Abstract
This paper presents a unified continuous and discrete model covering all device operating regions of double-gate MOSFETs for the first time. With a specific variable transformation method, the 1-D Poisson’s equation in the Cartesian coordinate for double-gate MOSFETs is transformed into the corresponding form in the cylindrical coordinate. Such a transformed cylindrical Poisson’s equation results in a simple algebraic equation, which correlates the (inversion-charge induced) surface potential to the field and allows the long-channel drain-current formula to be derived from the Pao–Sah integral. This model can be readily applied to predict the effects of both continuous and discrete doping variations. The short-channel-effect model is also developed by solving the 2-D Poisson’s equation using the eigenfunction-expansion method. The accuracy of both long-channel and short-channel models is confirmed by the numerical calculations and TCAD simulations.
Highlights
Double-gate MOSFET has been adopted in the past as the mainstream structure of logic devices to replace the conventional planar MOSFETs to achieve improved control of the short-channel effects [1]–[5]
By overcoming the above challenges for both continuous and discrete doping profiles, we extend our previous work and develop a unified double-gate MOSFET model capable of predicting the effect of both continuous and discrete dopant variations
Compared with the surface-field based GAA nanowire MOSFET model [31], the challenging task for double-gate MOSFET modeling is that the integration constant h in Eqs. (6) and (11) needs to be determined from the central potential while the potential distribution along the channel is still unknown
Summary
Double-gate MOSFET has been adopted in the past as the mainstream structure of logic devices to replace the conventional planar MOSFETs to achieve improved control of the short-channel effects [1]–[5]. It should be reminded that Eq (11) provides a highly accurate approximation of the electric-field related function β(τ ) by assuming a constant p(τ ), it is only used to estimate dβ/dτ when calculating the M integral. Compared with the surface-field based GAA nanowire MOSFET model [31], the challenging task for double-gate MOSFET modeling is that the integration constant h in Eqs. It is well known that the mobile-charge induced surface field in subthreshold region is much lower than when the surface potential begins to be “pinned” (i.e., (βs − 2) (βc − 2)) This subthreshold relation is no longer valid when the device enters the strong inversion region. The mobile-charge induced surface field increases rapidly with the gate voltage so that a different relation (βs − 2) (βc − 2) holds in the strong inversion region.
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