Two-Dimensional Analysis of Narrow Gate Effects in Micron and Submicron Mosfets

Variations of the device characteristics due to the geometry effects in narrow gate MOSFETs, such as threshold voltage shift and subthreshold characteristics, are important factors in designing next generation MOS-VLSI circuits. It is well known that numerical methods, using the exact 2 -D solutions of the transport equation and Poisson's equation for studying the geometry effect of small MOSFETs, are more accurate than simple charge-control analysis. The 2-D numerical model of Ji and Sah demonstrated important design features of the threshold voltage of narrow gate MOSFETs. However, studies of MOSFET characteristics using 2-D numerical analysis, which take into account the effects of all the device parameters, such as gate oxide thickness, backgate bias, and substrate doping, are lacking. Particularly, the analysis of the subthreshold characteristic for narrow gate MOSFETs was not reported before. The ideas in Ji-Sah's depletion approximation model, as well as their analysis method, have been extended to take into account the electrons and holes in the numerical solution of Poisson's equation. Using a super-minicomputer (VAX-11/750), a new 2-D program (NAROMOS-II) using the finite difference method has been developed in this thesis. Based on the 2-D results and device physics, a threshold voltage model and a subthreshold characteristics model for CAD of MOS-VLSI are proposed to describe the geometry effect of narrow gate MOSFETs. These models are based on the extraction of four model parameters: two for the threshold voltage model, and two for the subthreshold characteristics model. All of these model parameters can be verified numerically or experimentally. Results for the threshold voltage model compare favorably with numerical and reported experimental data. Dependences of the device performance on the device parameters are then investigated, using the above analysis techniques. Simple forms of the models of the threshold voltage shift and subthreshold characteristics are also developed, based on the 2-D results. It is shown that good agreement is obtained between the model, experimental data and 2-D numerical results. Proposed models of the threshold voltage shift and subthreshold characteristics for submicron MOSFETs also show good agreement between numerical results and modeled results.