- Email: [email protected]
Impact of process parameters on pattern formation in the maskless plasmonic computational lithography
Current Applied Physics 15 (2015) 698e702
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Impact of process parameters on pattern formation in the maskless plasmonic computational lithography Sang-Kon Kim a, b a b
Department of Applied Physics, Hanyang University, Ansan, Kyunggi-do 426-791, Republic of Korea Department of Science, Hongik University, Seoul 121-791, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2015 Received in revised form 17 March 2015 Accepted 20 March 2015 Available online 21 March 2015
The extraordinary optical transmission through a sub-wavelength size metal-aperture and metamaterials has been tremendous interests for the untilization of the surface plasmon polariton (SPP). Its technology, however, is hard to apply for the optical lithography process. In this study, a maskless plasmonic lithography (MPL) is modeled and simulated for 15-nm critical dimension (CD). The near-field intensity with the plasmonic phenomena of aperture shapes is described due to aperture parameters by using a scattering matrix (S-matrix) analysis method and the finite difference time domain (FDTD) method. MPL parameters of bowtie structures are optimized and improved for the imperfection of the resist pattern. The most dominant parameter on CD is gap size of bowtie by Taguchi method. © 2015 Elsevier B.V. All rights reserved.
Keywords: Lithography Lithography simulation Metamaterials Surface plasmon Plasmonic lithography Diffraction limit
1. Introduction Lithography technology has been developing the semiconductor industry according to Moore's law over 40 years. The current immersion ArF lithography locates at the crossroads of a decision on the next generation lithography (NGL) technology in terms of the improved limit of exposure wavelength and numerical aperture (NA) in Rayleigh's equation (HP ¼ k1 l/NA). As a favorite successor of the immersion ArF lithography, extreme ultraviolet (EUV) lithography has been researching for 1 nm technology nodes. Xray lithography and the massively parallel e-beam lithography cannot provide effective cost for mass production. Multiple patterning such as quadruple patterning is confronted with the huge increase of cost of ownership (CoO) and overlay difficulty. Under such conditions, the high transmission through a subwavelength size metal-aperture has been tremendous interests for the maskless plasmonic lithography (MPL) [1,2]. The physical origin of this enhanced transmission is the excitation of surface plasmon polariton (SPP), which is the coupled mode excitation of an electromagnetic wave and free charges on a metal surface. MPL has advantages for low cost, the high-intensity nanometer-scale light spot
beyond diffraction limit, and applicability of conventional light sources and resist materials [3,4]. To extend the scope of practical applications for SPP, MPL needs to be rigorously analyzed to ensure that it satisfies the demands of the semiconductor industry in terms of its ultimate resolution, pattern depth, overlay, and throughput. In this study, MPL process is modeled and simulated for 15-nm critical dimension (CD). The impact of process parameters on pattern formation is described to understand the effects of the pattern formation and optimize process parameters. 2. Maskless plasmonic lithography MPL in Fig. 1 includes maskless plasmonic illumination (wavelength, aperture shapes, and thickness), prebake (time and temperature), exposure (Dill parameters (A, B, and C) and dose), postexposure bake (PEB) (diffusion coefficient, time, and temperature), and development (rate function time and surface inhibitor), as shown in Table 1 [5e7]. Plasmonic illumination is performed by using an S-matrix analysis method and the FDTD method [8e11]. For resist flow of spin-coating, level-set method and a relative equation of NaviereStokes equation are, respectively,
Dt fðx; tÞ þ ð1 bkðx; tÞÞkVfðx; tÞk ¼ 0; E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.cap.2015.03.016 1567-1739/© 2015 Elsevier B.V. All rights reserved.
(1)
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
699
Fig. 1. Schematic flow of maskless plasmonic lithography: spin-coating, prebake, plasmonic illumination, exposure, post-exposure bake, and development.
! v3 H v3 S þ H 3 þ U2 H 3 ¼ U2 ; vX 3 vX 3
photoactive compound [PAC] is determined by.
(2)
where f(t) is a level-set function, k(t) is mean curvature, b is constant value, and H, S, and U are dimensionless parameters [6,7]. For the sovent evaporation-diffusion of prebake, the concentration rate (M) after bake can be determined from.
dM ¼ kevap $M; dt
kevap ¼ Ar eEa =kb T ;
(3)
where kevap is evaporation rate constant, Ar is Arrhenius coefficient, Ea is activation energy, kb is Boltzmann constant, and T is absolute temperature. For exposure model, the reaction of intensity and
Table 1 MPL parameters of 15-nm pattern formation. Source Type: Gaussian Pulse, Polarization: x-direction, Amplitude (V/m): 1, Central wavelength (nm): 800, 365, and 248, Temporal width (fs): 2, Duration of Gaussian Source (No. of widths): 10. Structure parameters Layer 1: 50-nm, dielectric constant: 2.2, properties: Insulator, Layer 2: 24-nm, properties: Gold, (Bowtie Geometry) Triangle altitude: 20, Radius of Curvature: 10, Thickness: 24, Gap size: 10, Layer 3: 50-nm, dielectric constant: 2, properties: Insulator. Prebake Temperature: 90 C, Warmup Time: 1 s Prebake Time: 60 s, LN Arrhenius: 40.89 1/min. Activation Energy: 34.32 kcal/mol, Exposure parameters Exposure Dose: 20 mJ/cm2, A: 0.01 1/mm, B: 0.3 1/mm, C: 0.01 cm2/mJ. Post-exposure baking parameters Diffusion length: 0.035 mm, Temperature: 100 C, Time: 80 s, Exponent n: 2, Resist type: Positive. Development parameters Development Model: Mack model, Rmin: 6.5 105 nm/s, Rmax: 0.1 mm/s, n: 0.01, Mth: 0.36, time: 50 s. 2D resist profile Contact hole: 15-nm, average sidewall angle: 70.32 .
vI ¼ aI; vz
d½PAC ¼ C$½PAC$I; dt
(4)
where a (¼A[PAC] þ B) is the optical absorption coefficient and A, B, and C are Dill's parameters [7]. For PEB model, the acid diffusion equation of the non-chemically-amplified resist (non-CAR) is
! dM v2 M v2 M ¼ DH þ 2 ; dt vx2 vy
(5)
where M is dissolution inhibitor (or PAC) and DH is the acid diffusion coefficient [6,7]. For development model, Mack model and raytrancing model are, respectively,
RðMÞ ¼ Rmax
ða þ 1Þð1 MÞn þ Rmin ; a þ ð1 MÞn
a¼
ðn þ 1Þ ð1 Mth Þn ; ðn 1Þ (6)
Pn ðx; y; zÞ ¼ Pn1 ðx; y; zÞ þ b S n1 ðx; y; zÞRn1 ðx; y; zÞDt;
(7)
where R(M) is development rate, Rmax (or Rmin) is the maximum (or minimum) development rate, Mth is the threshold inhibitor concentration, n is the reaction order, b S n is the unit vector of the trace direction, Pn is ray position, and Rn is the surface evolution rate [6,7]. The imperfection of resist pattern is possibly attributed to the imperfect of aperture structure and the roughness of the metal surface, so that this resist pattern can be further improved by optimizing lithography conditions. 3. Analysis and discussion SPP transmittance is calculated at 1-nm distance from the bottom of a gold layer by using an S-matrix analysis method [8,9]. For transmittance spectrum of a 100-nm gold thickness due to hole's radiuses in Fig. 2(a), the localized surface plasmon resonance (LSPR) shifts to lower energy when hole's radius becomes smaller, as same as Ref. [12,13]. LSPR positions in Fig. 2(b) are affected by the orders of fractal patterns. For the increasing orders, the intensity enhancement becomes larger and has a spot position. In simulation conditions of 100-nm a-width, 100-nm gold thickness, and incident light with 60 angle to surface in Fig. 2(c), LSPR shifts to lower
700
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
Fig. 2. Plasmonic effects of transmittance with wavelengths in terms of plasmonic structures such as (a) circle array and (b)e(d) rectangle array.
Fig. 3. Near-field intensities for circle array and rectangle array (a) and (b) in single silicon layer and (c) and (d) in double silicon layers.
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
Fig. 4. Simulation results of intensity for gap size, curvature radius, thickness, and triangle altitude in the optically resonant metallic bowtie nanoantenna. Linear graph is a fitting function of y ¼ Ax þ B for each of simulation results. Insert is bowtie structure.
energy due to the decreasing b-width. In simulation conditions of 100-nm b-width and incident light with 20 angle to surface in Fig. 2(d), LSPR shifts to red wavelength due to the decreasing of awidth [14]. The different LSPR shifts of a (or x)-width and b (or y)width in rectangle shape originate from the polarizationdependent optical property of rectangle array. Fig. 3 shows near-field intensity in silicon layers with the refractive index of 12 þ 0j and 0.05a thickness by using the Smatrix analysis method. For the simulation conditions of wave frequency (u ¼ 0.5) and gap distances (h ¼ 0.5a), intensity of single and double silicon layers is changed due to aperture parameters at circle and rectangle array [15]. The smaller aperture size is, the smaller the full width at half maximum (FWHM) of lower intensity is. When a is 100-nm, FWHM is 50-nm. Although SPP of double layer can be expected more than SPP of single layer, the amplitude of intensity is a little higher than that of single layer. Fig. 4 shows intensity FWHM due to structure parameters of metallic bowtie in Table 1 by using the FDTD method [10,11]. The
701
smaller gap size, curvature radius, and triangle altitude are, the smaller intensity FWHM is. The thinner thickness is, the less change of intensity FWHM is. Bowtie structure can provide intensity FWHM of 1 -nm using optimized structure parameters in Fig. 4. However, the sufficient aspect rate of critical dimension is required for etch process. For gap size, curvature radius, thickness, and triangle altitude, fitting functions are y ¼ 0.0814 x þ 23.03, y ¼ 0.36 x þ 17.3, y ¼ 0.0027 x þ 24.44, and y ¼ 0.1834 x þ 17.02, respectively. Fig. 5 shows the sensitivity of MPL simulation parameters in Table 1. The most effective factor of each process is used to find the most effective process by Taguchi method [7]. For the parameters of metallic bowtie, insert of Fig. 5 shows the plots of corresponding signal-to-noise ratio (S/N) effects, which are defined as the ratio of the mean (signal) to the standard deviation (noise). The inclined line of parameter (Gap Size) means significant effects. Hence, the most dominant factor is the gap size of bowtie structure in illumination process. According to the sensitivity of MPL simulation parameters on CD, gap size is the most dominant factor and illumination process is the most dominant process in MPL process. 4. Conclusions According to simulation results of plasmonic structures by using a scattering matrix (S-matrix) analysis method and the finite difference time domain (FDTD) method, a maskless plasmonic lithography (MPL) can be modeled for 15-nm critical dimension (CD) in a non-chemically-amplified resist (non-CAR). The near-field intensity at resonance wavelength was changed due to sizes and shapes of apertures and number of layers. The localized surface plasmon resonance (LSPR) positions have blue and red shifts due to the decreasing the x-width and y-width in rectangle pattern, respectively. For MPL with bowtie structure, the most dominant process and parameter for CD are illumination process and gap size of bowtie, respectively. For semiconductor, photovoltaic, and biosensor devices, our research can provide a feasibility of below 10-nm CD by using MPL with low cost and application of conventional illumination light sources and resist materials. However, the sufficient aspect rate of CD should be obtained for etch process.
Fig. 5. Parameter sensitivity of simulation parameters on resist patterns in MPL. Parameters sensitivities are normalized by the sensitivity of gap size because gap size is the most dominant parameter. Insert is graphs of average ratio for signal vs. noise.
702
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation on Korea (NRF) (2009-0074676) funded by the Ministry of Education, Science and Technology. References [1] D.K. Gramotnev, S.I. bozhevolnyi, Plasmonics beyond the diffraction limit, Nat. Phot. 4 (2010) pp.83epp.91. [2] S. Kawata, Plasmonics: future outlook, Jpn. J. Appl. Phys. 52 (2013) 010001. [3] S. Kim, H. Jung, Y. Kim, J. Jang, J.W. Hahn, Resolution limit in plasmonic lithography for practical applications beyond 2x-nm half pitch, Adv. Mater. 24 (2012) OP337eOP344. [4] L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D.B. Bogy, X. Zhan, Maskless plasmonic lithography at 22 nm resolution, Sci. Rep. 1 (2011) pp.175. [5] Y. Li, F. Liu, Y. Ye, W. Meng, K. Cui, X. Feng, W. Zhang, Y. Huang, Two-surfaceplasmon-polariton-absorption based lithography using 400 nm femtosecond laser, Appl. Phys. Lett. 104 (2014) 081115. [6] S.-K. Kim, Impact of process parameters on pattern formation of the selfaligned multiple patterning process, J. Nanosci. Nanotechnol. 14 (2014)
9454e9458. [7] S.-K. Kim, Sensitivity of process parameters on pattern formation of lithoecureelithoeetch process, Jpn. J. Appl. Phys. 51 (2012) 06FC02. [8] V. Liu, S. Fan, S4: a free electromagnetic solver for layered periodic structures, Comput. Phys. Comm. 183 (2012) 2233e2244. [9] S.-K. Kim, Aerial image formation of quantum lithography for diffraction limit, Curr. Appl. Phys. 12 (2002) 1566e1574. [10] J.A. Schuller, E.S. Barnard, W. Cai, Y.C. Jun, J.S. White, M.L. Brongersma, Plasmonics for extreme light concentration and manipulation, Nat. Mater. 9 (2010) 193e204. [11] A. Sundaramurthy, P.J. Schuck, N.R. Conley, D.P. Fromm, G.S. Kino, W.E. Moerner, Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas, Nano Lett. 6 (2006) 355e360. [12] Y.-C. Chang, S.-C. Lu, H.-C. Chung, S.-M. Wang, T.-D. Tsai, T.-F. Guo, Highthroughput nanofabrication of infra-red and chiral metamaterials using nanospherical-lens lithography, Sci. Rep. 3 (2013) 3339. [13] W. Yue, Z. Wang, Y. Yang, J. Li, Y. Wu, L. Chen, B. Ooi, X. Wang, X.-X. Zhang, Enhanced extraordinary optical transmission (EOT) through arrays of bridged nanohole pairs and their sensing applications, Nanoscale 6 (2014) 7917e7923. [14] F.J. Garcia-Vidal, E. Moreno, J.A. Porto, L. Martin-Moreno, Transmission of light through a single rectangular hole, Phys. Rev. Lett. 95 (2005) 103901. [15] W. Suh, M.F. Yanik, O. Solgaard, S. Fan, Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs, Appl. Phys. Lett. 82 (2003) 1999.
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Impact of process parameters on pattern formation in the maskless plasmonic computational lithography Sang-Kon Kim a, b a b
Department of Applied Physics, Hanyang University, Ansan, Kyunggi-do 426-791, Republic of Korea Department of Science, Hongik University, Seoul 121-791, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2015 Received in revised form 17 March 2015 Accepted 20 March 2015 Available online 21 March 2015
The extraordinary optical transmission through a sub-wavelength size metal-aperture and metamaterials has been tremendous interests for the untilization of the surface plasmon polariton (SPP). Its technology, however, is hard to apply for the optical lithography process. In this study, a maskless plasmonic lithography (MPL) is modeled and simulated for 15-nm critical dimension (CD). The near-field intensity with the plasmonic phenomena of aperture shapes is described due to aperture parameters by using a scattering matrix (S-matrix) analysis method and the finite difference time domain (FDTD) method. MPL parameters of bowtie structures are optimized and improved for the imperfection of the resist pattern. The most dominant parameter on CD is gap size of bowtie by Taguchi method. © 2015 Elsevier B.V. All rights reserved.
Keywords: Lithography Lithography simulation Metamaterials Surface plasmon Plasmonic lithography Diffraction limit
1. Introduction Lithography technology has been developing the semiconductor industry according to Moore's law over 40 years. The current immersion ArF lithography locates at the crossroads of a decision on the next generation lithography (NGL) technology in terms of the improved limit of exposure wavelength and numerical aperture (NA) in Rayleigh's equation (HP ¼ k1 l/NA). As a favorite successor of the immersion ArF lithography, extreme ultraviolet (EUV) lithography has been researching for 1 nm technology nodes. Xray lithography and the massively parallel e-beam lithography cannot provide effective cost for mass production. Multiple patterning such as quadruple patterning is confronted with the huge increase of cost of ownership (CoO) and overlay difficulty. Under such conditions, the high transmission through a subwavelength size metal-aperture has been tremendous interests for the maskless plasmonic lithography (MPL) [1,2]. The physical origin of this enhanced transmission is the excitation of surface plasmon polariton (SPP), which is the coupled mode excitation of an electromagnetic wave and free charges on a metal surface. MPL has advantages for low cost, the high-intensity nanometer-scale light spot
beyond diffraction limit, and applicability of conventional light sources and resist materials [3,4]. To extend the scope of practical applications for SPP, MPL needs to be rigorously analyzed to ensure that it satisfies the demands of the semiconductor industry in terms of its ultimate resolution, pattern depth, overlay, and throughput. In this study, MPL process is modeled and simulated for 15-nm critical dimension (CD). The impact of process parameters on pattern formation is described to understand the effects of the pattern formation and optimize process parameters. 2. Maskless plasmonic lithography MPL in Fig. 1 includes maskless plasmonic illumination (wavelength, aperture shapes, and thickness), prebake (time and temperature), exposure (Dill parameters (A, B, and C) and dose), postexposure bake (PEB) (diffusion coefficient, time, and temperature), and development (rate function time and surface inhibitor), as shown in Table 1 [5e7]. Plasmonic illumination is performed by using an S-matrix analysis method and the FDTD method [8e11]. For resist flow of spin-coating, level-set method and a relative equation of NaviereStokes equation are, respectively,
Dt fðx; tÞ þ ð1 bkðx; tÞÞkVfðx; tÞk ¼ 0; E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.cap.2015.03.016 1567-1739/© 2015 Elsevier B.V. All rights reserved.
(1)
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
699
Fig. 1. Schematic flow of maskless plasmonic lithography: spin-coating, prebake, plasmonic illumination, exposure, post-exposure bake, and development.
! v3 H v3 S þ H 3 þ U2 H 3 ¼ U2 ; vX 3 vX 3
photoactive compound [PAC] is determined by.
(2)
where f(t) is a level-set function, k(t) is mean curvature, b is constant value, and H, S, and U are dimensionless parameters [6,7]. For the sovent evaporation-diffusion of prebake, the concentration rate (M) after bake can be determined from.
dM ¼ kevap $M; dt
kevap ¼ Ar eEa =kb T ;
(3)
where kevap is evaporation rate constant, Ar is Arrhenius coefficient, Ea is activation energy, kb is Boltzmann constant, and T is absolute temperature. For exposure model, the reaction of intensity and
Table 1 MPL parameters of 15-nm pattern formation. Source Type: Gaussian Pulse, Polarization: x-direction, Amplitude (V/m): 1, Central wavelength (nm): 800, 365, and 248, Temporal width (fs): 2, Duration of Gaussian Source (No. of widths): 10. Structure parameters Layer 1: 50-nm, dielectric constant: 2.2, properties: Insulator, Layer 2: 24-nm, properties: Gold, (Bowtie Geometry) Triangle altitude: 20, Radius of Curvature: 10, Thickness: 24, Gap size: 10, Layer 3: 50-nm, dielectric constant: 2, properties: Insulator. Prebake Temperature: 90 C, Warmup Time: 1 s Prebake Time: 60 s, LN Arrhenius: 40.89 1/min. Activation Energy: 34.32 kcal/mol, Exposure parameters Exposure Dose: 20 mJ/cm2, A: 0.01 1/mm, B: 0.3 1/mm, C: 0.01 cm2/mJ. Post-exposure baking parameters Diffusion length: 0.035 mm, Temperature: 100 C, Time: 80 s, Exponent n: 2, Resist type: Positive. Development parameters Development Model: Mack model, Rmin: 6.5 105 nm/s, Rmax: 0.1 mm/s, n: 0.01, Mth: 0.36, time: 50 s. 2D resist profile Contact hole: 15-nm, average sidewall angle: 70.32 .
vI ¼ aI; vz
d½PAC ¼ C$½PAC$I; dt
(4)
where a (¼A[PAC] þ B) is the optical absorption coefficient and A, B, and C are Dill's parameters [7]. For PEB model, the acid diffusion equation of the non-chemically-amplified resist (non-CAR) is
! dM v2 M v2 M ¼ DH þ 2 ; dt vx2 vy
(5)
where M is dissolution inhibitor (or PAC) and DH is the acid diffusion coefficient [6,7]. For development model, Mack model and raytrancing model are, respectively,
RðMÞ ¼ Rmax
ða þ 1Þð1 MÞn þ Rmin ; a þ ð1 MÞn
a¼
ðn þ 1Þ ð1 Mth Þn ; ðn 1Þ (6)
Pn ðx; y; zÞ ¼ Pn1 ðx; y; zÞ þ b S n1 ðx; y; zÞRn1 ðx; y; zÞDt;
(7)
where R(M) is development rate, Rmax (or Rmin) is the maximum (or minimum) development rate, Mth is the threshold inhibitor concentration, n is the reaction order, b S n is the unit vector of the trace direction, Pn is ray position, and Rn is the surface evolution rate [6,7]. The imperfection of resist pattern is possibly attributed to the imperfect of aperture structure and the roughness of the metal surface, so that this resist pattern can be further improved by optimizing lithography conditions. 3. Analysis and discussion SPP transmittance is calculated at 1-nm distance from the bottom of a gold layer by using an S-matrix analysis method [8,9]. For transmittance spectrum of a 100-nm gold thickness due to hole's radiuses in Fig. 2(a), the localized surface plasmon resonance (LSPR) shifts to lower energy when hole's radius becomes smaller, as same as Ref. [12,13]. LSPR positions in Fig. 2(b) are affected by the orders of fractal patterns. For the increasing orders, the intensity enhancement becomes larger and has a spot position. In simulation conditions of 100-nm a-width, 100-nm gold thickness, and incident light with 60 angle to surface in Fig. 2(c), LSPR shifts to lower
700
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
Fig. 2. Plasmonic effects of transmittance with wavelengths in terms of plasmonic structures such as (a) circle array and (b)e(d) rectangle array.
Fig. 3. Near-field intensities for circle array and rectangle array (a) and (b) in single silicon layer and (c) and (d) in double silicon layers.
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
Fig. 4. Simulation results of intensity for gap size, curvature radius, thickness, and triangle altitude in the optically resonant metallic bowtie nanoantenna. Linear graph is a fitting function of y ¼ Ax þ B for each of simulation results. Insert is bowtie structure.
energy due to the decreasing b-width. In simulation conditions of 100-nm b-width and incident light with 20 angle to surface in Fig. 2(d), LSPR shifts to red wavelength due to the decreasing of awidth [14]. The different LSPR shifts of a (or x)-width and b (or y)width in rectangle shape originate from the polarizationdependent optical property of rectangle array. Fig. 3 shows near-field intensity in silicon layers with the refractive index of 12 þ 0j and 0.05a thickness by using the Smatrix analysis method. For the simulation conditions of wave frequency (u ¼ 0.5) and gap distances (h ¼ 0.5a), intensity of single and double silicon layers is changed due to aperture parameters at circle and rectangle array [15]. The smaller aperture size is, the smaller the full width at half maximum (FWHM) of lower intensity is. When a is 100-nm, FWHM is 50-nm. Although SPP of double layer can be expected more than SPP of single layer, the amplitude of intensity is a little higher than that of single layer. Fig. 4 shows intensity FWHM due to structure parameters of metallic bowtie in Table 1 by using the FDTD method [10,11]. The
701
smaller gap size, curvature radius, and triangle altitude are, the smaller intensity FWHM is. The thinner thickness is, the less change of intensity FWHM is. Bowtie structure can provide intensity FWHM of 1 -nm using optimized structure parameters in Fig. 4. However, the sufficient aspect rate of critical dimension is required for etch process. For gap size, curvature radius, thickness, and triangle altitude, fitting functions are y ¼ 0.0814 x þ 23.03, y ¼ 0.36 x þ 17.3, y ¼ 0.0027 x þ 24.44, and y ¼ 0.1834 x þ 17.02, respectively. Fig. 5 shows the sensitivity of MPL simulation parameters in Table 1. The most effective factor of each process is used to find the most effective process by Taguchi method [7]. For the parameters of metallic bowtie, insert of Fig. 5 shows the plots of corresponding signal-to-noise ratio (S/N) effects, which are defined as the ratio of the mean (signal) to the standard deviation (noise). The inclined line of parameter (Gap Size) means significant effects. Hence, the most dominant factor is the gap size of bowtie structure in illumination process. According to the sensitivity of MPL simulation parameters on CD, gap size is the most dominant factor and illumination process is the most dominant process in MPL process. 4. Conclusions According to simulation results of plasmonic structures by using a scattering matrix (S-matrix) analysis method and the finite difference time domain (FDTD) method, a maskless plasmonic lithography (MPL) can be modeled for 15-nm critical dimension (CD) in a non-chemically-amplified resist (non-CAR). The near-field intensity at resonance wavelength was changed due to sizes and shapes of apertures and number of layers. The localized surface plasmon resonance (LSPR) positions have blue and red shifts due to the decreasing the x-width and y-width in rectangle pattern, respectively. For MPL with bowtie structure, the most dominant process and parameter for CD are illumination process and gap size of bowtie, respectively. For semiconductor, photovoltaic, and biosensor devices, our research can provide a feasibility of below 10-nm CD by using MPL with low cost and application of conventional illumination light sources and resist materials. However, the sufficient aspect rate of CD should be obtained for etch process.
Fig. 5. Parameter sensitivity of simulation parameters on resist patterns in MPL. Parameters sensitivities are normalized by the sensitivity of gap size because gap size is the most dominant parameter. Insert is graphs of average ratio for signal vs. noise.
702
S.-K. Kim / Current Applied Physics 15 (2015) 698e702
Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation on Korea (NRF) (2009-0074676) funded by the Ministry of Education, Science and Technology. References [1] D.K. Gramotnev, S.I. bozhevolnyi, Plasmonics beyond the diffraction limit, Nat. Phot. 4 (2010) pp.83epp.91. [2] S. Kawata, Plasmonics: future outlook, Jpn. J. Appl. Phys. 52 (2013) 010001. [3] S. Kim, H. Jung, Y. Kim, J. Jang, J.W. Hahn, Resolution limit in plasmonic lithography for practical applications beyond 2x-nm half pitch, Adv. Mater. 24 (2012) OP337eOP344. [4] L. Pan, Y. Park, Y. Xiong, E. Ulin-Avila, Y. Wang, L. Zeng, S. Xiong, J. Rho, C. Sun, D.B. Bogy, X. Zhan, Maskless plasmonic lithography at 22 nm resolution, Sci. Rep. 1 (2011) pp.175. [5] Y. Li, F. Liu, Y. Ye, W. Meng, K. Cui, X. Feng, W. Zhang, Y. Huang, Two-surfaceplasmon-polariton-absorption based lithography using 400 nm femtosecond laser, Appl. Phys. Lett. 104 (2014) 081115. [6] S.-K. Kim, Impact of process parameters on pattern formation of the selfaligned multiple patterning process, J. Nanosci. Nanotechnol. 14 (2014)
9454e9458. [7] S.-K. Kim, Sensitivity of process parameters on pattern formation of lithoecureelithoeetch process, Jpn. J. Appl. Phys. 51 (2012) 06FC02. [8] V. Liu, S. Fan, S4: a free electromagnetic solver for layered periodic structures, Comput. Phys. Comm. 183 (2012) 2233e2244. [9] S.-K. Kim, Aerial image formation of quantum lithography for diffraction limit, Curr. Appl. Phys. 12 (2002) 1566e1574. [10] J.A. Schuller, E.S. Barnard, W. Cai, Y.C. Jun, J.S. White, M.L. Brongersma, Plasmonics for extreme light concentration and manipulation, Nat. Mater. 9 (2010) 193e204. [11] A. Sundaramurthy, P.J. Schuck, N.R. Conley, D.P. Fromm, G.S. Kino, W.E. Moerner, Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas, Nano Lett. 6 (2006) 355e360. [12] Y.-C. Chang, S.-C. Lu, H.-C. Chung, S.-M. Wang, T.-D. Tsai, T.-F. Guo, Highthroughput nanofabrication of infra-red and chiral metamaterials using nanospherical-lens lithography, Sci. Rep. 3 (2013) 3339. [13] W. Yue, Z. Wang, Y. Yang, J. Li, Y. Wu, L. Chen, B. Ooi, X. Wang, X.-X. Zhang, Enhanced extraordinary optical transmission (EOT) through arrays of bridged nanohole pairs and their sensing applications, Nanoscale 6 (2014) 7917e7923. [14] F.J. Garcia-Vidal, E. Moreno, J.A. Porto, L. Martin-Moreno, Transmission of light through a single rectangular hole, Phys. Rev. Lett. 95 (2005) 103901. [15] W. Suh, M.F. Yanik, O. Solgaard, S. Fan, Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs, Appl. Phys. Lett. 82 (2003) 1999.