# 2009 Research Summary

## Characterization and Monitoring of Photomask Edge Effects

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Marshal Miller and Andrew R. Neureuther

In semiconductor manufacturing, photolithography is used to define patterns on wafers. In practice, many approximations are made in order to simulate light propagation through mask openings, mainly that the mask is infinitely thin, which allows full chip-scale simulation. In practice, layers on the mask are 50-200 nm, on the order of 193 nm illumination. Scattering and diffraction off of corners and edges introduce phase errors not accounted for in the fast thin mask model. Using rigorous finite difference time domain (FDTD) simulation, tiny fractions of masks can be simulated accurately, taking into account electromagnetic effects. Our goal is to model these 3D mask effects in a fast way to scale up to better approximate thick mask features on a full chip.

The contribution of edges can be broken down into real and imaginary contributions. The real perturbations occur when light moves from one region to another. This causes an opening to appear electromagnetically smaller or larger than intended. Additionally, for a phase-shifting mask, materials are used to transmit light 180 degrees out of phase compared to other regions. The phase mismatch between the 2 regions can cause out-of-phase components to propagate through the mask resulting in a 90-degree, or imaginary transmission. This imaginary bias interacts with defocus causing an asymmetry in imaging through focus aberrations. As industry moves to the 22 nm node, these effects become large enough that accurately printing a circuit requires compensating for them.

Figure 1: Illustration for an attenuating phase shift mask of how field components moving between regions causes real and imaginary edge biases to arise

- [1]
- M. A. Miller, A. R. Neureuther, D.l P. Ceperley, J. Rubinstein, and K. Kikuchi, “Characterization and Monitoring of Edge Effects in Photomasks,”
*Proc. SPIE,*Vol. 6730, October 2007.