SUMMARYIn this paper, a simplified method for solving the Schro¨dinger-Poisson equation set in a quantum mechanical (QM) simulation is presented. This method simplifies the conventional Schro¨dinger and Poisson equations and then converts the simplification equation into an equivalent circuit form. During the QM simulation, the equivalent circuit model can replace the Schro¨dinger and Poisson's equations. In the equivalent circuit, the node voltages are taken as wave functions, and the electron concentration in the MOS inversion layer can be easily presented by solving the Schro¨dinger-Poisson equivalent circuit model. The simulation results are presented to demonstrate the quantum effects in the MOS inversion layer.

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SUMMARYIn this paper, we develop a three-dimensional (3-D) device simulator, which combines a simplified, decoupled Gummel-like method equivalent-circuit model (DM) with levelized incomplete LU (L-ILU) factorization. These complementary techniques are successfully combined to yield an efficient and robust method for semiconductor-device simulation. The memory requirements are reduced significantly compared to the conventionally used Newton-like method. Furthermore, the complex voltage-controlled current source (VCCS) is simplified as a nonlinear resistor. Hence, the programming and debugging for the nonlinear resistor model is much easier than that for the VCCS model. Further, we create a connectiontable to arrange the scattered non-zero fill-ins in sparse matrix to increase the efficiency of L-ILU factorization. Low memory requirements may pave the way for the widespread application in 3-D semiconductor-device simulation. We use the body-tied silicon-on-insulator MOSFET structure to illustrate the capability and the efficiency of the 3-D DM equivalent-circuit model with L-ILU factorization.

SUMMARYThe 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 equivalentcircuit 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 0 f1 and Q 0 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.

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