiménez J.R., Anera R.G., Jiménez del Barco L., Hita E., Pérez-Ocón F., Correction factor for ablation algorithms used in corneal refractive surgery with Gaussian-profile beams, OPT. EXPR., vol. 13, no. 1, pp , George D.S., Onischenko A., Holmes A.S., On the angular dependence of focussed laser ablation by nanosecond pulses in solgel and polymer materials, APPL. PHYS. LETT., vol. 84, no. 1, pp , Holmes A.S., Excimer laser micromachining with half-tone masks for the fabrication of 3-D microstructures, IEE PROC.-SCI. MEAS. TECHNOL., vol. 151, no. 2, pp , Dyer P.E., Karnakis D.M., Key P.H., et al., Excimer laser ablation for micro-machining: geometric effects, APPL. SURF. SCI., vol. 96-8, pp , Photonics West 26 9/9