previous up next contents
Prev: 5.2.2 Reflective Notching Up: 5.2 Benchmarks Next: 5.3 Coupling with Lithography

5.2.3 Phase Shifted Outriggers

The third and concluding example shows the patterning of a contact hole with phase shifted outriggers. For this example the intensity distribution is composed of five beams. Each of the beams consists of two phase shifted components. Similarly to the Gaussian beams in the first example, the five beams split up into a center beam and four beams shifted towards the corners. The equations describing the electrical field components are
$\displaystyle \mathrm{Mag_1}$ $\textstyle =$ $\displaystyle 1.00*\exp\{-0.01*[(x-40)^2+(y-40)^2]\}$  
$\displaystyle \mathrm{Mag_2}$ $\textstyle =$ $\displaystyle 0.50*\exp\{-0.01*[(x-20)^2+(y-20)^2]\}$  
$\displaystyle \mathrm{Mag_3}$ $\textstyle =$ $\displaystyle 0.50*\exp\{-0.01*[(x-20)^2+(y-60)^2]\}$  
$\displaystyle \mathrm{Mag_4}$ $\textstyle =$ $\displaystyle 0.50*\exp\{-0.01*[(x-60)^2+(y-20)^2]\}$  
$\displaystyle \mathrm{Mag_5}$ $\textstyle =$ $\displaystyle 0.50*\exp\{-0.01*[(x-60)^2+(y-60)^2]\}$  
$\displaystyle \mathrm{Mag_6}$ $\textstyle =$ $\displaystyle 0.10*\exp\{-0.01*[(x-40)^2+(y-40)^2]\}$  
$\displaystyle \mathrm{Mag_7}$ $\textstyle =$ $\displaystyle 0.05*\exp\{-0.01*[(x-20)^2+(y-20)^2]\}$  
$\displaystyle \mathrm{Mag_8}$ $\textstyle =$ $\displaystyle 0.05*\exp\{-0.01*[(x-20)^2+(y-60)^2]\}$  
$\displaystyle \mathrm{Mag_9}$ $\textstyle =$ $\displaystyle 0.05*\exp\{-0.01*[(x-60)^2+(y-20)^2]\}$  
$\displaystyle \mathrm{Mag_{10}}$ $\textstyle =$ $\displaystyle 0.05*\exp\{-0.01*[(x-60)^2+(y-60)^2]\}$  
$\displaystyle \mathrm{Pha_1}$ $\textstyle =$ $\displaystyle \sin(\pi*z/10)$  
$\displaystyle \mathrm{Pha_2}$ $\textstyle =$ $\displaystyle \mathrm{Pha_3} = \mathrm{Pha_4} = \mathrm{Pha_5} =
$\displaystyle \mathrm{Pha_6}$ $\textstyle =$ $\displaystyle \sin(-\pi*z/10+\pi/2)$  
$\displaystyle \mathrm{Pha_7}$ $\textstyle =$ $\displaystyle \mathrm{Pha_8} = \mathrm{Pha_9} = \mathrm{Pha_{10}} =
$\displaystyle r$ $\textstyle =$ $\displaystyle \sum_{i=1}^{10} \mathrm{Mag}_i \mathrm{Pha}_i.$ (5.3)

Fig. 5.4 shows two different time-steps of the evolving surface. The same perspective as for the example with the defect in Fig. 5.3 is chosen. The front part is again cut away and the outer shape of the evolving front is shaded in black.

Figure 5.4: Phase shifted outriggers benchmark example.
\begin{figure}\psfrag{0.8 mu}[b][b][0.8]{0.8 $\mu$m}
\psfrag{0.8 um}[t][t][0.8]{...

This example merges the requirements of the previous two examples including standing waves plus intersecting fronts forming a multitude of tips, ridges and odd structures. Even for this very complex example the cellular approach guarantees the stable evolution of the three-dimensional resist profile. The circular shape of the five beams emerges clearly and the sidewall slope vanishes with increasing development time.

The regularity of the standing waves in the cellular representation is excellent, which can be observed in the conformity of the openings formed where the evolving front reaches the bounding box at the backside of the simulation domain. Again we encounter regions with undefined surface normals, namely, the ridges on the left hand side of Fig. 5.4, revealing the phase shift between the different beams and the tips formed in the final structure on the right hand side, where four differently oriented planes intersect.

previous up next contents
Prev: 5.2.2 Reflective Notching Up: 5.2 Benchmarks Next: 5.3 Coupling with Lithography

W. Pyka: Feature Scale Modeling for Etching and Deposition Processes in Semiconductor Manufacturing