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Formation of polymeric pillars by using laser interference lithography is compared for nanosecond and picosecond laser pulses. The experimental results are explained by dynamics of laser-excited radicals. The shape of fabricated structures demonstrates that thermal accumulation and oxygen diffusion from the surrounding air make an influence on polymerization when the pulse duration is in the nanosecond range. By using picosecond laser pulses, the thermal accumulation and oxygen diffusion effects are not important for low repetition rate (500 Hz), and they become relevant only at the repetition rates higher than ≥ 1 kHz. It is shown that thermal accumulation is caused by a low-temperature diffusivity and heat accumulation at the polymer-glass interface, and it plays a significant role in the final shape of the structures fabricated using the nanosecond laser pulses.
© 2017 Optical Society of America
1. Introduction
In recent years, techniques based on photo-polymerization has been demonstrated the fabrication of complex 3D and 2D objects of dimensions required for practical applications in photonics [1,2], micro-optics [3–5], micro-fluidics [6–8] and biomedicine [9, 10]. Usually, such structures were fabricated using ultra-short laser pulses, but some investigations have been performed by employing low-cost lasers emitting picosecond [11, 12] or nanosecond [13] pulses and continuous wave (CW)-lasers as well [14]. Optimizing the photo-polymerization processes requires that an appropriate exposure energy to be delivered to the photopolymer material. That is because the induced photo-chemical kinetics depend on how the exposure energy is delivered [15]. Understanding of the photo-chemical and photo-physical processes, which occur during photo-polymerization is of extreme importance when attempting to improve the performance of a photopolymer material for given applications [16]. A typical photopolymer system consists initially of monomers and photoinitiators. Under the laser irradiation, the photoinitiators are excited by light absorption, resulting in the creation of radicals that are able to initiate the polymerization chain reactions (here we consider the most popular negative tone photoresists) [13]. The growth of chain radicals is restrained by termination reactions. When the material is exposed to an interference pattern, more monomers are polymerized in the bright region than in the dark region due to periodical intensity distribution [17]. This non-uniform irradiance distribution sets up monomer concentration gradients and results in diffusion of monomers from dark regions to the neighboring bright regions. Such irradiance allows having a controlled polymerization process, which can help find out the dominant processes that influence the shape of the final structures.
Here, we examined in detail the effect of pulse duration and pulse repetition rate to the photo-polymerization using an interference lithography technique [18]. Analysis of the pulse duration effect on the shape of the fabricated pillar is performed. Dynamics of radicals during a single pulse exposure was estimated, and it was revealed its influence on geometrical parameters of pillars and their variation for the ps- and ns-pulse exposure. It was found that polymerization by a ps-pulses is ~33 times less efficient than for the ns-pulses even if peak pulse intensity of the used ps-pulse is 3.5 times higher comparing to the ns-pulse. The analysis proved that thermal accumulation enhanced the polymerization process when pulse duration was in the ns-range. In the ps-range, the thermal accumulation for low repetition rate was negligible and became important at a higher repetition rate (≥ 1 kHz). Thermal accumulation at the polymer-glass interface was found to be significant and affected the shape of the pillars when the ns-laser pulses were applied.
2. Materials and methods
Comparison of photo-polymerization processes induced by nanosecond and picosecond laser pulses was performed by employing the laser interference lithography system [Fig. 1], which included a picosecond laser (Atlantic HE from Ekspla, pulse duration ~300 ps) or nanosecond laser (NL220 from Ekspla, pulse duration ~35 ns) operating at 532 nm wavelength. A diffractive optical element (DOE) (Holo-Or Ltd.) was used to split the laser beam into four identical beams. A diaphragm blocked undesirable high-order diffracted beams. A two-lens (L1 and L2) imaging system collected four beams on the sample surface where they interfered. The interference intensity distribution of four beams is constant in the vertical direction and fluctuates only in the lateral direction [depicted in Fig. 1 right]. The repetition rate of the nanosecond laser was set to 500 Hz, and it was chosen 500 Hz or 1 kHz in the case of the picosecond laser. The four-beam interference patterns with the period of 7.5 μm were recorded in SZ2080 photopolymer spin-coated on glass. The concentration of photoinitiator 4,4‘-bis(dimethyl-amino)-benzophenone was 1 wt%. Before the laser treatment, samples were dried for ~20 min at 95°C to evaporate the solvent and to solidify them. Photo-polymerization was initiated in a solid SZ2080 resist. The sample was irradiated from the polymer side [shown in Fig. 1]. After the exposure, samples were developed in 4-methyl-2-pentanone for 20 min to dissolve unexposed regions. All structures used for comparison of polymerization conditions were fabricated on the same specimen.
Fig. 1 Scheme of the experimental setup utilizing the laser interference lithography. Inset on the top right presents the comparison of the used laser pulses when the peak intensity of a picosecond laser pulse was 3.5 times larger compared to the peak intensity of a nanosecond laser pulse. Inset on the bottom right demonstrates an intensity distribution pattern of the four-beam interference.
3. Results and discussion
3.1 Effect of the pulse duration
Periodical pillar patterns were fabricated using the four-beam interference lithography with two different laser pulse duration (35 ns and 300 ps) at various laser exposure times (from 5 s to 240 s). To make a fair comparison between ns- and ps-pulse exposures, we searched for conditions with closest pulse peak intensities which can be used for a wide set of exposure doses. The pulse intensity of the ps-pulses was selected to be 3.5 times higher than the peak intensity of the used nanosecond pulses [inset in the top right of Fig. 1]:
where P is the average power of the laser, w0 is the radius of the beam on a sample; ν is the pulse repetition rate; τ is the pulse duration. The repetition rate and the beam radius on the sample were equal to ν = 500 Hz and w0 = 750 μm in all experiments. The average laser power was selected ~488 mW and ~15 mW for the ns-pulses and ps-pulses, respectively. Comparison of the structures fabricated using different laser pulse durations and exposure times is shown in Fig. 2. Morphology of the pillars in both cases was different and is summarized in Fig. 3. The diameter of the pillars was measured at the half of the pillar height. The data demonstrate that pillars, fabricated using ns-laser pulses, were wider and higher as compared with the pillars fabricated using ps-laser pulses. Furthermore, in the ps-case, the pillars started to grow only then the exposure time was longer than 40 s and they were too weak to survive the development process. By increasing the exposure time, the pillars manufactured using the ps-laser pulses were better crosslinked (a higher bulk modulus), but they were still too soft and collapsed due to capillary forces [19] acting during the drying process even if the exposure time was as long as 240 s [demagnified view in Fig. 2]. Meanwhile, in the ns-case, it was hard to distinguish the shape of the pillar after the 240 s exposure time [Fig. 2]. Furthermore, the diameter of the structure fabricated using the 5 s exposure time was already larger compared to the diameter of the structure fabricated in the ps-case and 240 s exposure time [Fig. 3].Fig. 2 Morphology of the structures fabricated using 300 ps and 35 ns laser pulses with different exposure times. The peak intensities of the used picosecond and nanosecond pulses were 11.3 MW/cm2 and 3.2 MW/cm2, respectively. Scale bars represent 5 μm.
Fig. 3 Diameter (a) and height (b) of the pillars vs. exposure time for 35 ns (black) and 300 ps (red) laser pulses with the 3.2 MW/cm2 and 11.3 MW/cm2 peak pulse intensities, respectively. The diameter was measured at the middle of the pillar height.
These experimental results can be explained as follows. It is well known that the size of the polymerized volume (voxel) is defined as the region where the density of radicals exceeds a certain minimum concentration (the threshold value) Rth [20]. Radicals are generated by the photolysis of photoinitiator molecules, and their concentration varies both spatially and temporally as it depends on various kinetic and transport processes [21]. The concentration of the radicals over the time is determined by their generation, termination and diffusion processes. The partial differential equation describing the dynamics of radicals can be represented by the equation:
where R is the density of radicals, t is time, D is the radical diffusion constant, σ1 is the effective single-photon cross-section for the generation of radicals, P is the density of primary initiator particles, N is the photon flux, kt is the chain reaction termination constant, kp is the propagation rate constant, M is the density of monomers.The laser power absorbed from a single pulse with the Gaussian spatial distribution in a volume unit can be written:
where I is the local laser intensity, z is the longitudinal coordinate, x is the transverse coordinate, α is the linear absorption coefficient, τ is the laser pulse duration.It is usually assumed that the energy density is proportional to the absorbed photon flow multiplied by the effective photon cross-section for the generation of radicals:
The photon flux spatially modulated in the case of a four-beam interference can be written:
where I0 is the peak intensity of the interference maximum, x is the transverse coordinate, Λ is the period of the interference intensity modulation.Then, the partial differential equation describing the radical generation by a single Gaussian beam pulse and their dynamics can be written as
The density of radicals generated by a single pulse can be estimated using Eq. (6). The estimated alteration of the radical density during the pulse at the interference maximum is shown in Fig. 4(a). The radical density generated with the 35 ns pulse and 3.2 MW/cm2 peak intensity (black line) at the end of a pulse is more than 30 times higher compared to the case of using the 300 ps pulse and 11.3 MW/cm2 peak intensity (red line). The temporal profiles of pulses (35 ns at FWHM – green, 300 ps at FWHM – blue) used in the estimation are shown in Fig. 4(a). An enlarged view of the radical density dynamics during the picosecond laser pulse is displayed in Fig. 4(b). The numerical analysis shows that the highest radical density is reached at the end of the laser pulse. Neither diffusion nor termination of radicals are dominant in this period and do not cause any significant change in the radical concentration until the end of the laser pulse. After the laser pulse, the radical density is decreasing due to the diffusion and termination processes. The dark period is defined as a time between two consecutive laser pulses, and it depends on the pulse repetition rate: for 500 Hz, it is 2 ms. Comparison of the radical density change in the interference maximum during the dark period in the ns- (black lines) and ps- (red lines) pulse cases for the different diffusion constants (10−9 cm2/s, 10−10 cm2/s, 10−11 cm2/s) is shown in Fig. 4(c) left. On the right side of Fig. 4(c), an enlarged view of the radical kinetics during the dark period for the ps laser pulse is depicted. For numerical analysis, the following process and material parameters were used: termination constant kt = 5x10−8 m3/(mol*s), the propagation constant kp = 5x10−8 m3/(mol*s), absorption constant α = 86.5 1/cm, peak intensity of the interference maximum I0 = 11.3 MW/cm2 (for the 300 ps laser pulse) or I0 = 3.2 MW/cm2 (for the 35 ns laser pulse), the period of the interference pattern Λ = 7.5 μm, the density of primary initiator particles P = 1 wt%, the density of monomers M = 99 wt%. It should be noted that calculations were made for a single laser pulse.
Fig. 4 a) Theoretical estimation of the radical density generated by a single laser pulse with the duration of 35 ns and with the 3.2 MW/cm2 peak intensity (black line) and for the 300 ps pulse with the 11.3 MW/cm2 peak intensity (red line); b) the radical density transient during the 300 ps laser pulse (the temporal profile is shown in the background); c) the radical density dynamics during the dark period for a 500 Hz system and different diffusion constant in the case of the 35 ns (black lines) and 300 ps (red lines) pulse durations with the peak pulse intensities 3.2 MW/cm2 and 11.3 MW/cm2, respectively. The right side depicts an enlarged view of the radical density variation during the dark period in the case of using the 300 ps pulse.
Simulation results show that for the larger diffusion constant, the decrease in the radical density in the region of the interference maximum is higher, but the termination process also plays a key role, especially for the higher density of radicals. In addition, the modeling results confirm that the longer laser pulse even at the lower peak intensity generates a larger number of radicals. It means that less number of laser pulses (or shorter exposure dose) is required to reach the threshold value of the radical density for longer laser pulses. If the number of laser pulses in both cases is the same, the region where radical density exceeds the photo-polymerization threshold is broader for the longer laser pulses. It indicates that the diameter of pillars obtained in the ns-pulse case (dns in Fig. 5(a)) is larger compared to the diameter of the structures fabricated in the ps-pulse case (dps in Fig. 5(a)). Furthermore, the difference in the height of the fabricated pillars for different exposure times [Fig. 3(b)] can be explained by the depletion of atmospheric oxygen, which inhibits the polymerization reaction. When the laser exposure time is short, the radicals created in the upper layer of polymer are consumed by oxygen scavenging, and the height of fabricated pillars is lower than the thickness of used polymer layer. By increasing the laser exposure time, the concentration of generated radicals is increasing and the consuming of the radicals by oxygen scavenging getting insufficient to limit the height of the fabricated pillars. The experimental results explain why the diameter of pillars formed by the ns-laser pulses is larger comparing with the use of ps-pulses, and why fewer laser pulses (shorter exposure time) are needed to fabricate the pillars in the ns-case but do not explain the final shape of pillars.
Fig. 5 a) Illustration of the difference between the radical density generated by the ns- and ps-laser pulses in the four beam interference case. Rth – threshold of radicals density; dps and dns – diameter of pillars fabricated by picosecond and nanosecond laser pulses, respectively; b) The transmission spectra of the used substrate (red line) and of the photopolymer SZ2080 with 1wt% 4,4‘-bis(dimethyl-amino)-benzophenone on the substrate (black line) when the thickness of the photopolymer was ~10 µm (the same as used in the experiments); c) Model of the heat accumulation effect to the shape of the pillars fabricated in nanosecond and picosecond cases. Pillars in nanosecond case were fabricated with 35 ns pulse duration, 3.2 MW/cm2 peak pulse intensity and 5 s exposure time, in picosecond case 300 ps pulse duration, 11.3 MW/cm2 peak pulse intensity and 240 s exposure time.
3.2 Effect of the pulse duration
The shape of the pillars was found not following the predictions of the photo-induced radical distribution. The following issues affecting polymerization has to be discussed:
- 1) The exponential decrease of the absorbed light intensity in the z-direction according to Beer-Lambert law do not clarify the shape of fabricated pillars as the laser power absorbed by the upper layer of polymer (from air side) is higher than at the lower side of polymer (close to the glass substrate). It means that diameter of the fabricated pillars should be wider at the top of the pillar comparing to the bottom side.
- 2) The interference field due to the incident and reflected from the substrate laser beams is negligible since the refractive indexes are similar (~1.5).
The pillar bottom widening effect in the ns-case can be explained by the depletion of atmospheric oxygen and the mismatch of thermal diffusivity at the boundary of polymer-glass. Indeed, concentration of oxygen up to 1018 cm−3 exist in polymers (e.g. in PMMA) [23, 24]. Oxygen inhibits the polymerization reaction and is usually consumed locally (by photogenerated radicals) before the actual reaction starts. Oxygen diffusion in PMMA was found to be dependent on crosslinking and twice slower in a fully crosslinked PMMA D = 2 x 10−8 cm2/s at 25° C as compared with a dried MMA solution [25] with Arrhenius activation energy of 38 kJ/mol. Hence, just 50 s is required for diffusion over the length of 10 μm. In the case of high pulse energies (ns pulses) and hence short exposure time (5 s) and fast polymerization, the consumption of the oxygen is faster than it is back-diffusion from the surrounding air. Obviously, no oxygen comes in from the glass side. Hence, there is a constant oxygen gradient over the height of the photoresist film such that oxygen concentration is highest at the photoresist-to-air interface. There, polymer conversion should be lowest as a larger fraction of the created radicals is consumed by the oxygen scavenging. In the case of the ps-pulsed setup, the polymerization is much slower, with fewer radicals generated per pulse [Fig. 4] and longer exposure time. In this case, the oxygen can diffuse in from the surrounding air as fast as it is consumed. No significant gradient is built up.
Furthermore, in the nanosecond case heating of the substrate is stronger, comparing it to the ps-case, as the difference between the used pulse energies is ~33 times. The maximum temperature jump due to a single pulse can be estimated from the absorbed energy:
where R – the light reflection coefficient, Fp = Ep/S is the fluence expressed per the pulse energy Ep over the surface area S, kB is the Boltzmann constant, ls = λ/(2) is the absorption depth with used laser wavelength and κ is the extinction coefficient, na = ρNA/M is the atomic density of material with mass density ρ and molar mass M, NA is the Avogadro number.In the ns-case, the portion of the pulse energy for one polymerized pillar is ~22 nJ when the pillar radius wr = 2.5 µm; the absorption depth ls ~4.234 x 10−5 m, when the laser wavelength λ = 532 nm and the extinction coefficient κ = 0.002; the atomic density of material na ~3.088 x 1021 number of atoms per bonds when ρ = 1.2 g/cm3 and M = 234 g/mol. Then, the temperature rise per a single pulse in the ns-case is ~44 K, while in the ps-case only ~1.4 K when the pulse energy for one polymerized pillar is ~0.7 nJ.
The calculations show that the difference in the temperature rise per a single pulse in the ns-case and the ps-case is significant when peak pulse intensities of both pulses are comparable. For the stabilization of temperature differences between upper side (air-polymer interface) and bottom side (polymer-glass interface) of 10 µm thickness (d) of SZ2080 sample with thermal diffusion constant χ ∼10−3 cm2/s [26, 27] is needed 1 ms (t = d2/χ). It is two times less than the time gap (tgap) between subsequent pulses when the pulse repetition rate is 500 Hz (tgap = 2 ms). This simple estimation shows that thermal accumulation in the experimental conditions with the used repetition rate of 500 Hz at the air-polymer interface do not occur. The experimental results show stronger polymerization at the glass-resist interface [Fig. 2]. It suggests that thermal accumulation occurs due to mismatch of thermal diffusivity at the boundary of polymer-glass, e.g., due to grain structure of the resist as the heat is localized on the nanoscale, at grain boundaries, and materials of low-temperature diffusivity [28]. Thermal diffusivity mismatch slows down the heat flux from the heated area, and it is leading to the longer cooling time for the heated area. That is further gained by exothermic nature of polymerization which is releasing the heat locally. Thermal accumulation at the polymer-glass interface and oxygen diffusion in polymer cause the pillar bottom widening in the ns-case [Fig. 5(c)]. In the nanosecond case, the heating of the substrate is stronger, comparing it to the ps-case, and the thermo-polymerization process already plays a significant role to the shape of the fabricated structures (as the higher temperature increases the photopolymerization rate [29–31]). In the ps-case, we were not able to observe the pillar bottom widening effect [Fig. 5(c)] even if the exposure time was as long as 240 s, and the peak pulse intensity of used picosecond pulses was about 3.5 times larger than that of used nanosecond pulses. In the picosecond case, the heating of the substrate was negligible as the maximum temperature jump due to a single pulse was proportional to the pulse energy (Tmax~Ep) [32, 33]. Furthermore, the polymerization in ps-case was much slower, and exposure time was longer. It leads to the uniform distribution of the oxygen as the diffusion of oxygen in the polymer from the surrounding air was as fast as its consumption. The thermal and oxygen depletion effects were observed in the ps-case when the repetition rate of pulses was increased more than twice. It means that the time gap between subsequent pulses was decreasing till 1 ms, and it was enough to observe the thermal accumulation and oxygen diffusion effects [Fig. 6]. More detailed results of experiments using different laser pulse repetition rate are described in the following section.
Fig. 6 a) Illustration of the experimental results using different pulse repetition rate of the lasers; b) Morphology of the structures fabricated with the 300 ps laser pulses and different repetition rate (1 kHz and 500 Hz) for the different number of the pulses when the laser pulse energy is 30 μJ and pulse peak intensity is ~11.3 MW/cm2. Scale bars represent 5 μm.
3.3 Effect of the repetition rate
Periodical structures were fabricated using different pulse repetition rates (1 kHz and 500 Hz) of the ps-laser and the number of laser pulses (5k −120k) while the peak intensity in both cases was the same [Fig. 6(a)]. When the repetition rate was 1 kHz, the dark period was two times shorter comparing with the case of the 500 Hz repetition rate. It means that, in the 1 kHz case, the radicals had less time to diffuse and react with other species (monomers, radicals, or inhibitors) during the dark period compared to the 500 Hz case. Theoretical estimation of the radical density for different durations of the dark period is shown in Fig. 4(c). The vertical cyan line in Fig. 4(c) shows the radical density for the 1 kHz case. The experimental results confirm that the polymerization reaction and monomer conversion took place in the dark period, and its duration influenced the formation of the structures. In Fig. 6(b), there are shown micrographs of the structures fabricated with the different pulse repetition rates (1 kHz and 500 Hz) and the number of laser pulses when the laser pulse duration was 300 ps and the pulse energy was equal to 30 μJ. In Fig. 7, the diameter and height for both cases and a different number of laser pulses are compared. The diameter and height of the fabricated pillars were higher in the 1 kHz case. Furthermore, the formation of pillars required less number of laser pulses. From Fig. 6(b), it is evident that in the 1 kHz case, the formation of structures started at 5k laser pulses, whereas, in the 500 Hz case, they started to grow only after irradiation with 20k pulses. In the case of 1 kHz and 1.2 x 105 pulses, the fabricated pillars survived the development process. Meanwhile, in the 500 Hz case and 1.2 x 105 laser pulses, the manufactured structures still did not have enough molecular weight and structural rigidity to withstand the development process. Moreover, it is clearly seen from Fig. 6(b) that by using 500 Hz repetition rate, the diameters of the pillars at the bottom and the top were close as the heating of the substrate was negligible and the oxygen diffusion due to long exposure time from the surrounding air was as fast as it is consumed. By using 1 kHz pulse repetition rate, the thermo-polymerization process and oxygen diffusion gradient due to twice shorter exposure time, already started to play a significant role in the shape of fabricated structures (pillars at the bottom are wider). It means that the radical density at the bottom was higher than at the top of polymer despite that the sample was irradiated from the top.
Fig. 7 The variation of geometrical parameters (diameter (a) and height (b)) of pillars fabricated by using 1 kHz (black) and 500 Hz (red) with the 300 ps (red) laser pulses and a different number of pulses. The diameter was measured in the middle of the structure height.
4. Conclusions
The effect of laser pulse duration and repetition rate to the polymerization process was analyzed. The experimental results demonstrated that structures, fabricated with the 35 ns-pulses, were taller and wider compared to the structures produced using the 300 ps-laser pulses even when the peak intensity of the ps- pulses was 3.5 times larger than that of the ns- pulses. The numerical analysis shows that the difference between the fabricated structures is determined by the radical density generated with a single laser pulse. Furthermore, the shape of the structures produced with the ns-pulses proposes that the photo-polymerization is enhanced by the thermo-polymerization process. In addition, the oxygen diffusion in the photopolymer from the surrounding air plays a significant role in the shape of fabricated pillars using ns-laser pulses. In the ps-case, the thermal accumulation and oxygen diffusion effects for low repetition rate is insignificant and becomes relevant only at a higher repetition rate. Structures manufactured with the higher pulse repetition rate are also taller and wider compared to the structures fabricated with the lower repetition rate when the other laser pulse parameters stay the same. The results exhibit that the losses of radicals between pulses, thermal accumulation and oxygen diffusion from the surrounding air are important for the final shape of the polymerized pillars and these effects can be used for the shape control of the polymerized structures.
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