Tunneling Theory Research Articles

Tunnelling amplitudes through localised external potentials from Feynman diagram summation

Currently there is no general theory of quantum tunnelling of a particle through a potential barrier which is compatible with QFT. We present a complete calculation of tunnelling amplitudes for a scalar field for some simple potentials using quantum field-theoretic methods. Using the perturbative S-matrix formalism, starting with the Klein–Gordon Lagrangian, we show that an infinite summation of Feynman diagrams can recover tunnelling amplitudes consistent with relativistic quantum mechanics. While this work does not include many-particle effects arising from a fully quantised QFT, it is necessary to investigate QFT corrections to tunnelling amplitudes.

Theory of Resonant Tunneling of Charge Carriers within the Framework of the Green’s Function Method and the Biorthogonal Formalism

Theory of Resonant Tunneling of Charge Carriers within the Framework of the Green’s Function Method and the Biorthogonal Formalism

PULSE TUNNEL EFFECT: FUNDAMENTALS AND PROSPECTS FOR APPLICATION

In the first part of the article discusses fundamental aspects of the pulsed tunneling effect as a unified mechanism for describing tunneling phenomena in various fields of physics are considered. The main provisions of the pulsed tunneling theory developed by Keldysh are analyzed. The features of the effect’s implementation in optics, nanoelectronics, perovskites and other materials are examined. The role of coherent radiation is shown. The prospects of regulating material properties and observing non-standard phenomena due to PTE are discussed. In the second part of the article discusses examines the subtleties of the pulsed tunneling effect as a fundamental mechanism of interaction of radiation with matter. The advantages of the ITE compared to the standard quantum tunneling effect are analyzed. Particular attention is paid to the role of radiation coherence and unidirectional polarization during pulsed exposure. The features of the manifestation of effects in optics, nanotechnology and biology are considered. The prospects for using ITEs to create new functional materials and effective technologies are shown.

The effect of Li(Ni0.9Co0.05Mn0.05)O2 on improving electrical properties of semi-conductive LDPE/EVA/CB composites

The conductive mechanism of the semiconductor shielding layer between the conductive core and the insulation layer of high-voltage direct current (HVDC) cables includes tunneling and over-diffusion theories; however, the ethylene vinyl acetate copolymer (EVA) matrix in the semi-conductive composite material expands when heated, leading to a break in the carbon black (CB) conductive networks, which results in an increase in resistivity and the formation of the positive temperature coefficient (PTC) effect. The addition of materials with negative temperature coefficient (NTC) properties can weaken the PTC effect while absorbing some free electrons to enhance the suppression of space charge injection into the insulating layer. Li(Ni0.9Co0.05Mn0.05)O2 (NCM) was prepared by sol–gel method, which was melted and mixed with low-density polyethylene (LDPE), EVA, and CB, and pressed and molded to obtain modified semi-conductive composites. The semiconducting composites were measured by resistivity, thermal stimulation depolarizing current method (TSDC), and pulsed electroacoustic method (PEA). The results showed that the composites had the best performance when the NCM doping was 2 wt%.

Dynamical tunneling across the separatrix.

The strong enhancement of tunneling couplings typically observed in tunneling splittings in the quantum map is investigated. We show that the transition from instanton to noninstanton tunneling, which is known to occur in tunneling splittings in the space of the inverse Planck constant, takes place in a parameter space as well. By applying the absorbing perturbation technique, we find that the enhancement invoked as a result of local avoided crossings and that originating from globally spread interactions over many states should be distinguished and that the latter is responsible for the strong and persistent enhancement. We also provide evidence showing that the coupling across the separatrix in phase space is crucial in explaining the behavior of tunneling splittings by performing the wave-function-based observation. In the light of these findings, we examine the validity of the resonance-assisted tunneling theory.

Application of smart sportswear based on multi-walled carbon nanotubes for safety in college physical education classes

As physical education advances, college physical education classrooms are becoming increasingly diverse, but this development also brings security concerns. Intelligent sportswear, serving as a real-time monitoring device for human data, can enhance safety for both teachers and students. This study focuses on developing a conductive filler for flexible piezoresistive sensors using modified multi-walled carbon nanotubes (MWCNTs). Firstly, the tunneling theory and permeability effects are employed to establish a sensing mechanism model and analyze the conductivity and piezoresistive effects. Subsequently, silane coupling agents (KH550) and sodium dodecyl benzene sulfonate (SDBS) are chosen to enhance the conductive filler’s performance. Finally, smart gloves, smart insoles, and smart vests are designed for the detection of hand pressure, foot pressure, and respiratory rate. This aims to enhance safety measures in physical education classrooms. Furthermore, their performance is validated through simulation experiments. Results indicate that MWCNTs were modified with KH550 and SDBS, showing improved conductivity with higher filler concentration. KH550-SDBS-MWNT/PU material demonstrates 108.3% increased elongation at break, 9% reduction in nonlinear error, enhanced linearity, and 2.972 sensitivity increase. Displacement deviation analysis reveals load change trends based on filler concentration. Empirical analysis of smart clothing, like smart insoles, aligns sensor data with theoretical principles, highlighting the potential for flexible sensor performance enhancement. In conclusion, the modified MWCNs have demonstrated potential for enhancing the performance of flexible sensors.

Ergodicity of complex dynamics and quantum tunneling in nonintegrable systems.

The instanton approximation is a widely used approach to construct the semiclassical theory of tunneling. The instanton path bridges the regions that are not connected by classical dynamics, but the connection can be achieved only if the two regions have the same energy. This is a major obstacle when applying the instanton method to nonintegrable systems. Here we show that the ergodicity of complex orbits in the Julia set ensures the connection between arbitrary regions and thus provides an alternative to the instanton path in the nonintegrable system. This fact is verified using the ultra-near integrable system in which none of the visible structures inherent in nonintegrability exist in the classical phase space, yet nonmonotonic tunneling tails emerge in the corresponding wave functions. The simplicity of the complex phase space allows us to explore the origin of the nontrivial tunneling tails in terms of semiclassical analysis in the time domain. In particular, it is shown that not only the imaginary part but also the real part of the classical action plays a role in creating the characteristic step structure of the tunneling tail that appears as a result of the quantum resonance.

Interaction of Cloud Dynamics and Microphysics During the Rapid Intensification of Super‐Typhoon Nanmadol (2022) Based on Multi‐Satellite Observations

AbstractUsing multi‐satellite observations, the cloud dynamic and microphysical characteristics were revealed during the rapid intensification (RI) of super‐typhoon Nanmadol (2022). As the storm intensifies, the eyewall contracts, the upper‐level divergence strengthens, and the cirrus cloud increases, leading to stronger upper‐level radial outflow and the vertical updraft. Meanwhile, it is found that there exists a dynamically attractive area in the outer rainbands, where particles grow effectively and form “a small amount of large particles” around 300 km from the eye. A theory of cloud dynamics‐microphysics interaction, called “tunnel theory,” is further proposed to explain the generation, accumulation, and concentrated downflow of large particles in the outer rainbands during RI. Results suggest the unique feature of particle distribution in the outer rainbands could be a potential indicator for RI.

Analysis of the Interaction Damage Mechanism and Treatment Measures for an Underpass Landslide Tunnel: A Case from Southwest China

Previous studies have analyzed the damage of tunnels and slopes as a single entity, ignoring the interaction effect between the tunnels and slopes, which will have an impact on the accuracy of the damage mechanism and the safety of the treatment measures. In this paper, three types of simulation models are established—the natural state, after tunnel excavation, and after reinforcement measures—considering a case study of an underpass landslide tunnel in southwest China. Based on the theory of underpass landslide tunnels and the strength reduction method, the interaction damage mechanism of this underpass landslide tunnel is revealed, and a reasonable treatment plan is proposed. The analysis results show the following: there is an obvious interaction effect between the tunnel collapse and the slope instability; a large number of mudstones common in the surrounding rock of the tunnel have rheological properties, which amplify the influence of the interaction effect of the tunnel through the landslide; and the proposed comprehensive treatment measures of “rescue inside the tunnel cave + tunnel slope treatment” have strong pertinence and effectiveness, and they fundamentally address the tunnel collapse and the slope instability of the tunnel.

Calculations of Constant-Height STM Images of Fullerene C60 Adsorbed onto a Surface

Constant-height scanning tunneling microscopy (STM) images of a C60 molecule adsorbed onto a surface were calculated using symmetry-adapted Hückel molecular orbitals (HMOs). Three adsorption orientations of C60 are considered. The interaction between the C60 molecule and the surface was treated using symmetry arguments only. Projection operators were used to generate symmetry-adapted HMOs of the molecule. These orbitals were then used to construct idealized constant-height STM images using the simple tunneling theory of Tersoff and Hamann. A comparison is made with published experimental STM maps. The results show that, for each orientation of C60, split orbitals of the same symmetry have similar appearances in the constant-height maps. They also show that the map of a molecular orbital of a complete degeneracy is dominated by only one or two of its components.

Charge trapping effect at the interface of ferroelectric/interlayer in the ferroelectric field effect transistor gate stack

We study the charge trapping phenomenon that restricts the endurance of n-type ferroelectric field-effect transistors (FeFETs) with metal/ferroelectric/interlayer/Si (MFIS) gate stack structure. In order to explore the physical mechanism of the endurance failure caused by the charge trapping effect, we first establish a model to simulate the electron trapping behavior in n-type Si FeFET. The model is based on the quantum mechanical electron tunneling theory. And then, we use the pulsed I d–V g method to measure the threshold voltage shift between the rising edges and falling edges of the FeFET. Our model fits the experimental data well. By fitting the model with the experimental data, we get the following conclusions. (i) During the positive operation pulse, electrons in the Si substrate are mainly trapped at the interface between the ferroelectric (FE) layer and interlayer (IL) of the FeFET gate stack by inelastic trap-assisted tunneling. (ii) Based on our model, we can get the number of electrons trapped into the gate stack during the positive operation pulse. (iii) The model can be used to evaluate trap parameters, which will help us to further understand the fatigue mechanism of FeFET.

Generalizing Fowler–Nordheim Tunneling Theory for an Arbitrary Power Law Barrier

Herein, the canonical Fowler–Nordheim theory is extended by computing the zero‐temperature transmission probability for the more general case of a barrier described by a fractional power law. An exact analytical formula is derived, written in terms of Gauss hypergeometric functions, that fully capture the transmission probability for this generalized problem, including screened interaction with the image potential. First, the quality of approximation against the so far most advanced formulation of Fowler–Nordheim, where the transmission is given in terms of elliptic integrals, is benchmarked. In the following, as the barrier is given by a power law, in detail, the dependence of the transmission probability on the exponent of the power law is analyzed. The formalism is compared with results of numerical calculations and its possible experimental relevance is discussed. Finally, it is discussed how the presented solution can be linked in some specific cases with an exact quantum‐mechanical solution of the quantum well problem.

631% room temperature tunnel magnetoresistance with large oscillation effect in CoFe/MgO/CoFe(001) junctions

We demonstrate tunnel magnetoresistance (TMR) ratios of up to 631% at room temperature (RT) using CoFe/MgO/CoFe(001) epitaxial magnetic tunnel junctions (MTJs). The TMR ratio increased up to 1143% at 10 K. The large TMR ratios resulted from fine-tuning of atomic-scale structures of the MTJs, such as crystallographic orientations and MgO interface oxidation by interface insertion of ultrathin CoFe and Mg layers, which are expected to enhance the well-known Δ1 coherent tunneling transport. Interestingly, the TMR oscillation effect, which is not covered by the standard coherent tunneling theory, also became significant. A 0.32-nm period TMR oscillation with increasing MgO thickness dominates the transport in a wide range of MgO thicknesses; the peak-to-valley difference of the TMR oscillation exceeds 140% at RT, which is attributed to the appearance of large oscillatory components in the resistance area product.

Three-Dimensional Mechanistic Modeling of Time-Dependent Dielectric Breakdown in Polycrystalline Thin Films

Time-dependent dielectric breakdown (TDDB) is a crucial issue for the dielectric reliability. In this work, we present a full three-dimensional mechanistic model for calculation of the TDDB process in polycrystalline thin films. The model is based on the multiphonon trap-assisted tunneling theory and takes into account the intrinsic three-dimensional discreteness of traps at the dielectric grain boundaries. The leakage current density is calculated by solving coupled three-dimensional master equation and Poisson equation. The net phonon emission associated with each charge trapping and release event is treated as a local point heat source, which then enters the Fourier heat equation for three-dimensional temperature distribution calculation. The generated trap is determined by local temperature and electric field, which is subsequently included in the next round of calculation of electric and thermal properties. A positive feedback loop gradually leads to an increase of trap density, temperature, and leakage current density, and finally the dielectric breakdown. Our model can, to a good approximation, reproduce the experimental leakage current density-voltage characteristics and the Weibull distribution of time to breakdown at different dielectric thicknesses, stress voltages, and environmental temperatures. We find that in realistic devices, the three-dimensional trap-to-trap transport of electrons contributes a non-negligible part to the leakage current when the dielectric approaches breakdown. Our approach of three-dimensional mechanistic simulation is computationally efficient such that evolution of ${10}^{3}$ traps during the TDDB process can be easily performed on a standard desktop computer.

A Physics-Based Dynamic Compact Model of Ferroelectric Tunnel Junctions

In this letter, we proposed a dynamic compact model for metal-ferroelectric-semiconductor (MFS) ferroelectric tunnel junctions (FTJ) based on their device physics. The voltage control over dynamic polarizations and the semiconductor surface potentials is achieved for full-region operations, supporting complex FTJ state transitions. A unified and smooth current model across different regions was proposed by formulating tunneling transports in FTJ with complicated barrier shapes from the first-principle tunneling theory. The model was extensively verified with both experimental data and technology computer-aided design (TCAD) simulations, featuring accurate descriptions of multi-states, frequency dependent programming, and circuit simulations.

Effect of formic acid on O2 + OH˙CHOH → HCOOH + HO2 reaction under tropospheric condition: kinetics of cis and trans isomers.

Formic acid (HCOOH) is one of the highly abundant acids in the troposphere. It is important in the formation of atmospheric aerosols and impacts the acidity of rainwater. In the present scenario, the model chemistry of HCOOH(FA) sources and sinks is poorly understood. In this work, we apply quantum chemical methods coupled with advanced statistical rate theories to understand the production of FA and its catalytic behavior under tropospheric conditions. The potential energy surfaces (PES) for O2 + OH˙CHOH and O2 + OH˙CHOH(+FA) reactions were constructed using the CCSD(T)/6-311++G(3df,3pd)//M06-2X/6-311++G(3df,3pd) level and rate constants for the production of FA were predicted using Rice-Ramsperger-Kassel-Marcus (RRKM)/master equation (ME) simulation with Eckart tunnelling and canonical variational transition state theory (CVT) with small curvature tunnelling (SCT) between the temperature range of 200-320 K and pressure range of 0.001 to 10 bar. The reaction follows the formation of cis and trans intermediates followed by spontaneous decomposition via concerted HO2 elimination to form stable post intermediates, which then leads to the straight formation of cis and trans formic acid. The current study also helps understand the role of cis and trans contribution to the total rate constants. The results show that O2 + OH˙CHOH is dominated by both cis and trans isomers; however, the trans isomer plays a more important role in the catalytic reaction. This result is due to the formation of a strong hydrogen-bonded complex in the trans isomer, which is dominated by the enthalpy factor rather than the entropy factor. The results predict that the catalytic effect of FA on the O2 + OH˙CHOH reaction is important when the concentration of FA is not included in the calculations; however, it has no effect under tropospheric conditions, when the FA concentration is included in the calculation. As a result, the total effective reaction rate constants are smaller. This work provides experimental/theoretical confirmation of Franco et al. who predicted that methanediol is the precursor for the FA formation, resolving an open problem in the kinetics of the gas phase reaction. O2 + OH˙CHOH and O2 + OH˙CHOH(+FA) probably explain other diol systems, which can help explain the formation of other atmospheric acids that affect aerosol formation and cloud evolution.

TOPcon route with quantum wells in GaInP/Si dual junction cell for efficiency enhancement

The GaInP/Si dual junction solar cell with Quantum Well and TOPCon technology has achieved 41.91 % efficiency in the simulation model. Quantum wells are proven to enhance the short circuit current without any significant degradation of open circuit voltage. The voltage preservation measure (for minimum reduction in open circuit voltage) is applied in design of Quantum well solar cell with the improvement in short circuit current, therefore the overall efficiency of dual junction cell is enhanced. In this work, the GaInP/Si dual junction solar cell is proposed by incorporating the InP quantum wells in the p-i-n region of GaInP top cell. Also, the TOPCon technology is applied at the rear side of the bottom c-Si solar cell. The quantum well increases the absorption of sub-bandgap photon energy. The buffer layer reduces the misfits between the lattice mismatched layers and tunnel oxide provides excellent passivation mechanism to increase the open circuit voltage. The ultrathin oxide layer provides extremely high electric field as described by the MIS tunneling theory. The electron and hole bound state energy and wavefunctions provides “miniband” formation and charge carrier trapping. The formation of type-A band structure in quantum well region and excellent electron mobility results in enhanced carrier transport. The GaInP/Si integrated model achieves efficiency of 33.30 % when the quantum wells are incorporated in the top cell. When the Combination of both QWs (in top cell) and TOPCon technology (in bottom cell) is applied, the model achieves 41.95 % efficiency. This model provides an excellent route toward achieving the 45 % efficiency limit of III-V/Si dual junction 2-terminal solar cell. The industry standard Silvaco TCAD platform is used for the calculation of the performance characteristics in AM1.5G environmental condition.

Features of tunneling current-voltage characteristics in dielectric films with Ni, Fe and Co nanoparticles, investigated by conductive AFM and within the framework of the theory of 1D-dissipative tunneling

Features of tunneling current-voltage characteristics in dielectric films with Ni, Fe and Co nanoparticles, investigated by conductive AFM and within the framework of the theory of 1D-dissipative tunneling

Improved Tunneling Property of p+Si Nanomembrane/n+GaAs Heterostructures through Ultraviolet/Ozone Interface Treatment

Here, heterostructures composed of p+Si nanomembranes (NM)/n+GaAs were fabricated by ultraviolet/ozone (UV/O3, UVO) treatment, and their tunneling properties were investigated. The hydrogen (H)-terminated Si NM was bonded to the oxygen (O)-terminated GaAs substrate, leading to Si/GaAs tunnel junctions (TJs). The atomic-scale features of the H-O-terminated Si/GaAs TJ were analyzed and compared to those of Si/GaAs heterojunctions with no UVO treatment. The electrical characteristics demonstrated the emergence of negative differential resistance, with an average peak-to-valley current ratio of 3.49, which was examined based on the band-to-band tunneling and thermionic emission theories.

Bardeen's tunneling theory applied to intraorbital and interorbital hopping integrals between dopants in silicon

We utilize Bardeen's tunneling theory to calculate intra- and interorbital hopping integrals between phosphorus donors in silicon using known orbital wave functions. While the two-donor problem can be solved directly, the knowledge of hoppings for various pairs of orbitals is essential for constructing multi-orbital Hubbard models for chains and arrays of donors. To assure applicability to long-range potentials, we rederive Bardeen's formula for the matrix element without assuming non-overlapping potentials. Moreover, we find a correction to the original expression allowing us to use it at short distances. We also show that accurate calculation of the lowest donor-pair eigenstates is possible based on these tunnel couplings, and we characterize the obtained states. The results are in satisfactory quantitative agreement with those obtained with the standard H\"uckel tight-binding method. The calculation relies solely on the wave functions in the barrier region and does not explicitly involve donor or lattice potentials, which has practical advantages. We find that neglecting the central correction potential in the standard method may lead to qualitatively incorrect results, while its explicit inclusion raises severe numerical problems, as it is contained in a tiny volume. In contrast, using wave functions obtained with this correction in the proposed method does not raise such issues. Nominally, the computational cost of the method is to calculate a double integral along the plane that separates donors. For donor separation in directions where valley interference leads to oscillatory behavior, additional averaging over the position of the integration plane is needed. Despite this, the presented approach offers a competitive computational cost as compared to the standard one. This work may be regarded as a benchmark of a promising method for calculating hopping integrals in lattice models.