Phonon-assisted Tunneling Research Articles

Tunneling Current in 4H-SiC p-n Junction Diodes

Heavily doped 4H-silicon carbide (SiC) epitaxial p-n junction diodes are fabricated, and their tunneling current under reverse-biased condition is investigated. Soft increase of the leakage current before avalanche breakdown is observed in the diodes with heavy reduced doping concentration. The temperature and electric field strength dependencies of the leakage current reveal that the leakage current is caused by a phonon-assisted tunneling process. An accurate parameter set for simulating the phonon-assisted tunneling current in 4H-SiC is obtained, which agrees well with the experimental results within a wide temperature range (100-500 K) regardless of the reduced doping concentration. In 4H-SiC p-n junction diodes, the Zener breakdown occurs at the maximum electric field strength of 5.7 MV/cm.

Electric field dependence of major electron trap emission in bulk β-Ga2O3: Poole–Frenkel effect versus phonon-assisted tunneling

Measurements of deep trap spectra in bulk β-Ga2O3 crystals showed the parameters of the two dominant centers with levels near Ec-0.8 eV (E2) and Ec-1 eV(E3) are affected the electric field during deep level transient spectroscopy (DLTS). Both DLTS spectra measurements of the emission rates of the E2 and E3 traps and measurements of emission rates as a function of electric field from capacitance decay curves obtained at a fixed temperature (380 K) show that, for strong electric field with magnitude above ∼5 × 105 V.cm−1, the emission rates of these traps increase with increasing field. For the E2 traps, the increase is driven by phonon assisted tunneling. This points to the trap being an acceptor, which is consistent with reported attribution of the center to substitutional Fe acceptors. For the E3 trap, the field dependence indicates the dominant mechanism is the Poole–Frenkel effect, operable for Coulombic centers. It is concluded that this commonly observed trap is a deep donor.

Critical properties and charge transport in ethylene bridged organosilica low-κ dielectrics

Organosilicate-glass-based low-κ films containing both terminal methyl groups and an ethylene bridge between the silicon atoms are spin-on deposited by using 1,2-bis(trimethoxysilyl)ethane and methyltrimethoxysilane, Brij30 template, and thermal curing. The chemical composition, porosity, and internal defects are studied using Fourier-transform infrared spectroscopy, x-ray photoelectron spectroscopy, electron energy loss spectroscopy, UV induced luminescence, and ellipsometric porosimetry. It was found that the studied films contain oxygen-deficient centers (Si—Si bonds). The high defect density of the states near the valence-band edge of the studied low-κ films leads to a relatively small bandgap value of about 6.3 eV. The current–voltage characteristics at different temperatures were analyzed using six theoretical charge transport models where the transport is limited by the traps ionization. It was found that the best qualitative and quantitative agreement between the calculations and experimental data is achieved by using the model of phonon-assisted electron tunneling between the neutral traps and is supplemented by considering the space charge and charge carrier kinetics. Since the thermal and optical energies of the traps in the studied films are 1.6 eV and 3.2 eV, respectively, it is concluded that the traps are responsible for the charge transport in the Si—Si bonds.

Phonon-assisted proton tunneling in the hydrogen-bonded dimeric selenates of Cs3H(SeO4)2.

In phases III and IV of Cs3H(SeO4)2, the vibrational state and intrabond transfer of the proton in the dimeric selenates are systematically studied with a wide range of absorbance spectra, a spin-lattice relaxation rate of 1H-NMR (T1 -1), and DFT calculations. The OH stretching vibrations have extremely broad absorption at around 2350 (B band) and 3050 cm-1 (A band), which originate from the 0-1 and 0-2 transitions in the asymmetric double minimum potential, respectively. The anharmonic-coupling calculation makes clear that the A band couples not only to the libration but also to the OH bending band. The vibrational state (nano-second order) is observed as the response of the proton basically localized in either of the two equivalent sites. The intrabond transfer between those sites (pico-second order) yields the protonic fluctuation reflected in T1 -1. Together with the anomalous absorption [νp2 phonon, libration, tetrahedral deformation (δ440), and 610-cm-1 band], we have demonstrated that the intrabond transfer above 70 K is dominated by the thermal hopping that is collectively excited at 610 cm-1 and the phonon-assisted proton tunneling (PAPT) relevant to the tetrahedral deformation [PAPT(def)]. Below 70 K, T1 -1 is largely enhanced toward the antiferroelectric ordering and the distinct splitting emerges in the libration, which dynamically modulates the O(2)-O'(2) distance of the dimer. The PAPT(lib) associated with the libration is confirmed to be a driving force of the AF ordering.

Modeling of the Vertical Leakage Current in AlN/Si Heterojunctions for GaN Power Applications

We present a model for the vertical conduction through an AlN/p–Si junction, which is used as a base for the growth of GaN power devices. First, we recall that for resistive silicon substrates, the ${I}$ – ${V}$ curves of the AlN/p–Si show a monotonic increase, interrupted by a plateau region. Then, to quantitatively explain this behavior, we propose a novel two-diode model. More specifically, we demonstrate that the AlN/p-Si structure can be split into the series connection of two substructures: 1) an equivalent AlN/n+-Si junction and 2) an equivalent n+-Si/p-Si diode. The n+ layer models the electron inversion layer in the silicon at the interface with the AlN layer. Technology Computer-Aided Design (TCAD) simulations were used to validate these two diode models. By comparing the leakage current of the AlN/p-Si structure with the current through the diodes, we demonstrate that within the plateau region, all the applied voltage drops on the equivalent n+-Si/p-Si junction, and the current through the diodes is limited by the reverse leakage current of the n+-Si/p-Si diode. The plateau ends as soon as impact ionization occurs in the Si substrate, due to the high electric field in the depletion region. After the plateau, the current through the diodes is again limited by charge injection from the inversion layer into the AlN, which occurs through a phonon-assisted tunneling mechanism (possibly trap-assisted).

Commensuration effects in layered nanoparticle solids

We have developed HiNTS, the {\bf Hi}erarchical {\bf N}anoparticle {\bf T}ransport {\bf S}imulator, and adapted it to study commensuration effects in two classes of Nanoparticle (NP) solids: (1) a bilayer NP solid (BNS) with an energy offset, and (2) a BNS as part of a Field-Effect Transistor (FET). HiNTS integrates the ab initio characterization of single NPs with the phonon-assisted tunneling transition model of the NP-NP transitions into a Kinetic Monte Carlo based simulation of the charge transport in NP solids. First, we studied a BNS with an inter-layer energy offset $\Delta$, possibly caused by a fixed electric field. Our results include the following. (1) In the independent energy-offset model, we observed the emergence of commensuration effects when scanning the electron filling factor $FF$ across integer values. These commensuration effects were profound as they reduced the mobility by several orders of magnitude. We analyzed these commensuration effects in a five dimensional parameter space, as a function of the on-site charging energy $E_C$, energy offset $\Delta$, the disorder $D$, the electron filling factor $FF$, and the temperature $k_{B}T$. We demonstrated the complexity of our model by showing that at integer filling factors $FF$ commensuration effects are present in some regions of the parameter space, while they vanish in other regions, thus defining distinct dynamical phases of the model. We determined the phase boundaries between these dynamical phases. (2) Using these results as a foundation, we shifted our focus to the experimentally much-studied NP-FETs. NP-FETs are also characterized by an inter-layer energy offset $\Delta$, which, in contrast to our first model, is set by the gate voltage $V_G$ and thereby related to the electron filling $FF$. We demonstrated the emergence of commensuration effects and distinct dynamical phases in these NP-FETs.

Charge transport mechanism in SiNx-based memristor

Amorphous silicon nitride is a key dielectric in silicon devices. The advantage of SiNx and Si3N4 over other dielectrics is that silicon nitride is compatible with silicon technology and is widely used in it. It is necessary to understand, experimentally and theoretically, the mechanism of charge transport in a memristor based on silicon nitride in the initial, high-resistance, and low-resistance states to develop a resistive memory element. At present, there is currently no single universal model of charge transport in a memristor based on silicon nitride. In our work, the charge transport of the initial, high, and low resistive states in an SiNx-based memristor is analyzed with four bulk-limited charge transport models. It is established that the Frenkel model of Coulomb traps ionization, Hill-Adachi model of overlapping Coulomb traps, and Makram-Ebeid and Lannoo model of multiphonon isolated traps ionization, quantitatively, do not describe the charge transport of the SiNx-based memristor in any state. The Nasyrov-Gritsenko model of phonon-assisted tunneling between traps gives a consistent explanation of the charge transport of the SiNx-based memristor in all states at temperatures above room temperature.

Light emission properties in a double quantum dot molecule immersed in a cavity: Phonon-assisted tunneling

Two main mechanisms dictate the tunneling process in a double quantum dot: overlap of excited wave functions, effectively described as a tunneling rate, and phonon-assisted tunneling. In this paper, we study different regimes of tunneling that arise from the competition between these two mechanisms in a double quantum dot molecule immersed in a unimodal optical cavity. We show how such regimes affect the mean number of excitations in each quantum dot and in the cavity, the spectroscopic resolution and emission peaks of the photoluminescence spectrum, and the second-order coherence function which is an indicator of the quantumness of emitted light from the cavity.

Phonon limited anisotropic quantum transport in phosphorene field effect transistors

Electron-phonon coupling limited transport in phosphorene metal oxide semiconductor field effect transistors (MOSFETs) is studied along the armchair (AC) and zigzag (ZZ) directions. In a multiscale approach, the unit cell of phosphorene is first relaxed, and the band structure is calculated using hybrid density functional theory (DFT). The transport equations are then solved quantum mechanically under the nonequilibrium Green’s function formalism using DFT-calibrated two-band k⋅p hamiltonian. The treatment of electron-phonon scattering is done under the self-consistent Born approximation in conjunction with deformation potential theory. It is found that optical phonon modes are largely responsible for degradation of ON-current apart from p-channel AC MOSFET where acoustic phonon modes play a stronger role. It is further observed that electron-phonon scattering is more pronounced in the ZZ direction, whereas the diffusive ON-current of p-MOSFET in a given direction is higher than n-MOSFET. Further study on the complex band structure of phosphorene reveals band wrapping within the bandgap region in the AC direction and multiple crossings in the ZZ direction. This signifies strong phonon-assisted tunneling in the ZZ direction in comparison with the AC direction. For completeness, drain current in the AC tunnel field effect transistor is calculated, and electron-phonon scattering is observed only in the near vicinity of the OFF-current.

Dynamical generation of synthetic electric fields for photons in the quantum regime

Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields in the minimal setup of two optical modes coupled by phonon-assisted tunneling where the phonon mode is undergoing self-oscillations. We use the quantum van-der-Pol oscillator as the simplest dynamical model for a mechanical self-oscillator that allows us to perform quantum master equation simulations. We identify a single parameter, which controls the strength of quantum fluctuations, enabling us to investigate the classical-to-quantum crossover. We show that the generation of synthetic electric fields is robust against noise and that it leads to unidirectional transport of photons also in the quantum regime, albeit with a reduced isolation ratio. Our study opens the path for studying dynamical gauge fields in the quantum regime based on optomechanical arrays.

Dynamically generated synthetic electric fields for photons

Static synthetic magnetic fields give rise to phenomena including the Lorentz force and the quantum Hall effect even for neutral particles, and they have by now been implemented in a variety of physical systems. Moving towards fully dynamical synthetic gauge fields allows, in addition, for backaction of the particles' motion onto the field. If this results in a time-dependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise self-consistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phonon-assisted photon tunneling. We study open, one-dimensional arrays, where synthetic magnetic fields are absent. However, we show that synthetic electric fields can be generated dynamically, which, importantly, suppress photon transport in the array. The generation of these fields depends on the direction of photon propagation, leading to a novel mechanism for a photon diode, inducing nonlinear nonreciprocal transport via dynamical synthetic gauge fields.

Polaronic interacceptor hopping transport in intrinsically doped nickel oxide

In this work, we revisit the issue of the nature of electronic transport in nickel oxide (NiO) and show that the widely used model of free small polaron hopping, initially raised to characterize transport in high-purity samples, is not appropriate for modeling intrinsically doped NiO. Instead, we present extensive evidence, collected by means of temperature- and frequency-dependent measurements of the electrical conductivity $\sigma$, that the model of polaronic inter-acceptor hopping can be used to consistently explain the electronic conduction process. In this framework, holes are localized to acceptors (Ni vacancies), forming a strongly bound, polaron-like state. They can only move through the film by hopping to a neighboring, at least partially unoccupied, acceptor. This renders the spatial overlap between neighboring polaronic wave functions a highly critical parameter. The signature of this process is the occurrence of two temperature regions of the DC conductivity, separated by about half the Debye temperature $\theta_D/2 \approx 200 K$. For $T > \theta_D/2$, holes are transferred by phonon-assisted hopping over the potential barrier between two sites, whereas phonon-assisted tunneling through the barrier dominates below that temperature. We also show that the degree of structural and electronic disorder plays a vital role in determining the characteristics of the transport process: high disorder leads to strong energetic broadening of the acceptor states such that hopping to more distant sites may be favored over transfer to nearest neighbors (variable range hopping). The assumption of high binding energies of the charge carriers at VNi is in accordance with the recent paradigm shift regarding the understanding of the electronic structure of NiO: holes doped into NiO couple to Ni 3d spins, thereby occupying deep polaron-like states within the band gap (Zhang-Rice bound doublets).

Electron tunneling through a coupled system of electron and phonon

We study the electron tunneling through a single level quantum dot in the presence of electron–phonon interaction. By using the Green’s function and canonical transformation methods, we calculated exactly the current. It is found that the current vs dot level exhibits satellite peaks even without occurring of phonon-assisted tunneling processes, and properties of the current are affected heavily by the strength of electron–phonon interaction and phonon temperature.

Temperature-Dependent Transient Absorption Spectroscopy Elucidates Trapped-Hole Dynamics in CdS and CdSe Nanorods.

Charge-carrier traps play a central role in the excited-state dynamics of semiconductor nanocrystals, but their influence is often difficult to measure directly. In CdS and CdSe nanorods of nonuniform width, spatially separated electrons and trapped holes display relaxation dynamics that follow a power-law function in time that is consistent with a recombination process limited by trapped-hole diffusion. However, power-law relaxation can originate from mechanisms other than diffusion. Here we report transient absorption spectroscopy measurements on CdS and CdSe nanorods recorded at temperatures ranging from 160 to 294 K. We find that the exponent of the power law is temperature-independent, which rules out several models based on stochastic activated processes and provides insights into the mechanism of diffusion-limited recombination in these structures. The data point to weak electronic coupling between trap states and suggest that surface-localized trapped holes couple strongly to phonons, leading to slow diffusion. Trap-to-trap hole hopping behaves classically near room temperature, while quantum aspects of phonon-assisted tunneling become observable at low temperatures.

Effect of phonon induced spin-flip processes on correlated quantum dot kinetics

We present a theoretical analysis of relaxation processes in a correlated quantum dot (QD) coupled to a reservoir in the presence of electron-phonon interaction. The effect of both electron-phonon interaction and Coulomb correlations on system's kinetics is analyzed by means of equations of motion for generalized non-equilibrium Green's functions. It is shown that phonon-assisted tunneling enhances the relaxation processes in a correlated quantum dot. Moreover, electron-phonon interaction changes stationary values and typical relaxation rates of the second-order correlation functions for localized electrons. In spite of the fact that electron-phonon interaction is spin independent, it strongly influences spin correlations in the presence of Coulomb interactions between localized electrons. This effect appears to be due to phonon-induced spin-flip processes of localized electrons.

Temperature-Dependent Characteristics of GaN Schottky Barrier Diodes with TiN and Ni Anodes**Supported by the National Key Research and Development Plan under Grant No 2017YFB0403000, and the Fundamental Research Funds for the Central Universities under Grant No JB181110.

The effect of temperature on the characteristics of gallium nitride (GaN) Schottky barrier diodes (SBDs) with TiN and Ni anodes is evaluated. With increasing the temperature from 25 to 175°C, reduction of the turn-on voltage and increase of the leakage current are observed for both GaN SBDs with TiN and Ni anodes. The performance after thermal treatment shows much better stability for SBDs with TiN anode, while those with Ni anode change due to more interface states. It is found that the leakage currents of the GaN SBDs with TiN anode are in accord with the thermionic emission model whereas those of the GaN SBDs with Ni anode are much higher than the model. The Silvaco TCAD simulation results show that phonon-assisted tunneling caused by interface states may lead to the instability of electrical properties after thermal treatment, which dominates the leakage currents for GaN SBDs with Ni anode. Compared with GaN SBDs with Ni anode, GaN SBDs with TiN anode are beneficial to the application in microwave power rectification fields due to lower turn-on voltage and better thermal stability.

Linewidth broadening and tunneling of excitons bound to N pairs in dilute GaAs:N

The exciton bound to a pair of nitrogen atoms situated at nearby lattice sites in dilute GaAs:N provides an energetically uniform electronic system, spectrally distinct from pairs with larger or smaller separations, and can even be grown with a uniform pair orientation in the crystal. We use photoluminescence excitation spectroscopy on an ensemble of N pairs to study the narrow continuous energy distribution within two of the individual exchange- and symmetry-split exciton states. Inhomogeneous linewidths of 50–60 μeV vary across the crystal on a mesoscopic scale and can be 30 μeV at microscopic locations indicating that the homogeneous linewidth inferred from previous time-domain measurements is still considerably broadened. While excitation and emission linewidths are similar, results show a small energy shift between them indicative of exciton transfer via phonon-assisted tunneling between spatially separated N pairs. We numerically simulate the tunneling in a spatial network of randomly distributed pairs having a normal distribution of bound exciton energies. Comparing the ensemble excitation-emission energy shift with the measured results shows that the transfer probability is higher than expected from the dilute pair concentration and what is known of the exciton wavefunction spatial extent. Both the broadening and the exciton transfer have implications for the goal of pair-bound excitons as a single- or multi-qubit system.

Conductivity relaxation and photocurrent generation in reduced graphene oxide-poly(9,9′-dioctyl-fluorene-co-bithiophene) composite with application in temperature sensing

The electrical transport properties and photocurrent generation in a reduced graphene oxide-poly(9,9′-dioctyl-fluorene-co-bithiophene) (RGO-F8T2) composite were investigated. The semiconducting nature of the RGO-F8T2 composite was jointly demonstrated by dc and ac conductivity measurements. The dc conductivity obtained from both dc and ac measurements follows the Arrhenius relationship with the activation energy of the order of 80 meV. The RGO-F8T2 composite also showed excellent temperature sensing properties. The temperature coefficient of resistance was compared to commercially available Platinum, Polysilicon, and Germanium temperature sensor. The conductivity relaxation mechanism in the RGO-F8T2 composite depicted the mechanism behind ac conduction. This was due to phonon assisted tunneling between the defect states. The density of states at the Fermi level increases by one order of magnitude for the temperature change of 301 to 433 K. The scaling of conductivity isotherms established the occurrence of intramolecular energy transfer from disordered to ordered chain segments or both in the composite. The photocurrent generation in the RGO-F8T2 composite thin film under simulated solar light illumination was also studied. Here, a linear variation of the photosensitivity with the variation of the incident light intensity was observed.

Impact of phonon scattering on digital characteristics and RF performance of graphene nanoribbon FETs

The switching capabilities and RF performance of graphene nanoribbon field-effect transistors (GNRFETs) in the presence of electron-phonon scattering are examined. Self-consistent atomistic simulations based on the nonequilibrium Green's function (NEGF) formalisms are used. We have studied the influence of incoherent transport on the most important digital parameters such as Ion, Ioff, Ion/Ioff, the subthreshold swing, and the drain-induced barrier lowering (DIBL) versus the channel length. Furthermore, the effects of phonon scattering on the gate capacitance and the transconductance are investigated in order to calculate the intrinsic cut-off frequency, switching delay, and the power-delay product of non-ballistic GNRFETs. We have shown that band-to-band tunneling regime is dominated by the phonon-assisted tunneling. Therefore, the off-current and the sub-threshold swing are deteriorated by this phenomenon. Furthermore, the scattering results in a decrease of intrinsic cut-off frequency and increase of the gate delay and energy consumed per switching event.

Phonon-assisted tunnelling in a double quantum dot molecule immersed in a cavity

The effects caused by phonon-assisted tunnelling (PhAT) in a double quantum dot (QD) molecule immersed in a cavity were studied under the quantum Markovian master equation formalism in order to account for dissipation phenomena. We explain how for higher PhAT rates, a stronger interaction between a QD and the cavity at off-resonance takes place through the resonant interaction of another QD and the cavity, where the QDs interact through tunnelling. A closer look at the system's allowed optical transitions as a function of PhAT rates showed coalescence of the transition energies, leading to a loss of spectroscopic resolution in the photoluminescence (PL) spectrum. This coalescence occurs at several exceptional points, suggesting a quantum dynamical phase transition.