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Direct laser patterning of self-assembled monolayer using elliptical laser beams: A theoretical parametric study
Optics & Laser Technology 43 (2011) 1377–1384
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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Direct laser patterning of self-assembled monolayer using elliptical laser beams: A theoretical parametric study Martin Y. Zhang 1, Mohammad Reza Shadnam 2, A. Amirfazli n Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G8
a r t i c l e i n f o
abstract
Article history: Received 8 December 2010 Received in revised form 30 March 2011 Accepted 30 March 2011 Available online 6 May 2011
A theoretical quantitative analysis of processing parameters for application of an elliptical laser beam to achieve maximum patterning area is the focus of this study. Direct laser patterning (DLP) of selfassembled monolayers (SAM) is achieved by localized heating of the sample above the SAM desorption temperature. Through use of elliptical laser beams in the present work, three goals are achieved by analyzing the heat diffusion model and related thermo-kinetics model: (1) optimal working conditions (combination of laser power, scanning velocity and aspect ratio) for DLP to produce maximum feature size, or highest processing velocity at a given power; (2) identification of conditions that reduces the potential thermal damage to the substrate; (3) shedding light on issues related to uniformity or homogeneity of heating a substrate using an elliptical laser beam. A heat diffusion model is employed to provide the resulting surface temperature caused by elliptical laser beams, and the coupled thermokinetics model is used to determine the final SAM coverage generated by DLP. Parametric analysis revealed that 70–150 mW can be used to pattern feature sizes in the range of 2–10 times of equivalent circular beam size. It is also found that each elliptical laser beam has a unique optimal aspect ratio to result in the widest feature size for a given laser power and scanning velocity. The edge transition width increases with an increase of the aspect ratio. Keeping the aspect ratio of elliptical laser beam small (i.e. b o 20), a sharp edge definition could be obtained; if an aspect ratio larger than 30 is used, a surface with gradual edge definition could be obtained. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Self-assembled monolayer Elliptical beam Patterning
1. Introduction A self-assembled monolayer (SAM) is a two-dimensional, onemolecule-thick film; it spontaneously forms when certain organic molecules, e.g. thiols and silanes, adsorb on a surface, i.e. noble metals and silica, respectively. SAMs are important for scientific and technological purposes, and they have a variety of applications in bio-technological devices, MEMS, and micro-fluidics [1–3]. Patterned SAM surfaces, i.e. surfaces having different wettability, charge, or biocompatibility in neighboring regions are useful for producing wall-less micro-fluidic channels, and chemical gradients, which is of interest for controlled liquid delivery on surface [4–5] and cell separation [6] applications. One of the most studied and used SAM systems is alkaline thiols placed on a gold film that is supported by a glass or silicon substrate, here we also consider such system.
n
Corresponding author. Tel.: þ1 780 492 6711; fax: þ1 780 492 2200. E-mail address: [email protected] (A. Amirfazli). 1 Current address: School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA. 2 Current address: R&D Incentive Practice, KPMG LLP, 777 Dunsmuir Street, Vancouver, BC, Canada V7Y 1K3. 0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.03.034
In the context of direct laser patterning (DLP) methodology for SAM patterning using circular beams [7–14], patterning with elliptical beams (by using cylindrical lenses, for instance), is considered in this study. In DLP, an initially formed homogeneous monolayer, e.g. 1-hexadecanethiol (HDT) SAM (hydrophobic) placed on gold film is irradiated by a laser beam, e.g. 488 nm CW argon ion laser beam [7,8] to form a bare region (because of thermal desorption of SAMs); then the bare region is backfilled by a second monolayer species, e.g. 16-mercaptohexadecanoic (MHA) acid SAM (hydrophilic) through solution deposition (details of SAM preparation procedure and the experimental set-up can be found elsewhere [8]). The procedure creates hydrophilic patterns on hydrophobic background that can control liquid spreading on a surface. In this way, DLP can be used to manipulate the surface properties. Note that the manipulation of surface properties is not limited to surface wettability; depending on the SAM’s tail group, surface charge or surface biocompatibility can be changed as well. Previously, patterns with feature sizes of 4–170 mm have been produced using laser beams with circular cross sections (various sizes and powers) in a single pass mode [7,8]. However, making features larger than 170 mm is of interest in many fields. For instance, a potential application is to enhance the efficiency of creating chemical
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gradient surface [15,16]. The findings of this study and especially the idea of coupling equations, describing the thermal response of the surface to chemical reactions resulting from heating can also be used for other areas such as welding process using laser beams [17], and oxidation of silicon wafer using laser [12,13] (a thermo-chemical process). Such an approach, if extended to consider pulsed laser applications, can also be useful for processes that involve photopolarization and photo-thermal effects, e.g. nano-patterning of indium tin oxide films [18]. Producing large areas using a typical circular beam needs high laser powers or multi-pass processing that (1) may be beyond the capability of a typical research laboratory laser system, or may damage substrate (the beam centerline) due to high laser powers needed and (2) can be a time-consuming process in multi-pass processing. A solution to overcome these problems is to expand the laser beam perpendicular to the scanning direction (making a beam with elliptical cross section). The heat diffusion model and temperature rise by an elliptical laser beam has been discussed in [19–21]; however, patterning SAMs with elliptical laser beams is not yet reported in the literature. Also, the concept of thermal Mach number (Mth) is introduced in this study for beams with elliptical cross section. In this study, we theoretically examine the feasibility of the idea of using elliptical laser beam in DLP and predict the practical range of working parameters to make largest possible feature sizes (patterning the largest possible area in a single pass); such a patterning enables achieving a desired feature size at minimal laser power, in minimal time. Another novel aspect of this study is the coupling of the thermal equation with a chemical kinetics equation describing the surface changes as a result of heating a surface. The theoretical predictions and quantitative analyses are made through adopting a previously developed heat diffusion model [19] for elliptical laser beams and coupling it to a kinetics model. There are two methods to find the feature sizes for a pattern: (1) The calculated feature sizes given by heat diffusion model which is associated with the 75–80% [22] SAM desorption; this is a simple and quick approach to quantitatively analyze the correlations between the feature size and processing parameters, i.e. laser power (for a 488 nm CW laser), scanning velocity, and aspect ratio of elliptical beam. (2) More accurate feature sizes defined by full SAM desorption can be found when a coupled thermo-kinetics model as described later in this study is used. The coupled model also sheds light on issues related to the homogeneity of the patterned sample (the edge resolution for patterning), which has application ranging from creating a chemical gradient along the surface, to more uniformly distributed laser welding or annealing zone. However, the second approach requires a more complex and time-consuming calculations. Therefore, on balancing the accuracy of the result and the time, one can choose a proper approach. We firstly discuss the change of the calculated feature size with change of the laser power, scanning velocity, and beam aspect ratio, to find how they affect feature size, and then determined the optimal combination of these parameters that results in the maximum feature size in a single pass processing. The correlation between the theoretically calculated feature sizes and chemical composition of the surface is demonstrated as well. The width of 0%, 50%, and 100% HDT coverage at different laser powers and aspect ratios are compared, and the edge resolution with respect to aspect ratio is analyzed at the end.
2. Model development 2.1. Heat diffusion model for surface temperature It is assumed that the laser beam is elliptical in cross section and the laser intensity has a Gaussian distribution along both
Fig. 1. (a) The temperature profiles obtained by solving the Eq. (3) are shown. Left half (solid line) shows the temperature profile along the y-axis that is wider than that of the x-axis (the scanning direction is along the minor axis, b 41, refer to the left inset). Right half (dashed line) shows the temperature profile along the x-axis that is wider than that of the y-axis when the scanning direction is along the major axis (b o 1, refer to the right inset). (b) Symmetric temperature profile centered on centerline of scanning beam (y¼0) is shown. This is the temperature field as a result of a circular beam (b ¼ 1). Feature size is determined by the width of the region (perpendicular to the scanning direction) that experiences temperature above 490 K [8], for HDT on gold system.
axes. The temperature distribution produced by elliptical laser beam is a function of the following parameters: laser power (P), laser beam size characterized by rx and ry as shown in Fig. 1a, scanning velocity (v), initial sample temperature (Ti) here assumed as 298 K, sample absorptivity (A), thermal conductivity (k), and thermal diffusivity (D). In this study, a reformulated form of the solution to the heat diffusion equation in [19] is employed: n h io pffiffiffi ðX þ Vu2 Þ2 Y2 Z2 Z 2 PA 1 exp 2 u2 þ 1 þ u2 þ b2 þ u2 Yðx,y,z,tÞ ¼ 3=2 du ð1Þ 2 p krx 0 ½ðu2 þ1Þðu2 þ b Þ1=2 where Y(x,y,z,t) denotes the temperature rise (see Eq. (2)); X¼ x/rx, Y¼y/rx, Z¼ z/rx, where x, y, z denote the stationary coordinates; b ¼ry/rx, is the aspect ratio of the elliptical beam; rx and ry are 2e-folding intensity radii along and perpendicular to the scanning direction, respectively, as shown in Fig. 1a; V¼ vrx/8D; ffi pffiffiffiffiffiffiffiffiffi u ¼ 2 2Dt 0 =rx , and t 0 ¼ t, where t is the time. It should be noted that in this work we have considered a continuous wave (CW) laser, whose duration of pulsed can be regarded as infinite. Compared with electron–phonon relaxation time, which is in
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the order of picoseconds, laser pulsed duration used here is much longer, and the laser heating effects caused by photon induced electron-phonon interactions could be neglected. Thus, diffusive heat conduction dominates the process here since CW laser is used. The actual temperature of the sample after heating the substrate is denoted as T; it can be obtained from the following equation: T ¼ Ti þ Y
ð2Þ
The position parameter (z) in the direction of depth of the sample is considered as zero, because only the surface temperature is important for SAM desorption [8]. Considering this and combining Eqs. (1) and (2), one has: n h io pffiffiffi ðX þ Vu2 Þ2 Y2 Z 2 PA 1 exp 2 u2 þ 1 þ u2 þ b2 T ¼ Ti þ 3=2 du ð3Þ 2 p krx 0 ½ðu2 þ 1Þðu2 þ b Þ1=2 The feature size (fs) can then be found knowing T after solving Eq. (3) (see Fig. 1b). For the specific case of patterning SAMs of HDT, it is shown that surface temperatures above 490 K will result in full desorption of HDT; hence creating bare region that can be functionized as discussed earlier. Considering this, fs will be a function of various parameters shown below: f s ¼ f s ðP,r x ,r y ,v,T i ,A, k,DÞ
ð4Þ
It is assumed that k and D are temperature-independent; A, Ti, and S are also assumed constant as shown in Table 1. The values provided in Table 1 are relevant to DLP processing of alkaline thiols films on a gold film supported by a glass substrate [7,8], but any other values can also be considered without the loss of generality of findings of this study. Considering Eq. (4), using p-theorem, a complete set of four dimensionless groups were obtained: (1) the dimensionless feature size is found as Fs ¼fs/r0; r0 is the 2e-folding intensity of the equivalent circular beam radius and considered a constant (see Table 1). (2) The beam aspect ratio is found as b ¼ry/rx; (3) the thermal Mach number is found as Mth ¼vrx/D; the numerator vrx can be viewed as an indication of the rate at which the energy is transferred into the sample, whereas the denominator D describes how heat diffuses through the substrate from the heated spot. (4) The laser power coefficient is defined as p ¼PA/(CpTiSv); the numerator PA denotes the energy of the laser beam per unit time, transferred into the sample, whereas the denominator CpTiSv denotes the energy stored in the sample, that is being diffused away from a heating spot. Therefore, the dimensionless feature size can be written as a function of the other three parameters as F s ¼ F s ðb, p,M th Þ
2.2. Thermo-kinetics model for SAM desorption We develop the thermo-kinetic model in the context of using DLP for patterning initially homogeneous SAMs of HDT. To comprehensively understand the final HDT composition on surface after application of DLP, and hence the accurate full HDT desorption width, a chemical kinetics model should be coupled to the above thermal model. The thermo-kinetics model used in this study is to describe the SAM desorption reaction, and calculate the final HDT coverage after DLP patterning (similar to our past experimentally study [8]). However, the principle provided here can easily be extended for other processes, e.g. oxidation of silicon for wafer processing. The rate of SAM desorption supported by gold substrate during the first few minutes is shown to be proportional to the surface coverage of SAMs [7], given by Eq. (6). The rate constant, the proportionality factor of this equation, is a temperature-dependent factor given by Eyring equation [23] dCðx,yÞ KB Tðx,y,tÞ DG ¼ exp Cðx,yÞ ð6Þ dt h RTðx,y,tÞ where C(x, y) denotes the coverage of HDT on the gold surface. In this case, C is decreasing, so dc/dt o0. T(x, y, t) represents the time-dependent temperature field given by Eq. (3) with replacing X by vt/rx, and Y by y/rx after the integration with respect to u has been carried out. KB, h, R, and DG are Boltzmann’s constant, Planck’s constant, universal gas constant and Gibbs free energy of activation of the HDT desorption reaction, respectively. DG is chosen to be 29.9 kcal/mol [22] in this study, as shown in Table 1. To find the final HDT coverage on the surface, Eq. (6) is numerically integrated with respect to time (t). Since the position x (parallel to the scanning direction) is a function of time (x ¼vt), the final HDT coverage is only a function of position y (perpendicular to the scanning direction). The equation relates the SAM desorption kinetics to the thermal model as: Z t1 KB DG CðyÞ ¼ Ci ðyÞexp dt ð7Þ Tðx,y,tÞexp RTðx,y,tÞ h t0 where C(y) denotes the HDT coverage after patterning (heating till HDT desorbs from surface) for each point on the surface. Ci(y¼1), represents the 100% initial HDT coverage. Eq. (7) at each given position y is solved numerically (using Maple 8 software), and the final HDT coverage is found.
3. Results and discussion
Table 1 Numerical values of the parameters to solve Eqs. (3) and (7); the beam is considered to be a 488 nm CW laser.
D, thermal diffusivity of soda lime glass (Erie) S, laser spot area r0, circular beam radius with spot area of 6000 mm2 Ti, initial sample temperature A, substrate absorptivity (measured) DG, Gibbs free energy of activation of HDT desorption
parameters for single-pass processing of large area using a laser beam with an elliptical cross section (i.e. an elliptical beam).
ð5Þ
The next section discusses our findings regarding the above functional relationship to determine the best processing
k, thermal conductivity of soda lime glass (Erie)
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0.872 W/(m K) 0.33 mm2/s 6000 mm2a 43.67 mm 298 K 0.44 29.9 kcal/mol
a In [8], when þ 10 cm lens was used, the removal intensity (average) threshold was reported as 2.5 kW/cm2. Maximum power studied in this study (maximum power of available laser) is 150 mW, thus maximum spot area would be 150 mW divided by 2.5 kW/cm2 (¼ 6000 mm2). The 2e-folding intensity of the equivalent circular laser beam is r0 ¼ 43.7 mm.
3.1. Heat diffusion approach According to the first method of finding the feature size i.e. width of the irradiated region that experiences temperatures above 490 K see Fig. 1a, one needs the temperature distribution of the surface. By solving the Eq. (3) numerically (using Maple 8 and values for constant parameters as given in Table 1), the temperature profiles along both axes (along the scanning direction and perpendicular to that) were obtained. Because of the ellipticity of the laser beam, the induced temperature distributions along the two axes are different. The left half (solid line) in Fig. 1a shows the temperature profile for the case where the beam is scanned along the minor axis of the ellipse (b 41), the temperature profile along y-axis is wider than that of x-axis. When the beam is scanned along the major axis of the ellipse (b o1), it is the opposite, i.e. the profile along x-axis is wider than
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that of y-axis, as indicated in right half of Fig. 1a (dashed line). In the rest of this study, the scanning direction is considered to be along minor axis (b 41) which is useful to pattern large areas in a single-pass processing. Effect of the aspect ratios on resultant temperature profiles is shown in Fig. 2, where the scanning velocity (v), laser power (P), and the spot area (S) are kept constant at 200 mm/s, 150 mW, and 6000 mm2, respectively (these values correspond to the available laser to us, i.e. Melles Griot 35 LAL Argon). It is clear that the beam with a larger aspect ratio can pattern a larger region in each scan (refer to the inset of Fig. 2). For very large aspect ratios (e.g. b Z 200, see Fig. 2), the temperature profile along y-axis is almost ‘flat’, with a relatively large feature size, while that of x-axis is ‘sharp’. In the limits for b values in the thousands, the elliptical beam can be regarded as a moving line source being scanned along the x-direction, and the temperature distribution found from above formulation agrees with calculated values from the moving rectangular source equation in [24], as shown in Fig. 3.
Fig. 2. The temperature distribution along both axes show the effect of beam aspect ratio (b). As shown in the inset, elliptical beams cover a larger region in each scanning compared to that of circular beams with the same spot area. The scanning velocity, laser power, and spot area are fixed at 200 mm/s, 150 mW, and 6000 mm2, respectively. Half of temperature field is shown due to the symmetry of the solution.
Fig. 3. Comparison of the temperature profiles obtained from both Eq. (3) and Ref. [22]. The solid line denotes the temperature profile obtained by solving Eq. (3), which is a Gaussian laser beam source, and the dashed line denotes the temperature profile calculated by solving Eq. (13) in [22] which is a rectangular source.
As for peak temperatures in Fig. 2, the circular beam has peak temperature of 987 K, when the aspect ratio equals to 23 and 200, the peak temperatures are 710 and 503 K, respectively. This can be physically explained when the aspect ratio increases, the region that the laser beam covers per unit time increases, so the energy per unit area that is transferred into the sample decreases resulting in a decrease in peak temperature. The peak temperature is important in DLP (or any other process); for example temperature above 1337 K (melting point for gold [25]), damages the gold film. Thus, this temperature determines the maximum power that can be used for patterning with a circular beam. For instance, for our experimental facilities, the maximum theoretical power for the given spot size can be 225 mW when the beam is circular, and it is 378 and 761 mW when elliptical beams with an aspect ratio of 23 and 200 are used, respectively. Of course, in practice due to imperfection in a thin gold film, it will damage at significantly lower temperature and hence when patterning of large areas are needed, application of circular beams is limited. Thus elliptical beams are safer than circular beams when considering substrate damage. The ability to have a more homogenous temperature field can also be useful for other processes such as welding, annealing or oxidation of silicon. Fig. 4 shows the change of dimensionless feature sizes with aspect ratio for the system parameters studied here. The calculated feature size increases with an increase of beam aspect ratio, but after a certain b value it begins to decrease. Therefore, there exists an optimal aspect ratio (denoted as bop), which corresponds to a maximum value of the dimensionless feature size denoted as (Fs)max. Note that by ‘‘optimal’’ we mean that largest area that can be processed in a single pass. When one continues to increase the aspect ratio beyond a certain limit, the peak temperature drops below the temperature threshold (490 K) where no full desorption can take place in the DLP process [7], and hence no patterning can be obtained. This aspect ratio is named as the maximum usable aspect ratio and denoted as bmax. Given the dimensionless nature of the presented results, using temperature limits for other process such as oxidation or annealing silicon, the findings or at least general trends here can be applied to other fields of interest. For a given scanning velocity, each power level results in a unique optimal aspect ratio, maximum dimensionless feature size, and maximum useable aspect ratio, as shown in Fig. 4. For
Fig. 4. Correlation of the dimensionless feature size and the beam aspect ratio at different laser power coefficients (laser powers). Feature size (the actual feature size) is theoretically calculated by the heat diffusion model by measuring the width of the surface experienced a temperature above 490 K. Velocity is kept as 200 mm/s. Other parameters are kept constant as listed in Table 1. Note the difference in the scale for inset and main figure results in difference in the shape of plotted curves.
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a fixed velocity, higher power coefficient (or laser power) results in larger maximum dimensionless feature size (Fig. 4). This is expected since for higher powers, the energy transferred into the sample would be more and heat will diffuse over a larger area and hence a larger feature size will result. However, application of high laser power with an elliptical beam can avoid substrate damage as discussed earlier. By extracting the maximum dimensionless feature size from plots similar to Fig. 4 at various scanning speeds, plots for the maximum dimensionless feature size can be obtained, (see for example Fig. S1 in the supplementary materials available online). For a given total laser power, increasing the scanning velocity means that the dwell time of the beam at any given location will be reduced. The reduction of the dwell time will result in lower energy transfer to the substrate at a given local. The consequence of lower energy transfer to the surface will be a smaller temperature rise, which is shown to result in narrower features, or smaller maximum dimensionless feature size (this can be seen in Fig. S1, in the supplementary material available online). Although some of these findings maybe intuitive, but this study provides a systematic and quantitative framework. It was also found that the maximum dimensionless feature size varies linearly with laser power (for each fixed velocity), and as explained, the maximum dimensionless feature size increases with an increase of laser power, and decreases with an increase of scanning velocity (see Fig. S1 in the supplementary materials available online). Noting the slopes of lines are larger at lower velocities, it can be concluded that the effect of scanning velocity on the maximum dimensionless feature size is more pronounced at lower velocities. This is to say, to create a large feature size one can control the resulting feature sizes more easily when the scanning speed is kept slow (i.e. o1000 mm/s; see Fig. 5). In order to keep the energy per unit scanned length high enough for full desorption, the aspect ratio should be limited to an upper value, called bmax. Each curve in Fig. 5 shows the maximum useable aspect ratio one can reach for each fixed scanning velocity, which increases with laser power, as explained. At higher scanning velocity, smaller maximum useable aspect ratio is seen in Fig. 5. Noting the slopes of curves are larger at higher powers and lower velocities in Fig. 5, it is clear that the effect of laser power on maximum useable aspect ratio is more pronounced at high powers, whereas that of scanning velocity is more significant at low velocities. It indicates larger maximum useable aspect ratio
Fig. 5. Maximum useable aspect ratio (extracted from plots similar to Fig. 4) is shown.
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Fig. 6. Maximum dimensionless feature size versus the optimal aspect ratio is found by measuring the maximum value of the dimensionless feature size and corresponding aspect ratio from family of graphs similar to Fig. S1. Scanning velocity and laser power are varied whereas other parameters are held constant as shown in Table 1. Heavy solid line is the linear fit to all data with the correlations given in the graph: (Fs)max ¼ 0.079bop þ 1.932 (cf. Eq. (8)).
are available when laser power is high (e.g. 4120 mW) and scanning speed is low (e.g. o1000 mm/s). Fig. 6 depicts the correlation between the maximum dimensionless feature size and the optimal aspect ratio. The correlation is linear (heavy line in Fig. 6), see Eq. (8), and indicate that two important factors in reaching a certain feature size are aspect ratio (which indicates the shape of laser beam) and laser power; scanning velocity (within the range considered) is not as important since data points with different velocities are close to each other (see Fig. 6). Finding such correlation is important as it enables one to know what should be the processing parameters for achieving the maximum feature size in a single pass ðF s Þmax ¼ 0:079bop þ 1:932
ð8Þ
The range of optimal aspect ratios (bop) for certain laser power to reach the maximum dimensionless feature size ((Fs)max) is shown in Fig. 6. Four dashed contours in this figure delimit the range of the maximum feature size that 70, 90, 120, and 150 mW can achieve. It also summaries that laser powers of 70–150 mW can be used to pattern feature sizes in the range of 2–10 times of equivalent circular beam size (r0) (i.e. an actual feature size from 85 to 450 mm). Fig. 6 also shows that specific parameter combination (the combination of the laser power and aspect ratio) results in specific maximum dimensionless feature size, and this dependence can be predicted, i.e. Eq. (8). For instance, if a dimensionless feature size of 5 (i.e. an actual feature size of 220 mm) is desired, a laser power of 120 mW should be used (based on DLP parameters for thiol SAM desorption [7,8], and the corresponding optimal aspect ratio is 39 (a more precise aspect ratio value depends on velocity; however, Eq. (8) provides a reasonably accurate value when one also considers experimental uncertainty). Of course, laser powers more than 150 mW can also result in a dimensionless feature size of 5 with a given lower aspect ratios, at a particular lower patterning speed. However, such setting would not be optimal from processing time to energy spent (i.e. higher power used). Generally, if one has a desired feature size to produce by DLP, one can use Eq. (8) to evaluate the appropriate aspect ratio. The correlation between the thermal Mach number (Mth) and the dimensionless feature size is shown in Fig. 7 (for 200 mm/s
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Fig. 7. Correlation of the dimensionless feature size and the thermal Mach number at different laser powers (laser power coefficients). Velocity is fixed at 200 mm/s. Other parameters are kept constant as listed in Table 1.
scanning velocity). With the increase of thermal Mach number, the dimensionless feature size increases (starting from zero) rapidly at first, reaches a maximum, and then drops down with the relatively slow slope. Similar to the optimal aspect ratio introduced above, the thermal Mach number that corresponds to the maximum feature size produced is called the optimal thermal Mach number, denoted as (Mth)op; the corresponding beam radius is called the optimal beam radius, denoted as (rx)op. The relationship between thermal Mach number and dimensionless feature size at other velocities such as 20, 1000, and 5000 mm/s also display the same trend as that of Fig. 7 (plots not shown for brevity). As discussed above, the numerator of thermal Mach number (vrx) is considered as an indication of the rate at which the energy is transferred into the sample (accumulation of energy), whereas the denominator (D) describes the rate of heat diffuses through the substrate from the heating spot (dispersion of energy). When the rate of energy dispersing is greater than or equal to that of accumulating (i.e. D Zvrx or Mth r1), no energy accumulation occurs. In other words, the energy will diffuse away at the rate of D once it reaches the substrate, therefore, the energy provided by the laser beam dominates the desorption reaction (for SAM patterning application). When the local energy intensity (rather than the average intensity) is high enough to induce, at least a local temperature of 490 K, it can produce a full SAM desorption; this applies to all the cases shown in Fig. 7 except the starting points. When the local energy intensity is lower than the minimal value needed to elevate the temperature to 490 K, no fully desorbed area will be produced. This explains the cutoff (intersecting curves with x-axis) seen on the left side of the curves in Fig. 7, i.e. where Fs ¼0. Similarly, the maximum point in Fig. 8 can be physically understood as when the local energy distribution reaches the optimal condition, which means the farthest distance away from the centerline of the heating spot with a temperature of 490 K. This results in optimal temperature field along the surface, hence the calculated feature size reaches the maximum value. As discussed above, the thermal footprint of laser beam similar in shape to that of the laser beam itself. Therefore, optimal patterning condition also indicates that the laser beam cross section (defined by rx and ry) has the optimal shape, and it produces a ‘‘smooth’’ and ‘‘large’’ feature size when the condition Mth r1 is meet.
Fig. 8. Comparison of the theoretically calculated temperature field on substrate surface (dashed line, read from right axis) by heat diffusion model, Eq. (3), and final SAM coverage (solid line, read from left axis) by thermo-kinetics model, Eq. (7). Laser power, scanning velocity, and aspect ratio are 150 mW, 200 mm/s, and 4, respectively.
When the rate of energy dispersing is less than that of accumulating (i.e. D ovrx, or Mth 41, which is not shown here for brevity), the energy accumulation occurs. As a result, both the energy provided by laser and the accumulation effect determine the desorption reaction for SAMs in DLP (or oxidation, silicon processing). Due to the energy accumulation, it can be easily understood that the energy will be accumulated in the heating spot, and thus the temperature of the heating area will be high, but areas far away from the centerline heating spot is low. Hence, a ‘‘sharp’’ temperature profile will be produced and the calculated feature size will be small (when maximum temperature is higher than 490 K) or even zero (when maximum temperature is less than 490 K). That is to say, in order to obtain a localized ‘‘sharp’’ and ‘‘small’’ feature size, the condition Mth 4 1 should be satisfied, i.e. a high scanning velocity should be used. This point is contrary to the goal of this study (process large area in a single pass), but an important process parameter, if one is to produce sub refraction feature sizes [26]. By extracting the optimal thermal Mach number from Fig. 7, the optimal value of vrx, the product of scanning velocity (v, which can be determined from Fig. 6) and optimal beam radius (rx)op, are known; by extracting the optimal aspect ratio from Fig. 4, the minor axis radius (rx) is known. Comparing Fig. 7 with Fig. 4, it is clear that with the same laser power and scanning velocity, both graphs have the same maximum dimensionless feature sizes, which means the optimal aspect ratio and optimal thermal Mach number should be satisfied at the same time. Hence, minor axis radii obtained from both plots are the same, and equal to the optimal beam radius. 3.2. Thermo-kinetics approach The second approach of characterizing the resulting feature sizes mentioned above is the coupled thermo-kinetics mode, i.e. Eq. (7). By solving this coupled kinetics model numerically, the final HDT coverage after patterning can be obtained. Fig. 8 shows comparison of the theoretically calculated laser-induced temperature field (dashed line, right axis) and the HDT coverage (solid line, left axis) of the surface for incident laser power, scanning velocity, and aspect ratio of 150 mW, 200 mm/s, and 4, respectively. Fig. 8 indicates a good agreement with the theoretical calculation results from both heat diffusion and thermokinetics models (for instance, as shown in Fig. 8, the percentage difference between both models is about 9.5%).
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Fig. 9. Comparison of the correlation between different desorption percentage of HDT and aspect ratios. Width of HDT desorption at different percentage are theoretically calculated by thermo-kinetics model given by Eq. (7). The laser power and scanning velocity are fixed as 150 mW and 200 mm/s, respectively.
Fig. 8 also shows three zones with constant HDT concentration, and two areas where HDT concentration changes rapidly with distance from centerline. The two areas with HDT concentration of 100% (1 in Fig. 8) are where substrate is not affected and the size of this area depends on width of other zones. In the area near the centerline, the HDT has been fully desorbed (HDT concentration is 0). The full desorption width is of course also weakly velocity-dependent which is not discussed here for brevity. One of the major differences between the surface temperature model and thermal-kinetics model is that the former model can only provide the calculated feature size (which is defined by the temperature threshold of 490 K), but the latter model provides detailed compositional information (any value from 0% to 100%) at any given point. Hence the width of transition zones in Fig. 8 and its chemical composition can be found. As presented in Fig. 9, the widths of three different desorption percentages (0%, 50%, and 100%, corresponds to HDT concentration of 1, 0.5, and 0) are compared. When plotting the width of any desorption percentage, the ‘‘desorption percentage’’ is theoretically defined as the desorption that one and only one molecular of SAM has been removed. Fig. 9 shows that with the increase of the aspect ratio, the width of any HDT desorption percentage increases at first. This means that a general broadening of edges of the feature width where HDT concentration is zero is observed along with increasing the feature size (zone with HDT concentration of 0). Fig. 9 also shows that when maximum feature size is obtained at bop, the edges (zone with variable HDT concentration, represented by the width of HDT desorption of 50%) is also the broadest. This means that for cases where edge definition need to be very sharp, a value below bop should be used. Fig. 9 also provides detail information about composition of the processed area for b values where no fully desorbed area will exist as pointed earlier, such information can be useful, for example, for processing chemical gradient [16]. As the aspect ratio increases (at a fixed laser power and scanning speed), the slope of the two curves where HDT concentration changes rapidly (see Fig. 10) i.e. drops down. To describe the transition quantitatively, the edge transition width (denoted as ET) is defined as the width of transition zone between full desorption and partial desorption. By measuring the length between the onset of partial desorption and the centerline for all of these curves, the edge transition widths are found to be 55, 70, and 130 mm for aspect ratio of 1, 20, and 50, respectively (refer to Fig. S3 in the supplementary materials available online). In
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Fig. 10. Changing behavior of theoretical final SAM coverage associated with the laser beam aspect ratio. The SAM coverage is obtained by calculating the thermokinetics model given by Eq. (7). Laser power and scanning velocity are fixed as 150 mW, and 200 mm/s, respectively. Only half of the curves are shown due to symmetry with respect to centerline. Widths of the edge transition zones are 55, 70, and 130. ET in this figure shows as an example of the edge transition width in the case with an aspect ratio of 20.
other words, at fixed laser power and scanning velocity, edge transition widths increase with increase of aspect ratio. The dependence of edge transition width (ET) on b is important for DLP since this effect can be either viewed as positive or negative by DLP users. If a surface with smooth and gradual edge definition such as an energy gradient is needed, then using elliptical laser beams with larger aspect ratio (i.e. b 430) is an ideal tool; however, if a sharp and rapid edge definition is required, one might have to either keep the laser aspect ratio small (i.e. b o20) or accept the large transition width as a cost for obtaining larger resulting feature size in a single pass mode.
4. Summary and conclusions A quantitative analysis of processing parameter for application of an elliptical beam to achieve the maximum processing area was the purpose of this study. DLP process was used as a case study and a parametric analysis of feature sizes of the patterned SAMs produced by DLP using CW elliptical laser beam is presented, but the findings can be general by just changing the constants. It is shown that scanning an elliptical laser beam along its minor axis has at least two advantages compared with circular beams: (1) it can pattern a larger region in each scan and (2) larger areas can be patterned without thermal damage to the substrate. Two different models were discussed: the heat diffusion model and coupled thermo-kinetics model. The heat diffusion model provides the surface temperature, which is numerically calculated by capturing the feature sizes associated with 75–80% HDT desorption (defined by 490 K theoretically). It is simple, quick, and precise enough for quantitative analysis regarding the corelationships between feature sizes and processing parameters (i.e. laser power, scanning velocity, and beam aspect ratio). Results from the heat diffusion model show that the feature size increases linearly with increase of laser power; whereas, the feature size increases with decrease of scanning velocity, and this effect is more pronounced at lower velocities (i.e. o1000 mm/s). Furthermore, the laser power and beam aspect ratio are an important determining factors for feature sizes than scanning speed. In order to increase/decrease the resulting feature size, when laser power is low (e.g. o90 mW), the first choice is to increase/decrease the incident laser power (other than decrease/increase the scanning
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velocity); while for high powers (e.g. 4120 mW), changing incident power is the only choice. Each elliptical laser beam has a unique optimal aspect ratio: for a given power and velocity, patterning with an elliptical beam at optimal aspect ratio can result in the widest feature size. The coupled thermo-kinetics model describing the final coverage of SAM on surface is a more accurate method compare to the thermal model to predict the final HDT coverage and hence the full HDT desorption width on the surface, but it is time-consuming to solve. The thermo-kinetics model is very useful to gain detail insight of SAM desorption percentage with respect to some specific processing conditions. It also provides edge resolutions information. The edge transition width increases with increase of aspect ratio. If a surface with gradual edge definition is needed, using elliptical laser beams with larger aspect ratio (i.e. b 4 30); however, if a sharp edge definition is the goal, one might have to either keep the laser aspect ratio small (i.e. b o20) or take the large transition zone as a cost for saving processing time.
Acknowledgment This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Canada Research Chair program.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at doi:10.1016/j.optlastec.2011.03.034.
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[6] Smith JT, Tomfohr JK, Wells MC, Beebe TP, Kepler TB, Reichert WM. Measurement of cell migration on surface-bound fibronectin gradients. Langmuir 2004;20:8279–86. [7] Shadnam MR, Kirkwood SE, Fedosejevs R, Amirfazli A. Thermo-kinetics study of laser induced desorption of self assembled monolayer from gold: case of laser micropatterning. J Phys Chem B 2005;109:11996–2002. [8] Shadnam MR, Kirkwood SE, Fedosejevs R, Amirfazli A. Direct patterning of self assembled monolayers on gold using a laser beam. Langmuir 2004;20:2667–76. [9] Balgar T, Franzka S, Hartmann N. Laser-assisted fabrication of submicronstructured hydrophilic/hydrophobic templates for the directed self-assembly of alkylsiloxane monolayers into confined domainst. Appl Phys A 2006;82:15–8. [10] Shadnam MR, Amirfazli A. Analysis of patterning nanometer thin organic monolayers by a laser: curvilinear paths and junctions. J Comput Theor Nanosci 2009;5:2054–9. [11] Mathieu M, Franzka S, Koch J, Chichlov BN, Hartmann N. Direct laser patterning of soft matter: photothermal processing of supported phospholipid multilayers with nanoscale precision. Small 2009;5:2099–104. [12] Scheres L, Klingebiel B, Maat J, Giesbers M, Jong H, Hartmann N, et al. Microand nanopatterning of functional organic monolayers on oxide-free silicon by laser-induced photothermal desorption. Small 2010;6:1918–26. [13] Klingebiel B, Scheres L, Franzka S, Zuilhof H, Hartmann N. Photothermal micro-and nanopatterning of organic/silicon interfaces. Langmuir 2010;26: 6826–31. [14] Iverson L, Younes-Metzler O, Martinez KL, Stamou D. Chemically specific laser-induced patterning of alkanethiol SAMs: characterization by SEM and AFM. Langmuir 2009;25:12819–24. [15] Wijesundara MBJ, Fuoco E, Hanley L. Preparation of chemical gradient surfaces by hyperthermal polyatomic ion-deposition: a new method for combinatorial materials science. Langmuir 2001;17:5721–6. [16] Meyyappan S, Shadnam MR, Amirfazli A. Fabrication of surface energy/ chemical gradients using self assembled monolayer surfaces. Langmuir 2008;24:2892–9. [17] Mazumder J. Laser welding: state of the art review. J Met 1982;34:16–24. [18] Miedzinski R, Ebothe´ J, Kozlowski G, Kasperczyk J, Kityk IV, Fuks-Janczarek I, et al. Laser induced microrelief superstructure of Ag/ITO seed-mediated nanocomposites. Superlattice Microstruct 2009;46:637–44. [19] Nissim YI, Lietolia A, Gold RB, Gibbons JF. Temperature distributions produced in semiconductors by a scanning elliptical or circular cw laser beam. J Appl Phys 1980;51:274–9. [20] Moody JE, Hendel RH. Temperature profiles induced by a scanning cw laser beam. J Appl Phys 1982;53:4364–71. [21] Ferrieu F, Auvert G. Temperature evolutions in silicon induced by a scanned cw laser, pulsed laser, or an electron beam. J Appl Phys 1983;54: 2646–9. [22] Shadnam MR, Amirfazli A. Kinetics of alkanethiol monolayer desorption from gold in air. Chem Commun 2005;38:4869–71. [23] Eyring H. The activated complex in chemical reactions. J Chem Phys 1935;3:107–15. [24] Carslaw HS, Jaeger JC. Conduction of heat in solids. second ed. Oxford: Clarendon Press; 1959 (pp. 270). [25] Goldsmith A, Waterman TE, Hirschhorn H,J. Handbook of thermophysical properties of solid materials, vol. 1. New York: Macmillan; 1961(pp. 313). [26] Kirkwood SE, Shadnam MR, Fedosejevs R, Amirfazli A. Mechanism for femtosecond laser pulse patterning of self-assembled monolayers on goldcoated substrates. J Phys Conf Ser 2007;59:428–31.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Direct laser patterning of self-assembled monolayer using elliptical laser beams: A theoretical parametric study Martin Y. Zhang 1, Mohammad Reza Shadnam 2, A. Amirfazli n Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G8
a r t i c l e i n f o
abstract
Article history: Received 8 December 2010 Received in revised form 30 March 2011 Accepted 30 March 2011 Available online 6 May 2011
A theoretical quantitative analysis of processing parameters for application of an elliptical laser beam to achieve maximum patterning area is the focus of this study. Direct laser patterning (DLP) of selfassembled monolayers (SAM) is achieved by localized heating of the sample above the SAM desorption temperature. Through use of elliptical laser beams in the present work, three goals are achieved by analyzing the heat diffusion model and related thermo-kinetics model: (1) optimal working conditions (combination of laser power, scanning velocity and aspect ratio) for DLP to produce maximum feature size, or highest processing velocity at a given power; (2) identification of conditions that reduces the potential thermal damage to the substrate; (3) shedding light on issues related to uniformity or homogeneity of heating a substrate using an elliptical laser beam. A heat diffusion model is employed to provide the resulting surface temperature caused by elliptical laser beams, and the coupled thermokinetics model is used to determine the final SAM coverage generated by DLP. Parametric analysis revealed that 70–150 mW can be used to pattern feature sizes in the range of 2–10 times of equivalent circular beam size. It is also found that each elliptical laser beam has a unique optimal aspect ratio to result in the widest feature size for a given laser power and scanning velocity. The edge transition width increases with an increase of the aspect ratio. Keeping the aspect ratio of elliptical laser beam small (i.e. b o 20), a sharp edge definition could be obtained; if an aspect ratio larger than 30 is used, a surface with gradual edge definition could be obtained. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Self-assembled monolayer Elliptical beam Patterning
1. Introduction A self-assembled monolayer (SAM) is a two-dimensional, onemolecule-thick film; it spontaneously forms when certain organic molecules, e.g. thiols and silanes, adsorb on a surface, i.e. noble metals and silica, respectively. SAMs are important for scientific and technological purposes, and they have a variety of applications in bio-technological devices, MEMS, and micro-fluidics [1–3]. Patterned SAM surfaces, i.e. surfaces having different wettability, charge, or biocompatibility in neighboring regions are useful for producing wall-less micro-fluidic channels, and chemical gradients, which is of interest for controlled liquid delivery on surface [4–5] and cell separation [6] applications. One of the most studied and used SAM systems is alkaline thiols placed on a gold film that is supported by a glass or silicon substrate, here we also consider such system.
n
Corresponding author. Tel.: þ1 780 492 6711; fax: þ1 780 492 2200. E-mail address: [email protected] (A. Amirfazli). 1 Current address: School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA. 2 Current address: R&D Incentive Practice, KPMG LLP, 777 Dunsmuir Street, Vancouver, BC, Canada V7Y 1K3. 0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.03.034
In the context of direct laser patterning (DLP) methodology for SAM patterning using circular beams [7–14], patterning with elliptical beams (by using cylindrical lenses, for instance), is considered in this study. In DLP, an initially formed homogeneous monolayer, e.g. 1-hexadecanethiol (HDT) SAM (hydrophobic) placed on gold film is irradiated by a laser beam, e.g. 488 nm CW argon ion laser beam [7,8] to form a bare region (because of thermal desorption of SAMs); then the bare region is backfilled by a second monolayer species, e.g. 16-mercaptohexadecanoic (MHA) acid SAM (hydrophilic) through solution deposition (details of SAM preparation procedure and the experimental set-up can be found elsewhere [8]). The procedure creates hydrophilic patterns on hydrophobic background that can control liquid spreading on a surface. In this way, DLP can be used to manipulate the surface properties. Note that the manipulation of surface properties is not limited to surface wettability; depending on the SAM’s tail group, surface charge or surface biocompatibility can be changed as well. Previously, patterns with feature sizes of 4–170 mm have been produced using laser beams with circular cross sections (various sizes and powers) in a single pass mode [7,8]. However, making features larger than 170 mm is of interest in many fields. For instance, a potential application is to enhance the efficiency of creating chemical
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gradient surface [15,16]. The findings of this study and especially the idea of coupling equations, describing the thermal response of the surface to chemical reactions resulting from heating can also be used for other areas such as welding process using laser beams [17], and oxidation of silicon wafer using laser [12,13] (a thermo-chemical process). Such an approach, if extended to consider pulsed laser applications, can also be useful for processes that involve photopolarization and photo-thermal effects, e.g. nano-patterning of indium tin oxide films [18]. Producing large areas using a typical circular beam needs high laser powers or multi-pass processing that (1) may be beyond the capability of a typical research laboratory laser system, or may damage substrate (the beam centerline) due to high laser powers needed and (2) can be a time-consuming process in multi-pass processing. A solution to overcome these problems is to expand the laser beam perpendicular to the scanning direction (making a beam with elliptical cross section). The heat diffusion model and temperature rise by an elliptical laser beam has been discussed in [19–21]; however, patterning SAMs with elliptical laser beams is not yet reported in the literature. Also, the concept of thermal Mach number (Mth) is introduced in this study for beams with elliptical cross section. In this study, we theoretically examine the feasibility of the idea of using elliptical laser beam in DLP and predict the practical range of working parameters to make largest possible feature sizes (patterning the largest possible area in a single pass); such a patterning enables achieving a desired feature size at minimal laser power, in minimal time. Another novel aspect of this study is the coupling of the thermal equation with a chemical kinetics equation describing the surface changes as a result of heating a surface. The theoretical predictions and quantitative analyses are made through adopting a previously developed heat diffusion model [19] for elliptical laser beams and coupling it to a kinetics model. There are two methods to find the feature sizes for a pattern: (1) The calculated feature sizes given by heat diffusion model which is associated with the 75–80% [22] SAM desorption; this is a simple and quick approach to quantitatively analyze the correlations between the feature size and processing parameters, i.e. laser power (for a 488 nm CW laser), scanning velocity, and aspect ratio of elliptical beam. (2) More accurate feature sizes defined by full SAM desorption can be found when a coupled thermo-kinetics model as described later in this study is used. The coupled model also sheds light on issues related to the homogeneity of the patterned sample (the edge resolution for patterning), which has application ranging from creating a chemical gradient along the surface, to more uniformly distributed laser welding or annealing zone. However, the second approach requires a more complex and time-consuming calculations. Therefore, on balancing the accuracy of the result and the time, one can choose a proper approach. We firstly discuss the change of the calculated feature size with change of the laser power, scanning velocity, and beam aspect ratio, to find how they affect feature size, and then determined the optimal combination of these parameters that results in the maximum feature size in a single pass processing. The correlation between the theoretically calculated feature sizes and chemical composition of the surface is demonstrated as well. The width of 0%, 50%, and 100% HDT coverage at different laser powers and aspect ratios are compared, and the edge resolution with respect to aspect ratio is analyzed at the end.
2. Model development 2.1. Heat diffusion model for surface temperature It is assumed that the laser beam is elliptical in cross section and the laser intensity has a Gaussian distribution along both
Fig. 1. (a) The temperature profiles obtained by solving the Eq. (3) are shown. Left half (solid line) shows the temperature profile along the y-axis that is wider than that of the x-axis (the scanning direction is along the minor axis, b 41, refer to the left inset). Right half (dashed line) shows the temperature profile along the x-axis that is wider than that of the y-axis when the scanning direction is along the major axis (b o 1, refer to the right inset). (b) Symmetric temperature profile centered on centerline of scanning beam (y¼0) is shown. This is the temperature field as a result of a circular beam (b ¼ 1). Feature size is determined by the width of the region (perpendicular to the scanning direction) that experiences temperature above 490 K [8], for HDT on gold system.
axes. The temperature distribution produced by elliptical laser beam is a function of the following parameters: laser power (P), laser beam size characterized by rx and ry as shown in Fig. 1a, scanning velocity (v), initial sample temperature (Ti) here assumed as 298 K, sample absorptivity (A), thermal conductivity (k), and thermal diffusivity (D). In this study, a reformulated form of the solution to the heat diffusion equation in [19] is employed: n h io pffiffiffi ðX þ Vu2 Þ2 Y2 Z2 Z 2 PA 1 exp 2 u2 þ 1 þ u2 þ b2 þ u2 Yðx,y,z,tÞ ¼ 3=2 du ð1Þ 2 p krx 0 ½ðu2 þ1Þðu2 þ b Þ1=2 where Y(x,y,z,t) denotes the temperature rise (see Eq. (2)); X¼ x/rx, Y¼y/rx, Z¼ z/rx, where x, y, z denote the stationary coordinates; b ¼ry/rx, is the aspect ratio of the elliptical beam; rx and ry are 2e-folding intensity radii along and perpendicular to the scanning direction, respectively, as shown in Fig. 1a; V¼ vrx/8D; ffi pffiffiffiffiffiffiffiffiffi u ¼ 2 2Dt 0 =rx , and t 0 ¼ t, where t is the time. It should be noted that in this work we have considered a continuous wave (CW) laser, whose duration of pulsed can be regarded as infinite. Compared with electron–phonon relaxation time, which is in
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the order of picoseconds, laser pulsed duration used here is much longer, and the laser heating effects caused by photon induced electron-phonon interactions could be neglected. Thus, diffusive heat conduction dominates the process here since CW laser is used. The actual temperature of the sample after heating the substrate is denoted as T; it can be obtained from the following equation: T ¼ Ti þ Y
ð2Þ
The position parameter (z) in the direction of depth of the sample is considered as zero, because only the surface temperature is important for SAM desorption [8]. Considering this and combining Eqs. (1) and (2), one has: n h io pffiffiffi ðX þ Vu2 Þ2 Y2 Z 2 PA 1 exp 2 u2 þ 1 þ u2 þ b2 T ¼ Ti þ 3=2 du ð3Þ 2 p krx 0 ½ðu2 þ 1Þðu2 þ b Þ1=2 The feature size (fs) can then be found knowing T after solving Eq. (3) (see Fig. 1b). For the specific case of patterning SAMs of HDT, it is shown that surface temperatures above 490 K will result in full desorption of HDT; hence creating bare region that can be functionized as discussed earlier. Considering this, fs will be a function of various parameters shown below: f s ¼ f s ðP,r x ,r y ,v,T i ,A, k,DÞ
ð4Þ
It is assumed that k and D are temperature-independent; A, Ti, and S are also assumed constant as shown in Table 1. The values provided in Table 1 are relevant to DLP processing of alkaline thiols films on a gold film supported by a glass substrate [7,8], but any other values can also be considered without the loss of generality of findings of this study. Considering Eq. (4), using p-theorem, a complete set of four dimensionless groups were obtained: (1) the dimensionless feature size is found as Fs ¼fs/r0; r0 is the 2e-folding intensity of the equivalent circular beam radius and considered a constant (see Table 1). (2) The beam aspect ratio is found as b ¼ry/rx; (3) the thermal Mach number is found as Mth ¼vrx/D; the numerator vrx can be viewed as an indication of the rate at which the energy is transferred into the sample, whereas the denominator D describes how heat diffuses through the substrate from the heated spot. (4) The laser power coefficient is defined as p ¼PA/(CpTiSv); the numerator PA denotes the energy of the laser beam per unit time, transferred into the sample, whereas the denominator CpTiSv denotes the energy stored in the sample, that is being diffused away from a heating spot. Therefore, the dimensionless feature size can be written as a function of the other three parameters as F s ¼ F s ðb, p,M th Þ
2.2. Thermo-kinetics model for SAM desorption We develop the thermo-kinetic model in the context of using DLP for patterning initially homogeneous SAMs of HDT. To comprehensively understand the final HDT composition on surface after application of DLP, and hence the accurate full HDT desorption width, a chemical kinetics model should be coupled to the above thermal model. The thermo-kinetics model used in this study is to describe the SAM desorption reaction, and calculate the final HDT coverage after DLP patterning (similar to our past experimentally study [8]). However, the principle provided here can easily be extended for other processes, e.g. oxidation of silicon for wafer processing. The rate of SAM desorption supported by gold substrate during the first few minutes is shown to be proportional to the surface coverage of SAMs [7], given by Eq. (6). The rate constant, the proportionality factor of this equation, is a temperature-dependent factor given by Eyring equation [23] dCðx,yÞ KB Tðx,y,tÞ DG ¼ exp Cðx,yÞ ð6Þ dt h RTðx,y,tÞ where C(x, y) denotes the coverage of HDT on the gold surface. In this case, C is decreasing, so dc/dt o0. T(x, y, t) represents the time-dependent temperature field given by Eq. (3) with replacing X by vt/rx, and Y by y/rx after the integration with respect to u has been carried out. KB, h, R, and DG are Boltzmann’s constant, Planck’s constant, universal gas constant and Gibbs free energy of activation of the HDT desorption reaction, respectively. DG is chosen to be 29.9 kcal/mol [22] in this study, as shown in Table 1. To find the final HDT coverage on the surface, Eq. (6) is numerically integrated with respect to time (t). Since the position x (parallel to the scanning direction) is a function of time (x ¼vt), the final HDT coverage is only a function of position y (perpendicular to the scanning direction). The equation relates the SAM desorption kinetics to the thermal model as: Z t1 KB DG CðyÞ ¼ Ci ðyÞexp dt ð7Þ Tðx,y,tÞexp RTðx,y,tÞ h t0 where C(y) denotes the HDT coverage after patterning (heating till HDT desorbs from surface) for each point on the surface. Ci(y¼1), represents the 100% initial HDT coverage. Eq. (7) at each given position y is solved numerically (using Maple 8 software), and the final HDT coverage is found.
3. Results and discussion
Table 1 Numerical values of the parameters to solve Eqs. (3) and (7); the beam is considered to be a 488 nm CW laser.
D, thermal diffusivity of soda lime glass (Erie) S, laser spot area r0, circular beam radius with spot area of 6000 mm2 Ti, initial sample temperature A, substrate absorptivity (measured) DG, Gibbs free energy of activation of HDT desorption
parameters for single-pass processing of large area using a laser beam with an elliptical cross section (i.e. an elliptical beam).
ð5Þ
The next section discusses our findings regarding the above functional relationship to determine the best processing
k, thermal conductivity of soda lime glass (Erie)
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0.872 W/(m K) 0.33 mm2/s 6000 mm2a 43.67 mm 298 K 0.44 29.9 kcal/mol
a In [8], when þ 10 cm lens was used, the removal intensity (average) threshold was reported as 2.5 kW/cm2. Maximum power studied in this study (maximum power of available laser) is 150 mW, thus maximum spot area would be 150 mW divided by 2.5 kW/cm2 (¼ 6000 mm2). The 2e-folding intensity of the equivalent circular laser beam is r0 ¼ 43.7 mm.
3.1. Heat diffusion approach According to the first method of finding the feature size i.e. width of the irradiated region that experiences temperatures above 490 K see Fig. 1a, one needs the temperature distribution of the surface. By solving the Eq. (3) numerically (using Maple 8 and values for constant parameters as given in Table 1), the temperature profiles along both axes (along the scanning direction and perpendicular to that) were obtained. Because of the ellipticity of the laser beam, the induced temperature distributions along the two axes are different. The left half (solid line) in Fig. 1a shows the temperature profile for the case where the beam is scanned along the minor axis of the ellipse (b 41), the temperature profile along y-axis is wider than that of x-axis. When the beam is scanned along the major axis of the ellipse (b o1), it is the opposite, i.e. the profile along x-axis is wider than
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that of y-axis, as indicated in right half of Fig. 1a (dashed line). In the rest of this study, the scanning direction is considered to be along minor axis (b 41) which is useful to pattern large areas in a single-pass processing. Effect of the aspect ratios on resultant temperature profiles is shown in Fig. 2, where the scanning velocity (v), laser power (P), and the spot area (S) are kept constant at 200 mm/s, 150 mW, and 6000 mm2, respectively (these values correspond to the available laser to us, i.e. Melles Griot 35 LAL Argon). It is clear that the beam with a larger aspect ratio can pattern a larger region in each scan (refer to the inset of Fig. 2). For very large aspect ratios (e.g. b Z 200, see Fig. 2), the temperature profile along y-axis is almost ‘flat’, with a relatively large feature size, while that of x-axis is ‘sharp’. In the limits for b values in the thousands, the elliptical beam can be regarded as a moving line source being scanned along the x-direction, and the temperature distribution found from above formulation agrees with calculated values from the moving rectangular source equation in [24], as shown in Fig. 3.
Fig. 2. The temperature distribution along both axes show the effect of beam aspect ratio (b). As shown in the inset, elliptical beams cover a larger region in each scanning compared to that of circular beams with the same spot area. The scanning velocity, laser power, and spot area are fixed at 200 mm/s, 150 mW, and 6000 mm2, respectively. Half of temperature field is shown due to the symmetry of the solution.
Fig. 3. Comparison of the temperature profiles obtained from both Eq. (3) and Ref. [22]. The solid line denotes the temperature profile obtained by solving Eq. (3), which is a Gaussian laser beam source, and the dashed line denotes the temperature profile calculated by solving Eq. (13) in [22] which is a rectangular source.
As for peak temperatures in Fig. 2, the circular beam has peak temperature of 987 K, when the aspect ratio equals to 23 and 200, the peak temperatures are 710 and 503 K, respectively. This can be physically explained when the aspect ratio increases, the region that the laser beam covers per unit time increases, so the energy per unit area that is transferred into the sample decreases resulting in a decrease in peak temperature. The peak temperature is important in DLP (or any other process); for example temperature above 1337 K (melting point for gold [25]), damages the gold film. Thus, this temperature determines the maximum power that can be used for patterning with a circular beam. For instance, for our experimental facilities, the maximum theoretical power for the given spot size can be 225 mW when the beam is circular, and it is 378 and 761 mW when elliptical beams with an aspect ratio of 23 and 200 are used, respectively. Of course, in practice due to imperfection in a thin gold film, it will damage at significantly lower temperature and hence when patterning of large areas are needed, application of circular beams is limited. Thus elliptical beams are safer than circular beams when considering substrate damage. The ability to have a more homogenous temperature field can also be useful for other processes such as welding, annealing or oxidation of silicon. Fig. 4 shows the change of dimensionless feature sizes with aspect ratio for the system parameters studied here. The calculated feature size increases with an increase of beam aspect ratio, but after a certain b value it begins to decrease. Therefore, there exists an optimal aspect ratio (denoted as bop), which corresponds to a maximum value of the dimensionless feature size denoted as (Fs)max. Note that by ‘‘optimal’’ we mean that largest area that can be processed in a single pass. When one continues to increase the aspect ratio beyond a certain limit, the peak temperature drops below the temperature threshold (490 K) where no full desorption can take place in the DLP process [7], and hence no patterning can be obtained. This aspect ratio is named as the maximum usable aspect ratio and denoted as bmax. Given the dimensionless nature of the presented results, using temperature limits for other process such as oxidation or annealing silicon, the findings or at least general trends here can be applied to other fields of interest. For a given scanning velocity, each power level results in a unique optimal aspect ratio, maximum dimensionless feature size, and maximum useable aspect ratio, as shown in Fig. 4. For
Fig. 4. Correlation of the dimensionless feature size and the beam aspect ratio at different laser power coefficients (laser powers). Feature size (the actual feature size) is theoretically calculated by the heat diffusion model by measuring the width of the surface experienced a temperature above 490 K. Velocity is kept as 200 mm/s. Other parameters are kept constant as listed in Table 1. Note the difference in the scale for inset and main figure results in difference in the shape of plotted curves.
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a fixed velocity, higher power coefficient (or laser power) results in larger maximum dimensionless feature size (Fig. 4). This is expected since for higher powers, the energy transferred into the sample would be more and heat will diffuse over a larger area and hence a larger feature size will result. However, application of high laser power with an elliptical beam can avoid substrate damage as discussed earlier. By extracting the maximum dimensionless feature size from plots similar to Fig. 4 at various scanning speeds, plots for the maximum dimensionless feature size can be obtained, (see for example Fig. S1 in the supplementary materials available online). For a given total laser power, increasing the scanning velocity means that the dwell time of the beam at any given location will be reduced. The reduction of the dwell time will result in lower energy transfer to the substrate at a given local. The consequence of lower energy transfer to the surface will be a smaller temperature rise, which is shown to result in narrower features, or smaller maximum dimensionless feature size (this can be seen in Fig. S1, in the supplementary material available online). Although some of these findings maybe intuitive, but this study provides a systematic and quantitative framework. It was also found that the maximum dimensionless feature size varies linearly with laser power (for each fixed velocity), and as explained, the maximum dimensionless feature size increases with an increase of laser power, and decreases with an increase of scanning velocity (see Fig. S1 in the supplementary materials available online). Noting the slopes of lines are larger at lower velocities, it can be concluded that the effect of scanning velocity on the maximum dimensionless feature size is more pronounced at lower velocities. This is to say, to create a large feature size one can control the resulting feature sizes more easily when the scanning speed is kept slow (i.e. o1000 mm/s; see Fig. 5). In order to keep the energy per unit scanned length high enough for full desorption, the aspect ratio should be limited to an upper value, called bmax. Each curve in Fig. 5 shows the maximum useable aspect ratio one can reach for each fixed scanning velocity, which increases with laser power, as explained. At higher scanning velocity, smaller maximum useable aspect ratio is seen in Fig. 5. Noting the slopes of curves are larger at higher powers and lower velocities in Fig. 5, it is clear that the effect of laser power on maximum useable aspect ratio is more pronounced at high powers, whereas that of scanning velocity is more significant at low velocities. It indicates larger maximum useable aspect ratio
Fig. 5. Maximum useable aspect ratio (extracted from plots similar to Fig. 4) is shown.
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Fig. 6. Maximum dimensionless feature size versus the optimal aspect ratio is found by measuring the maximum value of the dimensionless feature size and corresponding aspect ratio from family of graphs similar to Fig. S1. Scanning velocity and laser power are varied whereas other parameters are held constant as shown in Table 1. Heavy solid line is the linear fit to all data with the correlations given in the graph: (Fs)max ¼ 0.079bop þ 1.932 (cf. Eq. (8)).
are available when laser power is high (e.g. 4120 mW) and scanning speed is low (e.g. o1000 mm/s). Fig. 6 depicts the correlation between the maximum dimensionless feature size and the optimal aspect ratio. The correlation is linear (heavy line in Fig. 6), see Eq. (8), and indicate that two important factors in reaching a certain feature size are aspect ratio (which indicates the shape of laser beam) and laser power; scanning velocity (within the range considered) is not as important since data points with different velocities are close to each other (see Fig. 6). Finding such correlation is important as it enables one to know what should be the processing parameters for achieving the maximum feature size in a single pass ðF s Þmax ¼ 0:079bop þ 1:932
ð8Þ
The range of optimal aspect ratios (bop) for certain laser power to reach the maximum dimensionless feature size ((Fs)max) is shown in Fig. 6. Four dashed contours in this figure delimit the range of the maximum feature size that 70, 90, 120, and 150 mW can achieve. It also summaries that laser powers of 70–150 mW can be used to pattern feature sizes in the range of 2–10 times of equivalent circular beam size (r0) (i.e. an actual feature size from 85 to 450 mm). Fig. 6 also shows that specific parameter combination (the combination of the laser power and aspect ratio) results in specific maximum dimensionless feature size, and this dependence can be predicted, i.e. Eq. (8). For instance, if a dimensionless feature size of 5 (i.e. an actual feature size of 220 mm) is desired, a laser power of 120 mW should be used (based on DLP parameters for thiol SAM desorption [7,8], and the corresponding optimal aspect ratio is 39 (a more precise aspect ratio value depends on velocity; however, Eq. (8) provides a reasonably accurate value when one also considers experimental uncertainty). Of course, laser powers more than 150 mW can also result in a dimensionless feature size of 5 with a given lower aspect ratios, at a particular lower patterning speed. However, such setting would not be optimal from processing time to energy spent (i.e. higher power used). Generally, if one has a desired feature size to produce by DLP, one can use Eq. (8) to evaluate the appropriate aspect ratio. The correlation between the thermal Mach number (Mth) and the dimensionless feature size is shown in Fig. 7 (for 200 mm/s
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Fig. 7. Correlation of the dimensionless feature size and the thermal Mach number at different laser powers (laser power coefficients). Velocity is fixed at 200 mm/s. Other parameters are kept constant as listed in Table 1.
scanning velocity). With the increase of thermal Mach number, the dimensionless feature size increases (starting from zero) rapidly at first, reaches a maximum, and then drops down with the relatively slow slope. Similar to the optimal aspect ratio introduced above, the thermal Mach number that corresponds to the maximum feature size produced is called the optimal thermal Mach number, denoted as (Mth)op; the corresponding beam radius is called the optimal beam radius, denoted as (rx)op. The relationship between thermal Mach number and dimensionless feature size at other velocities such as 20, 1000, and 5000 mm/s also display the same trend as that of Fig. 7 (plots not shown for brevity). As discussed above, the numerator of thermal Mach number (vrx) is considered as an indication of the rate at which the energy is transferred into the sample (accumulation of energy), whereas the denominator (D) describes the rate of heat diffuses through the substrate from the heating spot (dispersion of energy). When the rate of energy dispersing is greater than or equal to that of accumulating (i.e. D Zvrx or Mth r1), no energy accumulation occurs. In other words, the energy will diffuse away at the rate of D once it reaches the substrate, therefore, the energy provided by the laser beam dominates the desorption reaction (for SAM patterning application). When the local energy intensity (rather than the average intensity) is high enough to induce, at least a local temperature of 490 K, it can produce a full SAM desorption; this applies to all the cases shown in Fig. 7 except the starting points. When the local energy intensity is lower than the minimal value needed to elevate the temperature to 490 K, no fully desorbed area will be produced. This explains the cutoff (intersecting curves with x-axis) seen on the left side of the curves in Fig. 7, i.e. where Fs ¼0. Similarly, the maximum point in Fig. 8 can be physically understood as when the local energy distribution reaches the optimal condition, which means the farthest distance away from the centerline of the heating spot with a temperature of 490 K. This results in optimal temperature field along the surface, hence the calculated feature size reaches the maximum value. As discussed above, the thermal footprint of laser beam similar in shape to that of the laser beam itself. Therefore, optimal patterning condition also indicates that the laser beam cross section (defined by rx and ry) has the optimal shape, and it produces a ‘‘smooth’’ and ‘‘large’’ feature size when the condition Mth r1 is meet.
Fig. 8. Comparison of the theoretically calculated temperature field on substrate surface (dashed line, read from right axis) by heat diffusion model, Eq. (3), and final SAM coverage (solid line, read from left axis) by thermo-kinetics model, Eq. (7). Laser power, scanning velocity, and aspect ratio are 150 mW, 200 mm/s, and 4, respectively.
When the rate of energy dispersing is less than that of accumulating (i.e. D ovrx, or Mth 41, which is not shown here for brevity), the energy accumulation occurs. As a result, both the energy provided by laser and the accumulation effect determine the desorption reaction for SAMs in DLP (or oxidation, silicon processing). Due to the energy accumulation, it can be easily understood that the energy will be accumulated in the heating spot, and thus the temperature of the heating area will be high, but areas far away from the centerline heating spot is low. Hence, a ‘‘sharp’’ temperature profile will be produced and the calculated feature size will be small (when maximum temperature is higher than 490 K) or even zero (when maximum temperature is less than 490 K). That is to say, in order to obtain a localized ‘‘sharp’’ and ‘‘small’’ feature size, the condition Mth 4 1 should be satisfied, i.e. a high scanning velocity should be used. This point is contrary to the goal of this study (process large area in a single pass), but an important process parameter, if one is to produce sub refraction feature sizes [26]. By extracting the optimal thermal Mach number from Fig. 7, the optimal value of vrx, the product of scanning velocity (v, which can be determined from Fig. 6) and optimal beam radius (rx)op, are known; by extracting the optimal aspect ratio from Fig. 4, the minor axis radius (rx) is known. Comparing Fig. 7 with Fig. 4, it is clear that with the same laser power and scanning velocity, both graphs have the same maximum dimensionless feature sizes, which means the optimal aspect ratio and optimal thermal Mach number should be satisfied at the same time. Hence, minor axis radii obtained from both plots are the same, and equal to the optimal beam radius. 3.2. Thermo-kinetics approach The second approach of characterizing the resulting feature sizes mentioned above is the coupled thermo-kinetics mode, i.e. Eq. (7). By solving this coupled kinetics model numerically, the final HDT coverage after patterning can be obtained. Fig. 8 shows comparison of the theoretically calculated laser-induced temperature field (dashed line, right axis) and the HDT coverage (solid line, left axis) of the surface for incident laser power, scanning velocity, and aspect ratio of 150 mW, 200 mm/s, and 4, respectively. Fig. 8 indicates a good agreement with the theoretical calculation results from both heat diffusion and thermokinetics models (for instance, as shown in Fig. 8, the percentage difference between both models is about 9.5%).
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Fig. 9. Comparison of the correlation between different desorption percentage of HDT and aspect ratios. Width of HDT desorption at different percentage are theoretically calculated by thermo-kinetics model given by Eq. (7). The laser power and scanning velocity are fixed as 150 mW and 200 mm/s, respectively.
Fig. 8 also shows three zones with constant HDT concentration, and two areas where HDT concentration changes rapidly with distance from centerline. The two areas with HDT concentration of 100% (1 in Fig. 8) are where substrate is not affected and the size of this area depends on width of other zones. In the area near the centerline, the HDT has been fully desorbed (HDT concentration is 0). The full desorption width is of course also weakly velocity-dependent which is not discussed here for brevity. One of the major differences between the surface temperature model and thermal-kinetics model is that the former model can only provide the calculated feature size (which is defined by the temperature threshold of 490 K), but the latter model provides detailed compositional information (any value from 0% to 100%) at any given point. Hence the width of transition zones in Fig. 8 and its chemical composition can be found. As presented in Fig. 9, the widths of three different desorption percentages (0%, 50%, and 100%, corresponds to HDT concentration of 1, 0.5, and 0) are compared. When plotting the width of any desorption percentage, the ‘‘desorption percentage’’ is theoretically defined as the desorption that one and only one molecular of SAM has been removed. Fig. 9 shows that with the increase of the aspect ratio, the width of any HDT desorption percentage increases at first. This means that a general broadening of edges of the feature width where HDT concentration is zero is observed along with increasing the feature size (zone with HDT concentration of 0). Fig. 9 also shows that when maximum feature size is obtained at bop, the edges (zone with variable HDT concentration, represented by the width of HDT desorption of 50%) is also the broadest. This means that for cases where edge definition need to be very sharp, a value below bop should be used. Fig. 9 also provides detail information about composition of the processed area for b values where no fully desorbed area will exist as pointed earlier, such information can be useful, for example, for processing chemical gradient [16]. As the aspect ratio increases (at a fixed laser power and scanning speed), the slope of the two curves where HDT concentration changes rapidly (see Fig. 10) i.e. drops down. To describe the transition quantitatively, the edge transition width (denoted as ET) is defined as the width of transition zone between full desorption and partial desorption. By measuring the length between the onset of partial desorption and the centerline for all of these curves, the edge transition widths are found to be 55, 70, and 130 mm for aspect ratio of 1, 20, and 50, respectively (refer to Fig. S3 in the supplementary materials available online). In
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Fig. 10. Changing behavior of theoretical final SAM coverage associated with the laser beam aspect ratio. The SAM coverage is obtained by calculating the thermokinetics model given by Eq. (7). Laser power and scanning velocity are fixed as 150 mW, and 200 mm/s, respectively. Only half of the curves are shown due to symmetry with respect to centerline. Widths of the edge transition zones are 55, 70, and 130. ET in this figure shows as an example of the edge transition width in the case with an aspect ratio of 20.
other words, at fixed laser power and scanning velocity, edge transition widths increase with increase of aspect ratio. The dependence of edge transition width (ET) on b is important for DLP since this effect can be either viewed as positive or negative by DLP users. If a surface with smooth and gradual edge definition such as an energy gradient is needed, then using elliptical laser beams with larger aspect ratio (i.e. b 430) is an ideal tool; however, if a sharp and rapid edge definition is required, one might have to either keep the laser aspect ratio small (i.e. b o20) or accept the large transition width as a cost for obtaining larger resulting feature size in a single pass mode.
4. Summary and conclusions A quantitative analysis of processing parameter for application of an elliptical beam to achieve the maximum processing area was the purpose of this study. DLP process was used as a case study and a parametric analysis of feature sizes of the patterned SAMs produced by DLP using CW elliptical laser beam is presented, but the findings can be general by just changing the constants. It is shown that scanning an elliptical laser beam along its minor axis has at least two advantages compared with circular beams: (1) it can pattern a larger region in each scan and (2) larger areas can be patterned without thermal damage to the substrate. Two different models were discussed: the heat diffusion model and coupled thermo-kinetics model. The heat diffusion model provides the surface temperature, which is numerically calculated by capturing the feature sizes associated with 75–80% HDT desorption (defined by 490 K theoretically). It is simple, quick, and precise enough for quantitative analysis regarding the corelationships between feature sizes and processing parameters (i.e. laser power, scanning velocity, and beam aspect ratio). Results from the heat diffusion model show that the feature size increases linearly with increase of laser power; whereas, the feature size increases with decrease of scanning velocity, and this effect is more pronounced at lower velocities (i.e. o1000 mm/s). Furthermore, the laser power and beam aspect ratio are an important determining factors for feature sizes than scanning speed. In order to increase/decrease the resulting feature size, when laser power is low (e.g. o90 mW), the first choice is to increase/decrease the incident laser power (other than decrease/increase the scanning
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velocity); while for high powers (e.g. 4120 mW), changing incident power is the only choice. Each elliptical laser beam has a unique optimal aspect ratio: for a given power and velocity, patterning with an elliptical beam at optimal aspect ratio can result in the widest feature size. The coupled thermo-kinetics model describing the final coverage of SAM on surface is a more accurate method compare to the thermal model to predict the final HDT coverage and hence the full HDT desorption width on the surface, but it is time-consuming to solve. The thermo-kinetics model is very useful to gain detail insight of SAM desorption percentage with respect to some specific processing conditions. It also provides edge resolutions information. The edge transition width increases with increase of aspect ratio. If a surface with gradual edge definition is needed, using elliptical laser beams with larger aspect ratio (i.e. b 4 30); however, if a sharp edge definition is the goal, one might have to either keep the laser aspect ratio small (i.e. b o20) or take the large transition zone as a cost for saving processing time.
Acknowledgment This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Canada Research Chair program.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at doi:10.1016/j.optlastec.2011.03.034.
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