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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 291–298
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Enhancement of height resolution in direct laser lithography

Hyug-Gyo Rhee and Yun-Woo Lee  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 291-298 (2012)
http://dx.doi.org/10.1364/OE.20.000291


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Abstract

To address the requirements of multi-level semiconductors, we propose a new technique for overcoming the height limitation of direct laser lithography. In the proposed system, an original source beam is fed into an interference generator that divides the input beam by 50: 50 into two output beams. After going through an imaging lens, these two beams make two focusing spots, which are slightly separated in the axial direction. In the overlapped region, these two spots generate a small interferogram that shortens the depth of focus. By using this phenomenon, we are able to overcome the height limitation of direct laser lithography. The governing equations are also derived in this manuscript by using the Gaussian beam model.

© 2011 OSA

1. Introduction

In the proposed system, an original source beam is fed into an interference generator that divides the input beam by 50: 50 into two output beams. After going through an imaging lens, these two beams make two focusing spots, which are slightly separated in the axial direction. In the overlapped region, these two spots generate a small interferogram that shortens the DOF. By using this phenomenon, we are able to overcome the height limitation of direct laser lithography. The details of the proposed method are presented in Section II. The governing equations are derived in Section III by using the Gaussian beam model [10

10. B. E. A. Saleh and M. C. Teich, “Beam optics,” in Fundamentals of Photonics (John Wiley & Sons, Inc., New York, 1991), Chap. 3.

]. In Section IV, we show some experimental results.

2. Direct laser lithographic system with the interference generator

In order to fabricate a fine pattern, we adopted an autofocusing control that makes the lithographic beam continuously focus on the target surface during the fabrication. A well-known astigmatic scheme [12

12. D. K. Cohen, W. H. Gee, M. Ludeke, and J. Lewkowicz, “Automatic focus control: the astigmatic lens approach,” Appl. Opt. 23(4), 565–570 (1984). [CrossRef] [PubMed]

, 13

13. H.-G. Rhee, D.-I. Kim, and Y.-W. Lee, “Realization and performance evaluation of high speed autofocusing for direct laser lithography,” Rev. Sci. Instrum. 80(7), 073103 (2009). [CrossRef] [PubMed]

] was introduced in our system to build a high speed precision autofocusing mechanism. An LD, a couple of cylindrical lenses, a quadrant detector, and a computer controlled motor were used. The maximum speed of our autofocusing mechanism is up to 150 Hz. The red line in Fig. 2 represents the auxiliary laser beam, of which the wavelength is 650 nm. The interference generator divides the input beam by 50: 50 into two output beams. One of them is reflected on the flat mirror and maintains the plane wave, while the other slowly converges on the focal area, as shown in Fig. 3
Fig. 3 Interference generator: PBS, polarized beam splitter; QWP: quarter wave plate. A Haidinger fringe is observed when we put a screen at plane A.
. These two beams make two focusing spots, which are slightly separated in the axial direction, as shown in Fig. 4
Fig. 4 (a) Axially separated two focused beam. (b) Intensity profile without and (c) with the interference. The parameter zo is known as the Rayleigh range [10].
. In the overlapped region, these two spots generate a small interferogram that shortens the DOF.

3. Governing equations

Light propagates in the form of waves, and obeys the wave equation. In the case of monochromatic light, the wave function is a harmonic function of time, so we simply use the Helmholtz equation instead of the original wave equation. One of the simplest solutions of the Helmholtz equation is
U(x,y,z)=A(x,y,z)exp[jkz],
(3)
where A(x, y, z) and k denote the amplitude and the wave number, respectively. In most cases, A(x, y, z) is assumed to be constant, but this assumption does not hold near the focal point because the beam power is concentrated within a small cylinder surrounding the beam axis of the focal area. From Eq. (3) and the Helmholtz equation, A(x, y, z) must satisfy

(2x2+2y2)A(x,y,z)j2kzA(x,y,z)=0.
(4)

One basic solution of Eq. (4) is

A(x,y,z)=A1q(z)exp[jkx2+y22q(z)],where1q(z)=1z+jz0=1z+z02zj1λz0+λz2z0=1R(z)j1πW2(z).
(5)

In Eq. (5), A1 is a constant. R(z) and W(z) are measures of the wavefront radius of curvature and beam width, respectively. Substituting Eq. (5) into Eq. (3), we can obtain

U(x,y,z)=A1jz0W0W(z)exp[x2+y2W2(z)]exp[jkzjkx2+y22R(z)+jς(z)],wherethephaseretardationofGaussianbeamς(z)=tan1zz0.(seeFig.5(a))
(6)

Then the optical intensity I can be expressed as,

I(x,y,z)=|U(x,y,z)|2=|A1jz0|2(W0W(z))2exp[2x2+y2W2(z)]
(7)

At any position on the z-axis, the intensity in Eq. (7) is a Gaussian function of the radial distance (x2 + y2)1/2, as shown in Fig. 5(b)
Fig. 5 (a) Τhe phase retardation ζ(z) along with the optical axis, and (b) contour plot of the intensity distribution at focal plane (z = 0).
. Moreover, on the optical axis (x = 0, y = 0), the intensity has a maximum value at z = 0 (exact focal point) and gradually drops with increasing |z|, reaching half its maximum value at z = ±z0, as shown in Fig. 4(b). Note that 2z0 is known as the DOF. Then the wave functions U1 and U2 in Fig. 4(a) can be expressed as

U1(x,y,z)=A0W0W(z+α)exp[x2+y2W2(z+α)]exp[jk(z+α)jkx2+y22R(z+α)+jς(z+α)],andU2(x,y,z)=A0W0W(zα)exp[x2+y2W2(zα)]exp[jk(zα)jkx2+y22R(zα)+jς(zα)].
(8)

From Eq. (8), the interfered intensity Inew is derived as

Inew(x,y,z)=|U1+U2|2=I(x,y,z+α)+I(x,y,zα)+2I(x,y,z+α)I(x,y,zα)cos[φ1φ2].whereφ1φ2=k2αkx2+y22[1R(z+α)1R(zα)]+ς(z+α)ς(zα).
(9)

4. Experimental results

5. Conclusions

References and links

1.

M. Haruna, M. Takahashi, K. Wakahayashi, and H. Nishihara, “Laser beam lithographed micro-Fresnel lenses,” Appl. Opt. 29(34), 5120–5126 (1990). [CrossRef] [PubMed]

2.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33(11), 3556–3566 (1994). [CrossRef]

3.

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999). [CrossRef] [PubMed]

4.

J.-M. Asfour and A. G. Poleshchuk, “Asphere testing with a Fizeau interferometer based on a combined computer-generated hologram,” J. Opt. Soc. Am. A 23(1), 172–178 (2006). [CrossRef] [PubMed]

5.

J. H. Burge, “Fabrication of large circular diffractive optics,” in Diffractive Optics and Micro-Optics, OSA Tech. Dig. 10 (1998).

6.

H.-G. Rhee and Y.-W. Lee, “Improvement of linewidth in laser beam lithographed computer generated hologram,” Opt. Express 18(2), 1734–1740 (2010). [CrossRef] [PubMed]

7.

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010). [CrossRef] [PubMed]

8.

J. W. Goodman, “Analog optical information processing,” in Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, Singapore, 1996), Chap. 4.

9.

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, and S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82(18), 3125–3127 (2003). [CrossRef]

10.

B. E. A. Saleh and M. C. Teich, “Beam optics,” in Fundamentals of Photonics (John Wiley & Sons, Inc., New York, 1991), Chap. 3.

11.

D.-I. Kim, H.-G. Rhee, J.-B. Song, and Y.-W. Lee, “Laser output power stabilization for direct laser writing system by using an acousto-optic modulator,” Rev. Sci. Instrum. 78(10), 103110 (2007). [CrossRef] [PubMed]

12.

D. K. Cohen, W. H. Gee, M. Ludeke, and J. Lewkowicz, “Automatic focus control: the astigmatic lens approach,” Appl. Opt. 23(4), 565–570 (1984). [CrossRef] [PubMed]

13.

H.-G. Rhee, D.-I. Kim, and Y.-W. Lee, “Realization and performance evaluation of high speed autofocusing for direct laser lithography,” Rev. Sci. Instrum. 80(7), 073103 (2009). [CrossRef] [PubMed]

14.

L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33(31), 7334–7338 (1994). [CrossRef] [PubMed]

15.

A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt. 39(13), 2107–2115 (2000). [CrossRef] [PubMed]

16.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56(9), 930–933 (1986). [CrossRef] [PubMed]

17.

T. Doi, T. V. Vorburger, and P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23(3), 135–143 (1999). [CrossRef]

OCIS Codes
(120.4610) Instrumentation, measurement, and metrology : Optical fabrication
(120.4640) Instrumentation, measurement, and metrology : Optical instruments

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: November 3, 2011
Revised Manuscript: December 1, 2011
Manuscript Accepted: December 2, 2011
Published: December 20, 2011

Citation
Hyug-Gyo Rhee and Yun-Woo Lee, "Enhancement of height resolution in direct laser lithography," Opt. Express 20, 291-298 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-291


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References

  1. M. Haruna, M. Takahashi, K. Wakahayashi, and H. Nishihara, “Laser beam lithographed micro-Fresnel lenses,” Appl. Opt.29(34), 5120–5126 (1990). [CrossRef] [PubMed]
  2. M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.33(11), 3556–3566 (1994). [CrossRef]
  3. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt.38(8), 1295–1301 (1999). [CrossRef] [PubMed]
  4. J.-M. Asfour and A. G. Poleshchuk, “Asphere testing with a Fizeau interferometer based on a combined computer-generated hologram,” J. Opt. Soc. Am. A23(1), 172–178 (2006). [CrossRef] [PubMed]
  5. J. H. Burge, “Fabrication of large circular diffractive optics,” in Diffractive Optics and Micro-Optics, OSA Tech. Dig. 10 (1998).
  6. H.-G. Rhee and Y.-W. Lee, “Improvement of linewidth in laser beam lithographed computer generated hologram,” Opt. Express18(2), 1734–1740 (2010). [CrossRef] [PubMed]
  7. J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express18(17), 18339–18346 (2010). [CrossRef] [PubMed]
  8. J. W. Goodman, “Analog optical information processing,” in Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, Singapore, 1996), Chap. 4.
  9. V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, and S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett.82(18), 3125–3127 (2003). [CrossRef]
  10. B. E. A. Saleh and M. C. Teich, “Beam optics,” in Fundamentals of Photonics (John Wiley & Sons, Inc., New York, 1991), Chap. 3.
  11. D.-I. Kim, H.-G. Rhee, J.-B. Song, and Y.-W. Lee, “Laser output power stabilization for direct laser writing system by using an acousto-optic modulator,” Rev. Sci. Instrum.78(10), 103110 (2007). [CrossRef] [PubMed]
  12. D. K. Cohen, W. H. Gee, M. Ludeke, and J. Lewkowicz, “Automatic focus control: the astigmatic lens approach,” Appl. Opt.23(4), 565–570 (1984). [CrossRef] [PubMed]
  13. H.-G. Rhee, D.-I. Kim, and Y.-W. Lee, “Realization and performance evaluation of high speed autofocusing for direct laser lithography,” Rev. Sci. Instrum.80(7), 073103 (2009). [CrossRef] [PubMed]
  14. L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt.33(31), 7334–7338 (1994). [CrossRef] [PubMed]
  15. A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt.39(13), 2107–2115 (2000). [CrossRef] [PubMed]
  16. G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett.56(9), 930–933 (1986). [CrossRef] [PubMed]
  17. T. Doi, T. V. Vorburger, and P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng.23(3), 135–143 (1999). [CrossRef]

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