Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design
Reexamination Certificate
1998-11-09
2001-09-25
Smith, Matthew (Department: 2768)
Computer-aided design and analysis of circuits and semiconductor
Nanotechnology related integrated circuit design
C716S030000, C716S030000, C430S270100, C430S030000, C703S013000, C438S579000
Reexamination Certificate
active
06295637
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a simulator for the post-exposure bake process of chemically amplified resists used in the lithography of deep submicron device fabrication.
BACKGROUND OF THE INVENTION
Lithography in the deep submicron era employs photoresists of very different working principles from the previous generations. Because of the reduced power level of the light sources at the wavelength of Deep Ultra-Violet(DUV), the resists employing the principles of chemical amplifications are developed, and are called the Chemically Amplified Resists(CAR).
As the resist film is exposed to the DUV light, the latent image of photoacids conforming to the photomask patterns is produced in the resist. After exposure, the resist film is baked at elevated temperature for the protection polymers to react with the photoacids, and this process is called the Post-Exposure Bake(PEB).
In the PEB process, the protection polymers in the resist undergo a catalytic reaction with the photoacids, and are gradually annihilated for the case of positive CARs. At the end of the PEB process, the resist in the exposed area is, thus, deprotected, and has a much larger etch rate than in the unexposed area. Namely, as a result of the PEB process, the exposed portions of the photoresist become soluble and can be readily washed away by the developer.
At the elevated temperature of PEB, both the reaction mechanism of protection polymers and photoacids and the diffusion mechanism of photoacids occur. The PEB model which includes the coupling of the two mechanisms was published in the literature and was granted U.S. Pat. 5,717,612 later (See, for example, L. Capodieci, A. Krasnoperova, F. Cerrina, C. Lyons, C. Spence, and K. Early, Novel post-exposure bake simulator: first results,“J. Vac. Sci. Technol., vol. B13, no. 6, pp. 2963-2967, 1995.). However, in the prior art, the reaction and diffusion mechanisms were modeled with fixed reaction constants and diffusion coefficient in the course of the bake process.
Because the reaction constants satisfy Arrhenius type of relations, the reaction rates have strong dependence on temperature. The temperature-time history, in turn, depends on the configurations of the bake apparatus and can be quite different between configurations. Hence, the reaction constants have to be modeled as time-dependent parameters in course of the PEB process.
Furthermore, the diffusion coefficient is reported to be dependent on both temperature and protection-site concentration.
Consequently, to physically model the PEB process, it is necessary to take into account the temperature-dependence and the protection-site-dependence of the reaction constants and the diffusion coefficient, and the temperature-time history of the bake apparatus.
SUMMARY OF THE INVENTION
Therefore, it is an object of the present invention to provide a method of simulating the post-exposure bake process of chemically-amplified resists which fulfills the following requirements:
(a) both the reaction mechanism of the protection polymers and the photoacids, and the diffusion mechanism of the photoacids are included, and are modeled by a set of reaction-diffusion equations;
(b) the reaction constant of the protection sites and the photoacids satisfy the Arrhenius expression;
(c) the acid-loss mechanism of the photoacids is modeled by a reaction with the reaction constant obeying the Arrhenius expression;
(d) the diffusion coefficient is expressed as the product of a temperature-dependent part and a part dependent on the protection-site concentration, wherein the temperature-dependent part also satisfies the Arrhenius expression; and the protection-site-dependent part satisfies an exponential expression;
(e) the temperature-time history is further given by a pair of exponential expression representing the heating and cooling phases of the bake apparatus.
(f) the above stated reaction constants and diffusion coefficient remain time-dependent in the entire course of PEB simulation.
The object is achieved in the present invention by providing a method of solving the set of reaction-diffusion equations with above stated conditions. The method comprises the steps of:
(g) discretizing the rectangular simulation area into equally spaced grids;
(h) computing the time stepsize based on a prescribed accuracy requirements;
(i) computing the protection-site concentration for the next time step, using the protection-site and photoacid concentrations of the current and the next time steps;
(j) computing the photoacid concentration in one direction for the intermediate time step in the middle of the current and the next time step;
(k) computing the photoacid concentration in the direction normal to the previous one for the next time step;
(l) repeating steps (i) to (k) until convergent solution is attained for the next time step;
(m) incrementing time step and repeating steps (h) to (
1
) until the end of the bake process.
The advantages of the present invention will be given in the detailed description of the preferred embodiments.
REFERENCES:
patent: 5717612 (1998-02-01), Capodieci
patent: 5889676 (1999-03-01), Kubo et al.
patent: 5985498 (1999-11-01), Levinson et al.
patent: 5999720 (1999-12-01), Inui
patent: 6049660 (2000-04-01), Ahn et al.
Lee, et al, “Characteristics of 193 nm Chemically Amplified Resist during Post Exposure Bake and Post Exposure Delay”, International Microprocesses and Nanotechnology Conference, 1999, pp. 92-93.
Acer Semiconductor Manufacturing Inc.
Smith Matthew
Speight Jibreel
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