Auther:2013-9-4

Process variations, such as defocus and lens aberrations, always exist in real lithography processes. Thus, fast and accurate lithography simulation considering process variations, especially the optical ones, is highly desirable. For optical imaging in Hopkins’ theory, it is rather expensive to calculate the four-dimensional transmission cross coefficient (TCC) and integrals. Although the sum of coherent systems (SOCS) method and the optimal coherent approximation achieve a significant speedup by eigen-analyzing the TCC and neglecting small eigenvalues, the TCC kernels are usually obtained under the nominal (best) process condition. For a different process condition, a simulator may have to repeat the costly eigen-decomposition and mask-kernel convolutions.

Recently, headed by Professor Shiyuan Liu, the Nanoscale and Optical Metrology (NOM) Group at Wuhan National Laboratory of Optoelectronics (WNLO) proposed a new method called convolution-variation separation (CVS) to enable efficient optical imaging calculations without sacrificing accuracy when simulating images for a wide range of process variations. The CVS method is derived from first principles using a series expansion, which consists of a set of predetermined basis functions weighted by a set of predetermined expansion coefficients. The basis functions are independent of the process variations and thus may be computed and stored in advance, while the expansion coefficients depend only on the process variations. Optical image simulations for defocus and aberration variations with applications in robust inverse lithography technology and lens aberration metrology have demonstrated the main concept and advantage of the CVS method.

The work was funded by the National Natural Science Foundation of China (Nos. 91023032, 51005091), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20120142110019), and the National Science and Technology Major Project of China (No. 2012ZX02701001). The work was published in Optics Letters (vol. 38, no. 13, pp. 2168-2170, 2013). 

Process variations, such as defocus and lens aberrations, always exist in real lithography processes. Thus, fast and accurate lithography simulation considering process variations, especially the optical ones, is highly desirable. For optical imaging in Hopkins’ theory, it is rather expensive to calculate the four-dimensional transmission cross coefficient (TCC) and integrals. Although the sum of coherent systems (SOCS) method and the optimal coherent approximation achieve a significant speedup by eigen-analyzing the TCC and neglecting small eigenvalues, the TCC kernels are usually obtained under the nominal (best) process condition. For a different process condition, a simulator may have to repeat the costly eigen-decomposition and mask-kernel convolutions.

Recently, headed by Professor Shiyuan Liu, the Nanoscale and Optical Metrology (NOM) Group at Wuhan National Laboratory of Optoelectronics (WNLO) proposed a new method called convolution-variation separation (CVS) to enable efficient optical imaging calculations without sacrificing accuracy when simulating images for a wide range of process variations. The CVS method is derived from first principles using a series expansion, which consists of a set of predetermined basis functions weighted by a set of predetermined expansion coefficients. The basis functions are independent of the process variations and thus may be computed and stored in advance, while the expansion coefficients depend only on the process variations. Optical image simulations for defocus and aberration variations with applications in robust inverse lithography technology and lens aberration metrology have demonstrated the main concept and advantage of the CVS method.

The work was funded by the National Natural Science Foundation of China (Nos. 91023032, 51005091), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20120142110019), and the National Science and Technology Major Project of China (No. 2012ZX02701001). The work was published in Optics Letters (vol. 38, no. 13, pp. 2168-2170, 2013).

Fig. 1. Optimized mask patterns under different defocus distributions.

Fig. 2. Separation and efficient simulation of image intensity under lens aberrations.