Bart Sorée

Impact of field-induced quantum confinement in tunneling field-effect devices

Being the working principle of a tunnel field-effect transistor, band-to-band tunneling is given a rigorous quantum mechanical treatment to incorporate confinement effects, multiple electron and hole valleys, and interactions with phonons. The model reveals that the strong band bending near the gate dielectric, required to create short tunnel paths, results in quantization of the energy bands. Comparison with semiclassical models reveals a big shift in the onset of tunneling. The effective mass difference of the distinct valleys is found to reduce the subthreshold swing steepness.

Figure of merit for and identification of sub-60 mV/decade devices

A figure of merit I60 is proposed for sub-60u2009mV/decade devices as the highest current where the input characteristics exhibit a transition from sub- to super-60u2009mV/decade behavior. For sub-60u2009mV/decade devices to be competitive with metal-oxide-semiconductor field-effect devices, I60 has to be in the 1-10u2009μA/μm range. The best experimental tunnel field-effect transistors (TFETs) in the literature only have an I60 of 6×10−3u2009μA/μm but using theoretical simulations, we show that an I60 of up to 10u2009μA/μm should be attainable. It is proven that the Schottky barrier FET (SBFET) has a 60u2009mV/decade subthreshold swing limit while combining a SBFET and a TFET does improve performance.

Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields: A rigorous approach

A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electron-phonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the evaluation of the Zener tunneling current under any three-dimensional potential profile. For a one-dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field, and a semiconductor under a non-uniform field using the WKB (Wentzel–Kramers–Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p-n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model, but a direct numerical treatment is required for low bias conditions.A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electron-phonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the evaluation of the Zener tunneling current under any three-dimensional potential profile. For a one-dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field, and a semiconductor under a non-uniform field using the WKB (Wentzel–Kramers–Brillouin) approximation. The obtained results agr...

A model determining optimal doping concentration and material’s band gap of tunnel field-effect transistors

We develop a model for the tunnel field-effect transistor (TFET) based on the Wentzel-Kramer-Brillouin approximation which improves over existing semi-classical models employing generation rates. We hereby introduce the concept of a characteristic tunneling length in direct semiconductors. Based on the model, we show that a limited density of states results in an optimal doping concentration as well as an optimal material’s band gap to obtain the highest TFET on-current at a given supply voltage. The observed optimal-doping trend is confirmed by 2-dimensional quantum-mechanical simulations for silicon and germanium.

Tensile strained Ge tunnel field-effect transistors: k-p material modeling and numerical device simulation

Group IV based tunnel field-effect transistors generally show lower on-current than III-V based devices because of the weaker phonon-assisted tunneling transitions in the group IV indirect bandgap materials. Direct tunneling in Ge, however, can be enhanced by strain engineering. In this work, we use a 30-band ku2009·u2009p method to calculate the band structure of biaxial tensile strained Ge and then extract the bandgaps and effective masses at Γ and L symmetry points in k-space, from which the parameters for the direct and indirect band-to-band tunneling (BTBT) models are determined. While transitions from the heavy and light hole valence bands to the conduction band edge at the L point are always bridged by phonon scattering, we highlight a new finding that only the light-hole-like valence band is strongly coupling to the conduction band at the Γ point even in the presence of strain based on the 30-band ku2009·u2009p analysis. By utilizing a Technology Computer Aided Design simulator equipped with the calculated band-t...

Low-field mobility in ultrathin silicon nanowire junctionless transistors

We theoretically investigate the phonon, surface roughness and ionized impurity limited low-field mobility of ultrathin silicon n-type nanowire junctionless transistors in the long channel approximation with wire radii ranging from 2 to 5u2009nm, as function of gate voltage. We show that surface roughness scattering is negligible as long as the wire radius is not too small and ionized impurity scattering is the dominant scattering mechanism. We also show that there exists an optimal radius where the ionized impurity limited mobility exhibits a maximum.

Quantum mechanical solver for confined heterostructure tunnel field-effect transistors

Heterostructure tunnel field-effect transistors (HTFET) are promising candidates for low-power applications in future technology nodes, as they are predicted to offer high on-currents, combined with a sub-60 mV/dec subthreshold swing. However, the effects of important quantum mechanical phenomena like size confinement at the heterojunction are not well understood, due to the theoretical and computational difficulties in modeling realistic heterostructures. We therefore present a ballistic quantum transport formalism, combining a novel envelope function approach for semiconductor heterostructures with the multiband quantum transmitting boundary method, which we extend to 2D potentials. We demonstrate an implementation of a 2-band version of the formalism and apply it to study confinement in realistic heterostructure diodes and p-n-i-n HTFETs. For the diodes, both transmission probabilities and current densities are found to decrease with stronger confinement. For the p-n-i-n HTFETs, the improved gate control is found to counteract the deterioration due to confinement.

Theory of hole mobility in strained Ge and III-V p-channel inversion layers with high-κ insulators

We present a comprehensive investigation of the low-field hole mobility in strained Ge and III-V (GaAs, GaSb, InSb, and In1−xGaxAs) p-channel inversion layers with both SiO2 and high-κ insulators. The valence (sub)band structure of Ge and III-V channels, relaxed and under biaxial strain (tensile and compressive) is calculated using an efficient self-consistent method based on the six-band k⋅p perturbation theory. The hole mobility is then computed using the Kubo–Greenwood formalism accounting for nonpolar hole-phonon scattering (acoustic and optical), surface roughness scattering, polar phonon scattering (III-Vs only), alloy scattering (alloys only) and remote phonon scattering, accounting for multisubband dielectric screening. As expected, we find that Ge and III-V semiconductors exhibit a mobility significantly larger than the “universal” Si mobility. This is true for MOS systems with either SiO2 or high-κ insulators, although the latter ones are found to degrade the hole mobility compared to SiO2 due t...

Novel Device Concepts for Nanotechnology: The Nanowire Pinch-Off Fet and Graphene Tunnelfet

We explain the basic operation of a nanowire pinch-off FET and graphene nanoribbon tunnelFET. For the nanowire pinch-off FET we construct an analytical model to obtain the threshold voltage as a function of radius and doping density. We use the gradual channel approximation to calculate the current-voltage characteristics of this device and we show that the nanowire pinch-off FET has a subthreshold slope of 60 mV/dec and good ION and ION/IOFF ratios. For the graphene nanoribbon tunnelFET we show that an improved analytical model yields more realistic results for the transmission probability and hence the tunneling current. The first simulation results for the graphene nanoribbon tunnelFET show promising subthreshold slopes.

Quantum transport in a nanosize silicon-on-insulator metal-oxide-semiconductor field-effect transistor

An approach is developed for the determination of the current flowing through a nanosize silicon-on-insulator metal-oxide-semiconductor field-effect transistors. The quantum-mechanical features of the electron transport are extracted from the numerical solution of the quantum Liouville equation in the Wigner function representation. Accounting for electron scattering due to ionized impurities, acoustic phonons, and surface roughness at the Si/SiO2 interface, device characteristics are obtained as a function of a channel length. From the Wigner function distributions, the coexistence of the diffusive and the ballistic transport naturally emerges. It is shown that the scattering mechanisms tend to reduce the ballistic component of the transport. The ballistic component increases with decreasing the channel length.