In optical lithography, a pattern defined in a photomask is transferred into a photosensitive film (photoresist). The photoresist processing steps for an exemplary pattern transfer into silicon dioxide on the top of a silicon wafer are sketched in Figure 1.
During exposure of the photoresist, photoacid generator (PAG) molecules are selectively converted into acid (A). Simulation of this process requires as an input the description of incident light, as well as the absorption and refractive index of the photoresist. This allows the computation of the light intensity distribution inside the photoresist, the so-called bulk image (for the simulation of the image formation, see Imaging).
The first model for photoresist exposure simulation was developed by Dill et al. It requires two parameters for characterization of the photoresist absorption properties, the so called A and B Dill parameters. Dill A represents the absorption that changes with exposure, while Dill B represents the absorption resulting from components that remain constant during exposure.
The local rate of PAG decomposition corresponds to the rate of acid generation. It depends on the current PAG concentration, the photoresist sensitivity Dill C, and image intensity I(x; y; z).
The goal of the PEB simulation is to obtain the resulting inhibitor concentration M after the specified PEB time. This concentration is the basic input data for the subsequent development simulation (see below). The following reactions have to be considered:
- Neutralization of acid A and base B: A + B --> XAB.
- Non-catalyzed inhibitor M deprotection: M --> XM.
- Acid catalyzed inhibitor deprotection: A +M --> A + XM.
- Acid loss due to thermal decomposition of acid molecules: A --> XA
- Diffusion of acid.
- Diffusion of base.
- In- and out-diffusion of chemical species.
XA, XAB, and XM, respectively denote the inert reaction by-products of acid decomposition, acid-base neutralization, and inhibitor deprotection. A fairly generic description is the so-called general Meta model which describes the PEB by a set of coupled PDEs.
DevelopmentDuring development, the acidic polymers are dissolved in the aqueous base
development liquid. The locally varying inhibitor concentration (i.e., degree of polymer deprotection) after PEB, results in highly selective photoresist dissolution behaviour. The exact mechanisms which determine the dissolution characteristics of the photoresist is still the subject of on-going research. A description of the photoresist development rate in dependence on the local inhibitor concentration is for instance given by the Mack model. Based on the resulting local development rates, the topography evolution during photoresist development can be simulated. An exemplary photoresist profile simulated with Dr.LiTHO, that can be used as input for subsequent etching or doping simulation, is shown in Figure 2.