Fabrication-resolution enhancement method based on low-energy multiple exposures

Laser direct writing (LDW) as a significant maskless lithography technique has been widely applied in scientific research and industrial manufacture. However, low fabrication resolution restricts its application in nanofabrication due to optical diffraction limit. This work presents a simple and novel way to improve the LDW fabrication resolution by multipleexposure method with a low energy laser beam. Experiments indicate that the method could increase the fabrication resolution by 33.3% for the same exposure depth, and is close to simulation results. It should be pointed out that principle of the method is universal, and may be instructive to improve the fabrication resolution of other maskless energy beam lithography techniques such as EBL and FIB. © 2015 Optical Society of America OCIS codes: (220.3740) Lithography; (200.0200) Optics in computing; (310.6628) Subwavelength structures, nanostructures. References and links 1. J.-H. Lee, C. Y. Koh, J. P. Singer, S.-J. Jeon, M. Maldovan, O. Stein, and E. L. Thomas, “25th Anniversary Article: Ordered Polymer Structures for the Engineering of Photons and Phonons,” Adv. Mater. 26(4), 532–569 (2014). 2. C. F. Guo, S. Cao, P. Jiang, Y. Fang, J. Zhang, Y. Fan, Y. Wang, W. Xu, Z. Zhao, and Q. Liu, “Grayscale photomask fabricated by laser direct writing in metallic nano-films,” Opt. Express 17(22), 19981–19987 (2009). 3. C. F. Guo, J. Zhang, J. Miao, Y. Fan, and Q. Liu, “MTMO grayscale photomask,” Opt. Express 18(3), 2621– 2631 (2010). 4. M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage,” Nat. Mater. 6(11), 824–832 (2007). 5. W. Gawelda, J. Siegel, C. N. Afonso, V. Plausinaitiene, A. Abrutis, and C. Wiemer, “Dynamics of laser-induced phase switching in GeTe films,” J. Appl. Phys. 109(12), 123102 (2011). 6. X. Sun, E. Thelander, P. Lorenz, J. W. Gerlach, U. Decker, and B. Rauschenbach, “Nanosecond laser-induced phase transitions in pulsed laser deposition-deposited GeTe films,” J. Appl. Phys. 116(13), 133501 (2014). 7. S. Privitera, S. Lombardo, C. Bongiorno, E. Rimini, and A. Pirovano, “Phase change mechanisms in Ge2Sb2Te5,” J. Appl. Phys. 102(1), 013516 (2007). 8. D. Bhattacharya, R. K. Singh, and P. H. Holloway, “Laser-target interactions during pulsed laser deposition of superconducting thin films,” J. Appl. Phys. 70(10), 5433–5439 (1991). 9. V. N. Tokarev and A. F. H. Kaplan, “An analytical modeling of time dependent pulsed laser melting,” J. Appl. Phys. 86(5), 2836–2846 (1999). 10. F. Xia, X. Zhang, M. Wang, S. Yi, Q. Liu, and J. Xu, “Numerical analysis of the sub-wavelength fabrication of MTMO grayscale photomasks by direct laser writing,” Opt. Express 22(14), 16889–16896 (2014). 11. J. Feng, Y. Zhang, B. W. Qiao, Y. F. Lai, Y. Y. Lin, B. C. Cai, T. A. Tang, and B. Chen, “Si doping in Ge2Sb2Te5 film to reduce the writing current of phase change memory,” Appl. Phys., A Mater. Sci. Process. 87(1), 57–62 (2007). 12. C. B. Peng, L. Cheng, and M. Mansuripur, “Experimental and theoretical investigations of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82(9), 4183–4191 (1997). 13. F. R. Liu, N. Bai, J. J. Zhao, X. X. Han, W. P. Zhou, X. Lin, and N. X. Sun, “An explanation of the crystallization of amorphous Ge2Sb2Te5 films induced by a short Gaussian laser pulse,” Appl. Phys. Lett. 103(5), 051905 (2013). #249670 Received 8 Sep 2015; revised 28 Oct 2015; accepted 28 Oct 2015; published 2 Nov 2015 © 2015 OSA 16 Nov 2015 | Vol. 23, No. 23 | DOI:10.1364/OE.23.029353 | OPTICS EXPRESS 29353 14. V. Weidenhof, I. Friedrich, S. Ziegler, and M. Wuttig, “Atomic force microscopy study of laser induced phase transitions in Ge2Sb2Te5,” J. Appl. Phys. 86(10), 5879–5887 (1999). 15. J. Liu, S. Liu, and J. Wei, “Origin of the giant optical nonlinearity of Sb2Te3 phase change materials,” Appl. Phys. Lett. 97(26), 261903 (2010). 16. F. R. Liu, X. X. Han, N. Bai, J. J. Zhao, J. M. Chen, and X. Lin, “Numerical simulation on the temperature field induced by a nanosecond pulsed excimer laser in the phase-change film,” Thin Solid Films 551, 102–109 (2014).


Introduction
Laser direct writing (LDW) technique has been widely applied to manufacture field due to its simplicity, flexibility and low cost.However, low fabrication resolution of traditional LDW restricts its applications in nanofabrication because of optical diffraction limit.To overcome the obstacle, several material-dependent or/and facility-dependent super-resolution methods have been developed recently, such as two-photon polymerization [1] and nonlinear-effect LDW [2,3].Owing to limitation of the methods, exploring universal approach based on physics principle rather than materials will be more meaningful for enhancing LDW fabrication resolution.
Generally, laser fabrication in size is decided by spot size of laser beam, but its effective size relies on energy density of laser pulse in fact due to Gaussian distribution of the laser beam.In other words, for a defined laser pulse width, the smaller the effective size, the lower the power, implying fabrication size could be decreased by using a lower energy laser pulse.Recently, multiple-exposure research of chalcogenides has been reported [4].W. Gawelda et al. observed an increase of crystallization degree in amorphous GeTe film with an increase of number of exposure by a low energy laser beam [5,6], accompanying with an height decrease in laser action region, indicating a phase-change depth desired can be crystallized layer by layer.Herein taking Ge 2 Sb 2 Te 5 as an example, we studied fabrication resolution enhancement (FRE) effect from laser-material interaction principle for the first time by multiple exposures using low-energy-density laser.The numerical simulation based on photothermal transformation and heat transfer theory shows an effective decrease in fabrication size and is consistent with our experimental results.The merits and demerits of the FRE effect are discussed also.Moreover, effectiveness of the FRE effect is not limited to Ge 2 Sb 2 Te 5 only.

Numerical simulation and theoretical analyses
The 50nm-thick Ge 2 Sb 2 Te 5 amorphous film samples were prepared by depositing Ge 2 Sb 2 Te 5 on cleaned Si substrates by radio-frequency magnetron sputtering (ULVAC ACS-400-C4) with power of 25 W, pressure of 0.18 Pa and duration of 900 s.Herein the substrates were cleaned ultrasonically for 10 min in turn immersed in athanol, acetone and de-ionized H 2 O, and then blow-dried by N 2 and baked for an hour at 120°C in a vacuum oven.The transmittivity and reflectivity spectrum (PerkinElmer Lambda 950) of the Ge 2 Sb 2 Te 5 film in visible region is shown in Fig. 1.The transmittivity and reflectivity of the Ge 2 Sb 2 Te 5 film at 532 nm were 10% and 38.5% on average, respectively.The absorption coefficient of the Ge 2 Sb 2 Te 5 film could be calculated according to the Lamber's law: where d is the film thickness, T is transmittivity, R is reflectivity, thus α = 3.67 × 10 7 m −1 .The FRE effect in phase-change region of the 50nm-Ge 2 Sb 2 Te 5 film sample during laser multiple exposures of a single point was simulated firstly in the cylindrical coordinates system.In the simulation, laser power was from 3.5 mW to 5 mW for a pulse of 50 ns, laser spot diameter was about 350 nm, model radius was 2500 nm, and the thickness of Ge 2 Sb 2 Te 5 and substrate were 50 nm and 950 nm, respectively.The multiple-exposure interval is 1s far longer than the characteristic thermal conduction time of Ge 2 Sb 2 Te 5 in our case, indicating the temperature accumulation between two adjacent pulses can be neglected.The initial temperature and Ge 2 Sb 2 Te 5 phase-change temperature were 293 K and 420 K, respectively [7].
Laser-induced phase change is generally attributed to the thermal effect.The spatial and temporal distribution of a laser pulse can be expressed as [8,9]: where P is the peak power of the laser spot center, τ p is the pulse width and ω is the waist of a Gaussian beam.
The thermal energy diffuses through electron-lattice coupling based on the famous twotemperature model.For a pulse width of 50 ns, the relationship τ e <<τ i <<τ p is fulfilled, where τ e and τ i is electron cooling and lattice heating time, respectively.In this case, lattice temperature and electron temperature are equal to the film temperature.As a result, twotemperature model can be simplified into the typical heat conduction equation [10]: Where T, ρ, c and k is the temperature, density, specific heat capacity and thermal conductivity, respectively.Here, (1-R) αI(r, t)e -αz refers to the absorbed laser energy density Q.
There are three kinds of heat exchange processes in the film-air system: the heat conduction, convective heat transfer and heat radiation.Considering the laser pulse is as short as 50 ns, the convective heat transfer and heat radiation can be ignored reasonably.Hence, thermal insulated boundary conditions can be taken into account as: and the thermal energy is conserved at the interface between the film and substrate, thus the interface conditions can be expressed as: where h i is the convective heat transfer coefficient, the subscript 1 and 2 refer to the Ge 2 Sb 2 Te 5 film and substrate, respectively.
According to the above model, the temperature field distributions of a single point varying with different powers and numbers of exposure were simulated for a 50 ns laser pulse.Optical and thermal parameters we adopted in the simulation are given in Table 1.And it should be noted that in multiple-exposure process, the phase-change in Ge 2 Sb 2 Te 5 film layer by layer is mainly attributed to the thermal conductivity because other parameters can be viewed as constants due to tiny variation.It is easy to see from Fig. 2 that sample temperatures corresponding to laser spot center are the highest always (marked each temperature in upper-left corner of Fig. 2) due to Gaussian distribution.Obviously, both radius and depth in phase-change region decided by 420 K isothermals have a decrease with a decrease in power from 5 mW to 4 mW.The 420 K isothermal vanishes when power declines to 3.5 mW because the highest temperature 392 K in Fig. 2(d) is smaller than the phase-change temperature of 420 K.For comparing FRE effect induced by lower-energy-laser multiple-exposure, we might as well select 20 nm as a basic phase-change depth, which corresponds to one-time exposure by a laser pulse (5 mW, 50 ns) as shown in Fig. 2(a).Compared with Figs.3(a), 3(b) and 2(b), it can be seen that there is an increase in both radius and depth in phase-change region with increasing number of exposure for the same laser pulse (4.5 mW, 50 ns).However, the radius corresponding to two-time exposures (Fig. 3(a)) has exceeded the one corresponding to onetime exposure under power of 5 mw (Fig. 2(a)), although the depth is not yet reaching 20 nm, indicating a lower energy pulse is needed.Figures 3(c)-3(f) show that difference of phasechange region under multiple exposures by using a pulse (4 mw, 50 ns).Although the radius and depth have also an increase with an increase in number of exposure, the radius for fourtime exposures shown in Fig. 3(e) has been much smaller than the one for one-time exposure shown in Fig. 2(a), demonstrating a remarkable FRE effect.What's more, it can be seen in Fig. 2 and Fig. 3 that the peak temperature of the film surface center decreases gradually with increasing number of exposure for a certain laser pulse.This is because thermal energy diffuses more easily due to the crystallization during multiple exposures.

Experiments verification
Exposure experiments were performed using a homemade LDW system adopting a frequency-doubled Nd:YAG 532 nm laser (Spectra Physics, Millennia Pro 2i) with a typical scan speed of 25 μm/s, repetition rate of 250 Hz and spot diameter of 350 nm focused by an objective lens (Nikon, NA 0.90, 100 × ).In the experiments, the pulse width and the exposure interval was 50 ns and 1 s (multiple exposures was performed by repeatedly scanning on one line), respectively, and the laser power was from 3 mW to 6 mW, corresponding energy density controlled by an acousto-optic modulator was from 156 mJ/cm 2 to 312 mJ/cm 2 .Experimental samples are the same as the ones in Section 2. Optical micrograph and morphology characterization were investigated by a confocal laser microscope (Olympus LEXT OLS4000) and an atomic force microscope (Veeco Dimension 3100), respectively.
For ease of measurement and observation, we wrote some lines by one-time exposure with laser power of 3 mW, 4 mW, 5 mW and 6 mW, respectively, for a defined 50 ns pulse width, as shown in optical image in Fig. 4(a), and AFM image in Fig. 4(b), indicating that both width and density-increase-induced sinkage in the lines increase gradually from left to right, while the line for 3 mW hadn't appeared due to too low energy.Figures 4(c) and 4(d) show width and sinkage in the lines corresponding to two-time, three-time and four-time exposures, respectively, under a power of 4 mW.Furthermore, the cross section analyses in Fig. 5(a) show that for one-time exposure with a laser pulse (5 mW, 50 ns), the width and sinkage are 300 nm and 0.9 nm, respectively.The same line depth of 0.9 nm but smaller width of 200 nm are shown in Fig. 5(b) for four-time exposures with a laser pulse (4 mW, 50 ns), showing an improvement in the fabrication resolution by 33% without sacrificing the exposure depth.Herein 0.9 nm in sinkage corresponds to about 17 nm phase-change depth, which can be calculated semi-qualitatively from the sinkage depth [14].The experimental results closely agree with the numerical simulation, and further verify the effectiveness of the FRE effect by the multiple-exposure technology.

Result and discussion
We have verified that reducing laser energy density can improve fabrication resolution, but in the meanwhile sacrificed efficient exposure depth.By means of multiple exposures with a low energy laser beam is able to effectively enhance the fabrication resolution for a certain exposure depth.Noted that each exposure can lead to a phase-change with a definite thickness due to limited-distance energy transfer, multiple exposures correspond a layer-by-layer phasechange process.When over crystallization temperature heated by the first laser pulse, the thermal conductivity increases in upper Ge 2 Sb 2 Te 5 layer due to crystallization, resulting in the next laser pulse energy can more easily transfer around.However, the radius increase in our numerical simulation is greater than depth increase in phase-change region during multiple exposures.This is because thermal diffusion is faster in vertical direction due to higher thermal conductivity of the Silicon substrate.In addition, the reflectivity of crystallization layer in Ge 2 Sb 2 Te 5 has an increase by 15% in fact under multiple exposures [6].This is responsible for which both the simulated width and depth in phase-change region are slightly larger than the experimental results because the laser energy absorbed in the simulation is higher than reality.What's more, the change of refractive index in multiple-exposure process [15] can be ignored due to very thin phase-change thickness in our case.
Obviously, the FRE effect needs a suitable energy density and acceptable number of exposure.For a certain LDW system, energy density must exceed a threshold to guarantee laser-matter interaction.However, energy density for a certain fabrication depth is not lower the better because more numbers of exposure to some degree will result in fabrication-size increase due to the positioning error of a LDW system.Therefore both number of exposure and energy density are important, and the matching and optimizing selection is necessary.In addition, exposure interval should be controlled to avoid the temperature field superposition during multiple exposures.Generally speaking, the effective heat transfer time is no more than 1 ms laser micro-nano manufacturing [16].As a result, the temperature accumulation with the exposure interval of 1s in our experiments can be neglected.
It is should be noted that multiple-exposure-induced FRE effect can be expanded to other materials also.Moreover, this method may be instructive to improve the fabrication resolution of other maskless lithography techniques like focused ion beam lithography and electron beam lithography, etc.

Table 1 .
Optical and thermal parameters [11-13] Parameter Value Density of Ge 2 Sb 2 Te 5 6200 kg/m 3 Specific heat of Ge 2 Sb 2 Te 5 202 J/kg•K Thermal conductivity of amorphous Ge 2 Sb 2 Te 5 0.17 W/m•K Thermal conductivity of crystalline Ge 2 Sb 2 Te 5 0.5 W/m•K Reflectivity of amorphous Ge 2 Sb 2 Te 5 film 38.5% Transmittivity of amorphous Ge 2 Sb 2 Te 5 film 10% Density of Si 2330 kg/m 3 Specific heat of Si 680 J/kg•K Thermal conductivity of Si 140 W/m•K

Fig. 2 .
Fig. 2. Local temperature field distribution of a single point after one-time exposure by a 50 ns laser pulse with different powers: (a) 5 mW; (b) 4.5 mW (c) 4 mW; (d) 3.5 mW.

Fig. 3 .
Fig. 3. Local temperature field distribution of a single point after multiple exposures by a 50 ns laser pulse with different powers and numbers of exposure: (a) 4.5 mW, two-time exposures; (b) 4.5 mW, three-time exposures; (c-f) 4 mW, two to five-time exposures.

Fig. 4 .
Fig. 4. Multiple exposures result on 50 nm-Ge 2 Sb 2 Te 5 film with different laser powers and numbers of exposure: (a) and (b) optical and AFM images of the line array after one-time exposure with power from 3 mW to 6 mW; (c) and (d) optical and AFM images of the line array after two to four-time exposures with the power of 4 mW.

Fig. 5 .
Fig. 5.The cross section of the exposure lines: (a) one-time exposure with the power of 5 mW; (b) four-time exposures with the power of 4 mW.