Modeling nanoscale quasi-ballistic MOS transistors: a circuit design perspective

The scaling of device technologies poses new challenges, not only in circuit design, but also in device modeling, especially because of the short-channel effects and the emergence of novel phenomena like ballistic transport. Nonetheless, it enables the design of ultra low-power analog and Radio Frequency (RF) circuits by allowing to push the operating points into moderate and eventually weak inversion regions, which are increasingly becoming the preferred regions of operation for such applications. Even though modern compact models have evolved to adequately model the short-channel effects in all regions of operation, there is a lack of simpler models that (a) reliably predict the physics of downscaled devices while (b) remaining continuous through moderate inversion and (c) aid the designer’s intuition through simple design methodologies. In this work, we extend the EKV charge based model to include the velocity saturation effect for weak inversion operation. Using the simple analytical model hence developed, we propose a design methodology for low-power analog circuit design. Then, we focus our attention on ballistic transport in MOSFETs, that is expected to dominate in the deeply scaled devices. Again, despite the extensive body of work available in the literature, most models remain deeply rooted in physics, consisting of fairly complicated equations, that are of little use for an intuitive understanding and design. In addition, the quasi-ballistic devices, which lie on the continuum between the ballistic and the diffusive devices, pose their own modeling challenges: a model for the quasi-ballistic devices would have to remain continuous between the ballistic and diffusive regimes. Most of the published works, based on the carrier flux transport over the source-channel potential barrier approach, seem to ignore the electrostatics in the rest of the channel. The shape of the electrostatic potential in the channel is approximated through polynomial functions, which is adequate for the very short-channel devices but not scalable to long channel quasi-ballistic devices. In this work, we study the role of the gate and the electrostatics in a ballistic channel by drawing on the insights gained from Monte-Carlo simulations on quasi-ballistic and ballistic doublegate MOSFETs. We propose a simple semi-empirical model of the channel charge, using which we develop an analytical model for the channel potential, both of which could be used as precursors to a scalable compact model that would encompass the ballistic, quasi-ballistic and drift-diffusion regimes.