Microelectronic Engineering 105 (2013) 103–106

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Microelectronic Engineering

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Enhanced Kretschmann structure for maskless surface plasmoninterference lithography

Xiaowei Guo a,⇑, Qiming Dong a, Ruiying Shi b, Shuhong Li b, Jinglei Du b

a School of Optoelectronic Information, University of Electronic Science and Technology, Chengdu 610054, Chinab Physics Department, Sichuan University, Chengdu 610064, China

a r t i c l e i n f o

Article history:Available online 27 December 2012

Keywords:Optical lithographySurface plasmonsInterferenceKretschmann structure

0167-9317/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.mee.2012.11.026

⇑ Corresponding author. Tel.: +86 28 83202342.E-mail address: gxw@uestc.edu.cn (X. Guo).

a b s t r a c t

Mask less surface plasmon interference lithography provides potential to obtain nanoscale feature sizewith large area at low cost. In this paper, we present a novel structure for mask less surface plasmoninterference lithography. It is an enhanced Kretschmann structure in which a dielectric layer with lowrefractive index is added between the prism and metal layer. Numerical results show that the additionaldielectric layer eliminates the inherent limit in classic Kretschmann structure that requires use of a prismwith high refractive index for lithography purpose. Also, the structure exhibits more flexibility in tuningthe spatial resolutions than classic Kretschmann structure. Both advantages lead to the structure morepractical in real use.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

A number of near-field patterning techniques have beenexplored recently to extend the resolution of optical lithographybeyond the conventional diffraction limits. The typical techniquesinclude evanescent field lithography [1,2] and plasmonic lithogra-phy [3–6]. In both cases resolution below 100 nm has been demon-strated by use of exposure wavelengths greater than 400 nm. Incomparison to the former, the latter offers larger exposure depthand better pattern contrast because of surface plasmon’s specialperformance in enhancement of optical near field. Among plas-monic lithography techniques, surface plasmon interferencelithography(SPIL) offers great promise for nanometer-scale pat-terning of large areas at low cost. At present SPIL behaves in twoways. One is the grating-assisted SPIL [3,4] and the other theprism-assisted SPIL [5,6]. The prism-assisted SPIL, however, ismore cost-effective than grating-assisted SPIL because no fine grat-ing is required. The prism-assisted SPIL reported is mainly basedon classic Kretschmann structure which consists of three layers,prism, metal and photoresist, from top to bottom. Due to strongrequirement of the prism with high refractive index, classicKretschmann structure is greatly limited in real use.

To solve the problem, in this paper we present an enhancedKretschmann structure for SPIL. Insert of a dielectric layer withlow refractive index between the prism and metal layer alleviatesthe need of high index prism and allows the tunability of spatialresolution.

ll rights reserved.

2. The enhanced structure and working principle

The enhanced Kretschmann structure is shown in Fig. 1. There isa dielectric layer inserted between the prism and the metal layersas compared to classic Kretschmann structure. The triangle prismis illuminated from above with a uniform, spatially coherent,monochromatic TM-polarized plane wave with wavelength k, inci-dent at angle h to the center line (or the base normal). Under totalinternal reflection, the evanescent wave arises at the interface be-tween the prism and the dielectric layers. When the wave vector ofthe evanescent field along the interface matches that of SPs on themetal layer, that is, ksp = k0npsinh, most of the incidence energytransmits the metal layer because of surface plasmon resonance.The resultant SPs at lower metal surface can be used for exposureof the photoresist. The interference pattern is formed in thephotoresist by two incidence beam.

For a thin metallic film surrounded by two materials, thedispersion relation for SPs can be written as follows [7],

tan hða2t2Þ ¼ � e2a1e1a2þ e2a3

e3a2

� �1þ e2a1

e1a2� e2a3e3a2

� �.

a2j ¼ k2 � k2

0ej; j ¼ 1;2;3ð1Þ

where k0 is the value of the wave vector of incidence light, k the va-lue of the wave vector of SPs. 1, 2 and 3 denote the values of permit-tivity in the region above, inside and below the metal layer,respectively. The thickness of metal layer t2 determines the wavevector of the SPs mode, and it should be small enough to ensurethe SPs modes on both interfaces couple each other.

Fig. 1. Schematic view of the enhanced Kretschmann structure.

104 X. Guo et al. / Microelectronic Engineering 105 (2013) 103–106

3. Unique features of the enhanced structures

The introduction of the dielectric layer actually increases twodegrees of freedom for the system, the refractive index and thethickness, which at least generates two advantages in lithography.One is the enhanced structure enables use of the prism with lowrefractive index if a dielectric layer with smaller refractive indexis used. Solving Eq. (1) obtains a series of SP mode solutions, which

Fig. 2. The transmission as a function of incidence angle at different refractive indices of tis 30 nm. The incidence wavelength is 365 nm at which the silver permittivity is e = �5.7and thickness are 1.5 and 150 nm, respectively.

Fig. 3. The transmission as a function of incidence angle at different combination ofstructure. The prism refractive index is 1.756 and other parameters are same as in Fig.

provides possibility to match the use of low dielectric refractive in-dex. Classic Kretschmann structure, however, can be regarded asan extreme case of the enhanced structure. The proximity of theprism will load and wipe out the SP wave [8]. In this case, the dis-persion relation for SPs is established by the following equation [5],

ksp ¼ k0½emer=ðem þ erÞ�12 ð2Þ

It is clear that there is only one SP solution which severely limits thechoice of the prism. Fig. 2 illustrates the difference. The incidencewavelength is 365 nm. The metal material is chosen to silver whoserefractive index and thickness are e = �5.7948 + 0.1265i atk = 365 nm and 30 nm, respectively. The refractive index of the re-sist is 1.6, a typical value for existing high resolution resists. InFig. 2(a), it shows the transmission as a function of incidence angleat different prism refractive indices in classic Kretschmann struc-ture. The transmission curve is obtained by using the multilayertransmission transfer matrix [9]. It is easily observed that obtainingan effective SPR requires use of a prism with the refractive indexabove 2.0. Under same conditions, insert of a dielectric layer with1.5 refractive index, e.g. PMMA, and 150 nm thickness can loosenthe choice range (see Fig. 2(b)). From Fig. 2(b), only use of the prismwith 1.79 refractive index generates an effective SPR. It is worth

he prism in (a) classic and (b) enhanced Kretschmann structure. The silver thickness948 + 0.1265i. The resist refractive index is 1.6. In (b), the dielectric refractive index

the dielectric and metal thicknesses in (a) classic and (b) enhanced Kretschmann2.

Fig. 4. The transmission as a function of incidence angle under the structureparameters as follows. The dielectric and metal thicknesses are 200 and 22 nm,respectively, and other parameters are same as in Fig. 3.

X. Guo et al. / Microelectronic Engineering 105 (2013) 103–106 105

pointing out the SPs excited in the enhanced structure are longrange SPs that are more sensitive to the angle change and thereforethe range of angle is narrower as compared to Krestchmann plas-mons. The narrower ranges of angle maybe require more preciseexperiment control. The other is that once the materials are speci-fied can tunable feature sizes be achieved by using different dielec-tric and metal thicknesses. Fig. 3(a) describes the transmission

Fig. 5. The interference pattern. (a) and (b) denote the int

conditions at different metal thicknesses in classic Kretschmannstructure. Here the prism refractive index is 1.755(ZF6) and otherparameters are same as in Fig. 2(a). It can be seen there is no SPRoccurring. All the guided wave modes are cut off at the total reflec-tion angle for the prism and resist, around 66�. In the enhancedstructures under the same conditions, however, the insert of thedielectric layer generates SPR signals where the dielectric refractiveindex is 1.5 (see Fig. 3(b)). The combination of the metal and dielec-tric thicknesses gives rise to different SP modes on the right of thetotal reflection angle. The SP modes are located at different reso-nance angles that evitably lead to different spatial resolutionsaccording to Eq. (3) shown as below. Moreover, it is interesting thatthe metal thickness monotonously corresponds to the resonanceangle, which indicates the interference lithography resolutionscan be arbitrarily engineered. The 15 nm variation of the silverthickness can produce the resonance angles ranging from 67� to83�.

4. Simulated fabrication of 55 nm feature size by using 365 nmwavelength

The resolution of the interference pattern in this structure iseasily deduced as,

R ¼ k=4ðnp sin hÞ ð3Þ

It is seen that high resolution can be obtained by reducing incidencewavelength or increasing the product of the prism refractive indexand the incidence angle. For example, use of 193 nm wavelength

erference field and the pattern contrast, respectively.

106 X. Guo et al. / Microelectronic Engineering 105 (2013) 103–106

with ZF6 glass prism theoretically offers the potential to obtain anultimate resolution of 27 nm and provides promising for fabricationof sub 32 nm node. For cost-effective purpose, we use 365 nmwavelength to fabricate 55 nm feature size. Other parameters aresame as in Fig. 3(b). According to Eq. (4), the resonance angle issolved to 71�. In Fig. 3(b), the blue line with 20 nm metal thicknesscorresponds to the resonance angle of 70�. Therefore, the metalthickness should be increased a little. Fig. 4 indicates the final metalthickness of 22 nm is required whereas the dielectric thickness is200 nm. The interference result is simulated by using a FDTD tech-nique [5]. In the FDTD technique, both the spatial area and the timeinterval are discretized. The Maxwell’s equations in differentialform can be solved directly and the iterative expressions have beengained. The material can be represented in the mesh of the squarecells. In our simulation, the cell size about 1 nm is used. Time stepsizes of less than 0.002 fs are used in order to satisfy the FDTD sta-bility criteria. The perfectly matched layer is used. Also, in this sim-ulation the complex dielectric constant of Ag dependent on thefrequency of the incidence light is described by Drude model

e2 ¼ e1 �x2p=ðx2 þ ixcÞ ð4Þ

with e1 the relative permittivity at infinite frequency, x the angularfrequency of the incidence light, xp the plasma frequency, and c thecollision frequency.

Finally, the interference pattern is shown in Fig. 5. Fig. 5(a) givesout the interference field intensity distribution. It can be seen thatthe exposure depth reaches about 160 nm that is enough for inter-ference realization. Here we defined the exposure depth by thepropagation length of the SPs when its electric field becomes zero.In Fig. 5(b), the pattern contrast as a function of decay depth isplotted. The definition of the pattern contrast is defined byV ¼ ðt2 � 1Þ=ðt2 þ 1Þ [5] in which t is the ratio of the electric field

Ez/Ex. The pattern contrast is very high up to 0.9 even if the decaydepth is over 400 nm which is far beyond the effective exposuredepth. Therefore, the simulations show the enhanced structure issufficient to fabricate 55 nm feature size.

5. Conclusion

In conclusion, we discuss an enhanced Kretschmann structurefor mask less SPIL. The structure is realized by using a dielectriclayer with low refractive index between the prism and metal layer.The simulated results demonstrate that the novel structure has theability to realize 55 nm spatial resolution. The cost-effective struc-ture is expected to contribute to the development of mask lessSPIL.

Acknowledgments

This work was supported by National Natural Science Founda-tion of China (No. 60906052).

References

[1] M.M. Alkaisi, R.J. Blaikie, S.J. McNab, et al., Appl. Phys. Lett. 75 (1999) 3560–3562.

[2] R. Blaikie, S. McNab, Appl. Opt. 40 (10) (2001) 1692–1698.[3] X.G. Luo, T. Ishihara, Appl. Phys. Lett. 84 (2004) 4780–4782.[4] D.B. Shao, S.C. Chen, Appl. Phys. Lett. 86 (2005) 253103–253107.[5] Xiaowei Guo, Jinglei Du, Yongkang Guo, Jun Yao, Opt. Lett. 31 (17) (2006) 2613–

2615.[6] K.V. Sreekanth, V.M. Murukeshan, J.K. Chua, Appl. Phys. Lett. 93 (2008) 093103.[7] H. Raether, Surface Plasmon On Smooth and Rough Surfaces and On Gratings,

SPring-Verlsilver, Berlin, 1988.[8] D. Sarid, Phys. Rev. Lett. 47 (1981) 1927–1930.[9] M. Born, E. Wolf, Principles of Optics, Pergamon, New York, 1964.