An equivalent-circuit modelling on vertical and horizontal integrations for MOS flat-band voltage simulation

The fixed oxide charge will cause the MOS capacitor (MOS-C) flat-band voltage to shift. We can observe the potential distribution to determine the MOS-C flat-band voltage. However, the potential distribution can be obtained from the integration of the electric field distribution. The integration of the electric field distribution is classified into the vertical and horizontal integrations. In this paper, we use the equivalent-circuit model to demonstrate the flat-band voltage of the non-ideal MOS-C. The equivalent-circuit model of Poisson's equation includes two fixed charges Q′_f1 and Q′_f2 in the oxide layer region. Because the horizontal integration method is the superposition method, the equivalent-circuit model for the horizontal integration is divided into 3 types. Hence, the flat-band voltage for the horizontal integration is equal to the sum of the V _G1, V_G2, and V_G3 for the flat-band condition. By comparison, the simulation results of the horizontal integration method approximate to the vertical integration method.