AVS 49th International Symposium
    Manufacturing Science and Technology Monday Sessions
       Session MS-MoA

Paper MS-MoA4
Mathematical Approaches to Optimal Control of Transient Enhanced Diffusion

Monday, November 4, 2002, 3:00 pm, Room C-109

Session: Control Issues in Electronics Manufacturing
Presenter: M.Y.L. Jung, University of Illinois
Authors: M.Y.L. Jung, University of Illinois
R. Gunawan, University of Illinois
R.D. Braatz, University of Illinois
E.G. Seebauer, University of Illinois
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Excessive transient enhanced diffusion (TED) of boron in silicon during rapid thermal annealing has been a major inhibitor to forming ultrashallow junctions for CMOS device applications. TED typically gives rise to a trade-off between junction depth X@sub j@ and sheet resistance @rho@ as a function of process variables. For example, increasing the ramp rate @beta@ or decreasing the maximum spike temperature T@sub M@ decreases X@sub j@ but increases @rho@. This tradeoff suggests there are optimum values of @beta@ and T@sub M@ to produce the best X@sub j@ and @rho@. The optimization of the temperature program is posed as a minimization problem with the objective function @PHI@, which is a function of the junction depth and the sheet resistance. The objective is selected such that: @PHI@=X@sub j@(T(t)) + w@rho@(T(t)) where w is a weighting factor. The constrained minimization problem is solved using sequential quadratic programming. Although current technology employs linear temperature trajectories, different parameterizations of the temperature program are used in the optimization to elucidate the true optimal trajectory. The rate of cooling is also included in the parameterization. All these calculations are performed using the process simulator FLOOPS. We describe how the kinetic parameters in this simulator were obtained using firmly grounded procedures for estimating rate parameters using the Maximum Likelihood Method together with multivariate statistics to quantify accuracy. We also describe a rigorous parameter sensitivity analysis by the finite difference method to investigate TED model behavior. These approaches lead to vast improvements in the ability of simulations to match experiment.