Three-dimensional resist development simulation with discrete models
Generation and representation of the resist structure. Initially polymer chains shorter than the specified average length (transparent circles connected by continuous lines) are added to the rectangular grid. Then, the remaining free cells are added to already existing polymer stubs (gray circles connected with dashed lines) to obtain the desired average chain length.
Influence of the orientation of the polymers, relative to the development front, on their dissolution time. To obtain dissolution times consistent with the macroscopic development rates, the gray polymers are (on average) assigned twice the dissolution times of the transparent polymers.
Schematic of the evolution of developing fronts. The figure illustrates the differences between continuous resist representation and a discrete representation on a regular cubic grid. The numbers denote the relative arrival times of the developer front resulting from the discrete (numbers in the squares) and the continuous modeling (numbers at the arcs). Development starts in the upper left cell. A constant development rate is assumed in the whole region. This systematic difference between continuous and discrete modelings is solely due to the simplified assumption of a regular (cubic) grid, not inherent to discrete models.
Sample resist profiles obtained with continuous (left; bottom CD value of ) and with discrete (right; average bottom CD value of ) resist representation and development simulation.
(a) Influence of the assumed average polymer size and variance (normal distribution) of the polymer dissolution time on the resulting line-edge roughness. The assumed polymer branching probability was 0.3. (b) Results for an assumed polymer branching probability of 0.5.
Key material and process parameters used in the simulations.
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