In this paper, fabrication of nano-scale 3-D features by total internal reflection generated single exposure counter propagating multiple evanescent waves interference lithography (TIR-MEWIL) in a positive tone resist is investigated numerically. Using a four incident plane waves configuration from an 364nm wavelength illumination source, the simulated results indicate that the proposed technique shows potential in realizing periodic surface relief features with diameter as small as 0.08λ and height-to-diameter aspect ratio as high as 10. It is also demonstrated that the sensitivity of multiple evanescent waves’ interference depends on the polarization and phase of the incident plane waves, and can be tailored to obtain different geometry features. A modified cellular automata algorithm has been employed to simulate three-dimensional photoresist profiles that would result from exposure to the studied evanescent waves interference configurations.
©2008 Optical Society of America
The growing importance of the nanotechnology research leads to the need for fabrication technique with the capability to fabricate nanometer scale features and one such technique is the optical lithography. Advanced projection optical lithography systems that employs 193nm wavelength laser source coupled with wavefront engineering schemes has the capability to achieve sub 50nm patterns. However, the cost of ownership of these sophisticated systems is exorbitantly high. Here comes the significance of near field optical lithography techniques, which are comparatively more economical than the projection technique since complicated projection optics is not required.
The underlying principle behind the high resolution capability of near-field optical lithography techniques lies in the capturing of high spatial frequency optical signals beyond the diffraction limit of the projection optics. These high spatial frequency optical signals are usually in the evanescence regime. In this paper, we propose a near-field optical lithography concept for fabricating nanoscale three dimensional periodic features, based on total-internal reflection (TIR) generated multiple evanescent waves interference. The TIR generated evanescent waves interference is an efficient technique for large area patterning of periodic high resolution features. This technique was initially studied for data storage applications in which periodic line features were patterned [1–6]. In these studies, laser sources with wavelengths in the visible regime were employed and a wide variety of photosensitive polymers and dye as recording media were explored. Recent works have also reported evanescent waves interference patterning, using UV lasers as irradiation source, on photoresist recording medium, which require higher exposure dose than polymers and dyes [7–10]. With the employment of irradiation sources with smaller wavelengths, the fabrication of sub-100nm features become the focus point, thereby demonstrating the feasibility of employing evanescent waves interference as a high resolution optical lithography option. In contrast to these previous works where patterning results from the interference of only two counterpropagating evanescent waves dealt with, this proposed work illustrates patterning with multiple evanescent waves interference. In addition to having the advantage of achieving two dimensional features patterning with single exposure, we would numerically demonstrate here that this approach allows phase modulation and polarization to effect geometry variation of the periodic features without altering the relative orientation between the incident beams. Also, in the context of lithography, it is important to understand and predict the final resist topology after exposure of the photoresist to the irradiation field. For this purpose, a modified cellular automata algorithm is employed to obtain the simulated results of three-dimensional post-development resist topologies that would result from the presented evanescent waves interference intensity profiles.
2. Theoretical model
For practical reasons, problems in science and technology are frequently studied through simulations. Computing techniques have enabled the solutions of such problems, before being investigated experimentally in the laboratory. This applies specifically in optical lithography, as new concepts and systems based on phenomenon have been widely employed over recent years for numerous applications with assumed configurations. In this study, the model assumes the configuration illustrated in Fig. 1(a). Four incident plane waves are directed into a prism with equal incident angle, θin, with respect to the Z axis. The incident plane waves are oriented such that the wave vectors for one pair is contained in the X-Z plane and that of the other pair is in the Y-Z plane. The prism is assumed to be in full optical contact with the photoresist layer. In practice, this may be achieved by introducing a thin layer of index-matching liquid between the prism and the photoresist, the refractive index value of the liquid should be chosen as close to that of the high index of prism as possible. Also, it is reported in the literature that a slight mismatch of refractive index values between that of the prism and liquid would still facilitate optical contact .
The X-Y plane at Z=0 represents the interface between the prism and the photoresist. Total internal reflections (TIR) of the incident plane waves is realized by having sin θin>sin-1(ntr/nin), where ntr and nin refer to the real refractive index values of the photoresist and that of the prism respectively. Shown in Fig. 1(b), the TIR of the incident plane waves, with incident vectors k⃗(1) in and k⃗(2) in, generate evanescent waves with wave vectors k⃗(1) e and k⃗(2) e, propagate parallel to the X-Y plane and in opposite direction along the X-axis. When four incident plane waves are employed as shown in Fig. 1(a), four evanescent waves would be generated, and the evanescent waves counter-propagate towards each other along the X-axis and Y-axis. For better referencing in the later discussion, the incident plane waves would be sequentially referred to as beam 1 to 4 in counter-clockwise manner around the Z-axis. Consequently, interference of the evanescent waves occurs, forming standing waves profiles with amplitude that decay exponentially in the negative Z direction. The glass prism and the photoresist used in the simulation are assumed to be homogenous and isotropic and therefore have scalar refractive index values. The refractive index values of the prism and the photoresist are nin=1.853 and n̂tr=1.684-i0.0007 respectively. The given values correspond to those of NLAF36 glass and AZ7220 (AZ Electronic Materials Ltd), positive tone photoresist sensitive to illumination with wavelength (assumed to be 364nm) in the UV range. The employed computation scheme is outlined in Fig. 2. Firstly, the positional intensity value of the evanescent waves interference, Ie(x,y,z) in the photoresist domain is computed for which the electric field amplitude |Ee|2 would be computed instead since the intensity is proportional the modulus square of the electric field amplitude given as Ie∝|Ψet|2.
Applying the general theoretical framework which we have reported previously , the analytical expression that describes the three-dimensional |Ee|2 interference profile of four counter-propagating evanescent waves is obtained in cartesian coordinates as follows,
where and A(w)z represent the electric field amplitude components corresponding to the x, y and z directions. The terms θw refers to the incident angle of the beam and ϕw refers to the azimuthal angle about the z-axis. The amplitude attenuation factor and the phase shift of the complex Fresnel transmission coefficients for s or p polarized incident plane waves are represented by τs /p and ηs /p respectively. The term Φw is the additional phase of an incident plane wave with respect to that of a chosen reference incident plane wave. The positional |Ψet|2 values would be subsequently used as inputs to compute the positional photoresist development rate, employing the conventional photoresist model . Finally, to simulate the photoresist development phenomenon, a cellular automata (CA) algorithm, modified from that reported by Karafydyllis, is employed [13, 14]. Employing the CA algorithm, the photoresist layer is meshed into identical cellular elements. In simulating the development process, the individual cell state at each time step is computed, taking into consideration of the influences of neighboring cells. The cell state after one time step dt from the time instance to, is given as . The subscripted alphabets i, j and k correspond to cell position along the x, y and z direction respectively. The term is qualitatively defined as the effective removed height of each cell normalized by the cell-height after resist dissolution by developing agent flowed from neighboring cell position mathematical description of this model is given as follows,
The differential cell state terms, dCadj, dCedg and dCvtx represent the change of the concerned cell state (cell for which the state to be solved) due to the flow of the developer from adjacent, edge and vertex cells positions respectively, given as,
in which I may represent either i, i+1 or i-1 and hence likewise for J and K. The Eqs. (2) to (4) show that the differential cell state terms are functions of positional development rates R,i,j,k which are, in this work, correlated to the positional intensity values of the evanescent waves interference in the photoresist layer as would be obtained from Eq. (1). The CA algorithm employed here differs from Karafydyllis’ in that (i) the influence on the concerned cell from all its neighbours are considered, (ii) factors accounting for “flow efficiency” of developer from neighbouring cells are introduced in the model and (iii) neighboring cells are identified as having either sequential” or simultaneous effect on the concerned cell. A neighbor with sequential effect will, only upon the complete dissolution of itself, influence the dissolution of the concerned cell. While one with simultaneous effect will influence as it is being dissolved itself.
In the following section, the |Ψet|2 distribution of the evanescent waves interference would be presented.
Results and discussion
3.1 Three-dimensional evanescent waves interference intensity profile
In the following section, the |Ψet|2 distribution for evanescent waves interference would be presented. The results are obtained with different schemes of polarization state assignment for the four incident plane waves. The simplest scheme is to have the same polarization state for all four incident plane waves. In the first instance, four s-polarized incident plane waves are employed. There is no phase difference between the incident plane waves. The interfacial and cross-sectional |Ψet|2 profile are shown in Fig. 3.
In the figures shown, the X-Y plane at Z=0 represent the interface between prism and the photoresist, and the negative Z positions refers to the corresponding depth in the photoresist layer. The intensity profiles in both cases are obtained with the incident beams directed such that they have θin value of 67°. The pitch size between the centres of subsequent high intensity regions are found to be less than that achievable by a conventional interference method with the same exposure wavelength and the incident angles. The interfacial |Ψet|2 profile indicates that the interference pattern results from a superposition of periodic linear fringes parallel to the Y axis and those parallel to the X-axis formed by interference between the evanescent waves that counter-propagate along X-axis and by those along the Y-axis, respectively. An evanescent wave generated by s-polarized incident plane wave maintains the polarization state of the incident plane waves. Thus, when four evanescent waves counter-propagate along the X and Y axial directions, interference between the evanescent waves that propagate along the same axis occurs but there would not be interference between the evanescent waves with wave vectors perpendicular to each other since the electric fields vectors are orthogonal to each other as well. The superposition of the interference fringes result in mid-intensity regions between adjacent high intensity regions and low intensity regions. When the incident plane waves are of p-polarization state, the corresponding interfacial |Ψet|2 profile shown in Fig. 3(b) is remarkably different from that produced by s-polarized incident plane waves. The cross sectional intensity profiles along the diagonal in both Figs. 3(a) and 3(b) shows the intensity decay exponentially with increasing depth into the photoresist layer. The electric field vector of the p-polarized incident plane wave can be resolved into two components, one parallel to the interface and the other parallel to the Z-direction. Hence, one can resolve the corresponding evanescent waves interference intensity profile into these two components as, |Ψet|2,xy the interference profiles due to the electric field components parallel to the x-y plane, and |Ψet|2 z that due to the electric field components parallel to the z-direction as in Fig. 4. The z-component electric fields for all the four evanescent waves interfere since they are parallel to each other. It is also observed that the |Ψet|2 xy profile is phase shifted by π2 from that of |Ψet|2 z profile. The incident angle value employed for the incident planes result in the electric field component parallel to the x-y plane to have larger amplitude than that of the z-component. As such, the |Ψet|2 xy profile defines the general interference profile shown in Fig. 4.
The presence of |Ψet|2 z translates to lower fringe contrast for the interference pattern. The effect of fringe contrast on the lithography performance would be discussed in greater detail later in this manuscript. A summary of analytical expressions for the interference profiles and periodicity is given in Table 1. In conventional interference lithography, the intensity patterns are defined not only by configured beam propagation, but are also sensitive to the phases and polarizations of the intersecting incident beams. This is expected to be true for the case of evanescent waves interference patterns too since the phase and polarization of the evanescent wave are dependent on the incident beam that generates it after TIR.. In this connection, we explore the possible evanescent wave interference patterns that can be achieved by modulating the phase and polarization states of the incident waves while maintaining the number of employed incident waves and their respective orientations as given in Fig. 1(a).
When all incident plane waves are of identical polarization states, introducing relative phase difference between any pair of incident waves in the same incidence plane would result in spatial displacement of the interference pattern but the general profile does not change. However, by using incident plane waves with different states of polarization and introducing relative phase difference, one would be able to modulate the interference between parallel electric fields of the evanescent waves. However, orthogonal electric fields do not interfere and adds to the background intensity to reduce the fringes contrast. The concept of employing incident beams to achieve interference patterns with different polarization states would still require that oppositely directed incident beams have parallel electric field components. In this regard, the interference profile generated when the evanescent waves generated by one pair of s-polarized counter-oriented incident beams is coupled to that of a p-polarized pair is investigated. It was observed that such a configuration would result in periodic features with dumb-bell shape geometry when a larger incident angle of 72° is employed. The contrast of each dumb-bell shaped feature can be modulated by introducing relative phase difference between counter-oriented incident plane waves. A possible method to realize phase difference is to place a high transmitting glass plate, with appropriately crafted thickness, in the path of one of the counter-oriented plane wave beams. It has been shown that slight amplitude difference between the counter-oriented incident plane wave beams would not result in significant distortion of the evanescent waves interference finges. In lithography context, optical intensity contrast of a feature directly influences its subsequent resist profile. For a dumb-bell shaped feature, the region at which intensity contrast is the most critical is across the waist since low intensity contrast at this region would most likely result in distorted resist profile. To investigate the optimum relative phase difference between the incident plane waves pair, different values of relative phase difference are introduced between the two pairs of counter-oriented incident plane waves. The phase shift assigned between counter-oriented incident plane waves 1 and 3 is represented by δ1,3 and that between incident plane waves 2 and 4 by δ 2,4. When δ a,b takes on a positive value, it means that the incident plane wave b has a phase lead with respect to incident plane wave a, where a refers to either 1 or 2 and b refers to 3 or 4. Conversely, a negative value would then mean a phase lag. For each pair of counter-oriented incident plane waves, the phase difference values are varied from - to 135° with step size of 45°. For each combination of δ 1,3 and δ 2,4, the variation of intensity contrast of the waist of an individual feature is shown in Fig. 5(a).
The combination of phase difference values which yield the highest intensity contrast across the waist region (shown by the dotted white line) are assigned to the respective incident plane waves pair. The corresponding intensity profile is shown in Fig. 5(b). From the result, it is observed that a few possible combinations of relative phase difference values can yield the highest contrast values. We have chosen the combination of δ 1,3=π 2 and δ 2,4=-π2. The result shown in Fig. 5(b) is that of normalized intensity values with the normalizing factor being the highest intensity value of the evanescent interference result that is obtained with the four p-polarized incident plane waves.
This configuration result in lower intensity values in the high intensity regions than those of the four p-polarized incident plane waves configuration. For study of optical lithography process, it is necessary to include the consideration of the photoresist reaction to the optical signal, the evanescent waves interference in this case. So far, by employing four s-polarized incident plane waves, four p-polarized incident plane waves and one s-polarized pair coupled to one p-polarized pair, the interference profiles of the three configurations have been shown. To further investigate the corresponding resist profiles that may result from the interference profiles, the positional development rate was computed for each of the three configurations and the CA method was employed to obtain the corresponding resist topology.
3.2 Three-dimensional resist structures
For this study, the same exposure time of 50s is used for all the cases. For computation simplicity, we have assumed that the highest intensity value of the evanescent wave interference generated by the four p-polarized incident plane waves correspond to a value of 1mW/cm2. For the same exposure duration, the photoresists in the three configurations receive different level of exposure dose since the respective highest positional intensity values are different. Hence it is expected that the three intensity profiles would require different development times to realize substantial depth in the corresponding topology. With lower intensity, it is expected that longer development time is required and vice versa. The photoresist exposed by the four p-polarized incident plane waves configuration is developed for 60 sec. Subsequently, the development duration for the two other cases, with lower intensity values, are estimated as follow, t′dev=I ref max>/I′max×trefdev where Iref max refers the maximum intensity value of the referenced set (i.e. the four p-polarized incident plane waves configuration),, I′max refers the maximum intensity value of the investigated set and trefdev refers to the development duration employed for the referenced set. The resultant resist topologies for the three configurations are shown in the following Fig. 6.
As the intensity decay exponentially with increasing distance away from the interface, the resultant features were shown to exhibit sidewall profiles that tapered in an exponential manner. Hence, to characterize the resist features, the width of the feature is taken at the halfheight position, zhalf which is defined as zhalf=(z max-z min)/2+z min, where z max refers to the highest point of the resist feature and z min refers to the lowest point. For the p-polarized incident plane waves configuration, the interference intensity profile results in cross-line grating as profiled by the dashed line. The width of the grating at zhalf is 36nm (≅0.10λ) with a pitch size of 126nm and the width of the intersection regions is 80nm (≅0.22λ). The height of the grating was found to be 255nm resulting in an height-to-width aspect ratio of 7.
As shown in Fig. 6(b), the nano-pillars, resulted from the s-polarized incident plane waves configuration, correspond to the low intensity regions. Each nano pillar has a height of 225nm and diameter of 28nm (0.08λ) at zhalf, with height-to-width ratio of almost 10. The nano-pillars are distributed in a square array format with average pitch size of 141.4nm along the diagonal direction and 105nm along the X and Y direction. The simulated results in Figs. 6(a) and 6(b) suggest that the diameter holes or the nano-pillar is smaller than the half of the pitch size. This is due to both intensity modulation by the photoresist as well as the exponential decay of the evanescent intensity in the direction away from the interface. For the third case shown in Fig. 6(c), saddle-like topologies are typically formed at two regions. One region is at the waist of each dumb-bell shaped low intensity region and the other between adjacent dumbbell-shaped regions as identified in the Fig. 6(c). The saddles at these two regions were found to have a height difference of 35nm. The resultant resist topology is that of periodic three-dimensional features since the saddles are located periodically. If the same benchmark that was used to characterize the feature width in previous two cases is applied, the resist contour in the X-Y plane at the position of zhalf=-60nm is obtained as shown in Fig. 7 below.
The result shows that at the half-height position, the resist contour is that of periodic dumb-bell shaped nanostructures. The result suggests that it is possible to realize the formation of periodic dumb-bell shaped nanostructures features albeit with precise control of resist thickness.
In this work, the three dimensional solutions for various phase and polarization modulated multiple evanescent waves interference have been obtained analytically. A modified CA algorithm is employed in tandem to simulate the corresponding resist topologies that would result from exposure to the presented evanescent interference fields. We have illustrated a single exposure counter-propagating multiple evanescent wave interference as means for fabricating three-dimensional surface relief features with resolution as high as 0.08λ and height-to-width aspect ratio of close to 10. With modulation of the state of polarization and relative phase difference between the incident plane waves, that generated the interfering evanescent waves, periodic features of different geometries can be achieved. It is demonstrated that cross-line grating, square array of nano-pillars and even dumb-bell shaped features are possible to be fabricated by using linearly polarized incident plane waves. This proposed fabrication concepts and nano-scale features can find potential applications in different areas ranging from photonic crystals fabrication, nano-field emitters, nano-needles arrays and nano-wells in biochips for biomedical applications, to nanoelectonics devices such as the dumbbell-shaped features for nano-scale frequency selective surface structure (FSS), coplanar waveguide fed antenna array , defected ground structure .
The financial support received through the MOE Academic Research Fund 3/08 is greatly acknowledged here. One of the authors Jeun Kee Chua also acknowledges the student scholarship awarded by NTU-Chartered-EDB fund.
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