Interference lithography is a powerful technique for high resolution patterning. It enables the generation of periodic grids with high aerial image contrast, and therefore provides for wide process latitude. It is relatively easy and inexpensive to implement, and it can provide a very high throughput. Its main drawback is the limited geometries that it can pattern. In its simplest form, interference lithography is capable of only generating single-period gratings. For this reason, if it is to be used in the fabrication of complex devices, interference lithography must be combined with a second exposure method, be it optical or electron beam based. Still, the production of a great number of nano-devices is enabled by high-resolution interference lithography. Many nano-photonic and nano-electromechanical devices rely on periodic geometries. Significantly, mass-produced microelectronic devices are becoming more and more grid-based as well. These large fields of application provide a strong incentive for the development of ultrahigh-resolution interference lithography.
In this paper we present patterning with interference lithography of gratings with 22-nm half pitch. This resolution is at the limit of the capabilities of any optical technique, and is comparable to the resolution of scanning electron-beams systems. It is achieved by combining the shortest practical optical wavelength, 157 nm, with immersion in a very high-index optical material and fluid, as described below. The results demonstrated in this paper indicate that a prototyping tool is feasible for resist evaluation and nano-scale device research at the resolutions required for future nano-photonic and microelectronic devices, nano-fluidic structures, and many other applications.
Recent results obtained elsewhere have been reported [1
1. B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE6154 (2006) (to be published).
2. H. Sewell, J. Mulkens, D. McCafferty, L. Markoya, B. Streefkerk, and P. Gräupner, “The next phase for immersion lithography,” Proc. SPIE6154 (2006) (to be published). [CrossRef]
], where a resolution of 26–32 nm half-pitch was achieved with immersion interference lithography at 193 nm. In this paper we describe the challenges facing implementation at sub-25 nm resolutions, and the engineering and materials solutions that we have devised in order to obtain the resolution of 22 nm.
In immersion interference lithography, the period of the pattern is defined by the source wavelength, the angle of incidence of the interfering beams, and the index of refraction of the coupling prism. In liquid immersion lithography, a liquid is introduced between the prism and the photoresist. However, if the index of the liquid is not high enough, the coupling efficiency of light out of the prism falls precipitously for incident angles above the critical angle. To take full advantage of the high index of the prism, either higher index liquids must be developed, or solid-immersion interference may be used. In the latter case, an air gap on the order of 10 nm is used to allow the evanescent wave to tunnel to the photoresist. Both approaches have been the subject of intense research at 193 nm. At this wavelength, the optical material with the practical highest index is sapphire (n ~1.92, leading to an effective wavelength in the prism of ~100 nm), while immersion liquids with index of ~1.65 have been employed. It is important to point out that in immersion lithography, whether liquid immersion or solid immersion, the index of the photoresist must also be high enough to allow efficient coupling of electromagnetic energy into it. At 193 nm, the index of available photoresists is ~1.7 [1
1. B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE6154 (2006) (to be published).
Transitioning to interference lithography at 157 nm has several advantages in terms of resolution. The vacuum wavelength is ~18% shorter. Furthermore, the index of refraction of sapphire is ~2.09, 9% higher than at 193 nm and leading to an effective wavelength in the prism of ~75 nm. These two considerations alone indicate that, for the same geometry and the same prism material there is a 25% resolution advantage at 157 nm. Furthermore, as is shown in this paper, there are important practical advantages as well. Chief among them is the availability of higher-index photoresists and high-index immersion fluids at 157 nm, enabling transfer of energy to the photoresist via propagating plane waves. It must be pointed out that at present the high-index immersion fluids are also highly absorptive. As shown in this paper, their absorptivity limits the gaps to below ~100 nm. Nevertheless, their use obviates the need to engineer systems, which are based on coupling the energy of evanescent waves across nanometer-size gaps.
Fig. 1. Schematic representation of the output portion of the interference system. The input beams are transverse electric (TE) polarized.
The coupling prism is fabricated in vacuum-ultraviolet (VUV) grade sapphire purchased from Crystal Systems, Inc. and cut and polished by Sydor Optics, Co. It is 6.35 mm thick and approximately 15 mm wide at the top. Sapphire is a birefringent crystal, with the ordinary and extraordinary components of the index of refraction differing by 2×10-3
at 157 nm [5
5. W. J. Tropf and M. E. ThomasE. D. Palik, “Aluminum Oxide (Al2O3) Revisited,” in Handbook of Optical Constants of Solids III, ed. (Academic Press, New York, 1998) pp. 653–682.
]. In order to avoid birefringence-induced depolarization of the interfering beams, the prism is cut such that the crystalline axis for the extraordinary ray is aligned parallel to the z-axis as shown in Fig. 1
. The projection of the extraordinary ray on each input face of the trapezoidal prism is perpendicular to the direction of the electric field vector, ensuring that the electric field aligns with one of the ordinary axes. Based on the tolerances on the crystal orientation with respect to the extraordinary ray prior to cutting, we estimate depolarization is under 3% for a TE polarized incident beam. As shown in Fig. 2
, the transmission of the sapphire prism along its 6.35-mm thickness is approximately 43% at 157 nm, with a ~145-nm cut-off wavelength. Of the 57% losses at 157 nm, we estimate that the Fresnel reflective losses are 24%, and 33% are due to absorption.
Fig. 2. Transmission of a 6.35-mm-thick VUV grade sapphire window measured in an Acton Research Corp. vacuum ultraviolet spectrometer purged with nitrogen. The transmission is 43% at 157.6 nm.
The interference experiments presented here employ a hydrocarbon-based immersion liquid with 157-nm index of 1.82 +/- 0.03 and an absorption coefficient of 5.75 µm-1 (base 10). The optical constants were measured in two steps. First, the absorption coefficient is determined from transmission measurements of liquid layers of different thicknesses. The four thicknesses used are obtained by spin-coating the liquid at different spin speeds on VUV grade CaF2 substrates. Transmission measurements are performed in an Acton Research Corporation VUV spectrometer. Film thicknesses are measured using a Woollam UV spectroscopic ellipsometer. Although the substrates are mounted vertically in the spectrometer, the liquid is viscous enough (viscosity 50 cP) that its thickness does not change during the transmission measurement. We confirmed this by performing ex-situ ellipsometric measurements on the coated substrates after the transmission measurements were performed.
Next, the index of refraction of the hydrocarbon liquid is determined by measuring the reflection of a thick layer (>500 nm) with a double-beam reflectance attachment in a Varian VUV spectrometer. The use of the thick layer simplifies the analysis, because the 157-nm absorption is high enough that back reflections off the underlying substrate can be neglected. The real part of the index is calculated from the measured Fresnel reflection, taking into account the absorption coefficient of the liquid and the angle of incidence. The measured index is 1.82±0.03, the margin of error being estimated from the uncertainty in the reflection measurements. The accuracy of this method of determining the index has been confirmed by cross-checking the results obtained in other, lower index fluids, with those obtained independently on a Woollam VUV ellipsometer.
The photoresist is a chemically amplified material. It is a dilution of the Rohm and Haas EPICTM 2340 photoresist, which is a 193-nm resist. Using the same procedure as for the immersion liquid, the 157-nm index of the photoresist is determined to be 1.74. Its absorption coefficient is estimated to be 6.1 µm-1 (base 10) using a similar technique to measure the absorption of the hydrocarbon based immersion liquid.
In the immersion lithography experiments described here, the thickness of the liquid layer is 30 nm. This thickness is chosen to enable practical throughput, given the high absorption coefficient of the liquid (see also next Section). Precise control of the thickness is achieved by spin coating it on the photoresist-covered silicon wafer at predetermined spin speeds. Since spin-coating provides an extremely precise means to deposit material to nanometer tolerances, this method enables accurate liquid spacings to be set over large areas, greatly simplifying staging and vibration control requirements.
The photoresist is spin coated to a thickness of 50 nm. Although this thickness appears small to practitioners of current-resolution lithography, it must be borne in mind that 22 nm features still present an aspect ratio of well over 2:1. The wafer is first cleaned in a He/O2 plasma for 2 minutes and primed in vapor hexamethyldisilazane (HMDS) for 1 min. Following spin-coating, a post-apply bake is performed at 130°C for 90 sec.
For the parameters summarized in Table 1
, the time constant, τ, is in the order of 1 hour. Thus, the applied pressure reduces the liquid thickness by a negligible amount during the exposure, whose duration is under one minute.
Table 1. Liquid Properties and Pressure Conditions
The transmission losses in the prism and immersion liquid necessitate an exposure dose at the prism of ~50 mJ/cm2, 20 times higher than that required in “dry” interference lithography with the same photoresist. The laser fluence at the prism being ~2 µJ/cm2/pulse, the exposure requires approximately 24,000 pulses, which are delivered in 24 seconds. The required dose agrees within 20% of predictions based on the transmission factors through the prism and 30 nm thick hydrocarbon fluid at 60° angle of incidence as discussed in the next section. This confirms to first order the 30 nm liquid layer spacing is maintained during exposure.
After exposure, the wafer is separated from the prism, and occasionally this step requires that it be distorted slightly by hand. Although we have not performed systematic studies, in general, no visual delamination of the photoresist is observed. The hydrocarbon immersion liquid is removed by spin-coating the wafer in a solvent for 60 sec. A photoresist post-exposure bake is then performed at 105°C for 75 sec, and the latent image developed in 0.26-N tetramethyl ammonium hydroxide (TMAH) developer for 30 seconds.
A scanning electron micrograph (SEM) is shown in Fig. 3
. The half-pitch is indeed 22 nm, as predicted by the wavelength, angle of incidence and index of the prism. This result demonstrates that optical methods can be employed to pattern at dimensions approaching 20 nm, well into the domain reserved until recently to particle beams. We note that the photoresist used in these studies has not been optimized for this application, except with regards to its thickness. In particular, the interaction between the immersion fluid and the photoresist is unoptimized. We did confirm that neither the rinse fluid nor hydrocarbon immersion fluid/rinse fluid combination altered the resist thickness of unexposed resist as measured with ellipsometry. However, in a separate set of experiments, we first patterned several resist coated wafers without the coupling prism under “dry” conditions, and subsequently exposed the patterned wafers to different combinations of rinse fluid and coupling fluid prior to development. If both fluids are used, distortions in the developed features could be observed in the top-down micrographs.
Fig. 3. SEM of patterned photoresist using interference lithography with a 30-nm-thick high-index absorptive immersion liquid. The pitch is 44 nm, as expected from the index of the sapphire prism, the laser wavelength and the angle of incidence of the interfering beams. The total exposure dose is 48 mJ/cm2.
Because of the physical contact between the prism and the liquid, care is taken to clean the prism between exposures using acetone and isopropanol, as well as an aqueous base cleaning solution (Cole-Palmer Micro-90 Solution). This procedure removes particulate contamination, and also any chemical or photo-induced residues from the liquid. Indeed, in separate experiments we noted that doses in excess of 300 mJ/cm2 are required to transform the immersion liquid into insoluble films, well above the exposure dose of the photoresist. In general, we typically achieve intimate contact over at least a quarter of the field size, enabling sufficient exposure area for the initial phases of resist evaluation and device research using electron beam, scanning probe, and focused optical techniques.
In this section we quantitatively analyze the coupling efficiency of laser light into the photoresist for different immersion media and gap sizes, under conditions that span the range from evanescent-wave solid immersion to propagating-wave liquid immersion. The results identify the trade-offs between gap size, liquid absorption coefficient, and throughput, and cast our results in a broader perspective.
The absorbed power in the resist for the film stack shown in Fig. 1
is calculated using Maxwell’s equations in a straightforward manner [7
7. P. H. BerningG. Hass, “Theory and Calculations of Optical Thin Films,” in Physics of Thin Films, ed. (Academic Press, New York, 1963), Vol. 1, pp. 69–121.
], and including complex indexes of refraction, n-jκ
, as needed. For the purpose of these calculations we treat the photoresist as a semi-infinite layer, since the photoresist absorption is sufficiently high to justify neglecting reflections from the photoresist-silicon interface.
Fig. 4. Schematic representation of electric field vectors in the multilayer system under consideration.
Referring to the geometry of Fig. 4
for two interfering TE-polarized coherent beams incident at angles ±θ, the electric field components in each layer have the form:
where Ei, Erp, Erliq, Etliq
, and Etr
, are the amplitude of incident, reflected, and transmitted electric fields in the prism, liquid, and resist, respectively. The parameters kx, kzp, kzliq
, and kzr
are the x and z components of the wavenumber in each layer. While kz
may be different in each medium, the continuity equations at the interfaces dictate that all the kx’s are the same:
where λ is the vacuum wavelength of the laser and np
is the index of refraction of the prism. The z-component of the wavenumber in each layer is:
The time-averaged power flow (i.e. the Poynting vector) in the photoresist, normalized to the peak intensity of the input beams, is given by the expression:
is the thickness of the liquid. Several fundamental dependencies are derived from Eqs. (3
–5). First, from "e5a">Eq. (5a)
and Eq. (3)
, the period of the intensity of the interference pattern is:
This period is independent of the index of the liquid or the resist, as indicated in the Introduction, and it is constant along the optical axis z. Second, from "e5a">Eq. (5a)
and ="e5b">Eq. (5b)
, the intensity contrast, defined in terms of the maximum and minimum values of the absorbed power at any given value of z, is unity. It is independent of the index of the prism, the liquid or the resist, and it is constant along the z-axis (as long as the beams are fully coherent). Thus, the period and intensity contrast are the same in the evanescent or propagating-wave regimes, i.e. above or below the critical angle.
However, the absolute intensity along the z-axis does depend on the various indexes and on the thickness of the liquid gap tliq
, and it also changes along the z-axis. Therefore, the liquid and photoresist, as well as the size of tliq
, have significant impact on the coupling efficiency of energy into the photoresist and on the robustness of the lithographic process. When the gap is filled with a non-absorptive fluid such as gaseous N2, κliq
→0, and the critical angle θcr
is defined by the familiar expression
For incident angles larger than θcr
, such as encountered in solid immersion lithography, kzliq
is purely imaginary (Eq. 4b
). As a result, the coefficient T in ="e5b">Eq. (5b)
decays nearly exponentially with tliq
, and without phase modulation, these being the hallmarks of the evanescent wave formed in the gap. Note that the exponential decay in the numerator of T is modulated by the terms in the denominator, which are non-zero in the typical case when kzr
is not equal to kzliq
. This deviation from simple exponential decay is due to the presence of the photoresist and its impact on the efficiency of energy coupling. In the more general case, when the gap is filled with an absorptive fluid, there is no special meaning for the critical angle. From ="e4b">Eq. (4b)
has an imaginary component for all values of θ
, and therefore T always decays nearly exponentially. This is a manifestation of the absorption in the liquid. The beam still represents a propagating wave, since kzliq
has also a real component, meaning that phase information is also propagated in the liquid.
(a) illustrates these considerations as they apply to 157-nm immersion lithography, at the specific angle of incidence of 60 degrees, and a sapphire prism (np
=2.09). The Fig. plots the calculated peak power at the liquid/resist interface normalized to the intensity of the input beams, as a function of the liquid gap size. The photoresist is assumed to have a complex index nr
=1.74 - j
0.176, based on the measured values discussed in the previous section. The three traces represent a nitrogen-filled gap, which is the case of high-resolution solid immersion; liquid immersion with a low-index, low-absorptivity liquid, of the type used in our previous work with a CaF2
3. M. Switkes and M. Rothschild, “Immersion lithography at 157 nm,” J. Vac. Sci. Technol. B 19, 2353 (2001). [CrossRef]
]; and liquid immersion with the high-index high-absorptivity liquid used in the present studies.
(a) clearly indicates that our choice of high-index, highly absorptive hydrocarbon liquid provides a significantly more relaxed value of tliq
than either the more transparent but lower-index fluid or a nitrogen filled gap. For instance, if throughput requirements dictate a coupling efficiency of 17%, the nitrogen gap must be less than 14 nm, the fluorocarbon liquid gap must be less than 19 nm, while the hydrocarbon liquid gap can be extended to 30 nm. There is a large gain in using a high-index, highly absorptive material compared to a low index, transparent fluid. A different way of viewing these results is shown in Fig. 5
(b). It is a series of contour plots of coupling efficiency, identifying the parameter values in the index-absorption space of immersion liquids, for the specific case of a 30-nm gap. As mentioned previously, this gap spacing has been chosen primarily due to absorption loss considerations. Even with the losses through the liquid, the incident doses are sufficiently low to allow minute scale exposures while also being below the threshold level where residues build up on the prism. For the combination of parameters used in Fig. 5
(b), if the desired coupling efficiency must exceed 20%, it is apparent that the liquid must have an index of at least 1.7. Furthermore, the required index is very sensitive to the absorption coefficient: a slightly higher absorption coefficient may necessitate an index of 1.9 or more. Conversely, even a modest reduction in absorption coefficient, achieved for instance by aggressive purification methods, can rapidly increase the coupling efficiency to 30%. Similar plots can, of course, be generated for other gaps, wavelengths, prism materials, and angles of incidence. They are useful in providing a mapping of the tradeoffs in throughput for various candidate fluids and interference geometries.
Fig. 5. (a) Coupling efficiency into resist as a function of liquid layer thickness using a sapphire coupling prism with index of 2.09, interfering beams intersecting at 60°, and vacuum wavelength of 157.6 nm. (b) Coupling efficiency into the photoresist for a 30-nm gap for several immersion fluids.
Finally, further work is required to determine the scalability of this process to higher throughputs and more general device prototyping. Even with the losses through the prism and coupling fluid, the required incident dose of ~50 mJ/cm2 is only ~2–5 times higher than the doses used in high throughput optical lithography. This exposure time is also still one to two orders of magnitude smaller than that of state of the art electron beam systems. The practical throughput and performance of the interference lithography system is instead gated by the necessity of performing optical contact, release, and cleaning in a repeatable, controlled fashion. Although recent developments in advanced optical and imprint lithography may be drawn upon, optical contacting is generally feasible under tightly controlled environmental conditions and not easily scaleable to high throughputs over large areas. A more careful engineering study is required to map out gap spacing control and generate a statistical database of defect rates in patterned wafers in a more automated, tightly regulated system.