Question

The interference pattern produced by two optical plane waves at oblique orientation with
respect to each other can be used in lithography. Suggest a set-up to produce gratings of
period 2 µm. Explain all steps. Discuss the practicality of the design

Answer 1

From elementary electromagnetism, one can easily deduce the period p of the inter- ference fringes at a substrate when two plane waves interfere, р (1.5) sin Q1 + sin 02 where is the wavelength, 01 and O2 are the incident angles for the left and the right arm, respectively (Fig. 1-5). When 61 = 12 = 0, Eq. (1.5) reduces to P= (1.6) 2 sin e Reference [23] provides a good description of IL and its history. Figure 1-6 illus- trates the MIT system setup. As drawn, the two incident angles are assumed equal. The split beams from an argon-ion laser (1 = 351.1 nm) are conditioned before in-

ER EL 02 ! Resist Substrate Figure 1-5: During interference lithography, the nominal fringe period p at the sub- strate is determined by the beam incident angles 01 and 02, and the laser's wavelength 1.

terfering at the substrate. The variable attenuator equalizes the power of the beams to maximize the fringe contrast. Polarizers in each arm ensure s-polarized4 light ex- posing the substrate. Spatial filters rid wavefront distortions by blocking undesired spatial frequencies. The focal length of the lens in the spatial filter is chosen to set the divergence of the beams, thereby defining the size of the interference region. The beams have a Gaussian intensity distribution. For good dose uniformity, the spot size on the substrate should be much larger than the desired patterning area. A phase error sensor located near the plane of the substrate measures fringe drift, which is mainly due to air index change, vibration, and thermal drift of the optical setup. A differential signal from two photodiodes yields the error signal that drives the ana- log controller for a phase displacement actuator (a Pockel's cell), which actuates to stabilize the fringes at the substrate. The distance from the spatial-filter pinhole to the substrate defines the radius of the expanding spherical wavefront. It is desirable for this distance to be large for reduced hyperbolic grating phase nonlinearities (23, 43, 44, 45). In practice however, turbulence, vibration, and thermal drift limit how large the propagation distance can be. In the MIT setup, this distance is nominally 1 m. Even with such large wavefront radii and the assumption of perfectly aligned beams, Figure 1-7 shows that the image diameter with subnanometer phase nonlinearity is only 2.8 mm. This assumes a 400 nm nominal grating period. Furthermore, if one considers a 20 mm x 20 mm square area, the discrepancy worsens to over 600 nm at the four corners of the square. 4 Also known as the transverse-electric (TE) polarization.

Laser (n=351.1nm) Beamsplitter Phase Displacement Actuator (e.g., Pockel's Cell) Variable Attenuator Polarizer Mirrors Spatial Filters 2 p= 20 2 sino Substrate Beamsplitter Phase Error Signal Controller K KHU G Figure 1-6: A schematic diagram of the traditional interference lithography system at MIT.

Theoretically, lenses may be used to collimate the beams after the spatial filter and thus eliminate the hyperbolic phase nonlinearity. However, it is questionable whether it is practical to fabricate, align and keep clean large optics capable of producing meter-sized gratings with nanometer phase nonlinearity. For the purpose of conducting pattern placement metrology or displacement mea- suring interferometry, it is most ideal to have linear gratings, but the requirement is not absolute. If the nonlinear phase in the IL-produced gratings is highly repeatable and well characterized, one can still use them and compensate for the nonlinearity via a look-up table. However, Ferrera showed conclusively that nanometer repeatability for traditional IL is improbable if not impossible to attain because of severe beam and substrate alignment requirements [23]. For example, he showed that in order to attain a repeatability of 3 nm over an area of 25 mm x 25 mm, the two interferometer arms dį and dR in Figure 1-7(a) must be matched to 150 nm. With much technical prowess, he was only able to demonstrate an experimental repeatability of 50 nm for

p= a 2 sino 0 (a) di dR C

22 Discrepancy from linear phase for dų = dR = 1 m (b) 2 5 nm 3 nm 1 1 nm y (mm) 0 0 nm -1 -1 nm -3 nm -5 nm - 1 0 2 x (mm) Figure 1-7: Nonlinear phase distortions due to the interference of two spherical waves with 1 m wavefront radii, assuming that the system is in perfect alignment and is set up for a nominal grating period of 400 nm. (a) The interference coordinates. (b) Phase discrepancy from an ideal linear grating. The region with subnanometer nonlinear phase is less than 2.8 mm in diameter.

400 nm period gratings over an area of 30 mm x 30 mm. Because of phase nonlinearity and repeatability issues, conventional IL is incapable of producing large-area linear gratings. 1.4.2 SBIL concept Figure 1-8 depicts the SBIL system concept. A grating beamsplitter splits the laser in two. The lithography interferometer optics closely resembles that of traditional IL but the grating image is much smaller than the total desired patterning area. The beams are Gaussian in nature. The 1/e2 intensity diameter at the substrate is typically 2 mm, but can be enlarged or reduced by adjusting the optical layout. The collimating lenses after the spatial filters ensure that the Gaussian beams interfere with each other at their waists, where the wavefronts are the most planarø. For a lithography laser wavelength of 351.1 nm, the system is intended for writing gratings with a period in the range of 200 nm to 2 pm. The substrate is mounted on a laser interferometer controlled air-bearing XY stage. Large gratings are fabricated by scanning the substrate at a constant velocity underneath the grating image.

Figure 1-9 illustrates how SBIL achieves a uniform exposure dose by overlapping scans. Figure 1-9(a) shows the grating image being scanned along the substrate. In order to stitch scans together, one must measure the fringe period with high accuracy. SBIL period measurement goal is 1 nm uncertainty over 1 mm-radius spot, which translates into an allowed percentage measurement error of only one-part-per-million (1 ppm). At the end of the scan the stage steps over by an integer number of fringe periods and reverses direction for a new scan. SBIL has the significant added complexity over IL of accurately synchronizing the interference image to a moving substrate. The scanning grating image is illustrated in Figure 1-9(b). The interference pattern has a Gaussian intensity envelope. The effective number of fringes in the grating image may be many thousands (i.e., 5,000 fringes in a grating image with a 2 mm 1/e2-diameter and a 400 nm period). Figure 1-9(c) shows the individual scan intensity envelopes in dashed lines and the sum of the envelopes in a solid line. A maximum step size is constrained by the desired dose uniformity. As plotted, a step size of 0.9 times the 1/e2-radius produces dose uniformity of better than 1%. Similar to IL, SBIL employs a fringe-locking controller to stabilize the fringes while writing. Unlike IL's homodyne approach, which stabilizes the fringes by sensing the differential intensity variations between two photodiodes, SBIL uses a heterodyne fringe-locking scheme. Since phase drifts are detected in the frequency domain, the

UV Laser (a) Grating Beamsplitter Stage Error Phase Error Signal Controller Variable Attenuator G Beamsplitter Phase Displacement Actuator Polarizer ot Mirror Beam Pickoffs Spatial Filter 20 Grating Patch Substrate Column Reference Mirror Stage Displacement Me ing Interferometer Stage Interferometer Mirror Air Bearing XY Stage Period: p = 2 2 sine Z X ОУ Figure 1-8: Scanning beam interference lithography system concept.

a) X Direction b) Intensity, scanning grating image Scanning Grating Image Air-bearing XY Stage Y Direction Х Resist- coated Substrate Grating Period, p c) Intensity, sum of overlapping scans Summed Intensity of Scans 1-6 Individual Scan (only intensity envelope shown) Х Figure 1-9: SBIL step-and-scan scheme. (a) Top view. The step and scan directions are x and y, respectively, which are also defined in Figure 1-8. To ensure good stitching between adjacent scans, the stage must step over by an integer number of fringe periods. (b) Gaussian intensity envelope of one scan. Period exaggerated. (c) Beam overlapping to create a uniform exposure dose.

heterodyne scheme is immune to laser intensity fluctuations, which can be quite significant over an hour time required to pattern a 300 mm grating. It should be noted that besides fringe motions due to the changing air index, the nonideal motion of the stage, if uncorrected, introduces additional errors in the written grating as well. For that reason, stage positioning error, especially along the sensitive x axis which is perpendicular to the fringe direction, is also compensated by fringe locking.