Prediction and Design of Capacitance Using the Finite Element Method

Abstract

Recently, the display devices predominantly manufactured in display industry are Liquid Crystal Displays (LCDs) and Organic Light Emitting Diodes (OLEDs). Both devices are controlled by the voltage or current through the Thin Film Transistor (TFT). Therefore, the design of the semiconductor or display depends on the capacitance formed between the electrodes and the insulator. In actual industrial manufacture lines, Critical Dimension (CD), which is a width of the pattern, overlay scattering of the electrode pattern and Optical Proximity Correction (OPC) influence in the Ultra Violet (UV) exposure process exist. Therefore these factors should be considered from the design stage. Also, according to the previous study, the capacitance is maximized like the fractal capacitance, or the characteristics of the device are changed according to the ratio between the capacitances in a plurality of transistors in a circuit. In this study, the electrode design was randomly generated and the capacitance was modeled through FEM-based simulation. We used Gmsh to divide the system into finite number of elements and calculate the electric potential by modeling the Laplace equation in weak form for GetDP, the FEM solver. In this thesis, we analyzed the effect of photolithography distribution on capacitance and suggest the optimal design of electrodes in a simple structure of metal-insulator-metal (MIM). The electrode of larger perimeter length has higher capacitance when the electrode area and the insulator thickness are consistent for different design of electrodes, which is the same principle as using the fringing field in the fractal capacitance. The electrode suggested in this research provides 62.4% higher capacitance compared to the simple polygon design.Maste