pubs.acs.org/Langmuir © 2010 American Chemical Society
Understanding Pattern Collapse in Photolithography Process Due to Capillary Forces S. Farshid Chini and A. Amirfazli* Department of Mechanical Engineering, University of Alberta Edmonton, AB T6G 2G8, Canada Received April 16, 2010. Revised Manuscript Received June 17, 2010 Photolithography is the most widely used mass nanoproduction process. Technology requirements demand smaller nanodevices. However, smaller features risk collapse during the drying of rinse liquid because of capillary forces. In the present study, progress is made on two fronts: (i) The importance of surface tension force (STF) on three-phase line on the pattern collapse is investigated. The STF was ignored in previous pattern collapse studies. It is found that inclusion of STF increases the pattern deformation. The calculated deformation error from neglecting STF increases by increasing contact angle, pattern height to width ratio, and trough to width ratio. The deformation error decreases with an increase in elasticity module of pattern. (ii) A more accurate representation for the interface curvature (and related Laplace pressure), that is, using Surface Evolver (SE) simulation rather than cylindrical interface model (CIM), is presented. Curvature values of two-line parallel and box-shaped patterns are derived from SE and compared with the curvature values from CIM. It was found that CIM for the case of two-line parallel overestimates the curvature value and for the case of box-shaped underestimates it. SE simulations also showed that the error of calculating curvature values using CIM for both shapes is only a function of LAR (ratio of pattern length to trough width). For LAR values less than 20, the curvature values from CIM are not accurate for calculating pattern deformation.
1. Introduction One of the problems during manufacturing of micro- and nanofeatures using photolithography is the collapse of features, the so-called “pattern collapse”. Pattern collapse is the lasting deformation (any or combination of bending, breaking, tearing, or peeling) of features due to unbalanced capillary forces. Pattern collapse is observed in microprocessor, MEMS, and NEMS manufacturing during drying the rinse liquid. Factors affecting pattern collapse can be categorized into three groups: (i) pattern’s geometry, (ii) rinse liquid and its related capillary forces, and (iii) pattern’s material. Each of these three categories is represented by few parameters in a model (e.g., pattern height can be one of the parameters in the geometry category). A comprehensive pattern collapse model should consider all parameters affecting the pattern deformation. By studying parameters of these three categories, we will show that the literature models lack two parameters affecting the deformation of isolated two-line parallel patterns. (See Figure 1.) By including these two parameters, we developed a new (more accurate) model to simulate the pattern collapse. 1.1. Pattern’s Geometry. In most cases, pattern’s geometry is dictated by the design requirements. As such, studying pattern’s geometry will guide one to determine if for a given geometry, to avoid pattern collapse, there is a need to change other factors such as the rinse liquid or the pattern’s material. To date, the basic geometrical parameter, affecting the pattern deformation, has been the pattern’s aspect ratio (AR, i.e., H/w; see Figure 1 for definition of H and w). Literature models have shown that manufacturing of denser features results in a higher AR value and a higher possibility of collapse (e.g., ref 1). In this study, a new geometrical parameter affecting the pattern collapse *Corresponding author. E-mail:
[email protected]. Tel: (780) 4926711. Fax: (780) 492-2200. (1) Yoshimoto, K.; Stoykovich, M. P.; Cao, H. B; de Pablo, J. J.; Nealey, P. F.; Drugan, W. J. J. Appl. Phys. 2004, 64, 1857–1865.
Langmuir 2010, 26(16), 13707–13714
is defined as the longitudinal aspect ratio (LAR, i.e., L/d; see Figure 1). The need for defining LAR in analysis of pattern deformation analysis is discussed in brief in the next subsection and in details in Section 3. 1.2. Rinse Liquid and Its Related Capillary Forces. To date, the rinsing liquid and its related capillary forces have been considered only in the context of the Laplace pressure, ΔP.2-12 It should be noted that for the cases that patterns are completely surrounded by liquid, the lateral capillary meniscus interaction force is also operative on the patterns.13 Lateral capillary meniscus interaction is attraction of two particles floating on a liquid. For the cases studied in this study, patterns are not surrounded by liquid, so lateral capillary meniscus interaction force does not exist. Also, even if lateral capillary meniscus interaction force was operative on the pattern, it was negligible compared with the Laplace pressure and surface tension force (STF).14 Laplace pressure in case of pattern collapse is the pressure difference across the liquid-air interface, shown in Figure 1, and is a function of rinse liquid surface tension (γ) and rinse (2) Yamashita, Y. Jpn. J. Appl. Phys. 1996, 35, 2385–2386. (3) Tanaka, T.; Morigami, M.; Atoda, N. Jpn. J. Appl. Phys. 1993, 32, 6059– 6064. (4) Cao, H. B.; Nealey, P. F. J. Vac. Sci. Technol., B 2000, 18, 3303–3307. (5) Kortera, M.; Ochiai, N. Microelectron. Eng. 2005, 78-79, 515–520. (6) Lee, H.-J.; Park, J.-t.; Yoo, J.-y.; An, I.; Oh, H.-K. Jpn. J. Appl. Phys. 2003, 42, 3922–3927. (7) Jincao, Y.; Matthews, M. A.; Darvin, C. H. Ind. Eng. Chem. Res. 2001, 40, 5858–5860. (8) Namutsu, H. J. Vac. Sci. Technol., B 2001, 19, 2709–2712. (9) Namatsu, H.; Yamazaki, K.; Kurihara, K. Microelectron. Eng. 1999, 46, 129–132. (10) Junarsa, I.; Stoykovich, M. P.; Yoshimoto, K.; Nealey, P. F. Proc. SPIE 2004, 5376, 842–849. (11) Jung, M.-H.; Lee, S.-H.; Kim, H.-W.; Woo, S.-G.; Cho, H.-K.; Han, W.-S. Proc. SPIE 2003, 5039, 1298–1303. (12) Tanaka, K.; Naito, R.; Kitada, T.; Kiba, Y.; Yamada, Y.; Kobayashi, M.; Ichikawa, H. Proc. SPIE 2003, 5039, 1366–1381. (13) Chandra, D.; Yang, S.; Soshinsky, A. A.; Gambogi, R. J. ACS Appl. Mater. Interfaces 2009, 1, 1698–1704. (14) Chandra, D.; Yang, S. Langmuir 2009, 25, 10430–10434.
Published on Web 07/20/2010
DOI: 10.1021/la101521k
13707
Article
Chini and Amirfazli Table 1. Surface Tensions and Contact Angles of Surfactant Solutions from Jung et al.11 a surfactant solution
Figure 1. (a) Schematic of an isolated two-line parallel pattern with rinse liquid in between. (b) Depicts the worst case scenario when neighboring spaces are free of any liquid.
interface curvature as
1 1 þ ΔP ¼ γ R1 R2
ð1Þ
where R1 and R2 are the principal radii of curvature at a point on the interface. To date, in pattern collapse studies, the rinse liquid interface is modeled simply with a cylindrical shape (e.g., refs 1 and 3-6). As such, ΔP is described as 2γ cos θ ð2Þ d Equation 2 reveals that variables related to rinse liquid and its related capillary forces are: the distance between two adjacent patterns (trough width, d, see Figure 1), γ and the contact angle (θ). It should be noted that θ in eq 2 is the equilibrium contact angle. However, receding contact angle,15 which may not be exactly equal to the equilibrium contact angle, is a more relevant value. As will be shown, the validity of the cylindrical shape assumption for the rinse interface (or eq 2) depends on the value of LAR. On the basis of literature models, selection of a rinse liquid with a small γ and large θ, to lower the capillary force, seems useful. (See eq 2.) Jincao et al.7 used a rinse liquid with low γ to decrease the Laplace pressure, but their rinse liquids have low solubility and other limitations, as stated in ref 7. Supercritical8,9,16-20 and freezedryings21 are processes with no or very low surface tension effects but are costly and have process limitations. Adding surfactant at concentrations near the critical micelle concentration (CMC) is another way of decreasing γ to improve pattern collapse.10-12 However, surfactants interact with patterns and can melt or cause them to dissolve. Drechsler et al.22 showed that at a one-tenth of CMC of cationic surfactants, θ increases by 10 with a slight change of γ.22 Increasing the θ is desirable for decreasing the Laplace pressure (see eq 2), and damage to the pattern due to surfactant concentration was minor. In this study, another contributor to capillary forces other than Laplace pressure will be included, that is, the horizontal projection of STF. STF is a concentrated force (CF) operating on the three-phase line. Three-phase line is where three bulk phases of solid, liquid, and gas meet. The STF is different from Laplace pressure and should be considered in the pattern collapse analysis. ΔP ¼
(15) Erbil, H. Y.; McHale, G.; Newton, M. I. Langmuir 2002, 18, 2636–2641. (16) Goldfarb, D. L.; De Pablo, J. J.; Nealey, P. F.; Simons, J. P.; Moreau, W. M.; Angelopoulos, M. J. Vac. Sci. Technol., B 2000, 18, 3313–3317. (17) Namutsu, H. J. Vac. Sci. Technol., B 2000, 18, 3308–3312. (18) Felix, N. M.; Tsuchiya, K.; Ober, C. K. J. Adv. Mater. 2006, 18, 442–446. (19) Simons, J.; Goldfarb, D.; Angelopoulos, M.; Messick, S.; Moreau, W.; Robinson, C.; Pablo, J. D.; Nealey, P. Proc. SPIE 2001, 4345, 19–29. (20) O’Neil, A.; Watkins, J. J. MRS Bull. 2005, 30, 967–975. (21) Tanaka, T.; Morigami, M.; Oizumi, H.; Ogawa, T. Jpn. J. Appl. Phys. 1993, 32, 5813–5814. (22) Drechsler, A.; Petong, N.; Bellmann, C.; Synytska, A.; Busch, P.; Stamm, M.; Grundke, K.; Wunnicke, O. Can. J. Chem. Eng. 2007, 84, 3–9.
13708 DOI: 10.1021/la101521k
surface tension (mN/m)
contact angle (degree)
ΔP/ΔPwater (%)
FSTF/ FSTF(water) (%)
A 22 12.5 96 7 B 20 54.7 52 24 C 21 53.5 56 25 a Capillary forces, that is, horizontal projection of STF and Laplace pressure, are normalized with respect to the values for water, that is, FSFT(water) and ΔPwater, respectively.
The STF is not an unknown quantity in other areas of application. Extrand and Kumagai23 using sessile drops placed on soft flat surfaces showed that the STF is of such magnitude that it can deform the surface (in the shape of a ridge) at the three-phase line. However, understanding and inclusion of the STF in pattern collapse study has been lacking. 1.2.1. Importance of Considering STF. To clarify the importance of considering the STF in pattern collapse, an order of magnitude comparison is performed between forces originated by Laplace pressure and STF. For simplicity, the comparison is performed for the case of cylindrical interface shape. Laplace pressure is exerted on the pattern’s side wall, so the force produced by Laplace pressure is 2γLH cos θ ð3Þ d STF is operative on the three-phase line of length L for the cylindrical interface (Figure 1), so the force generated by STF is Fpressure ¼
FSTF ¼ γL
ð4Þ
The ratio of the force originated by Laplace pressure to STF force is Fpressure 2H cos θ ¼ d FSTF
ð5Þ
Because H and d have the same order of magnitude, the STF is as important as Laplace pressure. An experimental example is provided to show the need for considering the effect of the STF on pattern deformation. Jung et al.11 prepared pattern with different dimensions (all line and space shape patterns) and filled the patterns’ troughs with water and changed the contact angle and surface tension by adding different surfactants to the water. In Table 1, pressure differences across the rinse liquid interface (Laplace pressure) for three of their surfactant solutions are shown. It is observed that Laplace pressure is higher when liquid is solution A (compared with solutions B and C). Therefore, considering the Laplace pressure as the only operative factor, maximum deformation should occur in the presence of solution A. Experimentally, however, Jung et al.11 observed that the lowest pattern deformation happens in the presence of solution A (compared with solutions B and C), unlike as predicted by Laplace pressure value alone. We calculated the horizontal projections of STFs for three different solutions using contact angle and surface tension values. (See Table 1.) It is observed that the horizontal projection of the STF is very small for solution A (compared with solutions B and C). Regarding Table 1, it should be noted that Laplace pressures are normalized by dividing them to Laplace pressures if the liquid was DI water. Horizontal projections of the STFs are also normalized by dividing them to the STF if the liquid was DI water. 1.3. Pattern’s Material. The effect of pattern’s material on the pattern deformation has been considered through (i) the (23) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1996, 184, 191–200.
Langmuir 2010, 26(16), 13707–13714
Chini and Amirfazli
Figure 2. (a) Surface tension forces at three phase line are shown. Horizontal projection of liquid-vapor phase surface tension (γLV) exerts a force on the pattern’s side wall. (b) Case of a flat interface (ΔP = 0) where γLV exerts a force on the pattern’s side wall. γLV, γSV, and γSL are liquid-vapor, solid-vapor, and liquid-solid surface tensions, respectively.
interaction of the pattern’s material and rinse liquid as manifested by θ and (ii) the modulus of elasticity for the pattern’s material (E ). However, yield stress,1 adhesion to the substrate,24-26 and swelling probability27 are other parameters that are not considered in this study and may be considered in future models. A proper material to decrease the pattern deformation is the one with a large E. However, such material with the ease of process implementation is not readily available or economical.1,3-6 Instead of changing the pattern’s material, one may change the stiffness of the existing pattern, for example, heating during rinsing, adding nanoparticles to form nanocomposites,28 flood exposing the patterns,29 and using sidewall profiles30,31 and buttressed zone plates.32 Application of the above methods is still uneconomical for mass production. In this article, a new model for predicting the pattern deformation is developed. Two parameters, that is, (i) STF and (ii) LAR are introduced in the analysis of pattern collapse. STF will be added to the existing analytical models, and pattern deformation will be analyzed. (Analysis is limited to the specific case of a twoline parallel pattern.) LAR is defined as a parameter to show the accuracy and limits for applicability of the cylindrical interface model (CIM) for calculating Laplace pressure. (Surface Evolver33 is applied to find the accuracy of CIM.) Using the newly developed model, effects of changing pattern’s material, pattern’s geometry, and rinse liquid on pattern deformation are studied.
2. Pattern Collapse Modeling Patterns are assumed to be two-line parallel patterns; the space between them is filled with the rinse liquid. To represent the worst case scenario, it is assumed that the described system is surrounded by a gas phase, and there is no rinse liquid outside the two-line parallel pattern. (See Figure 1.) Patterns are also modeled as simple clamped cantilever beams, and beam sway model of Deguchi et al.34 is applied for pattern deformation analysis. (See Figure 3.) For now, cylindrical shape is assumed for the rinse interface shape (similar to other literature, e.g., ref 3), and the next (24) Sanada, M.; Tamada, O.; Ishikawa, A.; Kawai, A. Proc. SPIE 2005, 5753, 988–995. (25) Kim, S.-K.; Jung, M.-H.; Kim, H.-W.; Woo, S.-G.; Lee, H. J. Nanotech. 2005, 16, 2227–2232. (26) Kawai, A. Proc. SPIE 1999, 3677, 565–573. (27) Kim, S.-K. J. Korean Phys. Soc. 2003, 42, S371–S375. (28) Shibata, T.; Ishii, T.; Nozawa, H.; Tamamura, T. Jpn. J. Appl. Phys. 1997, 36, 7642–7645. (29) Tanaka, T.; Morigami, M.; Oizumi, H.; Ogawa, T.; Uchino, S. Jpn. J. Appl. Phys. 1994, 33, L1803–L1805. (30) Choi, C.-H.; Kim, C.-J. J. Nanotechnol. 2006, 17, 5326–5332. (31) Fujikawa, Sh.; Takakai, R.; Kunitake, T. Langmuir 2006, 22, 9057–9061. (32) Olynik, D. L.; Harteneck, B. D.; Veklerov, E.; Tendulkar, M.; Liddle, J. Al.; Kilcoyne, A. L. D.; Tyliszcak, T. J. Vac. Sci. Technol., B 2004, 22, 3186–3190. (33) Brakke, K. A. Surface Evolver. Susquehanna University, PA; www.susqu.edu/ facstaff/b/brakke/evolver (accessed Sept 5, 2007). (34) Deguchi, K.; Miyoshi, K.; Ishii, T. Jpn. J. Appl. Phys. 1992, 31, 2954–2958.
Langmuir 2010, 26(16), 13707–13714
Article
Figure 3. Schematic of additive nature of the STF and Laplace pressure on the pattern deformation. Superposition assumptions are: (i) loads remain horizontal, (ii) elastic deformation (maximum stress is less than yield stress), and (iii) deformation with respect to height is very small.32
section defines the collapse criterion used based on this assumption. (See Section 4 for relaxing this assumption.) Lasting deformation is basically the definition of pattern collapse and occurs in two cases: (i) patterns (partly or completely) undergo the plastic deformation and (ii) elastic deformation causes sticking of tips of adjacent patterns. (Elastic deformation before sticking of pattern tips is not generally problematic.) For the following reason, the second case is more expected. Complete removal of the residue photoresist form the substrate after acid etching requires weaker bonding between photoresist and substrate (adhesion) compared with the bonding within the photoresist (cohesion). Furthermore, the maximum stress on the photoresist occurs at its base, where adhesion force is operative.3 As a result, in most of the cases, photoresist will be peeled off from the substrate before the base experiences plastic deformation. Therefore, simply here plastic analysis is not performed. The deformation mechanism of pattern is studied by comparing cohesive and restoring forces (first used by Tanaka et al.,3 but consideration of the STF was missing in their model). A simple example of cohesive and restoring forces is a spring being stretched. Cohesive force is the force exerted on the spring, and restoring force is its resistance force against stretching. At the equilibrium state, both restoring and cohesive forces are equal. Cohesive force in the case of the pattern collapse problem is composed of the Laplace pressure (ΔP) and horizontal projection of STF (Fx); see Figure 3. With increasing pattern deformation, ΔP increases and Fx remains almost unchanged. In elastic region, restoring force linearly increases with deformation. At the equilibrium, cohesive and restoring forces cancel each other. As such, the deformation can be calculated by mathematically setting the cohesive and restoring forces equal. During pattern deformation, Laplace pressure and horizontal projection of STF rotate as they remain perpendicular to the pattern. The current analytical model is unable to consider the force rotation. The force rotation can be combined by using a Finite Element model of the system.
3. Pattern Deformation Model: Inclusion of STF The STF can be understood by considering the Young equation (eq 6) at the three-phase line γSL - γSV ¼ γLV cos θ
ð6Þ
where γSL, γSV, and γLV are surface tensions of solid-liquid, solid-vapor, and liquid-vapor interfaces, respectively. Considering Figure 2a and eq 6, the horizontal force resulting from the normal component of STF to the pattern’s side wall acts as a CF along the three-phase line. The STF is not considered in previous pattern collapse studies, and a new term (in this context), STF deformation (δ2), should be added to deformation due to Laplace pressure (δ1). Also, as will be shown, considering the STF causes an indirect increase in DOI: 10.1021/la101521k
13709
Article
Chini and Amirfazli
Laplace pressure deformation, for example, deformation in models similar to that in ref 3. 3.1. Analytical Model for Calculation of δ2. Because the slope of the feature hardly changes as a result of pattern deformation, the cohesive force due to STF (Fx) remains almost constant as Fx ¼ γL sin θ
ð7Þ
Restoring force of a pattern (modeled as a beam) due to any CF as a function of deformation (δCF) is35 CF ¼
3δCF EI H3
ð8Þ
where I is the moment of inertia for cross sectional area of the beam/pattern and is I ¼
Lw3 12
ð9Þ
found from eqs 1 and 12 as
By comparing eq 7 with eq 8, deformation due to the STF is calculated as (note that δCF is replaced by δ2) δ2 ¼
4γH sin θ Ew3 3
ð10Þ
To elucidate the importance of STF in the pattern deformation model, consider a simple case of a flat interface where ΔP = 0. (See Figure 2b.) Literature suggests that collapse would never occur because δ1 is always zero. However, considering eq 10, definition of AR (= H/w), and the fact that if half of the d value is reached, then pattern is considered collapsed (tips of two patterns touch), one can derive eq 11 to find the maximum AR value for which, if exceeded, collapse will occur. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ed 3 AR ¼ 8γ sin θ
ð11Þ
For example, for values of E, d, γ, and θ of 4 GPa, 65 nm, 72 mN/m, and 60, respectively, if the AR value becomes greater than 8, then pattern will collapse. 3.2. Analytical Model for Calculation of δ1. Considering STF (Fx), in addition to changing directly the total deformation by δ2, also indirectly changes the δ1 through changing the Laplace pressure value. As will be shown, the effect of the STF on just δ1 is significant and must therefore be considered. The mechanism is as follows: δ2 increases the curvature of an already curved interface (squeezing the liquid in between the pattern) and Laplace pressure, ΔP, consequently. (See eq 13.) The increase in ΔP increases the δ1. As such, the literature formulation for finding δ1 (e.g., ref 3) needs modifications to account for the indirect effect of STF. Radii of curvature, in CIM model, by considering the total pattern deformation, δT (= δ1 þ δ2), are found as R1 ¼
d - 2δT , R2 ¼ ¥ 2 cosðθ - φT Þ
ð12Þ
where φT is the slope of the pattern at the three-phase line. (See Figure 3.) Laplace pressure (cause of the cohesive force) can be (35) Cook, D. R.; Young, W. C. Advanced Mechanics of Materials; Macmillan Publishing: New York, 1985; pp 70-72. (36) Chatain, D.; Lewis, D.; Baland, J.; Carter, W. C. Langmuir 2006, 22, 4237– 4243 .
13710 DOI: 10.1021/la101521k
Figure 4. Comparing restoring and cohesive pressures due to Laplace pressure by: (i) Tanaka’s model3 and (ii) current model for δ1, which considers the effect of STF on Laplace pressure deformation (AR = 6, H = 350 nm, d = 150 nm, θ = 15, E = 5.9 GPa, and γ = 72 mN/m).
ΔP ¼
2γ cosðθ - φT Þ d - 2δT
ð13Þ
Restoring pressure of a beam (conceptually is restoring force but to make the comparison easy and with uniform units, restoring force is divided by the pattern area) due to any capillary pressure (CP) related to the deformation (δCP) is35 CP ¼
8EIδCP LH 4
ð14Þ
Equations 13 and 14 should be set equal to one another to find δ1 (deformation due to Laplace pressure), similar to the Tanaka et al.3 approach. The procedure of equating eqs 13 and 14 is different from what is done for the models in literature (e.g., ref 3) because: (i) the effect of the STF on δ1 is considered and (ii) small deformation assumption (i.e., sin φ ≈ tan φ ≈ 4δ/3H) is relaxed. For the cases examined in this study, relaxation of small deformation assumption resulted in a negligible change (230) and under filling (ILH60 (which rarely happens), the error in using CIM becomes sensitive to θ as well. (See Figure 9a.) Therefore, in the prevalent range of contact angle, for both two-line parallel and box-shaped patterns, the error in using CIM compared with SE depends only on LAR value. For both two-line parallel and box-shaped patterns, the error in using CIM increases by decreasing the LAR value (Figure 9b and Table 8). It should be noted that in some cases, only a few percent error in curvature value may lead to incorrect prediction of pattern deformation or collapse (e.g., as shown in Figure 4). However, in some other cases, even 10% error is tolerable. For LAR values greater than 20, the relative error of using CIM in calculating the rinse interface curvature is
