US 12,405,570 B2
Method and device for compensating surface error of holographic grating substrate
Heshig Bayan, Changchun (CN); Shan Jiang, Changchun (CN); Yubo Li, Changchun (CN); Zhaowu Liu, Changchun (CN); Wei Wang, Changchun (CN); Wenhao Li, Changchun (CN); Shuo Li, Changchun (CN); and Yanxiu Jiang, Changchun (CN)
Assigned to CHANGCHUN INSTITUTE OF OPTICS, FINE MECHANICS AND PHYSICS, CHINESE ACADEMY OF SCIENCES, Changchun (CN)
Filed by Changchun Institute Of Optics, Fine Mechanics And Physics, Chinese Academy Of Sciences, Changchun (CN)
Filed on Aug. 22, 2024, as Appl. No. 18/812,069.
Claims priority of application No. 202311055791.3 (CN), filed on Aug. 22, 2023.
Prior Publication US 2025/0068123 A1, Feb. 27, 2025
Int. Cl. G03H 1/04 (2006.01); G03H 1/00 (2006.01)
CPC G03H 1/0486 (2013.01) [G03H 1/0005 (2013.01); G03H 2001/0094 (2013.01)] 3 Claims
OG exemplary drawing
 
1. A method for compensating a surface error of a holographic grating substrate, comprising steps:
obtaining a surface error distribution diagram corresponding to the holographic grating substrate by detecting the surface error of the holographic grating substrate;
obtaining a phase distribution of predetermined phases compensating for the surface error through simulation calculation; and
decomposing the phase distribution of the predetermined phases into a first coordinate matrix corresponding to phases of the holographic grating substrate in a point-to-point manner, exposing coordinate points of the predetermined phases, different from the phases of the holographic grating substrate, in the first coordinate matrix on photoresist disposed on a surface of the holographic grating substrate by stepping, scanning, and exposure, and developing to obtain a grating mask;
wherein a phase modulation principle of a scanning beam interference lithography system comprises:
interfering at beam waist positions of spatially filtered and collimated small-size Gaussian beams emitted by the scanning beam interference lithography system to form interference fringes; a phase of the interference fringes at a position (x,y) at time t is ϕph(x,y,t), a total exposure after scanning and exposure is:
D(x,y)=A(x,y){1+γ cos[2π/px+Φph(x,y)]},
wherein 2π/px+Øph (x,y) is an exposure phase distribution after stepping, scanning, and exposure, and Φph (x,y) is a phase distribution related to Øph (x,y,t), and a value of Øph (x,y,t) is changed to obtain a predetermined phase distribution Φph (x,y) of the surface of the holographic grating substrate;
detecting the surface error of the holographic grating substrate, and obtaining the phase distribution Φph,e(x,y) of the predetermined phases compensating for the surface error through the simulation calculation:

OG Complex Work Unit Math
measuring a displacement of a two-dimensional worktop by a displacement measurement apparatus and obtaining a second coordinate matrix H of the holographic grating substrate:

OG Complex Work Unit Math
wherein during a scanning and stepping process of the two-dimensional worktop, when not modulated, there is a phase distribution W of the phases of the holographic grating substrate one-to-one corresponding to coordinate points in the second coordinate matrix H, the phase distribution W is represented by:

OG Complex Work Unit Math
φ is a phase modulation term and is a feedback of a phase control apparatus through a displacement measurement of the two-dimensional worktop; phases of the interference fringes are directionally modulated by changing frequencies of phase modulators, φ is expressed as:

OG Complex Work Unit Math
after phase modulation, a phase distribution Wn of modulated phases one-to-one corresponding to the coordinate points in the second coordinate matrix is represented by:

OG Complex Work Unit Math
wherein the phase distribution Wn of the modulated phases is same as the phase distribution Φph,e(x,y) of the predetermined phases;
the step of decomposing the phase distribution of the predetermined phases into the first coordinate matrix corresponding to phases of the holographic grating substrate in the point-to-point manner, exposing the coordinate points of the predetermined phases, different from the phases of the holographic grating substrate, in the first coordinate matrix on photoresist disposed on the surface of the holographic grating substrate by stepping, scanning, and exposure, and developing to obtain the grating mask comprises:
accurately positioning the holographic grating substrate of a predetermined size from an exposure start point to an exposure end point by the displacement measurement apparatus to obtain the second coordinate matrix of the holographic grating substrate; and
corresponding the predetermined phases for compensating the surface error of the holographic grating substrate one-to-one to the coordinate points in the second coordinate matrix of the holographic grating substrate, feeding back a position of the holographic grating substrate by the displacement measurement apparatus in real time, and scanning and exposing the photoresist on the surface of the holographic grating substrate by a scanning beam interference lithography system, and then developing the photoresist to obtain the grating mask after surface compensation modulation.