One of the promising platforms for creating Majorana bound states is a hybrid nanostructure consisting of a semiconducting nanowire covered by a superconductor.Weanalyze the previously disregarded role of electrostatic interaction in these devices. Our main result is that Coulomb interaction causes the chemical potential to respond to an applied magnetic field, while spin–orbit interaction and screening by the superconducting lead suppress this response. Consequently, the electrostatic environment influences two properties of Majorana devices: the shape of the topological phase boundary and the oscillations of the Majorana splitting energy.Wedemonstrate that both properties show a non-universal behavior, and depend on the details of the electrostatic environment. We show that when the wire only contains a single electron mode, the experimentally accessible inverse self-capacitance of this mode fully captures the interplay between electrostatics and Zeeman field. This offers a way to compare theoretical predictions with experiments.

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Effects of the electrostatic environment on the Majorana nanowire devices

One of the promising platforms for creating Majorana bound states is a hybrid nanostructure consisting of a semiconducting nanowire covered by a superconductor. We analyze the previously disregarded role of electrostatic interaction in these devices. Our main result is that Coulomb interaction causes the chemical potential to respond to an applied magnetic field, while spin-orbit interaction and screening by the superconducting lead suppress this response. Consequently, the electrostatic environment influences two properties of Majorana devices: the shape of the topological phase boundary and the oscillations of the Majorana splitting energy. We demonstrate that both properties show a non-universal behavior, and depend on the details of the electrostatic environment. We show that when the wire only contains a single electron mode, the experimentally accessible inverse self-capacitance of this mode fully captures the interplay between electrostatics and Zeeman field. This offers a way to compare theoretical predictions with experiments.

The temperature and diameter dependences of capacitance and electron mobility in gated silicon nanowires are analyzed and discussed. The self-consistent solution of the 2D Schrodinger and Poisson equations is used to extract the inversion charge and capacitance curves as a function of the gate bias. Electron–phonon and surface-roughness scattering mechanisms are accounted for using the Fermi golden rule and the low-field electron mobility is computed using the Kubo–Greenwood approach. An understanding of the role of each scattering mechanism for a given nanowire width and temperature range is proposed highlighting oscillations of both capacitance and mobility at low temperature. These properties associated with one-dimensional structures result from electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity in the density of states.

https://iopscience.iop.org/article/10.1088/0268-1242/26/2/025001/pdf

Temperature and size dependences of electrostatics and mobility in gate-all-around MOSFET devices

The intrinsic properties of vertical InAs nanowire (NW) capacitors are investigated. The band structure is simulated using a Schrodinger-Poisson solver, taking the conduction band nonparabolicity into account. This is combined with a distributed RC model to simulate the current-voltage characteristics. It is found that the influence from the nonparabolicity is substantial for devices with a small nanowire diameter, resulting in an increased carrier concentration, a shift in the threshold voltage, and a higher intrinsic capacitance. These NW capacitors may be a suitable alternative in high frequency applications approaching 100 GHz, while maintaining a quality factor above 100.

Intrinsic Performance of InAs Nanowire Capacitors

The paper proposes analytical model for Gate-All-Around Metal Oxide Semiconductor Field Effect Transistor (GAA-MOSFET) for germanium channel including quantum mechanical effects. It is achieved by solving coupled Schrodinger-Poisson’s equation using variational approach. The proposed model takes quantum confinement effects to obtain charge centroid and inversion charge model. By using these models the quantum version of inversion layer capacitance, inversion charge distribution function and Drain current expressions are modelled and the performance evaluation of the developed model is compared with Silicon channel GAA-MOSFET. Analytically modelled expressions are verified by comparing the model with simulation results.

Analytical Quantum Model for Germanium Channel Gate-All-Around (GAA) MOSFET

We simulate room temperature capacitance-voltage characteristics of silicon (Si) nanowire gate-all-around MOS structures with radius les 10 nm using a self-consistent Schrodinger- Poisson solver in cylindrical coordinates with full treatment of the transverse quantum confinement. In this paper, we compare our simulation results with the latest capacitance measurements on single Si nanowire pMOS and nMOS devices in the subfemtofarad range. We also propose to probe the density-of-states features of the Si channel from the capacitance-voltage characteristics at room temperature measurements using dC/dV dependence and illustrate the idea by employing the latest measurements, our quantum and Medici (Synopsys) simulations, as well as a simplified analytical model.

Self-Consistent SchrÖdinger–Poisson Simulations on Capacitance–Voltage Characteristics of Silicon Nanowire Gate-All-Around MOS Devices With Experimental Comparisons

V. Ligatchev

Papers

Self-Consistent SchrÖdinger–Poisson Simulations on Capacitance–Voltage Characteristics of Silicon Nanowire Gate-All-Around MOS Devices With Experimental Comparisons