Two-dimensional finite element charge-sheet model of a short-channel MOS transistor

A two-dimensional charge-sheet model for short-channel MOS transistors has been developed. The unique feature of the model is that the effect of channel inversion layer charge is included as a nonlinear integral boundary condition on the two-dimensional electrostatic field in the transistor. The average inversion layer charge density and source-drain current are obtained directly from the model rather than from the electron density or electron quasi-Fermi level. The model retains all of the physical detail of more complex two-dimensional models such as sensitivity to source-drain profile shape, channel profile, and oxide field shape. This allows the model to represent the changes in drain current associated with short-channel effects while still allowing simple comparison with long-channel models. For long-channel transistors, the results of this model are identical to Brews' long-channel charge-sheet model. The accuracy of this model is verified by modeling a sequence of transistors with channel lengths between 4.6 and 1.1 μm. In short-channel transistors, effects previously attributed to high field mobility are explained by simple two-dimensional electrostatics. The simulations produced using this model have been compared to experimental measurements on an array of n-channel MOSFETs; the model is in good agreement for transistors with channel lengths as short as 1.1 μm. In this verification process, the model represented accurately the onset of subthreshold current, channel-length-induced threshold voltage offset, and drain-field-induced output conductance changes. From studies of numerical accuracy, we conclude that the charge-sheet model can easily simulate drain current with an accuracy which exceeds that required for most applications. To obtain 5% accuracy for drain current, a 146 element mesh is sufficient. Refinement of the 146 element mesh to a 455 element mesh gives a current which is accurate to 0.16%. Average computer time for a high current solution is 2.5 min on a DEC-20. The numerical solutions were obtained using general-purpose software for solving elliptic partial differential equations. We have been able to solve problems with exact solutions to test the correctness and accuracy of our codes. We also can easily change the physics included in our model and the geometry of the transistor. The finite element method used allows refinement of oblique triangles which is important in achieving computational efficiency. The program is portable and has been run on a DEC-20, a VAX 11780, a Cyber 175 and a Univac 1108.