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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19296–19309
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Accurate near-field lithography modeling and quantitative mapping of the near-field distribution of a plasmonic nanoaperture in a metal

Yongwoo Kim, Howon Jung, Seok Kim, Jinhee Jang, Jae Yong Lee, and Jae W. Hahn  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19296-19309 (2011)
http://dx.doi.org/10.1364/OE.19.019296


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Abstract

In nanolithography using optical near-field sources to push the critical dimension below the diffraction limit, optimization of process parameters is of utmost importance. Herein we present a simple analytic model to predict photoresist profiles with a localized evanescent exposure that decays exponentially in a photoresist of finite contrast. We introduce the concept of nominal developing thickness (NDT) to determine the proper developing process that yields the best topography of the exposure profile fitting to the isointensity contour. Based on this model, we experimentally investigated the NDT and obtained exposure profiles produced by the near-field distribution of a bowtie-shaped nanoaperture. The profiles were properly fit to the calculated results obtained by the finite differential time domain method. Using the threshold exposure dose of a photoresist, we can determine the absolute intensity of the intensity distribution of the near field and analyze the difference in decay rates of the near field distributions obtained via experiment and calculation. For maximum depth of 41 nm, we estimate the uncertainties in the measurements of profile and intensity to be less than 6% and about 1%, respectively. We expect this method will be useful in detecting the absolute value of the near-field distribution produced by nano-scale devices.

© 2011 OSA

1. Introduction

There is increasing interest in developing nanolithography to fabricate ultra-small features on a variety of integrated optical and electronic devices [1

1. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999). [CrossRef]

7

7. K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008). [CrossRef]

]. As derivatives of photolithography – the most widely used manufacturing approach over the last several decades – optical near-field lithographic techniques were developed to overcome the diffraction limit of light. Beyond the far-field cutoff of spatial frequencies, the higher frequency support of an evanescent field through subwavelength apertures was exploited to achieve finer features as small as a few tens of nanometers in size [1

1. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999). [CrossRef]

]. However, a major technical concern raised was extremely low transmission through apertures much smaller than the wavelength of the exposing light [2

2. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

]. The advent of optical nanoantennas [3

3. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006). [CrossRef] [PubMed]

, 4

4. L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006). [CrossRef] [PubMed]

], and metallic subwavelength apertures specifically tailored to couple surface plasmons (SP), conferred substantial benefits over conventional aperture-based sources in terms of drastic increases in near-field throughput [3

3. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006). [CrossRef] [PubMed]

7

7. K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008). [CrossRef]

]. Nevertheless, the rapid decay of the evanescent field from the exit plane of such nano-sources could still be problematic [3

3. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006). [CrossRef] [PubMed]

, 4

4. L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006). [CrossRef] [PubMed]

] due to shallow exposure depths available for only a few tens of nanometers in photoresists. Since the lithographic system setup and process have to be optimized strictly, this often renders lithographic processes hard to control and may result in poor contrast of fabricated patterns, eventually limiting the potential of nano-lithographic applications.

The entire process of photolithography, while technically complicated, can largely be divided into two processes: exposure and development [8

8. S. A. Campbell, The science and engineering of microelectronic fabrication (Oxford University Press, New York, 1996).

]. Given that a photoresist layer is formed with a certain initial thickness, the process parameters to be controlled are essentially exposure dose and developing time, depending on the use of a particular photoresist characterized by exposure contrast and dissolution rate in development. The optimization usually focuses on determining the exposure dose window, whereas the developing time can be readily set by the maximum thickness to be cleared. In near-field lithography, however, exposure and development conditions yielding the optimal result differ [1

1. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999). [CrossRef]

, 4

4. L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006). [CrossRef] [PubMed]

] from those required to transfer relatively large patterns with exposure light that can propagate through a thicker layer of the same photoresist without appreciable attenuation. Moreover, defining and optimizing relevant process parameters is even more challenging in practice, since exact theoretical predictions and non-perturbative measurements of the near-field distribution of metallic nanoantennas are difficult [9

9. S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996). [CrossRef]

, 10

10. R. Guo, E. C. Kinzel, Y. Li, S. M. Uppuluri, A. Raman, and X. Xu, “Three-dimensional mapping of optical near field of a nanoscale bowtie antenna,” Opt. Express 18(5), 4961–4971 (2010). [CrossRef] [PubMed]

] due to their high sensitivity to geometry and the local environment.

The intensity threshold method has been frequently used to estimate photoresist profiles by finding the isoexposure contour corresponding to the threshold dose of a photoresist [4

4. L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006). [CrossRef] [PubMed]

, 11

11. D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005). [CrossRef] [PubMed]

]. However, the method was found to yield a considerably inaccurate prediction when forming structures on the subwavelength scale [12

12. R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express 13(18), 7198–7208 (2005). [CrossRef] [PubMed]

] due to the oversimplified assumption of a stepwise photoresist response around the threshold. Recently, an improved model that takes a finite contrast of the photoresist response into account was suggested [13

13. E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008). [CrossRef] [PubMed]

], enabling a simple analysis of photoresist profiles produced by the nanoscale exposure localized in both the lateral and longitudinal directions. The effects of photoresist contrast as well as exposure decay length were evaluated based on the patterning depth and width [13

13. E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008). [CrossRef] [PubMed]

, 14

14. E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008). [CrossRef]

]. Experimental verification was also performed with several different exposure doses [15

15. Y. Kim, S. Kim, H. Jung, E. Lee, and J. W. Hahn, “Plasmonic nano lithography with a high scan speed contact probe,” Opt. Express 17(22), 19476–19485 (2009). [CrossRef] [PubMed]

], resulting in some discrepancy with the model, but qualitative consistency with the prediction.

2. Theoretical model for evanescent-field optical lithography

We develop a simple one-dimensional (1-D) development model for a photoresist exposed to evanescently decaying light fields that are localized to the nanometer scale. While the most accurate simulation of photolithography requires the entire fabrication process to be considered comprehensively [12

12. R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express 13(18), 7198–7208 (2005). [CrossRef] [PubMed]

], we make several assumptions in order to identify the critical process parameters and understand the behaviors characteristic to near-field lithography. First, the spatial distribution (aerial image) of exposed light in the photoresist is approximated by the irradiance at the entrance plane of the photoresist multiplied by a factor that accounts for the light’s evanescent decay along the direction of the photoresist depth with the exponential decay length. Second, we consider a positive-type photoresist with a dissolution rate that can be determined directly from the aerial image of exposure dose and is not affected by chemical diffusion or mechanical shrinkage due to post-exposure processes. The fundamental parameter characterizing the photoresist is its finite contrast with the maximum dissolution rate above the clearing dose. Finally, the removal of a photoresist is assumed to proceed only toward increasing depth, and the developing time physically limits the end point of the development process. The details of the theoretical model are described in the following subsections.

2.1 Near-field exposure

Near-field intensity distributions in the vicinity of metallic subwavelength apertures or plasmonic masks are complicated, and have to be calculated numerically via the finite-difference time-domain (FDTD) method, rigorous coupled-wave analysis (RCWA), and so on. The localized near-fields, however, usually have a smooth varying envelope on the nanometer scale in the lateral plane and decay exponentially along the direction normal to the exit plane [1

1. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999). [CrossRef]

, 6

6. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005). [CrossRef] [PubMed]

, 7

7. K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008). [CrossRef]

, 14

14. E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008). [CrossRef]

]. We assume an exposure dose Eex(x,y;z)to be Gaussian in the transverse direction (x,y) and decaying exponentially in the direction of increasing depth (z) in the photoresist, in the form of
Eex(x,y;z)=E0(x,y)exp(zβ)=Epexp[2(ρw)2]exp(zβ),
(1)
where the Gaussian profile is a function of radius ρ=(x2+y2)1/2 from its center with a peak exposure dose of Ep and has the FWHM diameter WFWHM=2ln2w. Away from the photoresist entrance plane atz=0, the exposure light is then attenuated by the decay constant β. This simplification allows us explore the general impact of near-field exposures as defined readily by peak dose, width, and decay length.

2.2 Photoresist parameters

A positive photoresist spun onto a substrate is basically a mixture of an alkaline soluble resin and a photosensitive dissolution inhibitor, often referred to as a photo-active compound (PAC) [8

8. S. A. Campbell, The science and engineering of microelectronic fabrication (Oxford University Press, New York, 1996).

]. The PAC prevents the resin from being dissolved in an alkaline solution unless the photoresist is exposed to ultraviolet (UV) light of sufficient energy. Above a certain threshold dose Ethof exposure, however, the PAC undergoes photochemical change to render the resin soluble in alkaline developers. The dissolution rate vDof the resin can be further enhanced with increasing exposure dose up to a second critical clearing dose Ecl, above which the dissolution rate saturates to its maximum atvcl. The differential dissolution rate between the exposed and unexposed photoresist permits the transfer of optical exposure patterns into positive development profiles. Such a chemical response can usually be specified by the photoresist contrast
Γ=1log10(Ecl/Eth),
(2)
which is inherent to photoresists, and represents the slope of the dissolution rate vD with respect to the logarithmic exposure dose log(Eex). The dissolution rate can be expressed as vD=vclη(Eex) by introducing a dose-dependent nonlinear function,

η(Eex)={0,forEex<Eth,Γlog10(Eex/Eth),forEthEex<Ecl,and1,forEclEex.
(3)

Here the dark erosion rate (a dissolution rate for unexposed (Eex<Eth) photoresists) is assumed to be negligible, as is often the case in well-optimized experiments.

2.3 Developing

We model the development process to remove the locally exposed photoresist at the dissolution rate vD, prescribed by the exposure dose distribution Eex(x,y;z), within a given time constraint τD. In this study the photoresist removal is assumed to proceed one dimensionally and only in the direction of increasing depth z.

The eliminated thickness at the end point of development carried out for τD is determined by constructing the isometric surface SE(x,y) that is defined by [11

11. D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005). [CrossRef] [PubMed]

]
τD=0SE1η(Eex)vcldz,
(4)
where the definite integral corresponds to the total time it takes for the development marching front to reach the depth SE(x,y), which should match the developing process time τD. By removing vcl from the integral, the above equation can be rewritten as

T0=0SE1η(Eex)dz.
(5)

T0=vclτDis the nominal developing thickness (NDT) that would have been removed when the same photoresist was completely exposed to the clearing light dose over its entire volume and subjected to the developing process for the time span τD. We take T0 as a convenient measure for the developing process span because it is physically more meaningful than using τD as an absolute developing time.

Substituting the expressions for η(Eex)from Eq. (3) and Eex(x,y;z) from Eq. (1) into Eq. (5), we find the analytic solution for the development profile SE(x,y):

SE(E0)={0,forE0<Eth,βln(E0/Eth)[1exp(γT0/β)],forEthE0<Ecl,βln(E0/Eth)β[(E0/Eth)γ/eγ]exp(γT0/β),forEclE0,andT0,forEcleT0/βE0.
(6)

The determinant parameters involved are T0, β, Eth, and γ, where γ=[ln(Ecl/Eth)]1 is an alternative parameter introduced for mathematical convenience, representing the photoresist contrast as Γ=γln102.3γ. The symbol e denotes Euler’s number (approximately 2.718). Given the exposure dose distribution at the entrance plane E0(x,y), the photoresist removal thickness SE as a function of position (x,y) can then be evaluated.

3. Numerical calculation of lithography profiles

3.1 Effect of peak exposure dose

3.2 Effect of developing time

Until T0 reaches the isoexposure depth Scl (within which the dissolution rate is the highest at its saturated value), the lowest depth of a profile SE(x,y) is kept identical with T0 as in Figs. 2(a-b). When T0exceedsSclas in Figs. 2(c-f), the dissolution gradually slows, and the actual removal thickness SE(x,y) always becomes smaller than the nominal process thickness T0. In principle the deepest profile achievable with the evanescent exposure is determined fundamentally by the isoexposure depth Sth. However, Figs. 2(d-f) suggest that this is the case provided that the developing process is carried out when the value of T0 is sufficiently larger than Sth.

3.3. Minimum NDT for optimizing the near-field lithographic features

In Fig. 3(a) the profile depth follows the constraint imposed by NDT (solid line) up to a certain point, and then asymptotically approaches the maximum at the threshold-dose isoexposure depth (black dashed-line), depending on the exposure dose level. We can estimate the minimum NDT by limiting the tolerance to fres (the ratio of the residual thickness to the maximum possible depth), so that the removal thickness SE(Ep) in Eq. (6) should be greater than (1fres)Sth(Ep).

For exposures less than dose-to-clear (i.e., Ep<Ecl or Ep<Ethe1/γ), the developing process is required to provide
To(β/γ)lnfres1
(8)
regardless of the exposure dose. With a fres less than 1%, the NDT then becomes T010.6β/Γ, which approximates to 106 nm for the parameters used in Fig. 3(a) (decay length β=30 nm, and the base-10-log contrast Γ=3).

For exposures greater than dose-to-clear (i.e., Ep>Ecl orEp>Ethe1/γ), the required NDT depends on the exposure dose as well, appearing in a somewhat complicated form given by
Toβ(   1γln(1fres)   +ln(EpEth)   1γ{ln[ln(EpEth)]+lnγ+1}),
(9)
which dictates T0 to be greater than that with exposures less than dose-to-clear. In general, the minimum NDT also varies with the photoresist contrast and the decay length of the exposure dose.

Generally, high-contrast photoresists are preferred for transferring exposure aerial images into fine patterns with large depths and steep edges. Since the contrast of a photoresist varies with the photoactive material used, baking procedures involved, exposure wavelength employed, and so on, understanding the impact of photoresist contrast on near-field lithography will help optimize such technical factors.

We characterized the photoresist profile (formed with an exposure dose four times the threshold) as a function of its contrast Γranging from one to ten. As shown in Fig. 3(b), it is also true for evanescent exposures that higher contrast permits deeper and steeper patterns given the same NDT. However, the apparent shortcomings of low-contrast photoresists can be remedied by extending the NDT (or equivalently the developing time). To put it differently, the photoresist contrast makes no fundamental difference to the best achievable topography.

4. Near-field lithography experiment for profiling of isointensity contour

4.1 Experimental setup

To measure the field distribution close to the surface of a nanoaperture, we placed an optical near-field scanning probe in close contact with the photoresist to be exposed. The nanoaperture was fabricated on a probe holding a pyramidal tip (height 5 μm) made of a 400-nm-thick silicon nitride (Si3N4, n=2.07) membrane. The tip apex has a flat surface and the diameter is 3 μm. On the nitride membrane, a 150-nm-thick aluminum film was deposited by ion-assisted thermal evaporation, and the root-mean-square (RMS) surface roughness was about 1.5 nm.

The bowtie-shaped aperture was milled by a focused ion beam (FIB) (SII SMI3050). Before the milling of the aperture, a 2 μm × 2 μm area and 300-nm-thick silicon nitride film was milled at the top using a 12 pA current ion beam to yield a 100-nm-thick Si3N4 membrane. The surface of the Si3N4 membrane was coated with a 2-nm-thick layer of Platinum (Pt) for precise milling of the nitride film, minimizing the charging effect. We milled the aperture from the Si3N4 membrane side in order to form sharp ridges at the bottom metal surface [18

18. J. B. Leen, P. Hansen, Y.-T. Cheng, and L. Hesselink, “Improved focused ion beam fabrication of near-field apertures using a silicon nitride membrane,” Opt. Lett. 33(23), 2827–2829 (2008). [CrossRef] [PubMed]

]. The bowtie-shaped nanoaperture with a 150 nm × 150 nm outline size and a 20 nm ridge gap distance was milled through the 100-nm-thick Si3N4 and 150-nm-thick aluminum layers under 30 kV acceleration voltage, 1 pA current, and 5 μs dwell time. The fabricated bowtie aperture is shown in Fig. 6(c)
Fig. 6 Cross-section of the developed pattern profile (under-filled black solid lines) and FDTD calculation results (dotted-lines) for the (a) xz-plane and (b) yz-plane. A scanning electron micrograph of bowtie-shaped nano aperture in experiment is shown in (c).
.

The probe was affixed to the laser direct writing system coupled with a 405 nm wavelength diode laser (CrystaLaser, BCL-025-405S). The aperture was illuminated with a laser beam focused by a high NA (0.8) objective lens (Nikon CFI LU Plan Epi ELWD 100×). The focused beam spot size was assumed to be about 625 nm (λ/ NAeff) based on the effective NA (NAeff=0.65) of illumination determined by the pyramidal tip geometry. The laser beam was polarized along the direction of the ridge gap. The laser power was measured at the plane between the objective lens and optical probe. The exposure dose was adjusted by changing the exposure time. In this experiment, the exposure time was varied in the range of several tens of milliseconds, and the error in exposure time was less than 0.2%. The 140-nm-thick positive-type photoresist (Donjin Semichem, DPR-i7201 diluted) was spun at 2000 rpm for 40 s on the 10 mm × 10 mm diced silicon wafer. The film was soft-baked at 100 °C for 100 s before exposure. Development of the photoresist after the exposure process was carried out with developing solution (AZ MIF 300), and the three-dimensional topography of the exposure profile in the photoresist was measured using an atomic force microscope (Park Systems, XE-100) with a high resolution sharp silicon tip (Nanosensors, SSS-NCHR, typical tip radius ~2 nm) in tapping mode.

4.2 Determination of the minimum NDT required for developing toward the threshold dose contour

The standard developing solution has a high saturated dissolution rate around several tens of nanometers per second (~50 nm/s). Since the development time is only a few seconds under the high dissolution rate, it is hard to control the NDT with several tens of nanometers. To determine the NDT with several tens of nanometers, we reduced the dissolution rate of the development process to 4 nm/s by diluting the developing solution with deionized water. The developing process was performed at 30 ± 0.1 C˚ and 30% relative humidity.

To determine the minimum NDT of the pattern profile, spot patterns were recorded on the same substrates with the same exposure dose. The laser power illuminated at the aperture was set at 120 nW with an exposure time of 30 ms. Since the NDT is given by T0=vclτD, we adjusted the NDT by changing the developing time. To determine the minimum NDT for the spot patterns recorded with the nano-aperture, we measured the maximum depth of the spot patterns for different NDTs.

Figure 4
Fig. 4 Developed photoresist maximum depth with respect to NDT. As NDT increases, the pattern depth increases until reaching the contour of threshold dose (S th). In this experiment the maximum depth of S E was expected to approach the 48.7 nm (red dotted-line). Above a NDT of 145 nm (dashed arrow), the pattern depth was expected to be similar to that of isoexposure at the threshold dose with a tolerance less than 1%.
shows the maximum depth of developed spot patterns with respect to NDT. The asymptotically approaching depth (Sth) is given as 48.7 nm, with the averaged value of the maximum depths at large NDT of 200 nm, 400 nm, and 800 nm. The experimental results were fitted to the calculation using Eq. (6) by setting the decay constant equal to 40 nm and contrast of photoresist Γ =3. From the fitted curve we obtained a minimum NDT of 145 nm with a tolerance of ~1% of the maximum depth of Sth for the isoexposure contour at the threshold dose.

According to the lithography model proposed in this work, the NDT should be larger than the minimum NDT to facilitate the development process toward the threshold contour. In practice, however, the developing is actually influenced by dark erosion, including dissolution of unexposed and exposed regions under the threshold dose level. Even though the dark erosion rate of a conventional photoresist is about 1% of the dissolution rate [19

19. MicroChemicals GmbH, “Development of Photoresists” (2007) http://www.microchemicals.eu/technical_information/development_photoresist.pdf

], it affects the pattern profile as NDT increases. To minimize the effect of dark erosion, the NDT should be given by a little bit larger than PR thickness to be removed (in general, initial thickness) in a conventional lithography. There is trade off, however, between removal depth and broadening of pattern width in near-field lithography. For the purpose of minimizing the effect of dark erosion, one should consider the rate of dark erosion and tolerance (fres) to optimize NDT during developing process.

To avoid pattern broadening due to dark erosion, we experimentally investigated the reasonable range of NDT by developing spot pattern samples with different NDTs. We recorded near-field spot patterns generated by a nano-aperture with a laser power of 120 nW and an exposure time of 10 ms. Developing the pattern samples within the range of 120 nm and 800 nm NDTs, we measured the maximum depths of the pattern profiles. The maximum depth of the pattern profiles was 17 nm, and the deviation of the depth was within ±1 nm when the NDT was varied from 120 nm to 800 nm. Thus, the experimental NDT value we used for the subsequent developing process of near field patterns was 500 nm, which is in the middle of the NDT range listed above and is sufficiently larger than minimum NDT from the fitting curve.

4.3 Measurement and analysis of the isointensity distribution of a bowtie-shaped nanoaperture

We measured the near-field distribution of a bowtie-shaped nanoaperture using the lithography model. We recorded several isointensity contours of the near field distribution with different exposure doses by changing the exposure time. Setting the laser power at 60 nW, we changed the exposure time from 20 ms to 60 ms in increments of 10 ms. At each exposure time we averaged five photoresist profiles measured with an AFM to obtain a three-dimensional profile. Because of the small AFM tip radius, we expected lateral and vertical profile measurement resolutions of about 2 nm and less than 0.1 nm, respectively. In the case of the profile with a depth of 41 nm, the deviation was about 2.56 nm, which was about 6% of the averaged value. The corresponding width was 121 nm in the x axis with a deviation of 6.18 nm, which was about 5% of the averaged width. The near-field distribution of the bowtie-shaped nanoaperture used in this experiment was calculated with a FDTD (XFDTD ver. 7.0). The total calculation volume was 500 nm × 500 nm × 500 nm in the xyz axis, and the mesh size was 2 nm × 2 nm × 2 nm in the xyz axis. In the analysis of isointensity surface (or contour) from FDTD calculations, we notice that the two peak at the ridges of bowtie aperture merge into a single peak when the maximum depth is about 6 ~10 nm. Figure 5
Fig. 5 (a) – (c) AFM measured three-dimensional profiles of developed patterns for different exposure times. From left (a) to right (c) in the upper row, the exposure time was 20, 30, and 50 ms, respectively, while the laser power was set at 60 nW. The isointensity surfaces from the three-dimensional near-field distribution using FDTD calculation are plotted in the bottom row (d) - (f), and the corresponding intensity was normalized to the intensity of the input plane. The intensity level of (d) - (f) are correspond to the peak intensity at the depth of 6.5, 21, and 41 nm, indicated in the inset of (a) - (c), respectively. The shape of the bowtie aperture is illustrated with white dotted lines, and white arrows indicate the polarization axis of illumination. The visualized space is 500 nm × 500 nm × 50 nm in x-y-z space.
show the three-dimensional profiles of isointensity surfaces obtained with exposure times of 20 ms, 30 ms, and 50 ms for the comparison of the experimental results [(a) - (c)] and FDTD calculations [(d) - (f)]. The experimental results representing the structures of the near-field distribution of a bowtie-shaped nanoaperture agreed well with the FDTD calculations.

In the quantitative analysis of the near-field distribution, we compared the results of the measurements and the calculations with respect to the cross-sectional profiles in both axes in Fig. 6. Since the threshold dose is an inherent property of a photoresist, we evaluated the absolute intensity of the isointensity contour corresponding to a photoresist profile. We obtained photoresist profiles at different exposure doses, and the cross-sections of the profiles are depicted in Figs. 6(a) and 6(b). Referring to the threshold dose of the photoresist (40 mJ/cm2 at 405 nm), we were able to determine the intensity of each isointensity contour with an error of less than 1.03%, for which the error in measurement of the threshold dose was about 1% [20

20. K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992). [CrossRef]

] and in exposure time control is about 0.25% (minimum illumination time of the electrical shutter was about 50 μs). The intensities corresponding to the profiles in Fig. 6 were 2.0, 1.3, 1.0, 0.80, and 0.67 W/cm2, as indicated in the order of the maximum depth. Note that unlike the method using NSOM, which measures the relative intensity distribution, this method measures the three-dimensional profile of the isointensity contour and also the absolute intensity value.

While comparing the experimental results and the calculations, however, we found that the intensity matching to the photoresist profile decreased by a factor of 3 (from 2 to 0.67 W/cm2) for a variation in maximum depth from 6.5 nm to 48 nm, and the calculated intensity of the isointensity contour decreased by a factor of 13 (from 0.40 to 0.03) for a similar range of depth variation. The absolute magnitude of each peak is indicated in the figure, and the intensity at the entrance of the aperture was assumed to be 1 for the calculation. Therefore, the photoresist profile was properly matched with the calculated intensity of the isointensity contour by comparing the maximum depth and width.

In order to clarify the difference between the experiment and the calculation in terms of the decay rate of the near field, we noted that the size of the beam spot resulted from the confinement of the near field at the beginning of the aperture exit. We presumed that the disagreement in the decay rate was due to the difference in the beam size confined in front of the exit of the nanoaperture since the near-field intensity of a large beam slowly decreases compared with that of a small beam. The beam sizes for the first peaks of the photoresist profile and the isointensity contour of FDTD calculation in Fig. 6 (a) were 70 nm and 37 nm, respectively. Using beam size, effective wavelength (λeff = 253 nm) in PR and a propagation vector kz=(2π/λeff)2(kx)2 in the direction of PR depth, we estimate a corresponding decay length, β=π/|kz|. Assuming kx=2π/(beamdiameter), we obtain the decay length is 36.4 nm and 18.7 nm for the beam size of 70 nm and 37 nm, respectively. From a simple exponential decay function (ez/β), we estimate that the intensity decreased by factors of 3.3 and 10.8, respectively, for the depth variation from 6.5 to 48 nm and it is found that these computations properly explain the discrepancy in decay rates of the near fields obtained by the experiment and the FDTD calculation.

In this experiment we were unable to clarify the origin of the beam spot broadening in the x-direction by a factor of ~2. We carefully fabricated the ridge of the aperture in the rear side with FIB to minimize the edge roundness and the gap distance between the ridges of the bowtie aperture was precisely measured by SEM with uncertainty ± 2 nm. We presumed that the finite size grains (estimated 50-100 nm in diameter) in the metal film and the rounded edges of the ridge aperture may have affected the confinement of the fields induced by the surface plasmon polariton and the near field of the diffracted light at the exit of the aperture. Further work is required to clearly investigate beam size broadening in the metal nanoaperture.

5. Conclusion

We experimentally determined the minimum NDT in order to determine the proper NDT for the development process that makes the exposure profile fit to the isointensity contour. Under the NDT condition, we measured the near field intensity distribution of a bowtie-shaped nanoaperture from the exposure profile. Using the threshold expose dose of the photoresist, this method can be used to measure not only the distribution, but also the absolute value of the intensity of each contour. We also analyzed the difference in decay rates of the near field distributions obtained experimentally and by calculation based on the initial beam size of the near field at the exit of the aperture. For maximum depth of 41 nm, we estimated the uncertainty in the measurement of the near-field profile and that in the measurement of the absolute intensity to be less than 6% and 1%, respectively. We expect the suggested method of near-field mapping based on an accurate lithography model to be useful for quantitative evaluation of nano-scale devices producing strong near-field distribution under a diffraction-limited scale, such as high transmission nanoapertures, nano probes for adiabatic concentration of light, nano antennas, and so on.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.2011-0030630).

References and links

1.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999). [CrossRef]

2.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

3.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006). [CrossRef] [PubMed]

4.

L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006). [CrossRef] [PubMed]

5.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004). [CrossRef]

6.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005). [CrossRef] [PubMed]

7.

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008). [CrossRef]

8.

S. A. Campbell, The science and engineering of microelectronic fabrication (Oxford University Press, New York, 1996).

9.

S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996). [CrossRef]

10.

R. Guo, E. C. Kinzel, Y. Li, S. M. Uppuluri, A. Raman, and X. Xu, “Three-dimensional mapping of optical near field of a nanoscale bowtie antenna,” Opt. Express 18(5), 4961–4971 (2010). [CrossRef] [PubMed]

11.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005). [CrossRef] [PubMed]

12.

R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express 13(18), 7198–7208 (2005). [CrossRef] [PubMed]

13.

E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008). [CrossRef] [PubMed]

14.

E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008). [CrossRef]

15.

Y. Kim, S. Kim, H. Jung, E. Lee, and J. W. Hahn, “Plasmonic nano lithography with a high scan speed contact probe,” Opt. Express 17(22), 19476–19485 (2009). [CrossRef] [PubMed]

16.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008). [CrossRef] [PubMed]

17.

L. Zhou, Q. Gan, F. J. Bartoli, and V. Dierolf, “Direct near-field optical imaging of UV bowtie nanoantennas,” Opt. Express 17(22), 20301–20306 (2009). [CrossRef] [PubMed]

18.

J. B. Leen, P. Hansen, Y.-T. Cheng, and L. Hesselink, “Improved focused ion beam fabrication of near-field apertures using a silicon nitride membrane,” Opt. Lett. 33(23), 2827–2829 (2008). [CrossRef] [PubMed]

19.

MicroChemicals GmbH, “Development of Photoresists” (2007) http://www.microchemicals.eu/technical_information/development_photoresist.pdf

20.

K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(110.4235) Imaging systems : Nanolithography
(220.4241) Optical design and fabrication : Nanostructure fabrication
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Imaging Systems

History
Original Manuscript: July 11, 2011
Revised Manuscript: August 29, 2011
Manuscript Accepted: August 29, 2011
Published: September 20, 2011

Citation
Yongwoo Kim, Howon Jung, Seok Kim, Jinhee Jang, Jae Yong Lee, and Jae W. Hahn, "Accurate near-field lithography modeling and quantitative mapping of the near-field distribution of a plasmonic nanoaperture in a metal," Opt. Express 19, 19296-19309 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19296


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References

  1. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett.75(22), 3560–3562 (1999). [CrossRef]
  2. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett.4(6), 1085–1088 (2004). [CrossRef]
  3. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett.6(3), 355–360 (2006). [CrossRef] [PubMed]
  4. L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express14(21), 9902–9908 (2006). [CrossRef] [PubMed]
  5. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett.84(23), 4780–4782 (2004). [CrossRef]
  6. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett.5(5), 957–961 (2005). [CrossRef] [PubMed]
  7. K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett.93(9), 093103 (2008). [CrossRef]
  8. S. A. Campbell, The science and engineering of microelectronic fabrication (Oxford University Press, New York, 1996).
  9. S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett.69(22), 3306–3308 (1996). [CrossRef]
  10. R. Guo, E. C. Kinzel, Y. Li, S. M. Uppuluri, A. Raman, and X. Xu, “Three-dimensional mapping of optical near field of a nanoscale bowtie antenna,” Opt. Express18(5), 4961–4971 (2010). [CrossRef] [PubMed]
  11. D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett.5(7), 1227–1230 (2005). [CrossRef] [PubMed]
  12. R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express13(18), 7198–7208 (2005). [CrossRef] [PubMed]
  13. E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology19(27), 275303 (2008). [CrossRef] [PubMed]
  14. E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys.103(8), 083550 (2008). [CrossRef]
  15. Y. Kim, S. Kim, H. Jung, E. Lee, and J. W. Hahn, “Plasmonic nano lithography with a high scan speed contact probe,” Opt. Express17(22), 19476–19485 (2009). [CrossRef] [PubMed]
  16. M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett.8(10), 3357–3363 (2008). [CrossRef] [PubMed]
  17. L. Zhou, Q. Gan, F. J. Bartoli, and V. Dierolf, “Direct near-field optical imaging of UV bowtie nanoantennas,” Opt. Express17(22), 20301–20306 (2009). [CrossRef] [PubMed]
  18. J. B. Leen, P. Hansen, Y.-T. Cheng, and L. Hesselink, “Improved focused ion beam fabrication of near-field apertures using a silicon nitride membrane,” Opt. Lett.33(23), 2827–2829 (2008). [CrossRef] [PubMed]
  19. MicroChemicals GmbH, “Development of Photoresists” (2007) http://www.microchemicals.eu/technical_information/development_photoresist.pdf
  20. K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng.17(1-4), 435–438 (1992). [CrossRef]

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