In a series of publications, we developed a compact model for nanotransistors in which quantum transport in a variety of industrial nano-FETs was described quantitatively. The compact nanotransistor model allows for the extraction of important device parameters as the effective height of the source-drain barrier, device heating, and the quality of the coupling between conduction channel and the contacts. Starting from a basic description of quantum transport in a multi-terminal device in Landauer–Büttiker formalism, we give a detailed derivation of all relevant formulas necessary to construct our compact nanotransistor model. Here we make extensive use of the the R-matrix method.

One major concern of channel engineering in nanotransistors is the coupling of the conduction channel to the source/drain contacts. In a number of previous publications, we have developed a semiempirical quantum model in quantitative agreement with three series of experimental transistors. On the basis of this model, an overlap parameter $0\le C\le 1$ can be defined as a criterion for the quality of the contact-to-channel coupling: A high level of C means good matching between the wave functions in the source/drain and in the conduction channel associated with a low contact-to-channel reflection. We show that a high level of C leads to a high saturation current in the ON-state and a large slope of the transfer characteristic in the OFF-state. Furthermore, relevant for future device miniaturization, we analyze the contribution of the tunneling current to the total drain current. It is seen for a device with a gate length of 26 nm that for all gate voltages, the share of the tunneling current becomes small for small drain voltages. With increasing drain voltage, the contribution of the tunneling current grows considerably showing Fowler–Nordheim oscillations. In the ON-state, the classically allowed current remains dominant for large drain voltages. In the OFF-state, the tunneling current becomes dominant.

We extend our previous semi-empirical model for quantum transport in a conventional nano-MOSFET to FDSOI transistors. In ultra-thin-body and -BOX (UTBB) FDSOI transistors, the electron channel can be treated as an electron waveguide. In the abrupt transition approximation, it is possible to derive an analytical approximation for the potential seen by the charge carriers. With these approximations we calculate the threshold voltage and the transfer characteristics, finding remarkably good agreement with experiments in the OFF-state given the relative simplicity of our model. In the ON-state, our theory fails because Coulomb interaction between the free charge carriers and the device heating is neglected in our approach.

We study field effect nanotransistor devices in the Si/SiO₂ material system which are based on lateral resonant tunneling between two parallel conduction channels. After introducing a simple piecewise linear potential model, we calculate the quantum transport properties in the R-matrix approach. In the transfer characteristics, we find a narrow resonant tunneling peak around zero control voltage. Such a narrow resonant tunneling peak allows one to switch the drain current with small control voltages, thus opening the way to low-energy applications. In contrast to similar double electron layer tunneling transistors that have been studied previously in III-V material systems with much larger channel lengths, the resonant tunneling peak in the drain current is found to persist at room temperature. We employ the R-matrix method in an effective approximation for planar systems and compare the analytical results with full numerical calculations. This provides a basic understanding of the inner processes pertaining to lateral tunneling transport.

In a number of previous publications, scattering theory for N-pole semiconductor quantum devices was developed. In the framework of the Landauer–Büttiker formalism, an S-matrix was constructed with the aid of an R-matrix providing a mapping of the in-going waves onto the out-going waves. These waves include propagating waves and evanescent waves, the latter of which decay exponentially in the leads which are connected to the active region of the N-pole device. In order to formulate the current conservation in the N-pole device, it is necessary to define the current S-matrix schematically as $\tilde{S}=k^{1/2}S{k}^{-1/2}$, where k contains the information about the k-vectors of the mentioned in- and out-going waves. In this paper, we show how the complete current S-matrix is calculated including the coupling between the propagating and evanescent components and coupling to the bound states in the active device region. One then finds a sub-matrix of $\tilde{S}$ which is unitary and which is restricted to the space of the propagating components. We demonstrate that current conservation is associated with the unitarity just of this sub-matrix.