To further decrease lithographic resolution, specific illumination modes are required for different mask patterns. The freeform pupil-shaping module is a standard component of lithography illumination systems at the 28 nm node and below. To ensure stable and uniform energy distribution at the optical pupil, a homogenization unit is used before the freeform pupil-shaping module. The current mainstream solution involves using a microlens array (MLA) for homogenization. The MLA divides the incident beam into a multitude of sub-beams, which are superimposed on the back focal plane of the condenser to obtain a homogeneous illumination field. Although a low-spatial-coherence excimer laser is used in lithography, it still produces interference patterns in the back focal plane of the condenser, significantly impacting pupil performance. In this paper, we propose a decoherence method based on the deformation design of MLAs that improves the uniformity without introducing additional elements.

In this paper, we propose a new design method for decoherent MLAs. First, considering the partial coherence of a laser, transmission of partially coherent light in the homogenization unit is modeled using mutual intensity theory. Based on the mutual intensity distribution in the back focal plane of the condenser, it can be concluded that the intensity distribution of the light field is modulated by the coherence length and related to the aperture function P(?,η). Changing this function not only affects the initial phase φ(m,n) of each sub-beam but also changes the frequency of sinc function. As a consequence, φ(m,n) affects the interference results and sinc function affects the amplitude modulation. Based on the aforementioned model, an optimized design of the mean value of the pitch size of the MLA was carried out. To increase the phase difference between the microlenses within the coherence length, degrees of freedom for pitch variation and border line tilting were introduced based on the optimized design described above.

First, the mean value of the pitch size of the MLA was optimized. The design results (Figs. 5 and 6) show that when the microlens pitch size is 0.5 mm, non-uniformity is at a minimum of 43.87% and energy utilization is 85.39%. While this optimization solution satisfies the energy utilization requirement of the freeform pupil-shaping module, it is not able to achieve a non-uniformity less than 40%. Introducing a small random pitch variable in the pitch size of the microlens, the design results (Figs. 8 and 9) show that non-uniformity is minimum at 41.53% and energy utilization is 84.16% at the amplitude of the pitch variation of 0.05 mm, which also satisfies the requirement for energy utilization. However, non-uniformity does not fulfill the aforementioned requirement yet. Making the microlens at the cylindrical border line in the xy plane introduces a tilt factor k, which is a random small quantity. The design results (Figs. 11 and 12) show that when the amplitude of the tilt factor is 5 μm, non-uniformity is at a minimum of 38.67%, and energy utilization is 82.74%, thereby fulfilling specifications. Combining the optimization solutions of pitch size variation and border line tilting, non-uniformity of 36.51% (Fig. 14) and energy utilization of 83.90% are achieved when the amplitude of the pitch variation is 0.03 mm and that of the tilting factor is 4 μm. This co-optimization approach results in a more significant reduction in non-uniformity, along with improved energy utilization.

In present paper, we propose a decoherence method based on the deformation design of MLA to improve homogeneity without introducing additional elements. First, the mean value of the pitch size of the MLA was optimally designed. Subsequently, degrees of freedom for pitch variation and border line tilting were introduced. The simulation results show that with the optimal combination of suitable pitch variation and border line tilting, non-uniformity and energy utilization reach 36.51% and 83.90%, respectively, which satisfy the requirements for the use of a freeform pupil-shaping module.