Modelling of solid-state and excimer laser processes for 3D micromachining

Transcription

1 Modelling of solid-state and excimer laser processes for 3D micromachining Andrew S. Holmes, Alexander I. Onischenko, David S. George, James E. Pedder Department of Electrical and Electronic Engineering Imperial College London Exhibition Road, London SW7 2AZ United Kingdom ABSTRACT An efficient simulation method has recently been developed for multi-pulse ablation processes. This is based on pulseby-pulse propagation of the machined surface according to one of several phenomenological models for the lasermaterial interaction. The technique allows quantitative predictions to be made about the surface shapes of complex machined parts, given only a minimal set of input data for parameter calibration. In the case of direct-write machining of polymers or glasses with ns-duration pulses, this data set can typically be limited to the surface profiles of a small number of standard test patterns. The use of phenomenological models for the laser-material interaction, calibrated by experimental feedback, allows fast simulation, and can achieve a high degree of accuracy for certain combinations of material, laser and geometry. In this paper, the capabilities and limitations of the approach are discussed, and recent results are presented for structures machined in SU8 photoresist. Keywords: laser ablation; excimer laser, solid-state laser; modelling; simulation; MEMS; microstructures 1. INTRODUCTION Laser micromachining by ablation is an attractive process for advanced manufacturing, offering great flexibility both in terms of the variety of materials that can be machined and the range of structures that can be produced. In addition to more traditional applications such as hole and via drilling, patterning of thin films and laser marking, new applications have emerged in recent years, particularly in the areas of micro-fluidics and micro-optics, that require more sophisticated operations such as machining of complex surface profiles into bulk material [1-5]. There are two basic approaches to laser micromachining: mask projection and direct-write (DW). Mask projection is normally reserved for excimer lasers, where the pulse energy is high but the beam quality is poor. With this approach, and with a normal binary mask (zero or 100% transmission), material is removed to the same depth in all exposed regions. Stepped multi-level structures can be produced in this kind of system by indexed mask projection, which involves a sequence of exposures with different static masks. Furthermore, in the limit where each mask is in place for only one pulse, the step heights can be reduced to sub-micron level to produce surfaces with effectively continuously varying surface height. This is the basis of so-called synchronous image scanning (SIS) [5]. Alternatively, variable height surfaces can be produced by mask- or workpiece-dragging [6], or by static projection using a half-tone mask [7]. For other laser types, in particular solid-state lasers, the combination of lower pulse energy, higher pulse repetition rate (PRR) and enhanced beam quality, make the direct-write approach more appropriate. In this case a focused laser spot is scanned over the workpiece, following a predefined tool path. Direct-write is particularly well suited to prototyping because it allows rapid transfer of a design from computer to workpiece without requiring a mask. Regardless of approach, the cost of process development and optimisation can be a barrier for some potential users of laser processing. In addition to finding the correct laser wavelength, pulse energy, pulse duration and processing environment for the material in question, there is, for each new device or structure, the task of converting a CAD design into either a set of mask patterns or a tool path, together with a numerical control file for the mask and/or workpiece Photonics West /10

2 stages. This is non-trivial for all but the most straightforward designs, and normally involves a number of iterations of the complete process cycle, with measurements being made on finished parts to provide feedback for correcting the mask or tool path design. Recently at Imperial College London we have started developing ablation simulation tools with a view to simplifying and speeding up this design process. The aim is to provide simulators that can predict the result of a specified machining process, and thereby provide feedback for iterative correction of the mask design or tool path. A significant body of literature exists on modelling of laser ablation (see, for example, [8,9]). This work has been focused mainly on the fundamental mechanisms of the laser-material interaction, and largely confined to the study of single-pulse ablation events, except in the case of hole-drilling models [10]. The methods used in such studies are computationally intensive, and too slow for simulation of practical multi-pulse ablation processes. For this latter application, a less fundamental, more computationally efficient approach is required. We have developed a simulation method based on pulse-by-pulse propagation of the etched surface, using an etch function to describe the laser-material interaction [11,12]. The etch function may be experimentally determined, or derived from more fundamental modelling carried out off-line. This kind of approach has been used by others to explain geometrical effects observed in particular machining situations [13,14], but not as the basis for a general simulation framework. In this paper, we review details of the method as applied to projection and direct-write processes, and present the results of recent experiments carried out to assess its performance by comparison with test structures machined in SU8 photoresist Projection ablation model 2. PROJECTION ABLATION The effect of a given laser pulse on the workpiece depends on the fluence distribution it produces over the partially etched surface, and on the response of the material to that fluence distribution. In considering the material response we assume that the local etch depth per pulse is given by an etch function that depends only on the local fluence and the surface orientation; any modification of the response by geometrical effects such as plume confinement are not taken into account. More importantly, we ignore the presence of the structure itself when calculating the fluence distribution. This means that any contribution to the fluence due to reflections from other parts of the surface is ignored, as is the possibility that one region of the surface may lie in the shadow of another region. These assumptions drastically simplify the fluence calculation, while at the same time limiting the range of machining situations that can be handled. For example, the simulator cannot be expected to perform well in very deep, high aspect-ratio cavities. With the above assumptions, the simulation process can be divided into two distinct stages: calculation of the fluence distribution in the vicinity of the workpiece, which needs to be carried out only once at the start of the process, and pulse-by-pulse propagation of the surface. We will now consider each of these in turn. Calculation of fluence distribution Figure 1 shows a typical optical set-up in a commercial laser micromachining workstation, comprising beam-shaping optics, a fly s eye homogeniser and a projection lens. The homogeniser splits the beam into a large number of sourcelets (typically 6x6), each of which is projected onto the mask from a different direction with the aid of a condenser lens. Overlapping different portions of the beam in this way improves the uniformity of illumination at the mask plane, and also reduces the spatial coherence of the illumination which helps to reduce diffraction-related ringing effects. In higher numerical aperture systems, the homogeniser has a further important effect in that the off-axis illumination components can allow vertical or undercut sidewalls to be produced. If the workpiece is neglected, then the fluence distribution in the region around the image plane is readily calculated by a combination of standard imaging and beam propagation theory [11]. The complex amplitude in the image plane due to a given sourcelet may be written, apart from a scaling factor, as: Ui ( x, y) τ( mx,my) [ i( α x + β y) k] P( x, y) = exp i i (1) Photonics West /10

3 where τ(x,y) is the mask transmission function, m is the magnification of the projection lens, P(x,y) is the point spread function of the imaging system, α i and β i are the direction cosines of the sourcelet in the image space, and k=2π/λ where λ is the wavelength of the radiation. It is assumed in (1) that the sourcelet is at infinity in the image space and hence provides plane-wave illumination. To calculate the corresponding amplitude distribution outside the image plane, it is convenient to use the angular spectrum of plane waves corresponding to (1), which may be written as: Ai ( k,k ) = A ([ k α k],[ k β k] ) D( k, k ) x y 0 x i y i x y (2) where A 0 (k x,k y ) and D(k x,k y ) are the Fourier transforms of τ(mx,my) and P(x,y) respectively. The function D(k x,k y ) is the aperture function of the imaging system. Given A i (k x,k y ), the complex amplitude at a position (x,y,z) outside the image plane due to the same sourcelet can be calculated as: U x,y,z = A k,k exp i k x + k y k z dk dk (3) i ( ) i ( x y ) [ ( x y z )] x y + where k z satisfies k z 2 2 x 2 y = k k k. For an excimer laser, the different sourcelets in the homogeniser can be assumed to be mutually incoherent, allowing the total energy flux vector at any point to be expressed as: w Φ with i * * [ U U U U ] = Φ i i Φ i = i i i i (4) 2 ik The coefficients w i are (time dependent) weightings for the different sourcelets, which are normalised so that the total energy flux across the image plane is equal to the instantaneous power in the laser pulse. Similarly we can define a local fluence vector by integrating (4) with respect to time over the duration of the laser pulse, giving: 1 * * F with w dt [ U U U U ] = F i i F i i i i (5) ik i = i 2 pulse Beam shaper Homogeniser Mask Workpiece Sourcelets Condenser lens Field lens Projection lens Image plane Fig. 1. Typical optical set-up for projection ablation with an excimer laser. Surface propagation algorithm In considering the material removal rate we need to take into account the fact that the radiation incident on any part of the surface generally consists of multiple waves with varying angles of incidence. Currently we assume that, in this situation, the local etch depth per pulse is a function only of the total energy per unit area crossing the surface. This is a reasonable assumption if the ablation process is essentially photothermal, and one that has been used in previous work. Photonics West /10

4 Under this assumption, and ignoring any angular dependence in the reflectivity of the material, the local etch depth δn due to a given pulse may be written as: δ n = f F. nˆ (6) where f( ) is the usual material etch function or ablation curve (AC), measured at normal incidence, and nˆ is a unit inward normal to the surface. The etched surface may be propagated simply by displacing points on the surface according to (6), with each point moving in the direction of the local normal as illustrated in Fig. 2. Alternatively, points may be propagated along the z-direction to maintain a uniform mesh in x-y, in which case the propagation distance is δ z δn / ( nˆ ˆz ). Both of these approaches can be made to work robustly provided appropriate measures are taken to avoid instabilities. ( ) before pulse F δn n x y after pulse δz z Fig. 2. Surface propagation due to single laser pulse Calibration for SU8 In order to implement the above model, it is necessary to know the ablation curve of the material. We have made detailed measurements at 248 nm wavelength for cross-linked SU8 photoresist. A special half-tone mask was used comprising a series of rectangular apertures, each with a different transmission level. The etch depths in the resulting structure were measured using a stylus profilometer, and used to construct an ablation curve. The fluence at maximum transmission was determined by replacing the half-tone mask by a normal binary mask containing a single aperture of known area, and then measuring the pulse energy incident at the workpiece. The advantage of using a half-tone mask in this kind of measurement is that it eliminates the usual errors associated with varying the laser fluence by means of the high-voltage supply or an attenuator. The overall scaling of the different fluence levels is still subject to error because of the energy measurement, but their relative magnitudes are guaranteed to be correct. Fig. 3 shows the measured ablation characteristic obtained at a maximum fluence of 1 J/cm 2. The material is seen to display a classic Beer s law or logarithmic ablation characteristic for fluences above about 200 mj/cm 2. However, as for many polymer materials, the ablation rate at lower fluence levels is greater than predicted by the simple Beer s law model, and also there is no abrupt ablation threshold. A 5 th order polynomial function, shown as a bold line in Fig. 3, was found to give a close approximation to the ablation characteristic for fluences above 56 mj/cm Simulation of half-tone ablation in SU8 To test the validity of the model, a comparison was made between the surface shapes of simulated and experimental test structures machined in SU8. A half-tone test mask was designed specifically for his purpose, comprising a rectangular aperture with a variable transmission profile in one axis as shown in Fig. 4a. Details of the mask design and transmission function are contained in [7]. The profile was designed to produce structures with a range of depths and surface orientations, in addition to abrupt steps in surface height. Fig. 4b shows an example structure formed by an exposure of 600 pulses at 1 J/cm 2 fluence (100% transmission value). Laser machining was carried out using a commercial KrF excimer laser workstation with a 5X, 0.15 NA projection lens. The mask was illuminated by a 6x6 fly s eye homogeniser with an effective NA in the image space of The experimental profiles were extracted from SEM images with the aid of custom analysis software. Photonics West /10

5 Etch depth per pulse (microns) Experimental data (halftone mask) Beer's law fit Polynomial fit (5th order) Fluence (mj/sq.cm) Fig. 3. Measured SU8 ablation curve, together with Beer s law (logarithmic) and 5 th order polynomial best fit analytical approximations. Mask transmission (%) Position (mm) (a) (b) Fig. 4. (a) Mask transmission function of half-tone test mask, and (b) corresponding structure produced in SU8 by projection ablation at 248 nm wavelength (600 pulses at 1 J/cm 2 fluence). Figure 5 compares the experimental and simulated profiles for exposures of 200, 400, 600 and 800 pulses at a fluence of 1 J/cm 2. For the regions where experimental data could be obtained, the agreement between the simulated and experimental profiles is extremely good. For example, the percentage error in surface height, defined as 100*(h sim -h expt )/max{h sim }, lies within a ±8% band for all four structures, and within ±4% for the 600 pulse exposure. The simulator appears to over-estimate the etch rate slightly at intermediate depths, but to compensate for this in parts of the structure that are deeper and/or have steeper gradient. We believe this occurs because the assumptions contained in (6) about the angular dependence of ablation rate are not quite correct; this aspect requires further investigation. To Photonics West /10

6 date we have verified only that other factors, such as the uncertainty in the relative weightings of the homogeniser sourcelets, cannot explain the observed discrepancies. Fig. 5. Comparison of simulated (solid lines) and experimental (circles) surface profiles produced by different numbers of pulses at a fluence of 1 J/cm Direct-write ablation model 3. DIRECT-WRITE ABLATION Direct-write micromachining differs from projection ablation in that the ablation event accompanying each pulse is localised around a focal spot, rather than being distributed over the workpiece. The optical set-up tends to be relatively simple, typically comprising a beam expander, iris, scanner, and objective lens, as shown in Fig. 6. The desired structure is produced by scanning the laser spot over the workpiece according to a specified trajectory or tool path. Complex structures are usually built up layer-by-layer, with the workpiece height being adjusted to keep the machined surface at or near the focal plane. Raw s.s. laser beam Beam expander Iris Scanner (2-axis) Objective Workpiece Fig. 6. Typical set-up for direct-write laser micromachining with a solid-state laser. Photonics West /10

7 Because ablation always occurs at the focal spot, the ablation events due to successive pulses are expected to be broadly similar, at least in materials that ablate cleanly i.e. in a largely deterministic way. Based on this premise, the surface height s(x,y) may be propagated on the n th laser pulse according to the following simple algorithm: s ( x, y) s( x, y) + h( x x, y ) (7) n y n where h(x,y) is the shape of the ablation crater formed by a single laser pulse, which we refer to as the single shot crater (SSC), and (x n,y n ) is the lateral position of the laser spot at the time of the pulse. In (7) the surface height is taken to increase in the direction of propagation of the laser beam. In general the function h(x,y) may depend on the local gradient, surface morphology, or past exposure history. These effects may be incorporated into the simulation at the expense of simulation speed, which can otherwise be extremely fast. Modelling the single shot crater In general, prediction of the single shot crater shape is a complex problem, requiring both a physical model of the lasermaterial interaction, and knowledge of the spatial and temporal characteristics of the laser spot. Even with an appropriate model, this approach is of limited use as it requires direct measurement of the beam profile at focus. We have taken the more pragmatic route of measuring the SSC shape directly. This can be done easily using equipment that is available in most R&D labs. Fig. 7a shows an experimental SSC shape extracted from SU8 using a white light interferometer (Zygo New View 200). This crater was formed by a diode-pumped solid-state laser operating at 355 nm wavelength, with a pulse duration of around 20 nsec, a pulse energy of 20 µj, and a nominal spot diameter of 17 µm. Note that the depth axis is expanded, and the crater is actually much shallower than it is wide. (a) Y, microns relative error, % X, microns (c) 0 (b) Fig. 7. (a) Experimental single-shot crater in SU8 formed by ablation at 355 nm wavelength; (b) best-fit simulated crater assuming Gaussian laser spot and exponential ablation curve; (c) contour plot showing fitting accuracy. One issue with using a measured SSC directly in multi-pulse simulation is that any stochastic features in the crater are reproduced in an unrealistic way in the simulation output. For this reason, there is some merit in using an idealised crater shape that is in some sense a best-fit to the experimental crater. Stochastic effects can then be re-introduced during the simulation process. We have developed a simulator that can construct best-fit SSC shapes by combining standard forms for the laser fluence profile and the laser-material interaction. This fitting process works by assuming Photonics West /10

8 that the local etch depth in the crater can be related directly to the local fluence F(x,y) through an ablation curve f( ). Under this local dependence assumption (LDA), the crater shape can be written as: ( x, y) f ( F( x, y) ) h = (8) The LDA assumption in (8) is physically reasonable when thermal diffusion is low on the timescale of the laser pulse, as is expected for polymer machining by nanosecond pulses. Fig. 7b shows a best-fit SSC for the experimental crater in Fig. 7a, assuming an ablation curve of the form f(f) = α -1 exp[-γ ln(f/f th )/(F/F th 1)] and a Gaussian fluence profile. Fig. 7c shows a map of the fitting error as a percentage of the maximum simulated crater depth, which remains below 10% except near irregularities in the experimental crater. Crater interactions A further advantage of using idealised craters is that the SSC can be modified in a systematic way to account for factors such as surface gradient or exposure history by modification of the ablation curve. For example, SU8 shows evidence of memory effects when machined at 355 nm, with the SSC becoming larger when there has been prior exposure near to the current site. An important practical consequence of this is that simulations based on an unmodified SSC generally under-estimate the depths of machined structures. The origin of this effect is still unknown, although it probably arises from transient heating of the surface, or from permanent modification of the material in the heat affected zone of the earlier pulses. We have found that crater interactions of the kind outlined above can be accounted for in a phenomenological way by locally reducing the threshold fluence by an amount that depends on the distance η from the location of the previous pulse. For example, Fig. 8 shows a Zygo plot of a trench machined by a series of pulses on a 5 µm pitch, together with cross-sections showing the experimental profile (line 1), a simulation using an unmodified SSC (line 2), and a simulation in which the threshold fluence is modified according to the trial function F th (η) = F th ( )[1 a 1 exp(-η 2 /a 2 2 )], with a 1 = 0.8 and a 2 = 12 µm. An important point here is that, provided the function F th (η) is chosen correctly and calibrated on an appropriate test structure, it should not require re-calibration when the pulse-to-pulse separation is adjusted. (a) (b) Fig. 8. (a) Calibration trench formed in SU8 using same laser parameters as for Fig. 7. Crater spacing is 5 µm. (b) Cross-sectional profiles of 1-experimental trench, 2-simulated trench ignoring interactions, and 3-simulated trench including interactions Simulation of complex direct-write structures in SU8 We have tested our DW simulator on more complex designs such as the one shown in Fig. 9. This structure, which comprises a stepped pyramid inside a square cavity, requires a total of 53,000 laser pulses, and can be simulated in around 10 seconds on a 1.2 GHz IBM-compatible personal computer. While this is longer than the time taken to fabricate the structure (approx 3.5 secs at 15 khz PRR), it is considerably shorter than the time taken to make measurements of the surface shape, as would be required to provide feedback for correction of the tool path. Photonics West /10

9 (a) (b) Fig. 9. Panoramic views of (a) simulated and (b) fabricated pyramid structures. Fig. 10 shows a cross-section through the experimental structure of Fig. 9 (line 1), compared to simulated cross-sections ignoring and including crater interactions (lines 2 and 3 respectively). The surface height error for the latter is within a ±10% band over 80% of the surface. While already good enough to provide useful information for tool path generation, this needs further improvement. The errors around the perimeter of the structure, near the base of the bounding wall, are thought to be due mainly to problems with the Zygo measurement. However, the simulator also over-estimates the height of the first step at the top of the pyramid, and the reason for this is currently unclear. Fig. 10. Cross-sectional profiles of 1-experimental structure, 2-simulation ignoring interactions and 3-simulation including interactions. 4. CONCLUSIONS We have been developing software tools for simulation of projection ablation and direct-write laser micromachining. These are based on pulse-by-pulse propagation of the machined surface, using a parameterised model for the lasermaterial interaction that may be calibrated either by more fundamental physical modelling or by experiment. The long term aim is to provide simulators that can give quantitative feedback for use in the iterative design of mask sets or tool paths. Such simulators would reduce the requirement for prototyping, and hence lower the cost of process development. Fast simulation is essential for this kind of application, and consequently the models we have developed contain a large number of simplifying assumptions. Nevertheless, as the SU8 results presented here indicate, they are capable of Photonics West /10

10 making predictions that are sufficiently accurate to be useful in mask or tool path design. Future refinements in the short term are likely to include proper provision for angular dependence of the ablation rate, and treatment of stochastic effects such as the development of surface roughness during the machining process. 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. REFERENCES 1. J.P.H. Burt, A.S. Goater, C.J. Hayden, J.A. Tame, Laser micromachining of biofactory-on-a-chip devices, SPIE vol. 4637, pp , W. Pfleging, W. Bernauer, T. Hanemann, M. Torge, Rapid fabrication of microcomponents UV-laser assisted prototyping, laser micro-machining of mold inserts and replication via photomolding, Microsyst. Technol., 9, pp , A.S. Holmes, G. Hong, K.R. Pullen, K.R. Buffard, Axial-flow microturbine with electromagnetic generator: design, CFD simulation and prototype demonstration, Proc. MEMS 2004, 17 th IEEE Int. Conf. on MEMS, Maastricht, The Netherlands, Jan 2004, pp A. Braun, K. Zimmer, B. Hösselbarth, J. Meinhardt, F. Bigl, R. Mehnert, Excimer laser micromachining and replication of 3D optical surfaces, Appl. Surf. Sci., , pp , K.L. Boehlen, I.B. Stassen Boehlen, Laser micromachining of high-density optical structures on large substrates, SPIE vol. 5339, pp , N.H. Rizvi, P.T. Rumsby, M.C. Gower, New developments and applications in the production of 3D microstructures by laser micro-machining, SPIE vol. 3898, pp , A.S. Holmes, Excimer laser micromachining with half-tone masks for the fabrication of 3D microstructures, IEE Proc. Sci. Meas. & Technol., 151(2), pp , N. Bityurin, A. Malyshev, Bulk photothermal model for laser ablation of polymers by nanosecond and subpicosecond pulses, J. Appl. Phys., 92, pp , S. Tosto, Modeling and computer simulation of pulsed-laser-induced ablation, Applied Physics A: Materials Science & Processing, 68, pp , V.N. Tokarev, J. Lopez, S. Lazare, F. Weisbuch, High-aspect-ratio microdrilling of polymers with UV laser ablation: experiment with analytical model, Applied Physics A: Materials Science & Processing, 76, pp , C. Paterson, A.S. Holmes, R.W. Smith, Excimer laser ablation of microstructures a numerical model, J. Appl. Phys., 86(11), pp , A.I. Onischenko, D.S. George, A.S. Holmes, F. Otte, Efficient pocketing simulation model for solid state laser machining and its application to a sol-gel material, SPIE vol. 5339, pp , H.J. Kahlert, U. Sarbach, B. Burghardt, B. Klimt, Excimer laser illumination and imaging optics for controlled microstructure generation, SPIE vol. 1835, pp , P.E. Dyer, D.M. Karnakis, P.H. Key, P. Monk, Excimer laser ablation for micro-machining: geometric effects, Appl. Surf. Sci., 96(8), pp , Photonics West /10