Numerical optimization of a showerhead system for the distribution of gas flow uniformity

A vector showerhead gas delivery system is widely applied to integrated circuit manufacturing equipments, including process chamber, and the uniformity of gas distribution is one of the key factors to affect the process uniformity. The uniformity of gas distribution is taken as an objective to drive the optimization design of the vector showerhead system. In order to solve the problem that the conventional parameter optimization methods for the showerhead porous face plate need a pre-determined topology and narrow the parameter dimension that leads to a poor system resolution, an equivalent impedance model is proposed to describe the showerhead porous face plate in the optimization strategy. This model translates the optimization problem of the holes structure and layout into optimizing the flow impedance feature of the showerhead face plate, and then a high-resolution optimization model can be established for the distribution of the impedance. The nonuniformity of gas distribution of the optimal showerhead system is reduced from 0.36% to 0.03% (under the process condition of 1.0417×10^-4 kg/s of nitrogen and 266 Pa). A CFD numerical experiment is applied to test the performance of the optimal showerhead system under the varied conditions that the inlet mass flow is 6.2500×10^-5 1.6667×10^-4 kg/s and the pressure is 133-665 Pa. The result shows that the performance of the optimal showerhead system is better than the compared one at the entire range of the process condition, and the nonuniformity is under 0.35%. Finally, 3 topology adjustment cases for the layouts and structures of the holes on the showerhead face plate are shown, and the optimal geometry configuration instances are illustrated correspondingly.