Higher-Order Macroscopic Transport Models

Macroscopic transport models are normally derived from the semi-classical Boltzmann transport equation which is often used to describe carrier transport in contemporary MOS transistors down to gate-lengths as small as 10 nm. Quantum-mechanical effects perpendicular to the transport direction have to be considered in an accurate description. While the classic drift-diffusion model begins to loose its accuracy for gate-lengths smaller than about 500 nm, energy-transport models give an improvement only down to about 100 nm. Recent research indicates that the important window of gate-lengths from 100 down to about 25 nm can be covered by a six moments model or an even higher-order moments model. Various challenges on the road to such an approach exist which will be covered in this project. Of fundamental importance is the closure relation applied for the highest-order moment since this issue determines both the accuracy and the numerical stability of the resulting transport model. In addition to the fact that higher-order models give a better approximation of Boltzmann`s equation they also provide more information about the distribution function which can be used to model non-local hot-carrier effects more accurately. These effects include impact ionization, hot-carrier tunneling, and the overestimation of hot-carrier diffusion known from energy-transport models. The goal of this project is the formulation of a robust, fit- parameter-free higher-order model which can be used for predictive simulations down to a still-to-be-determined minimum feature size. To this end the transport parameters will be extracted from rigorous solutions of Boltzmann`s equation for a suitably chosen infinitely long device. This approach guarantees that the validity of the transport model can be clearly determined because the transport parameters cannot be adjusted to artificially extend the validity of a transport model to smaller devices.

Macroscopic transport models are normally derived from the semi-classical Boltzmann transport equation which is often used to describe carrier transport in contemporary MOS transistors down to gate-lengths as small as 10 nm. Quantum-mechanical effects perpendicular to the transport direction have to be considered in an accurate description. While the classic drift-diffusion model begins to loose its accuracy for gate-lengths smaller than about 500 nm, energy-transport models give an improvement only down to about 100 nm. Recent research indicates that the important window of gate-lengths from 100 down to about 25 nm can be covered by a six moments model or an even higher-order moments model. Various challenges on the road to such an approach exist which will be covered in this project. Of fundamental importance is the closure relation applied for the highest-order moment since this issue determines both the accuracy and the numerical stability of the resulting transport model. In addition to the fact that higher-order models give a better approximation of Boltzmann`s equation they also provide more information about the distribution function which can be used to model non-local hot-carrier effects more accurately. These effects include impact ionization, hot-carrier tunneling, and the overestimation of hot-carrier diffusion known from energy-transport models. The goal of this project is the formulation of a robust, fit- parameter-free higher-order model which can be used for predictive simulations down to a still-to-be-determined minimum feature size. To this end the transport parameters will be extracted from rigorous solutions of Boltzmann`s equation for a suitably chosen infinitely long device. This approach guarantees that the validity of the transport model can be clearly determined because the transport parameters cannot be adjusted to artificially extend the validity of a transport model to smaller devices.