Scan angle error measurement based on phase-stepping algorithms in scanning beam interference lithography.

In this paper, a doubled-period grating (DPG) method is proposed to measure the scan angle error in scanning beam interference lithography (SBIL), together with a high-resolution two-dimensional stage and phase-stepping algorithms. A reference grating, which was the doubled period of the interference field, is adapted to diffract the incident left and right beams to form an interferogram captured by a CCD camera. The phase-stepping algorithm was applied to calculate the phase of the interferogram. First, by translating the stage, the reference grating lines were adjusted parallel to the scan direction by comparing the phase of the interferogram between the starting point and the ending point. Next, by rotating the stage step by step, the phase of the interferogram was obtained at each step as well as the phase slope. The scan angle error was considered to be least when the slope was minimum. Finally, a grating mask with a size of 100×100 mm2 was fabricated to verify the feasibility of the method. The scan angle error was measured with a precision of less than 12.65 µrad, which indicates the effectiveness of the proposed method to fabricate high-quality gratings in the future.

Long-range in situ picometer measurement of the period of an interference field.

A scanning reference grating (SRG) method is proposed for high-precision in situ measuring and controlling the period of a long-range interference field. The reference grating is produced with the in situ interference field; then it is used to obtain phase shift signal when scanning in the interference field. With the phase shift signal collected by the SRG system, before the exposure process of the holographic grating fabrication, the period and the period uniformity of the holographic grating can be evaluated directly from the interference field; then optical adjustment can be applied until the grating period is tuned to any certain desired value. Experiments of measurement and adjustment are conducted, and an interference field with period value of 833.335 nm±10 pm in 60 mm range is reached. The proposed method gives an efficient way to fabricate large gratings of an accurate period; furthermore, it provides a reliable tool that may lead us to picometer-level optical metrology and fabrication for the most advanced lithographic equipment and in other scientific fields.

Two-dimensional gold matrix method for encoding two-dimensional optical arbitrary positions.

In this study, a novel two-dimensional spatial coding pattern called two-dimensional Gold matrix method is proposed for general two-dimensional positioning. Considering the difficulty in representing a two-dimensional position in a single binary matrix, constructing a matrix while each submatrix refers to its location is a challenging mathematical problem. The general two-dimensional signal can be labeled by the two-dimensional Gold matrix, which results from a preferred pair of two m-sequences. For a pseudorandom m-sequence, the span-n property of the two-dimensional Gold matrix states that every n×n submatrix is unique and the decoding is fast and convenient. Numerical simulation and a proof-of-principle experiment are performed, and experimental results verified that the two-dimensional Gold matrix method is effective for high resolution and large range two-dimensional measurements.

Precision fringe period metrology using an LSQ sine fit algorithm.

High-precision grating fabrication is a precondition of grating-based displacement measurement techniques. Likewise, the value of high-precision fringe period is an essential parameter in the grating fabrication process, especially in scanning beam interference lithography. In this paper, a procedure for measuring the fringe periods of interference beams is introduced. The procedure includes signal acquisition and signal processing. The precisions of both the configuration for acquisition and the algorithm for processing are discussed. Experiments for fringe period measurement are also conducted, and an average value of 564.374 nm with a standard deviation of 1.5 pm is obtained, reaching a repeatability of 2.6 ppm. The value of precision period lays a solid foundation for the fabrication of high-precision gratings.

Eightfold optical encoder with high-density grating.

A novel grating interferometer configuration with eightfold optical subdivision to achieve ultrahigh resolution using a special symmetrical prism is proposed. The optical subdivision is enhanced by four times compared to traditional linear optical encoders. In this work, we take advantage of a high linear density grating of 1780 lines/mm, which is combined with an eightfold optical subdivision configuration. As a result, a high resolution of 68.6 pm is achieved. The apparatus adopts a symmetrical measurement configuration to reduce the error arising from environmental fluctuations. The verification experiments involve high optical subdivision, long- and short-range displacement measurement, and stability, with all results compared to those obtained with a commercial interferometer. The excellent agreement of the results demonstrates the effectiveness of our proposed system.