Diffraction-grating beam splitter, interferometric-lithography nanopatterning with a multilongitudinal-mode diode laser

Nanopatterning has wide applicability in areas including nanofluidics, nanomagnetics, biophotonics, metamaterials, and others. For research and for developing applications that have yet to reach broad acceptance and high volumes, conventional optical lithography using semiconductor industry tools is too expensive. E-beam and ion-beam nanopatterning have exquisite resolution and pattern flexibility but are limited in throughput and areal coverage. Nanoimprint lithography has master and wafer-scale issues.

Interferometric lithography (IL) with a partially reflective beam splitter or with Lloyd’s mirror is limited in the area by the coherence length of the laser source since the two arms of the interferometer are matched in length at the center of the pattern but vary in length as the print area is increased in the dimension perpendicular to the grating lines.¹ Often, a large-scale IL apparatus requires vibration and phase controls, which are disadvantageous in a manufacturing environment. IL with a grating beam splitter has lower coherence requirements, and generally shorter propagation distances from the beam splitter to the sample and, therefore, can be extended more readily to wafer-scale.² 

Off-axis illumination is a well-known single-sideband approach to extending the resolution of projection lithography.^3,4 Off-axis, oblique illumination along with a phase shifting mask⁴ and a variable transmittance pupil filter have been used in projection lithography systems to improve the resolution.⁵ 

Light sources often represent a significant share of the total cost of a large-area IL nanopatterning system. Progress in high-power diode lasers has made commercially available, at low-cost (∼$100), blue and UV single transverse- (TEM₀₀), multilongitudinal-mode lasers at 0.1- to 1.0-W power levels. In contrast, single longitudinal mode lasers with comparable powers are significantly (100×–1000×) more expensive. Diode lasers have been used for direct laser writing,^6–11 interferometric lithography,^12–18 multibeam laser interferometric lithography,¹⁹ laser ablation lithography,²⁰ plasmonic lithography,²¹ Talbot lithography,²² and mask aligner systems.²³ Light-emitting diodes have also been used as a source for low-cost lithography.^24,25

This work takes advantage of the grating-based approach and oblique incidence on a binary phase mask designed to result in equal 0th- and 1st-order diffraction intensities using a low-cost diode laser. The combined advantages of these techniques not only reduce the cost but also make the setup quite simple and readily applicable to volume manufacturing. A high-power (∼150 mW) single transverse mode (TEM₀₀), multilongitudinal mode diode laser is used as a light source. An achromatic, dual-grating approach is introduced and demonstrated to accommodate the multiple longitudinal modes of the diode laser and produce a large depth-of-field.

The multiple longitudinal modes of low-cost diode lasers require an achromatic approach to interferometric lithography. Take the center wavelength as λ₀ and the overall linewidth as Δλ with a mode spacing $δλ∼λ02/(2n′L)$⁠, where L is the laser cavity length and n′ = n + λ∂n/∂λ is the effective index. Four configurations with different degrees of compensation for a multilongitudinal mode, TEM₀₀ laser source are shown in Fig. 1.

Figure 1(a) is Lloyd’s mirror arrangement often used with single-frequency lasers.¹ The angles are all fixed at θ₀ by the geometry. Each longitudinal mode interferes only with its counterpart from the opposite direction since only pairs at the same frequency are time stationary, $⟨eiωkte−iωjt⟩=δk,j$⁠. Each mode produces a grating pattern at a period X_k = λ_k/(2sin θ₀), resulting in a moiré pattern $I(x,z)=∑k(Ak/2)[1+cos((4πsinθ0/λk)x)]$⁠, where A_k is the intensity in the kth mode. The gratings from each longitudinal mode are in phase and reinforce each other only in the narrow bands indicated by dark vertical lines in the figure. The width of the in-phase regions is X_ΛLloyd{X_RLloyd} ∼ {4Δλ/σδλ}σλ²/[8 sin(θ₀)Δλ], where σ is a parameter that depends on the distribution of power among the modes and the nonlinearity of the resist. X_ΛLloyd is evaluated without the quantity in the curly brackets on the right side of the equation which is included in the evaluation of X_RLlyod. The pattern repeats because the modes are equally spaced, the repeat distance X_RLloyd is given by a 2π phase shift between individual modal patterns.

Off-axis illumination of a phase grating [Fig. 1(b)] with period d at multiple wavelengths λ_k at an incidence angle θ_o results in 0th-order transmission at θ₀ and −1st-order diffraction at $θ−1,k=sin−1⁡(sinθ0−λk/d)$⁠. The 0-order angle, θ₀, set by the geometry, is identical for all wavelengths; however, the 1st-order diffraction angle, θ_−1,k is different for each wavelength. The result is that the individual fringe patterns resulting from each longitudinal mode are at the same period, but there is a wavelength-dependent tilt of the fringe pattern from the surface normal as a result of the diffraction angle asymmetry resulting in a z-dependence and a limited depth-of-field. The intensity of the interference pattern at the wafer surface is given by

where A_k is the intensity in the kth longitudinal mode. The x-dependent term, 2π(sin θ₀-sin θ₀+ λ_k/d)x/λ_k = 2πx/d, is independent of k. However, the z-dependent term varies with λ_k as θ₀ is the same for all wavelengths while θ_−1,k is different for each λ_k,

A plot of the z-dependence of I(0,z) and I(d/2,z) for the current experiments (λ₀ = 405 nm; d = 600 nm; Δλ = 1 nm; and δλ ∼ 0.025 nm) is shown in Fig. 2 assuming all A_k are equal.

The mask-wafer gap dependence is characterized by two lengths: Z_Λ1 the distance over which the IL contrast response decays to ∼50% of its peak value, set by the overall envelope linewidth, Δλ; and Z_R1 the distance over which the pattern repeats as a result of the equal spacing between the modes, set by the mode spacing, δλ. Expanding Eq. (2) to the lowest order in the small parameters Δλ/λ and δλ/λ gives Z_Λ1{Z_R1}={4Δλ/σδλ} σd²cos θ/(2Δλ). The number of repeats is determined by the coherence length associated with each individual mode. The regions of coherent addition of the modal interference patterns are shown as the dark horizontal lines in Fig. 1(b), each with a width 2Z_Λ1, and spacing Z_R1.

An achromatic configuration is needed to provide a large interferometric volume that allows freedom in the placement of the wafer relative to the mask. Figure 1(c) uses a single grating, at a period 2d; a beam block to eliminate any 0-order transmission, and a relay system to provide for interference between the ±1st-order beams.²⁶ The system is achromatic, each longitudinal mode produces a grating at a pitch d with vertical fringes so there is no z-dependence. As indicated by the dark triangle above the sample, the sample can be placed anywhere within this volume, in contrast to the narrow bands available for the chromatic configuration in Fig. 1(b).

The beam block is necessary because, for coherent normal incidence illumination, even small intensities in the 0th-order result in a z-dependent variation in the pattern with a period Z_R0 given by $ZR0=λ/(1−cosθ1,k)$⁠. For the present experiments writing a 600 nm period pattern, λ = 405 nm, d = 1200 nm, and cos θ = 0.94, giving Z_R0 ∼ 6.9 μm and requiring precision placement and parallelism between the grating mask and the wafer. Attempts to eliminate the 0th-order intensity, such as adjusting the grating parameters or the beam block shown in Fig. 1(c), either make the mask more difficult to produce²⁷ or the system larger and more complex. Another significant disadvantage of this configuration is that the system scales in volume as W³, where W is the width of the printed pattern. Most of this volume is in the region after the grating beam splitter, so vibration and air-current control become difficult issues, particularly in a manufacturing environment.

Figure 1(d) shows an alternative, two grating mask configuration, closely related to achromatic lithography first introduced for the fabrication of 100-nm period gratings with broadband excimer lasers.^28–31 The first grating, at a period 2d, is used to provide slight variations in the angle of incidence to the second grating mask. The diffraction from a second mask at period d is symmetric about the normal for all wavelengths resulting in a large volume available for IL as indicated by the dark triangle above the sample. The 1st-order diffraction angle of mask 1 is the Littrow angle for mask 2 for all wavelengths. For mask 1 at normal incidence (⁠$sinθ01=0$ superscripts refer to the specific mask) $sin⁡θ1,k1=λk/2d$⁠. Then after the second mask,

and for each k, the diffracted orders are symmetric about the surface normal, the interferometric period is d and the fringes are normal to the sample surface. As shown in Fig. 1(d), the longer wavelengths diffract to higher angles compared to shorter wavelengths but the symmetry about the surface normal, and the period of the interferometric pattern, is maintained for all λ_k. The IL process is considerably more forgiving to mismatch in the power density of the two interfering beams than it is to the presence of any 0 order in the configuration of Fig. 1(c). Modern photoresists (PR) have a sufficiently nonlinear response that good patterns result even when the difference between the intensities of the interfering beams is as much as 20%.¹ Misalignment of the system will reintroduce a z-dependence. Two examples are a slight tilt φ between the two grating masks, equivalent to misaligning the input beam by an angle φ from normal incidence, and a deviation of the 2× relationship between the grating periods, one at 2d and the other at d + ε. Following the same procedure as outlined above for the single grating case, the results are $ZΛ2tilt{ZR2tilt}∼({4Δλ/σδλ}(σd2cosθ)/(2Δλ)[4d(cosθ)2/λ0φ])$⁠. The expressions are written as the dephasing (repeat) distance for the oblique incidence, single grating case times an enhancement inversely proportional to the deviation from alignment. The comparable expressions for the grating period mismatch case are $ZΛ2p{ZR2p}∼{4Δλ/σδλ}(σd2cosθ/2Δλ)[d/ε[1+λ2/4d2[1−(λ/2d)2]]−1]$⁠. Importantly, in this configuration, the gap between the beam splitter, the second grating mask and the sample, the region where the two interferometric beams propagate independently, can be very small (<1 mm), significantly reducing the sensitivity to vibrations and air currents. This makes this configuration particularly suitable for large-area manufacturing operations. As in the system of Fig. 1(c), the spacing between the first and second grating masks serves to allow blocking of any 0-order transmission of the first grating mask. This is a common mode region insensitive to vibrations, but, of course, differential variations in the refractive properties of the air or any other immersion medium across the 1st-order diffracted beams have to be minimized.

A 50 cm diameter, 6 mm thick, fused silica glass window was used as a mask substrate. An ∼500-nm-thick spin-on-glass (SOG) coating was deposited onto the surface of the substrate. SOG, fully transparent at 405 nm, is a relatively soft, easy to etch medium, with good etch controllability. The SOG coated substrate was hotplate baked at a temperature of 200 °C. The refractive index of the SOG layer after baking was measured by ellipsometry as 1.45 at 405 nm, in good agreement with the Cauchy coefficients provided by the manufacturer.

A 150-nm thick layer of back-anti-reflection-coating (BARC) ICON-16™ was applied by spin coating atop the SOG layer. The sample was hotplate baked at a temperature of 190 °C for 180 s. This was followed by spin coating of a layer of I-line negative photoresist (NR7-500™) to a thickness of about 500 nm. The soft bake temperature and time were 150 °C and 180 s, respectively. The next step was to make use of IL in Lloyd’s mirror arrangement [Fig. 1(a)] with a single mode, frequency-tripled YAG laser source¹ (Coherent Infinity 40-100) operating at 355 nm to make a one-dimensional pattern of period 600 nm on the photoresist coated substrate. The energy dosage was ∼128 mJ/cm². The exposed PR-BARC-substrate was baked and developed as described above. The substrate was further hard-baked after the development at 100 °C for 60 s in order to improve the mechanical stability of the photoresist pattern prior to etching. An oxygen plasma was used to etch the exposed BARC layer between the PR lines. Gas flow rate, process pressure, RF power, and inductively coupled plasma (ICP) power were 30 sscm, 15 mTorr, 25 W, and 300 W, respectively. The photoresist patterned glass substrate was then etched using CF₄ to transfer the grating pattern into the SOG layer, at a gas flow rate of 21 sscm, a pressure of 15 mTorr, an RF power of 100 W, and an ICP power of 300 W. Following the SOG etch, the photoresist pattern was removed using an acetone spray gun and the remaining layer of BARC was etched away with an oxygen plasma. The required etching depth for minimizing the 0-order intensity for mask 1 and equalizing the 0th and −1st transmission intensities for mask 2 was obtained empirically after a few attempts by iteratively checking the optical performance and changing the etching time. The etch depth for mask 2 was estimated before fabrication using simulation done in Lumerical™ FDTD.³² For mask 1, an ideal phase grating would have no power in the transmitted 0 order and ∼41% of the power in each of the ±1 diffracted orders. For the present experiments, a 0-order power of ∼8% was achieved. For mask 2, the difference between the 1st-order and 0th-order intensities was about 8%, with only 11% reflected.

The first experiment was in Lloyd’s mirror configuration [Fig. 1(a)]. The diode laser was used as a source to expose a silicon sample coated with positive photoresist SPR 505 to create a one-dimensional pattern. The developed sample is shown in Fig. 3. IL gave multiple very small grating regions seen as intensely colored bands in the photo of the developed sample. These regions correspond to the vertical bands shown in Fig. 1(a). The relative path lengths vary across the field in this Lloyd’s mirror configuration; the persistence of the different bands of constructive interference shows that the coherence length of each individual mode is at least several cm long. The width of each band is ∼300 μm, and the repeat distance is 9.6 mm. Fitting Eqs. (1) and (2) to these values gives σ ∼ 2.5 and δλ ∼ 0.025 nm. These values will be used in analyzing additional configurations.

Two grating mask optical schemes were investigated corresponding to Figs. 1(b) and 1(d). An inexpensive (∼$100) TEM₀₀ diode laser with N ∼ 40 longitudinal modes and hence different wavelengths represented by λ_k (δλ ∼ 0.025 nm; Δλ ∼ 1 nm) was used for these experiments.³³ The angle of incidence of the 405 nm laser was chosen as 19.7° onto an ∼600 nm period grating, the Littrow angle for this grating period and wavelength, resulting in an IL pattern period of 600 nm. The alignment for the patterning process basically involves two steps. The photoresist coated substrate surface is initially made parallel to the mask surface using a green (nonactinic) laser. The expanded green laser is approximately normally incident on the mask while the actinic 405-nm diode laser is incident obliquely. Both the sample and the mask are held in tip tilt stages. The 1st-order light diffracted reflected from the sample and the mask grating surface are made to interfere on a screen. Diffraction of both the incident beam onto the mask and the reflected beam from the surface shifts the interference pattern to the side where it is easy to monitor without affecting the exposure process. The tip tilt stage is used to finely tune the position of the wafer until both the wafer and mask surface are parallel with a fringe pattern showing only about 4–5 fringes, resulting from the residual surface flatness variations and bowing of the wafer and the mask. Once the wafer and the mask are aligned, the green laser path is blocked, and the 405-nm diode laser path is opened to expose the wafer. A schematic of the patterning process is shown in Fig. 4. For the laser parameters determined in Lloyd’s mirror exposure, Z_Λ1 ∼ σd² cos θ/(4Δλ) ∼ 202 μm and Z_R1 ∼ d² cos θ/δλ ∼ 13 mm.

A 1-mm diameter collimated green laser beam is incident normal to the mask. Light diffracted by the mask in transmission, reflected from the sample, and diffracted on passing through the mask emerges parallel to and displaced from the incident beam. The distance between the symmetric double diffracted beams, L_2diff= 4G[tan(sin⁻¹(λ_probe/d))], is proportional to the gap between the mask and the sample. In the present case, (λ_probe = 532 nm, d = 600 nm) is 7.7 times the gap.

Developed exposures made with this system with a mask-sample gap of ∼1 mm showed a clear grating pattern but with insufficient contrast to fully develop the resist as a result of the short Z_Λ1 and practical gap alignment considerations. This is consistent with the estimated z-dependence. The two grating mask system, described above, was developed to resolve this issue. For a single transverse and longitudinal mode laser, the single mask scheme works very well and is suitable for large-area patterning, as demonstrated below.

The Littrow angle is the angle of incidence at which the 0th-order diffraction angle is equal to the −1st-order diffraction angle (θ₀ = −θ₋₁). The wavelength-dependent Littrow angle θ_L for a grating of period d is given by $sinθL=λ/2d$⁠. When light is incident with each mode at the Littrow angle on grating mask 2, the 1st-order diffracted angle is symmetric with respect to the surface normal for all wavelengths and the interferometric intensity pattern is constant at period d independent of z.

For optimum efficiency, mask 1 should be a binary phase mask where the transmitted first orders dominate. Experimentally, the 1st-order intensity is about six times that of the 0th-order intensity and hence is close to the efficient use of the laser power. Mask 2 has an equal intensity in 1st-order and 0th-order diffraction when light is incident at the Littrow angle. The fabrication process of mask 1 is the same as mask 2 except for the etch depth and the periodicity.

A schematic of the patterning setup is shown in Fig. 5(a), and the photograph of the experimental setup is shown in Fig 5(b). The 405 nm diode laser is expanded and is normally incident on mask 1 and obliquely incident on mask 2 after diffraction from mask 1. Both masks are initially made parallel to each other by setting them perpendicular to the incident collimated beam by monitoring the back reflection. A 1-mm aperture, placed about 40 cm away from mask 1 is used for this purpose (φ < 0.07° = 1.2 mrad). The sample surface is made parallel to the mask 2 surface using a green laser as described above for the single mask exposure. The green laser is incident obliquely on mask 2. Both the sample and the mask are held in tip tilt stages. The sample is on a three-axis stage with a precision in the z-direction of about 10 μm. The sample and the mask are made highly parallel (4–5 interference fringes) as discussed in Sec. III C. Once this alignment is done, the sample is moved as close as possible to the mask. During the course of this movement, the tip tilt screws are adjusted to maintain the interferogram at about 4–5 fringes. For the laser parameters and the approximate angular mismatch of φ ∼ 0.07°, the estimated $ZΛ2tilt{ZR2tilt}∼{4Δλ/σδλ}σd2cos⁡θ/2Δλ[4d(cosθ)2/λ0φ]∼0.9m{52m}$⁠. The mask grating periods were measured as d₁ = 1198 nm and d₂ = 590 nm and for a period mismatch of d₂ d₁/2 = ε = 9 nm, and $ZΛ2p{ZR2p}∼{4Δλ/σδλ}σd2cosθ/2Δλ[d/ε[1+(λ2/4d2[1−(λ/2d)2])]−1]∼25mm{145cm}$⁠. For these parameters, the period mismatch is the dominant limitation on the gap distances.

The silicon sample was spin coated with a layer of BARC (ICON-16) at 3000 rpm and hotplate baked at 190 °C for 60 s. This was followed by spin coating of positive photoresist SPR-505 (diluted 1:1) at 3000 rpm resulting in a thickness of about 250 nm. The soft bake time and temperature for the photoresist were 90 s and 90 °C, respectively. The incident beam power was about 500 μW over a 1-cm diameter area for an exposure time of 40 s. The exposed sample was postbaked at a temperature of 110 °C for 60 s and developed in MF-26 developer for 25 s. Figure 6(a) is an optical image of diffraction from the sample showing good uniformity. A top-down SEM image of the developed sample is shown in Fig. 6(b). For an ∼0.5 mm gap, a well-exposed uniform pattern across the full area was achieved. Figure 6(c) shows a 45° SEM showing the approximately vertical sidewalls that are a consequence of the resist nonlinearity.

High contrast, fully developed patterns were obtained for gap distances from 0.25 to 10 mm; however, at the larger gaps, the developed pattern was more rounded at the top of the PR lines, indicating a reduced contrast, consistent with the Z_Λ estimates. For a 0.5 mm gap exposure, the fill factor of the developed resist was measured at five locations: the center of the pattern and four points near the perimeter separated by 90°. The pattern was uniform with a linewidth of 260 ± 30 nm; improved results can be achieved with additional attention to beam quality and power density averaging across the laser transverse beam pattern.

An oblique incidence experiment [Fig. 1(b)] was also carried out using the single mask scheme with a single longitudinal mode laser. I-line negative photoresist NR7-500 was used. The period was 500 nm. For this experiment, a frequency tripled, pulsed YAG laser (Coherent infinity 40-100) having an emission wavelength of 355 nm was used. The laser operated in a single mode and hence there was no z-dependence issue. The angle of incidence onto the 500 nm period mask grating was close to 21°. The silicon sample was spin coated with ICON-16 and then photoresist was spin coated at 3000 rpm onto the silicon substrate. The soft bake temperature and time were 150 °C and 60 s, respectively. Exposure time and exposure dose were 13 s and 120 mJ/cm², respectively. An optical image and SEM of the developed sample are shown in Figs. 7(a) and 7(b) respectively. The size of the sample was approximately 12 × 25 mm².

A cost-effective, large-area nanopatterning technique has been demonstrated. A low-cost, ∼$100, commercially available, TEM₀₀, multilongitudinal mode diode laser was used as the source. A two-mask achromatic configuration was demonstrated with easily produced spin-on-glass-based diffraction phase masks having an optimal diffraction efficiency for patterning. To the best of our knowledge, this is the first use of spin-on-glass for easily customized phase masks whose diffraction efficiency can be varied by etching to meet the requirements of the optical arrangement. The presence of only two orders makes the technique simple and avoids complexities often encountered in techniques with additional diffraction orders. In contrast to previously demonstrated achromatic arrangements, the mask-to-beam splitter sample gap is quite small, ∼1 mm or less, providing immunity to vibrations and air-current induced phase shifts, making this technique well suited to manufacturing environments and suitable for immersion extensions. The current technique is scalable and is capable of large-area patterning. Efforts are underway to pattern 100-mm diameter samples using a diode laser.

This work is based upon the work supported primarily by the National Science Foundation (NSF) under Cooperative Agreement Nos. EEC-1160494 and CMMI 1635334. Any opinions, findings, and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

The data that support the findings of this study are available from the corresponding author upon reasonable request.