A quasi-3D analytical threshold voltage model of small geometry MOSFETs

Numerical 2D and 3D models of MOSFETs, which have been developed so far, are accurate but take enormous computer time and memory for their implementation. It restricts their use only to the design and development of submicron devices. A computationally faster, analytical quasi-3D model for the threshold voltage of small geometry MOSFETs, which should be useful for VLSI circuit simulation, has been presented in this paper. The model is based on a rigorous 2D analytical model. An equivalence between the analytical 2D model and the Yau's charge sharing model has been established, and the same has been utilized to incorporate the narrow width effect. The important features of the present work are: (1) realistic channel implantation profiles for nMOSFETs have been used in developing the 2D model; (ii) the effect of birds' beaks on the lateral confinement of charges in the channels of oxide isolated MOSFETs has been considered in a simple manner; and (iii) the fringing of electric field near the edges of channels (widths) has also been considered empirically. The simulated values of the threshold voltages exhibiting 2D and 3D effects compare well with those obtained using a numerical 3D simulator (MICROMOS) and with available experimental data. The model is also capable of predicting the inverse narrow width effect observed in MOSFETs with fully recessed field oxide.