Birefringence Due to Dislocations in CaF₂ for Lithography Optics

As lithography moves to ever-shorter wavelengths to achieve the resolution required to produce finer features for semiconductor device miniaturization, conventional silica optics must be replaced with a material that is less absorbent at shorter UV wavelengths. Calcium fluoride is used for some optical elements at 193 nm, and is the optical material of choice for the 157 nm wavelength from fluorine excimer lasers. However, much concern has emerged about its birefringence. An intrinsic component of the birefringence might be reduced by alloying it with barium fluoride, but stress-induced birefringence from dislocations also must be considered.

The concentration of dislocations can be expressed as L, the length of the dislocation per unit volume, which is usually quoted in cm/cc. In ionic solids a typical value for L is 105 cm/cc, which corresponds to a root mean square (rms) strain on the order of 10^-4, said A.M. Stoneham of the Department of Physics and Astronomy, University College London (London). An rms strain on the order of 3×10^-7 (L cm/cc)^½ is to be expected. The piezo-optic constants that link the strain tensor to the birefringence are on the order of unity for CaF₂, so the birefringence will also have a distribution with an rms value on the order of 3×10^-7 (L cm/cc)^½. Stoneham said these estimates indicate that the rms birefringence will be less than the acceptable average value of 10^-7 only if the dislocation densities are essentially zero.

Dislocation-induced stresses will create some regions with positive birefringence and others with negative birefringence, so that there will be some cancellations for any optical path. Stoneham suggested that, for an optical system with a very short scale length — such as the ideal random alloy — this compensation will probably solve the problem. However, the number of dislocations met by the optical path can be estimated. Stoneham estimated that the compensation by sign fluctuations in the strain, and hence in the birefringence, will effectively reduce the birefringence by a little more than a factor of 10 to 10^-5. This is far higher than the acceptable value of 10^-7.

Stoneham concluded that dislocation-induced birefringence must be taken seriously, especially if (Ca, Ba)F₂ optics are to be employed. He believes it will be difficult to reduce dislocation-induced birefringence to acceptable levels without eliminating dislocations almost completely. Further problems may arise from UV-induced defect processes causing material property changes with time.

For further details, see Semiconductor Science and Technology , May 2002, p. L15.

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