Modeling of Surrounding Gate MOSFETs With Bulk Trap States

We report a simple analytical model for surrounding gate MOSFETs including bulk traps. Based on the depletion approximation and the assumption that bulk traps are uniformly distributed inside the bandgap, we solved Poisson's equation in cylindrical coordinates and derived the general solution of potential distribution. Extraction of threshold voltage and subthreshold slope were conducted. The analytical solution yields good agreement with MEDICI simulations confirming the model. The model predicts a linear threshold voltage drop, depending on the trap density, as the diameter of the device decreases when the channel is fully depleted