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An Efficient Simulation System for Inclined UV Lithography Processes of Thick SU-8 Photoresists Zaifa Zhou, Qingan Hang, Senior Member, IEEE, Zhen Zhu, and Weihua Li, Member, IEEE
Abstract—A 2-D simulation system based on a 2-D dynamic cellular automata method, integrating aerial image simulation, exposure simulation, post-exposure bake simulation, and development simulation modules is presented for inclined ultraviolet (UV) lithography processes of thick photoresists such as SU-8 photoresists. To verify the simulation system, a series of experiments have been performed for SU-8 2000 series photoresists under UV source with 365 nm (2.6 mW/cm2 ) radiation. The simulation results demonstrate to be in agreement with the experimental results. This is useful to optimize the inclined UV lithography processes of SU-8 photoresists, and to accurately design and control the dimensions of some SU-8 microstructures. Index Terms—Inclined lithography, light intensity distribution, lithography simulation, microelectromechanical systems (MEMS), SU-8 photoresist.
I. Introduction FTER THE INITIAL report of inclined ultraviolet (UV) exposure scheme of thick photoresists [1], the inclined UV lithography of thick photoresists such as SU-8 photoresists is widely employed in microelectromechanical systems (MEMS) area to fabricate various microstructures effectively and economically [2]–[8], such as mixing microchannel [6], micro-optic components [7], and so on. The line width of the SU-8 microstructures varies from several micrometers to over 10 µm, compared with the designed line width, for different UV lithography conditions. Many complicated factors such as UV light distribution, exposure time and development time should be determined and optimized for the fabrication of various MEMS elements. It is not practical to determine the best fabrication parameters for the UV lithography processes of thick SU-8 using the traditional repeated experiment method. Simulation is widely acknowledged to be ideally suited for the optimization of lithography processes, since simulation is efficient to understand the fundamental effects of individual lithography step parameters. Although simulation software for the thin photoresist lithography processes has been
A
Manuscript received March 29, 2010; revised October 13, 2010; accepted December 20, 2010. Date of publication January 13, 2011; date of current version May 4, 2011. This work was supported by the National High Technology Program, under Contract 2007AA04Z342, and by the Innovation Foundation of Southeast University of China, under Contract 3206000501. The authors are with the Key Laboratory of MEMS of the Ministry of Education, Southeast University, Nanjing 210096, China (e-mail: zfzhou@seu. edu.cn;
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSM.2011.2105511
Fig. 1. Exposure schemes for (a) vertical and (b) inclined UV lithography processes.
commercialized [9]–[14], the lithography processes of thick SU-8 cannot be accurately implemented by the software specified for the thin photoresists, since the thick SU-8 has properties different from the thin photoresists. Recently, some attention has been paid to the conventional (vertical) UV lithography process simulations of thick photoresists [15]–[19]. Unlike the vertical UV lithography process, the UV light in inclined lithography has an arbitrary incident angle between 0° and 90° from the vertical line on the substrate, as shown in Fig. 1. Since the exposure schemes for vertical and inclined UV lithography processes are different, some models used for vertical UV lithography simulations cannot be directly adopted for the inclined UV lithography simulations. We have presented an aerial image model to estimate the patterned widths of the UV lithography process of thick SU-8 [20]. However, the accuracy of the simulation results is limited since only the UV light distribution can be considered and the light absorption coefficient of the SU-8 is assumed to be a constant during the whole exposure process in the aerial image model [20]. As the inclined UV lithography of thick SU-8 is increasingly utilized to produce MEMS elements, a more efficient and systematic simulation system for the inclined UV lithography processes of thick SU-8 are believed to be more interesting and informative. In this paper, we present a 2-D simulation system based on a 2-D dynamic cellular automata method [19], integrating aerial image simulation, exposure simulation, post-exposure bake (PEB) simulation, and development simulation modules for the inclined UV lithography processes of thick SU-8. A series of simulations for various lithography conditions have been conducted using the simulation system and the corresponding experiments have been implemented to verify the simulation
c 2011 IEEE 0894-6507/$26.00
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Fig. 3. Schematic diagram of the light distribution calculation for inclined UV lithography processes of thick SU-8.
Fig. 2. Basic steps for the inclined UV lithography processes of thick SU-8. (a) Exposure. (b) PEB. (c) Development.
results. All studies are carried out on SU-8 2000 series photoresists under UV source with 365 nm (2.6 mW/cm2 ) radiation. The results confirm the validity of the proposed simulation system and this is useful to accurately design and control the dimensions of some SU-8 microstructures. This paper is organized as follows. The basic process steps and the models for the inclined UV lithography processes of the SU-8 are introduced in Section II. The implementation of the simulation system based on the improved 2-D dynamic cellular automaton method is described in Section III, and the system structure is given. Comparisons, analysis, and discussions of the simulation and experimental results for the inclined UV lithography processes are given in Section IV. The conclusions are drawn in Section V. II. Inclined UV Lithography Models The inclined UV lithography of thick SU-8 includes three steps: exposure, PEB, and development, as shown in Fig. 2. During the first step, the SU-8 is exposed to the UV light, and the photoreaction initiator decomposes and generates an acid within the photoresist. For the subsequent PEB step, the photogenerated acid catalyzes the reaction between the resin and the cross-linking agent to produce a highly cross-linked polymer network which is significantly less soluble than the polymer resin without cross-linking reaction. In this way, the acid catalyzed cross-linking reaction determines the etching rate distribution within the photoresists. At last, the photoresist etching rate is determined by the extent of the cross-linking reaction during the PEB process, in terms of the normalized concentration of the cross-linked sites. Some photoresists will then be removed away in the development solution according to the corresponding etch rates to obtain the final photoresist profiles. The models for the inclined UV lithography include
aerial image simulation model, exposure simulation model, PEB simulation model, and development simulation model. A key aspect in the inclined UV lithography processes is that the incident UV is always reflected at the interface between the SU-8 and a substrate. The reflected UV will be transmitted into other unexposed SU-8, leading to the crosslinking reactions of these SU-8. So it is important to incorporate the effects of the reflected UV light, besides the diffraction and refraction effects, on the light intensity distribution into the SU-8, as illustrated in Fig. 3. The aerial image model for vertical UV lithography processes cannot be directly adopted for the incline UV lithography simulation for their different exposure schemes. The paraxial approximation approach, used for the modeling of vertical UV lithography, can also be employed for the modeling of inclined UV lithography. By transforming the axis direction to the direction of the inclined UV light and shifting the Fresnel number horizontally, the final equation incorporating diffraction, refraction, and reflection effects to calculate the total inclined UV light intensity distribution at point P (IP ) can be calculated using the “mask shifting method” [20], [21]. Following the equation formation for the vertical UV lithography of thick SU-8 [18], it can be expressed as IP = Ii + Ir (1 − R1 )Ilamp = · {[c(u2 ) − c(u1 )]2 + [s(u2 ) − s(u1 )]2 } 2 (1 − R1 )Ilamp + · R2 {[c(u4 ) − c(u3 )]2 + [s(u4 ) − s(u3 )]2 } 2 (1) 2(n /n ) 2 1 u2i = · (xi −x−(z − p1 +p2 ) λ1 (z − p1 + p2 )/ cos θ · tan θ)2 , i=1, 2 (2) u2i =
2(n2 /n1 ) · (xi −x−(2d + p1 −z + p2 ) λ1 (2d + p1 −z + p2 )/ cos θ i = 3, 4 (3) · tan θ)2 ,
where Ilamp is the original intensity of the incident UV light. Ii and Ir are the light intensities from the direct incident
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UV light and the reflected UV light by the SU-8/substrate u interface, respectively. c(u) = 0 cos(πy2 /2)dy and s(u) = u 2 0 sin(πy /2)dy are the Fresnel integrals, u(u1 and u2 ) are the Fresnel numbers. n1 and n2 are the refractive indices of air (n1 = 1) and SU-8 (n2 = 1.67), respectively. d represents the thickness of the SU-8 layer, p1 is the air gap between the photoresist and mask, and p2 is the distance between the photoresist and the image mask. The relationship between p2 and p1 is deduced to be p2 · n1 · cos δ = p1 · cos θ · n2 . R1 is the reflection coefficient at the air/SU-8 interface defined by δ − n2 / cos θ 2 δ − n2 cos θ 2 ) + ( nn11 cos ) )/2, and R2 is the R1 = (( n1n/1 cos cos δ + n2 cos θ cos δ + n2 cos θ reflection coefficient at the SU-8/substrate interface, dependent on the refractive index of the substrate n3 (n3 = 3.42 for silicon). The relationship among the UV light incident angle (δ), the refractive angle in SU-8 (θ), and the inclined angle α (to the horizon as shown in Fig. 3) of the obtained SU-8 photoresist structures are expressed as follows according to Snell’s law: θ = sin−1 (n1 sin δ/n2 )
(4)
α = 90° − θ.
(5)
According to (4) and (5), α will always be greater than 53° if the SU-8 is exposed in the air medium, for the limitation by the air/photoresist refraction. To overcome this limitation and fabricate SU-8 structures with smaller inclined angles, index matching materials such as glycerol (refractive index ∼1.6) or water (refractive index ∼1.33) can be adopted as exposure medium to correct the refraction effect [3], [6]. By using glycerol as index matching materials, the inclined angle of the SU8 structures can be reduced to about 19°. The simulation of the inclined exposure with index matching materials can also be implemented using this model, only by replacing the refractive index of air by that of the index matching material in (1)–(3). Based on the obtained inclined UV light intensity distribution into the SU-8, the exposure kinetics in the SU-8 can be implemented using exposure simulation models. However, the original Dill model [9] developed for thin photoresist lithography is insufficient to describe the nonlinear effects in the thick photoresists. Unlike the thin photoresists, the nonlinear effects in the thick photoresists, such as the concentration distribution of photoresist components, will significantly affect the exposure processes. In order to accurately describe these nonlinear effects, an improved Dill model [19] is developed to describe the exposure kinetics for vertical UV lithography of thick SU-8. The UV light runs across the SU-8 in an inclined optical path for inclined UV lithography, so the improved Dill model cannot be adopted for the inclined UV lithography simulation. Some modification to the improved Dill model is necessary to satisfy the requirements of inclined UV lithography simulation, as expressed as follows: ∂I(x, z, t) ∂z = −I(x, z, t)[A(z)m(x, z, t) + B(z)] αi (x, z, t) = A(z)m(x, z, t) + B(z) I(x, z, t) = I0 (x, z) · exp(− 0
l
αi (x, z, t)dz)
(6) (7) (8)
CA (x, z, t) = 1 − m(x, z, t)
(9)
where the SU-8 is divided into several layers, and αi is the absorption coefficient for the ith layer. I0 (x, z) is the light intensity from the aerial image simulation. m(x, z, t) and CA (x, z, t) denote the normalized photoacid generator concentration and photoacid concentration, respectively. z (µm) is the variable to indicate the photoresist depth (the distance from top to bottom of the SU-8 layer). l indicates the distance that the UV light passes through in the SU-8. Unlike the vertical UV lithography processes, l is a variable dependent on δ or θ for the inclined UV lithography processes. The Dill parameters vary with the photoresist thickness A(z) = i1 + i2 · z + i3 · z2 (µm−1 ), B(z) = j1 +j2 ·z+j3 ·z2 (µm−1 ), C(z) = l1 +l2 ·z+l3 ·z2 (cm2 /mJ). i1 , i2 , i3 , j1 , j2 , j3 , l1 , l2 , and l3 are the constants obtained by fitting experimental results using the conventional “Dill graphical method” [22]. For SU-8 2000 series photoresists, the values for these constants are fitted to be i1 = −0.0031, i2 = 4.7878 × 10−6 , i3 = −3.0860 × 10−9 , j1 = 0.0079, j2 = −7.5510 × 10−6 , j3 = 4.0971 × 10−9 , l1 = 0.0865, l2 = −1.3078 × 10−4 , and l3 = 6.1193 × 10−8 . During the PEB process, the photoacid, as a catalyst, induces chemical reactions which result in cross-linking of epoxy resin. The acid catalyzes ring opening of epoxies and turns them into cross-linked sites. In this way, SU-8 resin transfers from a low-molecular-weight material to a highly cross-linked 3-D network [22], [23]. Since the acid concentration is not uniform in the SU-8, there is an acid diffusion process while the catalytic conversion is undergoing. The chemical reactions and diffusion of species happen simultaneously and couple with each other, so they must be considered simultaneously during the PEB process simulation. The coupled reaction-diffusion kinetics [24] is believed to be sufficient to describe the PEB process for the SU-8. Since the reaction orders for photoacid and cross-linked sites are 1 for the lithography of SU-8, here the equations for the PEB simulation can be expressed by q ∂Ccs ∂t = k1 (1 − Ccs )CA (10) ∂CA ∂t = ∇ • (D ∇CA ) − k2 CA
(11)
where Ccs is the normalized concentration of the cross-linked sites where epoxy rings become open, and one cross-linked site is created when one epoxy ring is open. q is a fitting parameter, D is the photoacid diffusivity, k1 is the site cross-linking reaction coefficient and k2 is the photoacid loss reaction coefficient. The acid catalyzed cross-linking reaction determines the etch rate distribution within the SU-8, and the Notch Model [25] has been proved to be efficient to describe the relationship between the dissolution rate and cross-linked site concentration. The SU-8 development is depth dependent for highaspect-ratio microstructures, and the swelling effect will significantly affect the pattern edge size and the sidewall profiles of the SU-8 structures. Thus the above Notch Model, should be modified to incorporate the depth-dependent dissolution rate effect, and the swelling model should be adopted to obtain the final development profiles [18], [19].
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III. Simulation System Combining the above models and the surface movement algorithms for etching simulation, the inclined UV lithography processes of the SU-8 photoresists can be implemented. Currently, algorithms for etching surface movement including cell removal methods, string methods, the ray-tracing methods, level-set methods, the static cellular automata methods, and the dynamic cellular automata methods [19], [26]–[33] have been presented for lithography simulations. Though the cellular automata methods were slow and inefficiency in its original approach (static cellular automata method) [29], it becomes faster and more efficient when a dynamic memory allocation scheme is adopted (dynamic cellular automata method) [19], [33]. Furthermore, compared with other methods, the advantages of cellular automata methods for photoresist etching simulation also include the ease to handle topological changes and adaptive mesh methods. However, these are not the main reasons why we still carry on the inclined UV lithography simulation using dynamic cellular automata method. For example, the level-set methods are also very competitive in fabrication process simulation. We target on the dynamic cellular automata method for the implementation of the inclined UV lithography of thick SU-8 mainly for the following two reasons. First, increasing efforts have been poured into the research about structure analysis using the cellular automata method in MEMS design, so this makes the seamless link of fabrication process simulation and structure performance analysis possible [34]–[36]. Second, some researches to incorporate MEMS fabrication process simulation profiles, which are obtained using cellular automata methods, into the finite element analysis software are in progress in our laboratory [37]. The finite element analysis of some microstructures obtained by fabrication process simulations has been implemented, and this is believed to be attractive for related researchers in MEMS area. Currently, the performance of the original 2-D dynamic cellular automata method [29] has been further improved by using a novel time compensation value calculation method and novel update rules, and the improved 2-D dynamic cellular automata method have been used for the vertical UV lithography simulations [19]. Based on the improved 2-D dynamic cellular automata method, above mentioned aerial image simulation model, exposure simulation model, PEB simulation model and development simulation model have been extended to a 2-D simulation system for the inclined UV lithography of SU-8 photoresists. Fig. 4 shows the system structure of the simulation system. The simulation system is developed using C/C++ language based on Borland C++ Builder 6.0. After the initial conditions are specified and the process parameters are input, (1)–(3) are adopted to complete the aerial image simulation, to obtain the inclined UV light intensity distribution into the SU-8 for the following exposure simulation. The improved Dill simulation model as described by (6)–(9) are then used to describe the decomposition of the photoreaction initiator and generation of acids within the SU8 according to the light intensity distribution. After that, the PEB model is adopted to express the acid catalyzed crosslinking reaction and the acid diffusion in the SU-8. During
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Fig. 4. Simulation system structure for the inclined UV lithography process of thick SU-8.
the final development process, the etch rate distribution into the SU-8 is calculated by the Notch Model, and some SU-8 will be removed according to the etch rate distribution using the improved 2-D dynamic cellular automata method. The final development profiles can be visualized and output for analysis. IV. Simulations, Experiments, and Discussions To investigate the performance of the simulation system, a series of experiments and simulations have been performed using SU-8 2000 series photoresists under UV source with 365 nm (2.6 mW/cm2 ) radiation. Although the “hard contact” exposure method is employed in our experiments, the air gap between the mask and the SU-8 cannot be avoided during the exposure process, because it is not practical to prevent the nonuniformity of the resist surface and thickness derived from spin coating and soft baking [38]. In the following simulations, the air gap between the mask and the SU-8 is assumed to be 15 µm. A. Lithography Processes with Reflection Structures During the inclined UV lithography processes of the SU8, the incident UV light is reflected at the SU-8/substrate interface. The reflected UV light will be transmitted into other unexposed SU-8, usually creating reflected induced structures. Fig. 5 shows the simulation and experimental results of the inclined UV lithography processes on bare silicon wafer for 23.5° UV incident angle. The designed line/space of the SU8 structure is 50 µm/75 µm. The SU-8 was spin coated on 3 in diameter silicon wafers (thicknesses = 430±10 µm) to form photoresist layers with thickness of 140±12 µm. After exposing the SU-8 to the UV light for 240 s, the first step PEB condition was 65 °C/12 min and the second step PEB condition was 95 °C/35 min. Finally, the photoresist was developed in SU-8 developer for 12 min at 20 °C with ultrasonic agitation. Fig. 5(a) and (b) shows the simulated light intensity distribution into the SU-8 at the beginning and in the end of the exposure process, respectively. The simulated UV light intensity distributions reveal that the light absorption coefficient of the SU-8 will increase with the exposure time increases, leading to the decreases of the light intensity at the bottom of the SU-8 layer. In other words, the light absorption coefficient
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Fig. 5. Simulation and experimental results of the inclined lithography of the SU-8 for 23.5° UV incident angle with reflected UV on bare silicon wafer: exposure time = 240 s, development time = 12 min, line/space = 50/75 µm. (a) Predicted light intensity distribution at the beginning of the exposure process. (b) Predicted light intensity distribution at the end of the exposure process. (c) Simulation result. (d) Experimental result.
of the SU-8 is not a constant during the exposure processes. The reason lies in that the cross-linked polymer has higher absorption coefficient than the SU-8 before cross-linking. The results indicate that our aerial image model [20] is not accurate enough to estimate the development profiles of the SU-8, because the attenuation function of UV light intensity used in the aerial image model [20] assumes that the light absorption coefficient of the SU-8 is a constant during the whole exposure process. Since both the exposed and unexposed SU-8 is absorbing material, the reflected UV light will be absorbed when passing through the SU-8. For a normal exposure time, the energy of the reflected UV is relatively low to initiate full cross-linking of the SU-8. Thus the effects of the reflection are slightly observed at the bottoms of the SU-8 structures, as shown in Fig. 5(c) and (d). The largest line width variation between the experimental and simulation profiles in Fig. 5(c) and (d) is less than 1.72 µm. The inclined angle α of the SU-8 structure is also successfully predicted by the simulation system. Compared with the designed values by calculation using (4) and (5), the deviation of the measured inclined angle of the
simulation result is less than 1°. The experimental result also verifies the simulation result for this case, as shown in Table I. As the energy of the reflected UV light is increased enough, solid structures can be formed by the reflected UV light. The energy of the reflected UV light can be increased by extending exposure time or by using reflective substrates (Alcoated silicon wafer) [2]. Fig. 6 shows the simulation and experimental results with extended exposure time to form solid reflection structures on bare silicon wafer for 23.5° UV incident angle. Here the 140 ± 12 µm thickness SU-8 spin coated on 3 in diameter silicon wafers is exposed to the UV light for 600 s, and other lithography conditions are kept unchanged. As shown in Fig. 6, the solid reflection structures are successfully produced by extending the exposure time. The simulation result is in agreement with the experimental result, and the inclined angle α of the SU-8 structures is also predicted by the simulation system, as shown in Table I. Since more factors [including UV light distribution, exposure dose (time), PEB conditions, development time, and others] can be considered in this simulation system presented in this paper, the simulation accuracy has been increased, compared with
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Fig. 6. (a) Simulation result and (b) experimental result of the inclined UV lithography of the SU-8 under 600 s exposure on bare silicon wafer: development time = 12 min, line/space = 50/75 µm.
Fig. 7. Simulation and experimental results for 30° UV incident angle with TiO2 film as antireflection layer: exposure time = 240 s, development time = 12 min, line/space = 30/30 µm. (a) Predicted light intensity distribution. (b) Simulation result. (c) Experimental result.
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Fig. 8. (a) Simulation result and (b) experimental result of the inclined lithography of the SU-8 for 30° UV incident angle with TiO2 film as antireflection layer: exposure time = 240 s, development time = 12 min, line/space = 30/60 µm.
Fig. 9. (a) Simulation result and (b) experimental result of the inclined lithography of the SU-8 for 23.5° UV incident angle with TiO2 film as antireflection layer: exposure time = 240 s, development time = 12 min, line/space = 20/30 µm.
Fig. 10. Comparisons of the line width at different depths for SU-8 structures with different line/space and different development times.
[20]. Reference [20, Fig. 12] shows over 13.0% deviation of the bottom width between the experimental result and simulation result if the “threshold model” is adopted, while the largest line width variation between the experimental and simulation result in Fig. 6 is less than 1.96 µm (less than 4.0% deviation of the line width between the experimental and simulation results). B. Lithography Processes Without Reflection Structures Although the SU-8/substrate surface reflection can be employed for the fabrication of some novel microstructures, the
reflected induced patterns must be avoided for some other applications. Some antireflection materials (CK-6020L resist [3] or TiO2 ) should be employed to eliminate the wafer surface reflection. In our experiments, TiO2 film is used to absorbed UV light for antireflection purposes. Ti film was sputter-deposited on the top surface of the 3 in diameter glass wafers (thicknesses = 2600 µm), and then TiO2 film was formed by using heat treatment method or oxidation solutions. After that, 140 ± 12 µm thickness SU-8 was spin-coated on the TiO2 -coated glass wafers. Following the contact exposure for 240 s, the first step PEB condition was 65 °C/12 min and the second step PEB condition was 95 °C/35 min. Finally, the photoresist was developed in SU-8 developer at 20 °C with ultrasonic agitation. In this paper, the inclined UV lithography processes for different UV incident angles and line/space are investigated. Since the energy of the reflected UV can be neglected and the cross-linking reactions of SU8 can not be initiated, the effects of the reflection are not observed in the obtained SU-8 structures. Figs. 7 and 8 show the simulation and experimental results for the line/space of 30 µm/30 µm and 30 µm/60 µm with 30.0° UV incident angle, respectively. While the simulation and experimental results for the line/space of 20 µm/30 µm with 23.5° UV incident angle are shown in Fig. 9. The development time for Figs. 7–9 is 12 min. The simulation results demonstrate to be in good agreement with the experimental results for different cases, as shown in Figs. 7–9 and Table I. The largest line width variation between the experimental and simulation profiles in Figs. 7– 9 is less than 1.58 µm. The largest variation of the inclined angles between the simulation results and experimental results
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Fig. 11. (a) Simulation result and (b) experimental result for 30° UV incident angle with TiO2 film as antireflection layer: exposure time = 240 s, development time = 16 min, line/space = 30/30 µm.
TABLE I Inclined Angle α (to the Horizon) of the SU-8 Structures by Calculations Using (4) and (5), Simulations, and Experiments
useful to optimize the lithography process parameters and to predict the final development profiles. V. Conclusion
α Calculation (designed value) Simulation Experiment
Fig. 5 76.19°
Fig. 6 76.19°
Fig. 7 72.58°
Fig. 8 72.58°
Fig. 9 76.19°
Fig. 11 72.58°
76.69° 77.54°
77.01° 77.83°
72.79° 73.66°
72.90° 73.76°
76.91° 77.45°
73.02° 73.89°
is less than 1°. To efficiently evaluate and compare the simulation and experimental results in Figs. 7 and 8, the line width at different depth of the SU-8 structures was measured for both experimental results and simulation results, as shown in Fig. 10. The results reveal that the diffraction effect is enhanced with the decrease of the interval between two slits, leading to the line width of the SU-8 structure with line/space = 30/30 µm becomes a little bit larger than the SU-8 structure with line/space = 30/60 µm. Simulation and experimental results have demonstrated that, the SU-8 swelling during development will affect the size of pattern edges and sidewall profiles of the SU-8 microstructures [19], [38]–[40]. The swelling is assumed to result from the solvent molecules penetration into the cross-linked polymer in the exposed SU-8 produced by the acid catalyzed cross-linking reaction, so the diffusion length of the solvent molecules is related to the development time. To investigate the effects of development time, we have done some simulations and experiments for extended development time. Fig. 11 shows the simulation and experimental results for the line/space of 30 µm/30 µm, when the development time is extended to 16 min. The largest variation of the inclined angles between the simulation results and experimental results is less than 1°. The line width at different depth of the SU-8 structure for different development time was measured, as shown in Fig. 10. The results reveal that the line width of the SU-8 structure becomes larger with extended development time, and the simulation results are in agreement with the experimental results. The comparisons of experimental and simulations, resulting in a good agreement, indicate the accuracy and efficiency of the inclined UV lithography simulation system. The results reveal that appropriate process parameters are important to produce expected profiles, and numerical simulations are
An efficient 2-D simulation system based on the improved 2-D dynamical cellular automata method has been presented for the inclined UV lithography processes of thick SU-8 photoresists. A series of experiments have been designed and performed using 2000 series SU-8 to investigate the performance of the simulation system. The agreement of the simulation and experimental results indicates the effectiveness of our approaches. The simulation system is useful to optimize the process parameters for the inclined UV lithography of the SU-8 and to accurately design and control the dimensions of some SU-8 microstructures. Acknowledgment The authors would like to thank the Kayaku Microchem Company, Ltd., Tokyo, Japan, for providing some lithography parameters, Prof. D. Chen, J. Zhu, and Z. P. Ni for some experiments in the Key Laboratory for Thin Film and Microfabrication of the Ministry of Education, Shanghai Jiao Tong University, Shanghai, China. References [1] C. Beuret, G.-A. Racine, J. Gobet, R. Luthier, and N. F. de Rooij, “Microfabrication of 3-D multidirectional inclined structures by UV lithography and electroplating,” in Proc. IEEE MEMS, Jan. 1994, pp. 81–85. [2] M. Han, W. Lee, S. K. Lee, and S. S. Lee, “3-D microfabrication with inclined/rotated UV lithography,” Sens. Actuators, vol. A111, pp. 14–20, Jan. 2004. [3] K. Y. Hung, H. T. Hu, and F. G. Tseng, “Application of 3-D glycerolcompensated inclined-exposure technology to an integrated optical pickup head,” J. Micromech. Microeng., vol. 14, pp. 975–983, Jul. 2004. [4] Y. K. Yoon, J. H. Park, and M. G. Allen, “Multidirectional UV lithography for complex 3-D MEMS structures,” J. Microelectromech. Syst., vol. 15, pp. 1121–1130, Oct. 2006. [5] W. J. Kang, E. Rabe, S. Kopetzet, and A. Neyer, “Novel exposure methods based on reflection and refraction effects in the field of SU-8 lithography,” J. Micromech. Microeng., vol. 16, pp. 821–831, Jun. 2006. [6] H. Sato, D. Yagyu, S. Ito, and S. Shoji, “Improved inclined multilithography using water as exposure medium and its 3-D mixing microchannel application,” Sens. Actuators, vol. A128, pp. 183–190, Mar. 2006. [7] Z. Ling and K. Lian, “SU-8 3-D microoptic components fabricated by inclined UV lithography in water,” Microsyst. Technol., vol. 13, pp. 245– 251, Jan. 2007.
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[33] Z. F. Zhou, Q. A. Huang, W. H. Li, and W. Lu, “A novel 2-D dynamic cellular automata model for photoresist etching process simulation,” J. Micromech. Microeng., vol. 15, pp. 652–662, Mar. 2005. [34] P. Hajela and B. Kim, “On the use of energy minimization for CA based analysis in elasticity,” Struct. Multidisc. Optim., vol. 23, pp. 24–33, Jan. 2001. [35] E. Kita and T. Toyoda, “Structural design using cellular automata,” Struct. Multidisc. Optim., vol. 19, pp. 64–73, Mar. 2000. [36] Z. F. Zhou, Q. A. Huang, and W. H. Li, “Coupled fabrication process simulation and mechanical performance analysis of microstructures based on cellular automata,” in Proc. 5th IEEE Sensors, Oct. 2006, pp. 1061–1063. [37] F. J. Jian, “Study on interface between MEMS process simulation and finite element analysis (in Chinese),” M.S. thesis, Southeast Univ., Nanjing, China, Mar. 2009. [38] Y. J. Chuang, F. G. Tseng, and W. K. Lin, “Reduction of diffraction effect of UV exposure on SU-8 negative thick photoresist by air gap elimination,” Microsyst. Technol., vol. 8, pp. 308–313, Feb. 2002. [39] J. Hsieh, C. J. Weng, H. L. Yin, and H. H. Lin, “Realization and characterization of SU-8 micro cylindrical lenses for in-plane micro optical systems,” Microsyst. Technol., vol. 11, pp. 429–437, Jun. 2005. [40] Y. Luo, X. D. Wang, C. Liu, Z. F. Lou, D. N. Chu, and D. H. Yu, “Swelling of SU-8 structure in Ni mold fabrication by UV-LIGA technique,” Microsyst. Technol., vol. 11, pp. 1272–1275, Dec. 2005. Zaifa Zhou received the M.S. degree in electronic engineering from Southeast University, Nanjing, China, in 2004. He is currently working toward the Ph.D. degree from the Key Laboratory of MEMS of the Ministry of Education, Southeast University. His current research interests include ultraviolet lithography simulation of thick photoresists, low pressure chemical vapor deposition and reactive ion etch process simulation, silicon anisotropic etching simulation, and microstructure performance analysis for microelectromechanical systems based on fabrication process simulation. Qingan Huang (S’89–M’91–SM’95) received the B.S. degree from the Hefei University of Technology, Hefei, Anhui, China, in 1983, the M.S. degree from Xidian University, Shaanxi, China, in 1987, and the Ph.D. degree from Southeast University, Nanjing, China, in 1991, all in electrical engineering. His Ph.D. research concerned micromachined GaAs piezoelectric sensors. After graduation, he joined the faculty of the Department of Electronic Engineering, Southeast University, as an Assistant Professor. He became an Associate Professor in 1993, a Full Professor in 1996, and was specially awarded appointed Professor for Chang Jiang Scholar by the Ministry of Education in 2004. He was a Visiting Scholar with the Hong Kong University of Science and Technology, Kowloon, Hong Kong, in 1997. He has served as a Vice-Chairman with the Department of Electronic Engineering, Southeast University, since 1997, and is the Founding Director of the Key Laboratory of MEMS of Ministry of Education, Southeast University. He authored the book Silicon Micromachining Technology (Science Press, 1996), published over 80 peer-reviewed international journal/conference papers, and holds 25 Chinese patents. Dr. Huang was the winner of the Grade-I Natural Science Award of the Ministry of Education of China in 2002, and received the National Outstanding Youth Science Foundation Award. He has served as a reviewer for the following: Journal of Applied Physics, Applied Physics Letters, Journal of Micromechanics and Microengineering, Journal of Micro-ElectroMechanical Systems, IEEE Sensors Journal, Sensors and Actuators, and IEEE Electron Device Letters. He has served as the Editor-in-Chief of the Chinese Journal of Electron Devices and the Deputy Editor-in-Chief of the Chinese Journal of Sensors and Actuators. He served as the Conference Co-Chair for SPIE-Microfabrication and Micromachining Process Technology and Devices (vol. 4601, Nov. 2001) and a program member of the first five IEEE international conferences on sensors. He is currently serving on the Council for the National Plan of MEMS for the Ministry of Science and Technology of China.
ZHOU et al.: INCLINED UV LITHOGRAPHY PROCESSES OF THICK SU-8 PHOTORESISTS
Zhen Zhu received the B.S. and M.S. degrees in electronic engineering from Southeast University, Nanjing, China, in 2006 and 2009, respectively. He is currently with the Key Laboratory of MEMS of the Ministry of Education, Southeast University. His current major research interests include aerial image modeling for lithography simulations.
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Weihua Li (M’05) received the B.S. and M.S. degrees in electronic engineering from Southeast University, Nanjing, China, in 1982 and 1988, respectively. After graduation, he joined the Department of Electronic Engineering, Key Laboratory of MEMS of the Ministry of Education, Southeast University, as an Assistant Professor. He became an Associate Professor in 1997 and a Full Professor in 2003. He has published several books in China and holds four Chinese patents. His current research interests include the design of analog and digital IC, physics and technology of Si MOSFET, methodology of microelectromechanical systems design and computer-aided design, and semiconductor devices.
