Analytic Charge-Based Current Model of an Undoped Double-Gate MOSFET Considering the Lateral Electric Field

An analytical current model has been presented for an undoped symmetric double gate MOSFET based on the drift and diffusion of the inversion charges. First, using the one dimensional long channel (1D) Poisson’s equation perpendicular to the channel with mobile charges, a differential equation for charge of the channel is achieved which its solution gives the variation of the long channel charge concentration perpendicular to the channel. The 1D long channel potential is calculated by this long channel charge. The 2D short channel potential caused by the lateral electric field (which is important in short channel devices) is the solution of the 2D Laplace’s equation. Using this potential, the 2D variation of the short channel charge is extracted. Using the total calculated charge and the Gauss’s law at each point along the channel under the gate, the inversion charge in that point is calculated. Despite the existing models in which the inversion charge is calculated from the long channel charge perpendicular to the channel, in the proposed method it is shown that the 2D short channel charge (introduced by the lateral electric field) varies perpendicular to the channel too which affects calculating the inversion charge and must be taken into account in short channel devices. Finally, using the total inversion charge, the current is calculated. Good agreement between the results of the model and the results obtained by the Atlas software shows the validity of the proposed method.