Dynamic modeling of superresolution photoinduced-inhibition nanolithography

Zongsong Gan; Yaoyu Cao; Baohua Jia; Min Gu

doi:10.1364/OE.20.016871

Dynamic modeling of superresolution photoinduced-inhibition nanolithography

Zongsong Gan, Yaoyu Cao, Baohua Jia, and Min Gu

Optics Express
Vol. 20,
Issue 15,
pp. 16871-16879
(2012)
•https://doi.org/10.1364/OE.20.016871

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Zongsong Gan, Yaoyu Cao, Baohua Jia, and Min Gu, "Dynamic modeling of superresolution photoinduced-inhibition nanolithography," Opt. Express 20, 16871-16879 (2012)

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Abstract

A dynamical model based on the photo-physics and photo-chemistry processes for superresolution photoinduced-inhibition nanolithography (SPIN) under both single-photon and two-photon excitation is developed and validated by experimental results. Numerical simulation results for the dot fabrication predict that the theoretical single dot size can be infinitely reduced, which shows diffraction-unlimited feature of the SPIN. A small reaction constant of the inhibitor polymerization is crucial to realize a small dot size and high resolution. It is discovered both theoretically and experimentally that the dot minimum size and best resolution occur under different inhibition beam powers because of the influence from the inhibitor polymerization. Moreover, due to the consumption of the photo-inhibitor molecules in the inhibition process, the dot size may vary during the sequential fabrication.

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J. W. Perry, B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, and S. R. Marder, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]
M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref] [PubMed]
S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]
K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-dimensional spiral architecture photonic crystals obtained by direct laser writing,” Adv. Mater. 17(5), 541–545 (2005).
[Crossref]
M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]
J. Li, B. Jia, and M. Gu, “Engineering stop gaps of inorganic-organic polymeric 3D woodpile photonic crystals with post-thermal treatment,” Opt. Express 16(24), 20073–20080 (2008).
[Crossref] [PubMed]
M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. 27(20), 1824–1826 (2002).
[Crossref] [PubMed]
J. Serbin and M. Gu, “Experimental evidence for superprism effects in three-dimensional polymer photonic crystals,” Adv. Mater. 18(2), 221–224 (2006).
[Crossref]
T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324(5929), 913–917 (2009).
[Crossref] [PubMed]
Y. Cao, Z. Gan, B. Jia, R. A. Evans, and M. Gu, “High-photosensitive resin for super-resolution direct-laser-writing based on photoinhibited polymerization,” Opt. Express 19(20), 19486–19494 (2011).
[Crossref] [PubMed]
L. G. Lovell, B. J. Elliott, J. R. Brown, and C. N. Bowman, “The effect of wavelength on the polymerization of multi(meth)acrylates with disulfide/benzilketal combinations,” Polymer (Guildf.) 42(2), 421–429 (2001).
[Crossref]
J. H. Lee, R. K. Prud’homme, and I. A. Aksay, “Cure depth in photopolymerization: experiments and theory,” J. Mater. Res. 16(12), 3536–3544 (2001).
[Crossref]
N. Hayki, L. Lecamp, N. Desilles, and P. Lebaudy, “Kinetic study of photoinitiated frontal polymerization: influence of UV light intensity variations on the conversion profiles,” Macromolecules 43(1), 177–184 (2010).
[Crossref]
M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]
S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, “Photopolymerization model for holographic gratings formation in photopolymers,” Appl. Phys. B 77(6-7), 639–662 (2003).
[Crossref]
M. R. Gleeson and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. part I. modeling,” J. Opt. Soc. Am. B 26(9), 1736–1745 (2009).
[Crossref]
W. D. Cook, “Photopolymerization kinetics of dimethacrylates using the camphorquinone amin initiator system,” Polymer (Guildf.) 33(3), 600–609 (1992).
[Crossref]
J. P. Fouassier, “Photopolymerization reactions” in Polymer Handbook, 4th ed., J. Brandrup, E. H. Immergut, E. A. Grulke, eds. (Wiley, 1999), p. II/169.
I. V. Khudyakov and N. J. Turro, “Cage effect dynamics under photolysis of photoinitiators,” Des. Monomers Polym. 13, 487–496 (2010).
P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive index: an integral representation,” J. Opt. Soc. Am. A 12(2), 325–332 (1995).
[Crossref]
B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]
M. Gu, Advanced Optical Imaging Theory (Springer, 2000).
C. Y. Park and S. K. Ihm, “Percolation analysis on free radical linear polymerization with instantaneous initiation,” Polym. Bull. 24(5), 539–543 (1990).
[Crossref]
I. V. Khudyakov, W. S. Fox, and M. B. Purvis, “Photopolymerization of vinyl acrylate studied by photodsc,” Ind. Eng. Chem. Res. 40(14), 3092–3097 (2001).
[Crossref]
G. Odian, Principles of Polymerization, 4th ed. (John Wiley & Sons, Inc., 2004).

2011 (1)

Y. Cao, Z. Gan, B. Jia, R. A. Evans, and M. Gu, “High-photosensitive resin for super-resolution direct-laser-writing based on photoinhibited polymerization,” Opt. Express 19(20), 19486–19494 (2011).
[Crossref] [PubMed]

2010 (3)

N. Hayki, L. Lecamp, N. Desilles, and P. Lebaudy, “Kinetic study of photoinitiated frontal polymerization: influence of UV light intensity variations on the conversion profiles,” Macromolecules 43(1), 177–184 (2010).
[Crossref]

I. V. Khudyakov and N. J. Turro, “Cage effect dynamics under photolysis of photoinitiators,” Des. Monomers Polym. 13, 487–496 (2010).

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]

2009 (3)

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324(5929), 913–917 (2009).
[Crossref] [PubMed]

M. R. Gleeson and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. part I. modeling,” J. Opt. Soc. Am. B 26(9), 1736–1745 (2009).
[Crossref]

B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]

2008 (2)

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]

J. Li, B. Jia, and M. Gu, “Engineering stop gaps of inorganic-organic polymeric 3D woodpile photonic crystals with post-thermal treatment,” Opt. Express 16(24), 20073–20080 (2008).
[Crossref] [PubMed]

2006 (1)

J. Serbin and M. Gu, “Experimental evidence for superprism effects in three-dimensional polymer photonic crystals,” Adv. Mater. 18(2), 221–224 (2006).
[Crossref]

2005 (1)

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-dimensional spiral architecture photonic crystals obtained by direct laser writing,” Adv. Mater. 17(5), 541–545 (2005).
[Crossref]

2004 (1)

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref] [PubMed]

2003 (1)

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, “Photopolymerization model for holographic gratings formation in photopolymers,” Appl. Phys. B 77(6-7), 639–662 (2003).
[Crossref]

2002 (1)

M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. 27(20), 1824–1826 (2002).
[Crossref] [PubMed]

2001 (4)

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

L. G. Lovell, B. J. Elliott, J. R. Brown, and C. N. Bowman, “The effect of wavelength on the polymerization of multi(meth)acrylates with disulfide/benzilketal combinations,” Polymer (Guildf.) 42(2), 421–429 (2001).
[Crossref]

J. H. Lee, R. K. Prud’homme, and I. A. Aksay, “Cure depth in photopolymerization: experiments and theory,” J. Mater. Res. 16(12), 3536–3544 (2001).
[Crossref]

I. V. Khudyakov, W. S. Fox, and M. B. Purvis, “Photopolymerization of vinyl acrylate studied by photodsc,” Ind. Eng. Chem. Res. 40(14), 3092–3097 (2001).
[Crossref]

1999 (1)

J. W. Perry, B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, and S. R. Marder, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398(6722), 51–54 (1999).
[Crossref]

1995 (1)

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive index: an integral representation,” J. Opt. Soc. Am. A 12(2), 325–332 (1995).
[Crossref]

1992 (1)

W. D. Cook, “Photopolymerization kinetics of dimethacrylates using the camphorquinone amin initiator system,” Polymer (Guildf.) 33(3), 600–609 (1992).
[Crossref]

1990 (1)

C. Y. Park and S. K. Ihm, “Percolation analysis on free radical linear polymerization with instantaneous initiation,” Polym. Bull. 24(5), 539–543 (1990).
[Crossref]

Acebal, P.

Aksay, I. A.

J. H. Lee, R. K. Prud’homme, and I. A. Aksay, “Cure depth in photopolymerization: experiments and theory,” J. Mater. Res. 16(12), 3536–3544 (2001).
[Crossref]

Ananthavel, S. P.

Barlow, S.

Blaya, S.

Booker, G. R.

Bowman, C. N.

Brown, J. R.

Busch, K.

Cao, Y.

Carretero, L.

Chen, B.

B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]

Cook, W. D.

W. D. Cook, “Photopolymerization kinetics of dimethacrylates using the camphorquinone amin initiator system,” Polymer (Guildf.) 33(3), 600–609 (1992).
[Crossref]

Cumpston, B. H.

Desilles, N.

Deubel, M.

Dyer, D. L.

Ehrlich, J. E.

Elliott, B. J.

Erskine, L. L.

Evans, R. A.

Fimia, A.

Fox, W. S.

I. V. Khudyakov, W. S. Fox, and M. B. Purvis, “Photopolymerization of vinyl acrylate studied by photodsc,” Ind. Eng. Chem. Res. 40(14), 3092–3097 (2001).
[Crossref]

Gan, Z.

Gleeson, M. R.

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]

Gu, M.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]

J. Serbin and M. Gu, “Experimental evidence for superprism effects in three-dimensional polymer photonic crystals,” Adv. Mater. 18(2), 221–224 (2006).
[Crossref]

M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. 27(20), 1824–1826 (2002).
[Crossref] [PubMed]

Hayki, N.

Heikal, A. A.

Ihm, S. K.

C. Y. Park and S. K. Ihm, “Percolation analysis on free radical linear polymerization with instantaneous initiation,” Polym. Bull. 24(5), 539–543 (1990).
[Crossref]

Jia, B.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]

Juodkazis, S.

Kawata, S.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Khudyakov, I. V.

I. V. Khudyakov and N. J. Turro, “Cage effect dynamics under photolysis of photoinitiators,” Des. Monomers Polym. 13, 487–496 (2010).

I. V. Khudyakov, W. S. Fox, and M. B. Purvis, “Photopolymerization of vinyl acrylate studied by photodsc,” Ind. Eng. Chem. Res. 40(14), 3092–3097 (2001).
[Crossref]

Kowalski, B. A.

Kuebler, S. M.

Laczik, Z.

Lebaudy, P.

Lecamp, L.

Lee, I.-Y. S.

Lee, J. H.

J. H. Lee, R. K. Prud’homme, and I. A. Aksay, “Cure depth in photopolymerization: experiments and theory,” J. Mater. Res. 16(12), 3536–3544 (2001).
[Crossref]

Li, J.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]

Liu, S.

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]

Lovell, L. G.

Madrigal, R. F.

Marder, S. R.

Matsuo, S.

McCord-Maughon, D.

McLeod, R. R.

Misawa, H.

Mizeikis, V.

O'Duill, S.

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]

Park, C. Y.

C. Y. Park and S. K. Ihm, “Percolation analysis on free radical linear polymerization with instantaneous initiation,” Polym. Bull. 24(5), 539–543 (1990).
[Crossref]

Pereira, S.

Perry, J. W.

Prud’homme, R. K.

J. H. Lee, R. K. Prud’homme, and I. A. Aksay, “Cure depth in photopolymerization: experiments and theory,” J. Mater. Res. 16(12), 3536–3544 (2001).
[Crossref]

Pu, J.

B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]

Purvis, M. B.

I. V. Khudyakov, W. S. Fox, and M. B. Purvis, “Photopolymerization of vinyl acrylate studied by photodsc,” Ind. Eng. Chem. Res. 40(14), 3092–3097 (2001).
[Crossref]

Qin, J.

Röckel, H.

Rumi, M.

Scott, T. F.

Seet, K. K.

Serbin, J.

J. Serbin and M. Gu, “Experimental evidence for superprism effects in three-dimensional polymer photonic crystals,” Adv. Mater. 18(2), 221–224 (2006).
[Crossref]

Sheridan, J. T.

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]

Soukoulis, C. M.

Straub, M.

M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. 27(20), 1824–1826 (2002).
[Crossref] [PubMed]

Sullivan, A. C.

Sun, H. B.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Takada, K.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Tanaka, T.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Török, P.

Turro, N. J.

I. V. Khudyakov and N. J. Turro, “Cage effect dynamics under photolysis of photoinitiators,” Des. Monomers Polym. 13, 487–496 (2010).

Ulibarrena, M.

Varga, P.

Ventura, M. J.

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]

von Freymann, G.

Wegener, M.

Wu, X.-L.

Zhang, Z.

B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]

Adv. Mater. (2)

J. Serbin and M. Gu, “Experimental evidence for superprism effects in three-dimensional polymer photonic crystals,” Adv. Mater. 18(2), 221–224 (2006).
[Crossref]

Appl. Phys. B (1)

Des. Monomers Polym. (1)

I. V. Khudyakov and N. J. Turro, “Cage effect dynamics under photolysis of photoinitiators,” Des. Monomers Polym. 13, 487–496 (2010).

Ind. Eng. Chem. Res. (1)

I. V. Khudyakov, W. S. Fox, and M. B. Purvis, “Photopolymerization of vinyl acrylate studied by photodsc,” Ind. Eng. Chem. Res. 40(14), 3092–3097 (2001).
[Crossref]

J. Appl. Phys. (1)

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104(6), 064917 (2008).
[Crossref]

J. Mater. Res. (1)

J. H. Lee, R. K. Prud’homme, and I. A. Aksay, “Cure depth in photopolymerization: experiments and theory,” J. Mater. Res. 16(12), 3536–3544 (2001).
[Crossref]

J. Opt. Soc. Am. A (2)

B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

M. Gu, B. Jia, J. Li, and M. J. Ventura, “Fabrication of three-dimensional photonic crystals in quantum-dot-based materials,” Laser Photon. Rev. 4(3), 414–431 (2010).
[Crossref]

Macromolecules (1)

Nat. Mater. (1)

Nature (2)

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. 27(20), 1824–1826 (2002).
[Crossref] [PubMed]

Polym. Bull. (1)

C. Y. Park and S. K. Ihm, “Percolation analysis on free radical linear polymerization with instantaneous initiation,” Polym. Bull. 24(5), 539–543 (1990).
[Crossref]

Polymer (Guildf.) (2)

W. D. Cook, “Photopolymerization kinetics of dimethacrylates using the camphorquinone amin initiator system,” Polymer (Guildf.) 33(3), 600–609 (1992).
[Crossref]

Science (1)

Other (3)

J. P. Fouassier, “Photopolymerization reactions” in Polymer Handbook, 4th ed., J. Brandrup, E. H. Immergut, E. A. Grulke, eds. (Wiley, 1999), p. II/169.

G. Odian, Principles of Polymerization, 4th ed. (John Wiley & Sons, Inc., 2004).

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Fig. 1

Focus profiles of the fabrication laser beam with wavelengths of 488 nm (a) and 800 nm (b) for the single and two-photon excitation respectively, and inhibition beam with the wavelength of 375 nm (c) in the focal region. The calculated area is 2 μm by 2 μm.

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Fig. 2

(a): Dot sizes plotted as a function of the power of the inhibition laser beam. The power of the fabrication laser beam is 200 nW and the exposure time is 700 ms. The sizes of the dots in experiment were measured with a scanning electron microscope (SEM). The parameters used in the calculation are as follows: The absorption cross sections of initiators and inhibitors are 2.1 × 10⁻²¹ cm² and 5.9 × 10⁻²¹ cm², respectively; k_d = 5 × 10⁻⁵ s⁻¹, r_d = 5 × 10⁻⁵ s⁻¹; k_i = 3 × 10⁷ cm³mol⁻¹s⁻¹,r_i = 3.6 × 10⁵ cm³mol⁻¹s⁻¹; k_r = 1 × 10⁷ cm³mol⁻¹s⁻¹, r_r = 1 × 10⁷ cm³mol⁻¹s⁻¹; k_p = 2 × 10⁶ cm³mol⁻¹s⁻¹, r_kt = 1.2 × 10⁸ cm³mol⁻¹s⁻¹; k_t = 2.4 × 10⁷ cm³mol⁻¹s⁻¹, r_t = 1.6 × 10⁷ cm³mol⁻¹s⁻¹; τ₁, τ₂, τn₁ and τn₂ are set as 1 × 10² cm³mol⁻¹s⁻¹. The diffusion constant of the initiator/inhibitor radicals is 0.25µm²/s and the diffusion constant of the chain-initiating radicals is 0.05µm²s⁻¹. These values were obtained from the literatures [11, 13, 17, 19, 22, 25] and estimated from the fits to the experimental data. (b): Monomer conversion rate in the focal region at the XY plane for different levels of the inhibition beam powers. The laser beam power corresponds to the Fig. 2(a). Each of the calculated pattern area is 2 μm by 2 μm.

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Fig. 3

(a): The dot size is plotted as a function of the inhibition laser power with different reaction constants of the inhibitor radicals with monomers (normalized by the reaction constant of the initiator radicals with monomers). (b): Calculated achievable dot minimum size for different r_i/k_i values (the inhibition laser power range is 0-121 μW; other parameters are the same as those used in Fig. 2.

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Fig. 4

Dot size and the resolution plots as a function of the inhibition laser power. For the single-photon case (a), all the parameters used are the same as those in Fig. 2. For the two-photon fabrication case (b), all the parameters related to photo-inhibitor are the same as that used in Fig. 2.

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Fig. 5

The variation of the dot size and resolution with the inhibition laser power. The dots were fabricated with the fabrication beam power of 20 mW at the wavelength of 800 nm. The inhibition beam wavelength was 375 nm and the exposure time was 50 ms. (a): SEM image of the fabricated dots, the scale bar is 2 μm; (b): dot size and resolution date taken from the read box of the left SEM image. The black and red curves are the polynomial fitting of the experimental data to guide eyes. The formulation of the photoresin was composed of 0.02 wt% 2,5-bis(p-dimethylamino cinnamylidene) cyclopentanone, 0.5 wt% camphorquinone and 0.5 wt% ethyl4-(dimethylamino)benzoate as photoinitiator components, and 2.5 wt% TED as the photoinhibitor, and 96.48 wt% SR 349 (Sartomer Inc.). The fabrication beam laser operates at repetition rate of 80 MHz with a 140-femtosencond pulse width. The inhibition beam laser works at CW mode. These two beams are overlapped and introduced to an objective with numerical aperture 1.4. The dot fabrication exposure time is 50 ms. After fabrication, the gelated structure was washed out by rinsing the structure in pure isopropanol for 5 min, then in pure acetone for 2 sec and then in pure ethanol for 2 sec.

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Fig. 6

Simulation of four sequentially fabricated dots for different values of the inhibition beam laser power ((a) to (e)). The first fabricated dot is plotted in the up position, the second down, the third left and the forth right. All the parameters are the same as those used in Fig. 2. Each of the calculated pattern area is 2 μm by 2 μm.

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Equations (8)

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\frac{d P_{0}}{d t} = - σ_{E} I_{E} (P_{0} - P_{1}) + τ_{1} P_{1} + τ n_{1} P_{1}

\frac{d P_{1}}{d t} = σ_{E} I_{E} (P_{0} - P_{1}) - τ_{1} P_{1} - τ n_{1} P_{1} - k_{d} P_{1} + k_{r} P_{2}^{2}

\frac{d P_{2}}{d t} = 2 k_{d} P_{1} - 2 k_{r} P_{2}^{2} - k_{i} P_{2} M - k_{t} P_{3} P_{2} - r_{t} I_{2} P_{2} - r_{kt} I_{2} P_{2}

\frac{d P_{3}}{d t} = k_{i} P_{2} M + r_{i} I_{2} M - k_{t} (P_{3} + P_{2}) P_{3} - r_{t} I_{2} P_{3} - r_{kt} I_{2} P_{3}

\frac{d I_{0}}{d t} = - σ_{S} I_{S} (I_{0} - I_{1}) + τ_{2} I_{1} + τ n_{2} I_{1}

\frac{d I_{1}}{d t} = σ_{S} I_{S} (I_{0} - I_{1}) - τ_{2} I_{1} - τ n_{2} I_{1} - r_{d} I_{1} + r_{r} I_{2}^{2}

\frac{d I_{2}}{d t} = 2 r_{d} I_{1} - 2 r_{r} I_{2}^{2} - r_{i} I_{2} M - r_{t} (P_{3} + P_{2}) I_{2} - r_{kt} (P_{3} + P_{2}) I_{2}

\frac{d M}{d t} = - k_{p} P_{3} M