Wim Magnus

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.

Analytical model for point and line tunneling in a tunnel field-effect transistor

The tunnel field-effect transistor (TFET) is a promising candidate for the succession of the MOSFET at nanometer dimensions. In general, the TFET current can be decomposed into two components referred to as point tunneling and line tunneling. In this paper we derive a compact analytical model for the current due to point tunneling complementing the previously derived analytical model for line tunneling. We show that the derived analytical expression for point tunneling provides a more consistent estimate of the TFET current than a commercial device simulator. Both the line and point tunneling current do not show a fixed subthreshold-slope. Three key parameters for design of a TFET are: bandgap, dielectric thickness and source doping level. A small bandgap is beneficial for a high TFET on-current and a low onset voltage. Point tunneling and line tunneling show a strong dependance on gate dielectric thickness and doping concentration respectively.

Analytical model for a tunnel field-effect transistor

The tunnel field-effect transistor (TFET) is a promising candidate for the succession of the MOSFET at nanometer dimensions. Due to the absence of a simple analytical model for the TFET, the working principle is generally not well understood. In this paper a new TFET structure is introduced and using Kanepsilas model, an analytical expression for the current through the TFET is derived. Furthermore, a compact expression for the TFET current is derived and conclusions concerning TFET design are drawn. The obtained analytical expressions are compared with results from a 2D device simulator and good agreement at low gate voltages is demonstrated.

Strategy for electromagnetic interconnect modeling

In order to design on-chip interconnect structures in a flexible way, a computer-aided design approach is advocated in three dimensions, describing high-frequency effects such as current redistribution due to the skin effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by a scalar electric potential and a magnetic vector potential. These potentials are not uniquely defined and in order to obtain a consistent discretization scheme, a gauge transformation field is introduced. The displacement current is taken into account to describe current redistribution and a small-signal analysis solution scheme is proposed based upon existing techniques for fields in semiconductors.

Zero‐dimensional states in submicron double‐barrier heterostructures laterally constricted by hydrogen plasma isolation

The lateral dimensions of resonant tunneling AlGaAs‐GaAs double barrier heterostructures have been restricted by hydrogen plasma exposure. Ohmic contacts to the submicron diodes have been made by solid phase epitaxial growth of Ge on GaAs. The current‐voltage characteristics show a fine structure splitting that is inversely proportional to the lateral size of the diode. The results are interpreted as resonant tunneling through zero‐dimensional states in the quantum box confined by the AlGaAs barriers and a harmonic lateral confining potential.

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

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

Optimization of Gate-on-Source-Only Tunnel FETs With Counter-Doped Pockets

We investigate a promising tunnel FET configuration having a gate on the source only, which is simultaneously exhibiting a steeper subthreshold slope and a higher ON-current than the lateral tunneling configuration with a gate on the channel. Our analysis is performed based on a recently developed 2-D quantum-mechanical simulator calculating band-to-band tunneling and including quantum confinement (QC). It is shown that the two disadvantages of the structure, namely, the sensitivity to gate alignment and the physical oxide thickness, are mitigated by placing a counter-doped parallel pocket underneath the gate-source overlap. The pocket also significantly reduces the field-induced QC. The findings are illustrated with all-Si and all-Ge gate-onsource-only tunnel field-effect transistor simulations.

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...

Full quantum mechanical model for the charge distribution and the leakage currents in ultrathin metal–insulator–semiconductor capacitors

A method is presented for the evaluation of the charge distribution and quantum-mechanical leakage currents in ultrathin metal–insulator–semiconductor gate stacks that may be composed of several layers of materials. The charge distribution due to the finite penetration depth inside the insulating material stack is also obtained. The method successfully applies the Breit–Wigner theory of nuclear decay to the confined carrier states in inversion layers and provides an alternative approach for the evaluation of the gate currents to that based on the Wentzel–Kramers–Brillouin approximation or Bardeen’s perturbative method. A comparison between experimental and simulated current–voltage characteristics has been carried out.

Physical modeling of strain-dependent hole mobility in Ge p-channel inversion layers

We present comprehensive calculations of the low-field hole mobility in Ge p-channel inversion layers with SiO2 insulator using a six-band k⋅p band-structure model. The cases of relaxed, biaxially, and uniaxially (both tensily and compressively) strained Ge are studied employing an efficient self-consistent method—making use of a nonuniform spatial mesh and of the Broyden second method—to solve the coupled envelope-wave function k⋅p and Poisson equations. The hole mobility is computed using the Kubo–Greenwood formalism accounting for nonpolar hole-phonon scattering and scattering with interfacial roughness. Different approximations to handle dielectric screening are also investigated. As our main result, we find a large enhancement (up to a factor of 10 with respect to Si) of the mobility in the case of uniaxial compressive stress similarly to the well-known case of Si. Comparison with experimental data shows overall qualitative agreement but with significant deviations due mainly to the unknown morpholog...