How to describe polarization influence on imaging

Abstract

We give a general introduction into polarized imaging and report on a Jones-pupil approach for a complete evaluation of the resulting optical performance. The Jones pupil assigns a Jones matrix to each point of the exit pupil describing the impact of both the global phase and the polarization on imaging. While we can learn already a lot about the optical system by taking a close look at the Jones pupil -and starting imaging simulations from it -a quantitative assessment is necessary for a complete evaluation of imaging. To do this, we generalize the concept of scalar Zernike aberrations to Jones-Zernike aberrations by expansion of the Jones pupil into vector polynomials. The resulting method is nonparaxial, i.e. the effect of the polarization dependent contrast loss for high numerical apertures is included. The aberrations of the Jones-matrix pupil are a suitable tool to identify the main drivers determining the polarization performance. Furthermore, they enable us to compare the polarized and the unpolarized performance of the such characterized lithographic system.

Analytical analysis for impact of polarization aberration of projection lens on lithographic imaging quality

“…In addition, the linear fitting of IPE and BFS is performed using the standard linear model expressed as 4 PZ , 9 PZ , 16 PZ and the corresponding fitting lines under linear polarization illumination (0,1) are shown in Figure 3. The IPE and BFS of that and the corresponding fitting lines under linear polarization illumination (1,1) are shown in Compare with the corresponding ratios -2 in Eq. (21) and (22) …”

“…As a major source of the polarization effects in lithography system, polarization aberration of projection lens can cause various undesirable effects, such as image placement error (IPE), best focus shift (BFS) and critical dimension (CD) errors and so on, leading to the degradation of image quality and process window [1][2][3] . As high NA projection lenses and polarized illumination are used in lithography system, the impact of polarization aberration on lithographic imaging quality can't be ignored any more.…”

“…The RSS values of line relationships under illumination (1,1) .   ratios under linear polarization illumination(1,1) are calculated, which are shown intable 3 and table 4.…”

Polarization aberration compensation method by adjusting illumination partial coherent factors in immersion lithography

“…Several representations of PA have been proposed, such as Jones pupil, physical pupil, Mueller pupil ,Pauli pupil and 3D PA [9][10][11][12][13][14] . The impact of scalar wavefront aberration or PA on image performance had been studied well based on thin mask 11,13,[15][16][17] , and their work adopt the simplified Kirchhoff approach. The results reveal that PA can evidently induce the pattern critical dimension(CD) error, best focus shift (BFS) and pattern placement error (PE), thus degrading the performance of the resist image.…”

Analytical approach to the impact of polarization aberration on lithographic imaging

“…Although numerical computation is effective for lithographic process analysis, it is usually time consuming. Totzeck et al in [5] proposed a useful method, which was based on the concept of complex contrast for analyzing imaging quality and polarization aberrations, and it gave their theoretical demonstrations. The critical relationship between imaging quality and polarization aberration is very important for aberration adjustment and lithography process control.…”