Self-consistent Quantum Research Articles

Analysis of models for quantum transport of electrons in graphene layers

We present and analyze two mathematical models for the self-consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can move in all the plane ℝ2, the model takes the form of a system of massless Dirac equations coupled together by a self-consistent potential, which is the trace in the plane of the graphene of the 3D Poisson potential associated to surface densities. In this case, we prove local in time existence and uniqueness of a solution in Hs(ℝ2), for [Formula: see text] which includes in particular the energy space H1/2(ℝ2). The main tools that enable to reach [Formula: see text] are the dispersive Strichartz estimates that we generalized here for mixed quantum states. Second, we consider a situation where the particles are constrained in a regular bounded domain Ω. In order to take into account Dirichlet boundary conditions which are not compatible with the Dirac Hamiltonian H0, we propose a different model built on a modified Hamiltonian displaying the same energy band diagram as H0 near the Dirac points. The well-posedness of the system in this case is proved in [Formula: see text], the domain of the fractional order Dirichlet Laplacian operator, for [Formula: see text].

Boosting the voltage gain of graphene FETs through a differential amplifier scheme with positive feedback

We study a possible circuit solution to overcome the problem of low voltage gain of short-channel graphene FETs. The circuit consists of a fully differential amplifier with a load made of a cross-coupled transistor pair. Starting from the device characteristics obtained from self-consistent ballistic quantum transport simulations, we explore the circuit parameter space and evaluate the amplifier performance in terms of dc voltage gain and voltage gain bandwidth. We show that the dc gain can be effectively improved by the negative differential resistance provided by the cross-coupled pair. Contact resistance is the main obstacle to achieving gain bandwidth products in the terahertz range. Limitations of the proposed amplifier are identified with its poor linearity and relatively large Miller capacitance.

High-temperature interfacial electroluminescence in type-II broken-gap heterostructures based on InSb quantum dashes in n-InAs matrix

Room-temperature electroluminescence is observed for the first time in type-II heterostructures based on InSb quantum dashes embedded in a narrow-gap n-InAs matrix. The heterostructures exhibit positive luminescence at wavelengths in the range 3–4 μm. This is due to the interfacial radiative transitions of electrons from self-consistent quantum wells on the side of InAs matrix layers across the broken-gap type-II InSb/InAs heterointerface to quantum-well hole levels in the InSb quantum dashes, situated in the energy gap of the matrix near the InAs conduction-band bottom.

The Nexus graviton: A quantum of Dark Energy and Dark Matter

In a recently published paper called Nexus: A quantum theory of space-time, gravity and the quantum vacuum by the above author, a plausible self-consistent quantum theory of space-time, gravity and the quantum vacuum is provided. In this current paper the author focuses primarily on the graviton as described in Nexus as a solution to the enigmatic phenomena of Dark Energy and Dark Matter as well as includes corrections to the first paper.

Efficient self-consistent quantum transport simulator for quantum devices

We present a self-consistent one-dimensional (1D) quantum transport simulator based on the Contact Block Reduction (CBR) method, aiming for very fast and robust transport simulation of 1D quantum devices. Applying the general CBR approach to 1D open systems results in a set of very simple equations that are derived and given in detail for the first time. The charge self-consistency of the coupled CBR-Poisson equations is achieved by using the predictor-corrector iteration scheme with the optional Anderson acceleration. In addition, we introduce a new way to convert an equilibrium electrostatic barrier potential calculated from an external simulator to an effective doping profile, which is then used by the CBR-Poisson code for transport simulation of the barrier under non-zero biases. The code has been applied to simulate the quantum transport in a double barrier structure and across a tunnel barrier in a silicon double quantum dot. Extremely fast self-consistent 1D simulations of the differential conductance across a tunnel barrier in the quantum dot show better qualitative agreement with experiment than non-self-consistent simulations.

Nonstationary self-consistent model for an ensemble in the self-field

The behavior of a nonstationary system of charged particles interacting with the self-field is studied using integrals of motion for nonstationary systems. Numerical solutions are obtained for the sets of equations describing the characteristics of a system of particles. A nonstationary self-consistent quantum system is also analyzed. The proposed model can be useful for investigating the acceleration of charged particles by the self-field.

Exploiting Negative Differential Resistance in Monolayer Graphene FETs for High Voltage Gains

Through self-consistent quantum transport simulations, we evaluate the RF performance of monolayer graphene FETs in the bias region of negative output differential resistance. We show that, compared to the region of quasi-saturation, a voltage gain larger than 10 can be obtained, at the cost of a decrease in the maximum oscillation frequency of about a factor of 1.5--3 and the need for a careful circuit stabilization.

A Process Model of Quantum Mechanics

A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has the potential to address several paradoxes in quantum mechanics while remaining computationally powerful.

On Monolayer ${\rm MoS}_{2}$ Field-Effect Transistors at the Scaling Limit

The ultimate scaling limit of double-gate molybdenum disulfide (MoS2) field-effect transistors (FETs) with a monolayer thin body is examined and compared with ultrathin-body Si FETs by self-consistent quantum transport simulation in the presence of phonon scattering. Modeling of phonon scattering, quantum mechanical effects, and self-consistent electrostatics allows us to accurately assess the performance potential of monolayer MoS2 FETs. The results revealed that monolayer MoS2 FETs show 52% smaller drain-induced barrier lowering (DIBL) and 13% smaller subthreshold swing (SS) than 3-nm-thick-body Si FETs at a channel length of 10 nm with the same gating. With a requirement of DIBL , the scaling limit of monolayer MoS2 FETs is assessed to be 8 nm, comparing with 10 nm of the ultrathin-body Si counterparts due to the monolayer thin body and higher effective mass, which reduces direct source-to-drain tunneling. By comparing with the international technology roadmap for semiconductor (ITRS) target for high performance logic devices of 2023; double-gate monolayer MoS2 FETs can fulfill the ITRS requirements.

Theoretical comparison of Si, Ge, and GaAs ultrathin p-type double-gate metal oxide semiconductor transistors

Based on a self-consistent multi-band quantum transport code including hole-phonon scattering, we compare current characteristics of Si, Ge, and GaAs p-type double-gate transistors. Electronic properties are analyzed as a function of (i) transport orientation, (ii) channel material, and (iii) gate length. We first show that ⟨100⟩-oriented devices offer better characteristics than their ⟨110⟩-counterparts independently of the material choice. Our results also point out that the weaker impact of scattering in Ge produces better electrical performances in long devices, while the moderate tunneling effect makes Si more advantageous in ultimately scaled transistors. Moreover, GaAs-based devices are less advantageous for shorter lengths and do not offer a high enough ON current for longer gate lengths. According to our simulations, the performance switching between Si and Ge occurs for a gate length of 12 nm. The conclusions of the study invite then to consider ⟨100⟩-oriented double-gate devices with Si for gate length shorter than 12 nm and Ge otherwise.

Self-consistent quantum process tomography

Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors in tomography can not be fully corrected through oversampling or by performing a larger set of experiments. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner. The essential ingredient is to define a likelihood function that assumes nothing about the gates used for preparation and measurement. In order to make the resulting optimization tractable we linearize about the target, a reasonable approximation when benchmarking a quantum computer as opposed to probing a black-box function.

Electromagnetic cascade in high-energy electron, positron, and photon interactions with intense laser pulses

The interaction of high energy electrons, positrons, and photons with intense laser pulses is studied in head-on collision geometry. It is shown that electrons and/or positrons undergo a cascade-type process involving multiple emissions of photons. These photons can consequently convert into electron-positron pairs. As a result charged particles quickly lose their energy developing an exponentially decaying energy distribution, which suppresses the emission of high energy photons, thus reducing the number of electron-positron pairs being generated. Therefore, this type of interaction suppresses the development of the electromagnetic avalanche-type discharge, i.e., the exponential growth of the number of electrons, positrons, and photons does not occur in the course of interaction. The suppression will occur when 3D effects can be neglected in the transverse particle orbits, i.e., for sufficiently broad laser pulses with intensities that are not too extreme. The final distributions of electrons, positrons, and photons are calculated for the case of a high energy e-beam interacting with a counter-streaming, short intense laser pulse. The energy loss of the e-beam, which requires a self-consistent quantum description, plays an important role in this process, as well as provides a clear experimental observable for the transition from the classical to quantum regime of interaction.

Molecular modeling of the piezoelectric effect in the ferroelectric polymer poly(vinylidene fluoride) (PVDF)

In this work, computational molecular modeling and exploration was applied to study the nature of the negative piezoelectric effect in the ferroelectric polymer polyvinylidene fluoride (PVDF), and the results confirmed by actual nanoscale measurements. First principle calculations were employed, using various quantum-chemical methods (QM), including semi-empirical (PM3) and various density functional theory (DFT) approaches, and in addition combined with molecular mechanics (MM) methods in complex joint approaches (QM/MM). Both PVDF molecular chains and a unit cell of crystalline β-phase PVDF were modeled. This computational molecular exploration clearly shows that the nature of the so-called negative piezo-electric effect in the ferroelectric PVDF polymer has a self-consistent quantum nature, and is related to the redistribution of the electron molecular orbitals (wave functions), leading to the shifting of atomic nuclei and reorganization of all total charges to the new, energetically optimal positions, under an applied electrical field. Molecular modeling and first principles calculations show that the piezoelectric coefficient d 33 has a negative sign, and its average values lies in the range of d 33 ~ -16.6 to -19.2 pC/N (or pm/V) (for dielectric permittivity ε = 5) and in the range of d 33 ~ -33.5 to -38.5 pC/N (or pm/V) (for ε = 10), corresponding to known data, and allowing us to explain the reasons for the negative sign of the piezo-response. We found that when a field is applied perpendicular to the PVDF chain length, as polarization increases the chain also stretches, increasing its length and reducing its height. For computed value of ε ~ 5 we obtained a value of d31 ~ +15.5 pC/N with a positive sign. This computational study is corroborated by measured nanoscale data obtained by atomic force and piezo-response force microscopy (AFM/PFM). This study could be useful as a basis for further insights into other organic and molecular ferroelectrics.

Simulations of Shocked Methane Including Self-consistent Semiclassical Quantum Nuclear Effects

ABSTRACTA methodology is described for atomistic simulations of shock-compressed materials that incorporates quantum nuclear effects on the fly. We introduce a modification of the multi-scale shock technique (MSST) that couples to a quantum thermal bath described by a colored noise Langevin thermostat. The new approach, which we call QB-MSST, is of comparable computational cost to MSST and self-consistently incorporates quantum heat capacities and Bose-Einstein harmonic vibrational distributions. As a first test, we study shock-compressed methane using the ReaxFF potential. The Hugoniot curves predicted from the new approach are found comparable with existing experimental data. We find that the self-consistent nature of the method results in the onset of chemistry at 40% lower pressure on the shock Hugoniot than observed with classical molecular dynamics. The temperature change associated with quantum heat capacity is determined to be the primary factor in this shift.

Intrinsic region length scaling of heavily doped carbon nanotube p–i–n junctions

We investigated the dependence of the transport properties of heavily doped intratube single-walled carbon nanotube (SWCNT) p-i-n junctions on the length of the intrinsic region by using empirical self-consistent quantum transport simulations. When the length of the intrinsic region is scaled from a few angstroms to over 10 nanometers, the SWCNT p-i-n junction evolves from a tunneling diode with a large negative rectification and large negative differential resistance to one with a large positive rectification (like a conventional positive rectifying diode). The critical length of the intrinsic length is about 8.0 nm. Therefore, one can obtain nanoscale diodes of different performance types by changing the intrinsic region length.

Simulations of Shocked Methane Including Self-Consistent Semiclassical Quantum Nuclear Effects

A methodology is described for atomistic simulations of shock-compressed materials that incorporates quantum nuclear effects on the fly. We introduce a modification of the multiscale shock technique (MSST) that couples to a quantum thermal bath described by a colored noise Langevin thermostat. The new approach, which we call QB-MSST, is of comparable computational cost to MSST and self-consistently incorporates quantum heat capacities and Bose-Einstein harmonic vibrational distributions. As a first test, we study shock-compressed methane using the ReaxFF potential. The Hugoniot curves predicted from the new approach are found comparable with existing experimental data. We find that the self-consistent nature of the method results in the onset of chemistry at 40% lower pressure on the shock Hugoniot than observed with classical molecular dynamics. The temperature shift associated with quantum heat capacity is determined to be the primary factor in this shift.

Interlayer transport in disordered semiconductor electron bilayers

We study the effects of disorder on the interlayer transport properties of disordered semiconductor bilayers by performing self-consistent quantum transport calculations. We find that the addition of material disorder to the system affects the interlayer interactions leading to significant deviations in the interlayer transfer characteristics. In particular, we find that disorder decreases and broadens the tunneling peak, effectively reducing the interacting system to a non-interacting system. Our results suggest that the experimental observation of exchange-enhanced interlayer transport in semiconductor bilayers requires materials with mean free paths larger than the spatial extent of the system.

Modeling of a vertical tunneling graphene heterojunction field-effect transistor

Vertical tunneling field-effect-transistor (FET) based on graphene heterojunctions with layers of hBN is simulated by self-consistent quantum transport simulations. It is found that the asymmetric p-type and n-type conduction is due to work function difference between the graphene contact and the tunneling channel material. Modulation of the bottom-graphene-contact plays an important role in determining the switching characteristic of the device. Due to the electrostatic short-channel-effects stemming from the vertical-FET structure, the output I-V characteristics do not saturate. The scaling behaviors the vertical-FET as a function of the gate insulator thickness and the thickness of the tunneling channel material are examined.

Zener tunneling: Congruence between semi-classical and quantum ballistic formalisms

We compare the results of self-consistent ballistic quantum transport simulation of Zener tunneling in InAs, a direct bandgap semiconductor, with corresponding semi-classical solutions using the well-known Kane’s model and the Wentzel-Kramers-Brillouin (WKB) approximation. We find a qualitative difference between solutions obtained from Kane’s formulation and rigorous quantum-mechanical formalism. However, the WKB solution, with evaluation of action integral along the tunneling paths determined from the nearest neighbor sp3s* Hamiltonian, is shown to provide qualitative agreement. We discuss the issues involved in fitting semi-classical solutions with their quantum counterpart and also present a brief comparison of our results with experimental data.

Evidence for the Fourfold-Valley Confinement Electron Piezo-Effective-Mass Coefficient in Inversion Layers of $\langle \hbox{110}\rangle$ Uniaxial-Tensile-Strained (001) nMOSFETs

We have recently experimentally extracted the piezo-effective-mass coefficients of 2-D electrons via the gate tunneling current of (001) n-channel metal-oxide-semiconductor field-effect transistors under 〈110〉 uniaxial compressive stress. The results pointed to the existence of a piezo-effective-mass coefficient around the fourfold conduction-band valley in the out-of-plane (quantum confinement) direction. To strengthen this further, here, we provide extra evidence. First, explicit guidelines are drawn to distinguish all the piezo-effective-mass coefficients. Then, a self-consistent strain quantum simulation is executed to fit literature data of both the mobility enhancement and gate current suppression in the uniaxial tensile stress situation. It is found that neglecting the fourfold-valley out-of-plane piezo-effective-mass coefficient, as in existing band structure calculations, only leads to a poor fitting.