Preparation and testing of laterally graded multilayer with a double genetic algorithm and root mean square error optimization in differential deposition

Abstract

Lateral graded multilayer can realize reflection, collimation and focusing of hard X-ray, and are currently the research frontier and hotspot of synchrotron radiation and high-performance X-ray sources. To reduce the d-spacing error of graded multilayers, a root mean square error optimization method based on double genetic algorithm (DGA-RMSE) is proposed. The theoretical d-spacing distribution is obtained by optical design, and the range is 1.9 ∼ 3.1 nm. The optimized d-spacing distribution is obtained by convolution of particle beam function and continuous monotonic rate distribution line (RDL) which is constructed in the form of a polynomial. The GA is applied to optimize variables from the polynomial twice, and the RMSE of thickness error is optimized and converged to 0.0065 nm. The final thickness error which is measured by the grazing incidence X-ray reflectivity (GIXRR) is consistent with the theoretical calculation. The results show that DGA-RMSE can precisely select polynomial function of RDL, reducing the error in high-precision magnetron sputtering and mask technology.