Monica Sears


As semiconductor optical lithography is pushed to smaller dimensions, resolution enhancement techniques have been required to maintain process yields. For some time, the customization of illumination coherence at the source plane has allowed for the control of diffraction order distribution across the projection lens pupil. Phase shifting at the mask plane has allowed for some phase control as well. However, geometries smaller than the imaging wavelength introduce complex wavefront effects that cannot be corrected at source or mask planes. Three dimensional mask topography effects can cause a pitch dependent defocus (δBF), which can decrease the useable depth of focus (UDOF) across geometry of varying density. Wavefront manipulation at the lens pupil plane becomes necessary to provide the degrees of freedom needed to correct for such effects. The focus of this research is the compensation of such wavefront phase error realized through manipulation of the lens pupil plane, specifically in the form of spherical aberration. The research does not attempt to improve the process window for one particular feature, but rather improve the UDOF in order to make layouts with multiple pitches possible for advanced technology nodes. The research approach adopted in this dissertation includes rigorous simulation, analytical modeling, and experimental measurements. Due to the computational expense of rigorous calculations, a smart genetic algorithm is employed to optimize multiple spherical aberration coefficients. An analytical expression is formulated to predict the best focus shifts due to spherical aberration applied in the lens pupil domain. Rigorously simulated trends of best focus (BF) through pitch and orientation have been replicated by the analytical expression. Experimental validation of compensation using primary and secondary spherical aberration is performed using a high resolution wavefront manipulator. Subwavelength image exposures are performed on four different mask types and three different mask geometries. UDOF limiting δBF is observed on the thin masks for contact holes, and on thick masks for both one directional (1D) and two directional (2D) geometries. For the contact holes, the applied wavefront correction decreases the δBF from 44 nm to 7 nm and increases the UDOF to 109 nm, an 18% improvement. For the 1D geometries on a thick mask, the through pitch UDOF is increased from 59 nm to 108 nm, an 83% improvement. Experimental data also shows that an asymmetric wavefront can be tuned to particular geometries, providing a UDOF improvement for line ends under restricted processing conditions. The experimental data demonstrates that pupil wavefront manipulation has the capability to compensate for mask topography induced δBF. This dissertation recommends that corrective spherical aberration coefficients be used to decrease pitch dependent best focus, increase process yield, and ultimately expand the design domain over parameters such as mask materials and mask feature densities. The effect of spherical aberration applied in the pupil plane is to provide a wavefront solution that is equivalent to complex multiple-level mask compensation methods. This will allow the advantages of thicker masks to be explored for further applications in semiconductor optical lithography.

Library of Congress Subject Headings

Nanolithography; Masks (Electronics); Optics, Adaptive

Publication Date


Document Type


Student Type


Degree Name

Microsystems Engineering (Ph.D.)

Department, Program, or Center

Microsystems Engineering (KGCOE)


Smith, Bruce

Advisor/Committee Member

Palmer, Harvey


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