- Finding optimal photomask layouts and illumination settings.
- Off-axis illumination, optical proximity correction (OPC).
- No user intervention, very few preconditions.
- Mutual optimization for different features (e.g., chained/isolated contact hole set-up)
- Underlying optimizer: genetic algorithm (GA).
- Related Work: Rosenbluth et al., Smith, Oh et al., Socha et al., Granik, and Poonawalaa et al.
- Global optimization method.
- Non-analytical technique → requires little a priori
- knowledge of the search space.
- Easily adaptable to different tasks.
- Mimics “natural” evolution or, more precisely, breeding: selection, recombination, and mutation.
optional local optimizer, e.g., via LisBON
- GA uses binary “alphabet” → binary encoding of parameters. E.g., bin(5) = (101)2.
- Mask elements are restricted to rectangles → 2 vertices/4 parameters per element.
- Illumination subdivided in track/sector pixels.
- Each pixel can take transmission values of 0 or 1.
- Transformation into simulator’s representation (mesh grid).
- Up to 50 parameters (mutual optimization of two features).
- Merit of a solution is determined by aerial image computation and evaluation (Kirchhoff approach).
- Aerial image analysis is conducted at different de-focus positions (e.g, 0 – 400 nm).
- In a first step, aerial images are computed at low resolution (10 mesh-points).
- If obtained merit exceeds a pre-defined threshold, a finer grained (20 mesh-points) evaluation is conducted.
Mask Manufacturability Criterion
In order to obtain a producible mask, following conditions should be met:
- Elements should exhibit minimum dimensions and
- a minimum distance between elements should be
- Obtained CDs (critical dimensions) should match the target CD as closely as possible.
- For each feature and each defocus setting, target and computed CDs are compared.
- The difference is considered the CD badness.
- The overall merit is decreased
- Prevention of side-lobe-printing.
- Assurance of main-feature-printing.
- “Security Band” around threshold: both side-lobes and main features hitting this band decrease the overall merit.
- NA := 0.7,
- λ := 193 nm,
- High transmission (19.3 %) attenuated PSM
- Objective: Finding optimum mask and illumination set-ups for 140 nm x 170 nm contact holes
dense: 320 nm x 410 nm,
chain: x-pitch: 320 nm,