Optimization of Grayscale Lithography for the Fabrication of Flat Diffractive Infrared Lenses on Silicon Wafers

Abstract

Grayscale lithography (GSL) is an alternative approach to the standard binary lithography in MEMS fabrication, enabling the fabrication of complicated, arbitrary 3D structures on a wafer without the need for multiple masks and exposure steps. Despite its advantages, GSL's effectiveness is highly dependent on controlled lab conditions, equipment consistency, and finely tuned photoresist (PR) exposure and etching processes. This works presents a thorough investigation of the challenges of GSL for silicon (Si) wafers and presents a detailed approach on how to minimize fabrication inaccuracies, aiming to replicate the intended design as closely as possible. Utilizing a maskless laser writer, all aspects of the GSL are analyzed, from photoresist exposure parameters to Si etching conditions. A practical application of GSL is demonstrated in the fabrication of 4-μm-deep f#/1 Si Fresnel lenses for long-wave infrared (LWIR) imaging (8-12 μm). The surface topography of a Fresnel lens is a good case to apply GSL, as it has varying shapes and size features that need to be preserved. The final fabricated lens profiles show a good match with the initial design, and demonstrate successful etching of coarse and fine features, and demonstrative images taken with an LWIR camera.

Keywords: Fresnel lens; MEMS; grayscale; grayscale etching; infrared vision; multilevel.

Figure 1

The evolution of the patterns during the etching step. The patterned PR and the exposed Si are etched simultaneously and anisotropically. The transfer of the patterns from the PR to the Si happens steadily throughout the etching cycle.

Figure 2

(a) The test structure for dose calibration and (b) the test structure for selectivity measurements are relatively identical structures. The calibration design has more squares, so the linearization is accurate, and the interpolation relies on a sufficient number of measurements. (c) Part of the test structure that is used to optimize the development process. The width of the ramps increases gradually. The structures will be referred to as test structures A, B, and C in the text.

Figure 3

(a) The height of the columns is measured. (b) Y’ is the etched height of the of column Y. Column X has unetched PR and its total height is measured. (c) Removal of PR residues. X’ is measured and dX as a result. Calculated values: selectivity = Y’/Y, Si etch rate = X’/T, PR etch rate = (Χ − dX)/T, dX = X − X’.

Figure 4

Comparison of PR ramps when their designs are linearized and not. The unoptimized designs show an inward curve in which, in some areas, the difference between desired and actual height can reach values that will severely degrade the image quality. The optimized ramps exhibit excellent linearity.

Figure 5

Comparison of the first rings of a Fresnel lens. Each point is adjusted based on the exposure curve resulting on a similar but “scaled” mask.

Figure 6

SEM images of the selectivity measuring test structures B in Si. (a) On the left, the ramp is unoptimized. From the “shadow” on the sidewalls, it is visible that the ramp lags at gaining height. (b) The right optimized ramp starts to gain height earlier than the left one.

Figure 7

Selectivity and etching rates of Si and PR were examined. The flow rate of SF6 was held constant at 22.5 sccm. As the O₂ flow rate increased, the etching rate of the RP increased, while the rate of Si decreased slightly. Similarly, with a constant flow rate of O₂ at 8 sccm and a varying flow rate of SF6, an increase in SF6 flow rate led to an increase in the etching rate of both Si and PR.

Figure 8

SEM images of part of the test structure C. (a) When ramps are placed adjacently, without gaps in between, the slope flattens near the vertical walls. This results in less etched depth. (b) When ramps are spaced apart, the etched depth increases by 0.3 μm, reaching closer to the desired etch depth.

Figure 9

SEM images of the test structures C and B. (a) Multiple 14-μm-wide ramps were subjected to etching, resulting in a depth of ~4 μm. (b) The etching recipe demonstrated efficacy in etching structures of varying heights. The bottom right square, measuring approximately 80 nm in height, and the top left square, reaching approximately 4 μm in height, were both etched successfully. the 80 nm tall square retained its shape and height despite representing merely 2% of the height of the tallest square.

Figure 10

(a) SEM images of the last rings of a $f$#/0.5 Fresnel lens. The widths of the rings are in the range of ~14 μm. (b) Using AFM, the surface roughness (Ra) was measured at 3.5 nm. The total area scanned is 400 μm².

Figure 11

SEM images of rings of different widths, the etched depth varies from (a) 2.4 μm, (b) 3.0 μm, and (c) 3.9 μm. With the increment in the width of the ring, the discrepancy between the resultant and the targeted etch depths diminishes. This phenomenon can be attributed to the non-uniform development of the PR.

Figure 12

SEM images of rings of a lens with uniform development. (a) The cross-section of 29.8-μm-wide ring. The ramp initially flattens and then goes upward, from 4.07 μm to 3.66 μm, identical to the behavior that was observed also in Figure 8. (b) The wider rings have achieved the optimal etched depth of 4.08 μm.

Figure 13

SEM images of inner and outer rings of a lens. (a) The central ring achieves a step height of 4.2 μm. The verticality of the step change is excellent. (b) For outer rings, the measured step height is 3.9 μm. Both rings are very close to the 4 μm target step height.

Figure 14

Various SEM images showing Si Fresnel lenses. (a) shows the outer rings and (b) shows half of a Si Fresnel lens. (c) shows the cross-section of a Si lens.

Figure 15

(a) An “infrared” image taken (b) with the $f$#/1 and 1.2 cm diameter lens shown on and (c) attached to the camera housing using a custom mount as seen in image.