The action mechanism of the work done by the electric field force on moving charges to stimulate the emergence of carrier generation/recombination in a PN junction

It is discovered that the product of the current and the electric field in a PN junction should be regarded as the rate of work(power)done by the electric field force on moving charges(hole current and electron current),which was previously misinterpreted as solely a Joule heating effect.We clarify that it is exactly the work done by the electric field force on the moving charges to stimulate the emergence of non-equilibrium carriers,which triggers the novel physical phenomena.As regards to Joule heat,we point out that it should be calculated from Ohm’s law,rather than simply from the product of the current and the electric field.Based on this understanding,we conduct thorough discussion on the role of the electric field force in the process of carrier recombination and carrier generation.The thermal effects of carrier recombination and carrier generation followed are incorporated into the thermal equation of energy.The present study shows that the exothermic effect of carrier recombination leads to a temperature rise at the PN interface,while the endothermic effect of carrier generation causes a temperature reduction at the interface.These two opposite effects cause opposite heat flow directions in the PN junction under forward and backward bias voltages,highlighting the significance of managing device heating phenomena in design considerations.Therefore,this study possesses referential significance for the design and tuning on the performance of piezotronic devices.

Stress-induced potential barriers and charge distributions in a piezoelectric semiconductor nanofiber

The performance of a piecewise-stressed ZnO piezoelectric semiconductor nano?ber is studied with the multi-?eld coupling theory. The ?elds produced by equal and opposite forces as well as sinusoidally distributed forces are examined. Speci?c distributions of potential barriers, wells, and regions with effective polarization charges are found. The results are fundamental for the mechanical tuning on piezoelectric semiconductor devices and piezotronics.

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

The electric band energy variation in a bent piezoelectric semiconductor(PSC) nanowire of circular cross-section induced by the mechanical force is analyzed based on a six-band k · p method. The electric-mechanical fields are first obtained analytically in a cantilever bent PSC nanowire by solving the fully-coupled electro-mechanical equations. Then, the band energy is acquired numerically via the six-band Hamiltonian.By considering further the nonlinear coupling between the piezoelectric and semiconducting quantities, the contribution of the redistribution carriers to the electric field is analyzed from the Gauss’ s law. Numerical examples are carried out for an n-type Zn O nanowire in different locations induced by an applied concentrated end force. They include the electric potential, heavy hole(HH), light hole(LH), spin-orbit split-off(SO),and conduction band(CB) edges along the axial and thickness directions. Our results show that the applied force has a significant effect on the band energies. For instance, on the bottom surface along the axial direction, the bandgaps near the fixed end are greater than those near the loading end, and this trend is reversed on the top surface. Moreover,at a fixed axial location, the energy level of the lower side can be enhanced by applying a bending force at the end. The present results could be of significant guidance to the electronic devices and piezotronics.

Electric potential and energy band in ZnO nanofiber tuned by local mechanical loading

Recent success in strain engineering has triggered tremendous interest in its study and potential applications in nanodevice design. In this paper, we establish a coupled piezoelectric/semiconducting model for a wurtzite structure ZnO nanofiber under the local mechanical loading. The energy band structure tuned by the local mechanical loading and local length is calculated via an eight-band k·p method, which includes the coupling of valance and conduction bands. Poisson's effect on the distribution of electric potential inversely depends on the local mechanical loading. Numerical results reveal that both the applied local mechanical loading and the local length exhibit obvious tuning effects on the electric potential and energy band. The band gap at band edges varies linearly with the applied loading. Changing the local length shifts the energy band which is far away from the band edges. This study will be useful in the electronic and optical enhancement of semiconductor devices.

Dislocation Dissociation Strongly Influences on Frank-Read Source Nucleation and Microplasticy of Materials with Low Stacking Fault Energy

The influence of dislocation dissociation on the evolution of Frank-Read （F-R） sources is studied using a three- dimensional discrete dislocation dynamics simulation （3D-DDD）. The classical Orowan nucleation stress and recently proposed Benzerga nucleation time models for F-R sources are improved. This work shows that it is necessary to introduce the dislocation dissociation scheme into 3D-DDD simulation, especially for simulations on micro-plasticity of small sized materials with low stacking fault energy.

The mechanism to reform dynamic performance of an elastic wave-front in a piezoelectric semiconductor by the wave-carrier interaction induced from static biasing fields

The propagation of an elastic wave(EW)in a piezoelectric semiconductor(PSC)subjected to static biasing fields is investigated.It is found that there exist two coupling waves between electric field and charge carriers.One is stimulated by the action of the polarized electric field in the EW-front on charge carriers(EFC),and the other is stimulated by the action of initial electric field in biasing fields on dynamic carriers(IEC).Obviously,the latter is a man-made and tunable wave-carrier interaction.A careful study shows that IEC can play a leading role in remaking dynamic performance of the wave-front and an inter-medium role in transferring energy from biasing fields to EW-fronts.Hence,a method is proposed to reform the EW performance by biasing-fields:reforming the dispersivity of EW-fronts by promoting competition between IEC and EFC and inverting the dissipation by the IEC to transfer energy from biasing fields to EWfronts.The corresponding tuning laws on the phase-frequency characteristics of an EW show that the wave velocity can be regulated smaller than the pure EW velocity at a lowfrequency and larger than the pure piezoelectric wave velocity at a high-frequency.As for regulating the amplitude-frequency characteristics of the EW by the IEC,analyses show that EWs can obtain amplification only for those with relatively high vibration frequencies(small wave lengths).The studies will provide guidance for theoretical analysis of waves propagating in PSCs and practical application and design of piezotronic devices.

Size effects on the mixed modes and defect modes for a nano-scale phononic crystal slab

The size-dependent band structure of an Si phononic crystal(PnC)slab with an air hole is studied by utilizing the non-classic wave equations of the nonlocal strain gradient theory(NSGT).The three-dimensional(3D)non-classic wave equations for the anisotropic material are derived according to the differential form of the NSGT.Based on the the general form of partial differential equation modules in COMSOL,a method is proposed to solve the non-classic wave equations.The bands of the in-plane modes and mixed modes are identified.The in-plane size effect and thickness effect on the band structure of the PnC slab are compared.It is found that the thickness effect only acts on the mixed modes.The relative width of the band gap is widened by the thickness effect.The effects of the geometric parameters on the thickness effect of the mixed modes are further studied,and a defect is introduced to the PnC supercell to reveal the influence of the size effects with stiffness-softening and stiffness-hardening on the defect modes.This study paves the way for studying and designing PnC slabs at nano-scale.

Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.

A full-coupling model of PN junctions based on the global-domain carrier motions with inclusion of the two metal/semiconductor contacts at endpoints

A full-coupling model on the current-voltage(J-V)characteristics of PN junctions is put forward in the paper by taking into account both the whole junction and the two electrode regions consisting of metal/semiconductor(M/S)contacts.The depletion layer assumption proposed by the Shockley model is discarded.Gauss’law on the electric potential and the electric field is applied in the whole junction region such that the majority-carrier currents inside and outside the P/N barrier region are able to be exactly defined and clearly calculated.Then,the stable continuity equations of the electron and hole currents are established to show the current conversion between minority-and majority-carriers inside the whole PN junction region.By analyzing all the conversion procedure,the J-V characteristics of a PN junction are obtained with good agreement to the experimental results,which are closely dependent on the minority-carrier lifetime and doping concentrations.Obviously,the study on this topic possesses referential significance to mechanically tuning the performance of piezoelectric PN junctions and piezotronic devices.

Typical transient effects in a piezoelectric semiconductor nanofiber under a suddenly applied axial time-dependent force

Based on the mechanical motion equation,Gauss’s law,and the current continuity condition,we study a few typical transient effects in a piezoelectric semiconductor(PS)fiber to realize the startup and turning-off functions of common piezotronic devices.In this study,the transient extensional vibration induced by a suddenly applied axial time-dependent force is examined in a cantilevered n-type ZnO nanofiber.Neither the magnitude of the loadings nor the doping concentration significantly affects the propagation caused by disturbance of the axial displacement.However,both of the factors play an important role in the propagation caused by disturbance of the electron concentrations.This indicates that the electromechanical coupling effect can be expected to directly determine the electronic performance of the devices.In addition,the assumption of previous simplified models which neglect the charge carriers in Gauss’s law is discussed,showing that this assumption has a little influence on the startup state when the doping concentration is smaller than 1021 m-3.This suggests that the screening effect of the carriers on the polarized electric field is much reduced in this situation,and that the state is gradually transforming into a pure piezoelectric state.Nevertheless,the carriers can provide a damping effect,which means that the previous simplified models do not sufficiently describe the turning-off state.The numerical results show that the present study has referential value with respect to the design of newly multifunctional PS devices.

Effects of mechanical loadings on the performance of a piezoelectric hetero-junction

A fully-coupled model for a piezoelectric hetero-junction subjected to a pair of stresses is proposed by discarding the depletion layer approximation.The effect of mechanical loadings on PN junction performance is discussed in detail.Numerical examples are carried out for a p-Si/ZnO-n hetero-junction under a pair of stresses acting on the ntype ZnO portion near the PN interface,where ZnO has the piezoelectric property while Si is not.It is found that the bottom of conduction band is lowered/raised near the two loading points due to the decrease/increase in the electron potential energy there induced by a tensile-stress mode via sucking in majority-carriers from two outside regions,which implies appearance of a potential barrier and a potential well near two loading points.Furthermore,the barrier height and well depth gradually become large with increasing tensile stress such that more and more electrons/holes are inhaled in loading region from the n-/p-zone,respectively.Conversely,rising/dropping of conduction band bottom is brought out near the two loading points by a compressive-stress mode due to the increase/decrease in the potential energy of electrons by pumping out the majority-carriers from the loading region to the two outside regions.Therefore,a potential well and a potential barrier are induced near the two loading points,such that more and more electrons/holes are driven away from the loading region to the n-zone/p-zone,respectively,with the increasing compressive stress.These effects are important to tune the carrier recombination rate near the PN interface.Thus,the present study possesses great referential significance to piezotronic devices.

On the Transient Numerical Simulation of Solid Rocket Motor by Coupling Quasi One⁃Dimension Internal Flow with Three⁃Dimension Propellant Grain Burnback

The quasi one⁃dimension compressible flowfield coupled to the three⁃dimension propellant grain regression solved by the level⁃set method was used to simulate the transient internal ballistics of solid rocket motor.One⁃dimension flowfield instead of three⁃dimension can save computational cost on the premise of calculation accuracy because the radial and azimuthal variations parameters have little contribution to the internal flowfield.The grain regression in real⁃time could provide accurate geometrical information for simulation.A combination of flowfluid solver and grain regression can reappear in a relatively real internal ballistic flowfield,so it is good for further studying the instability of solid rocket motor.For level⁃set equations,the total variation⁃diminishing second⁃order Runge⁃Kutta method for temporal derivatives and a fifth⁃order weighted⁃essentially⁃non⁃oscillatory scheme for spatial derivatives were used.The total variation⁃diminishing MacCormack method was used to discrete the Euler equations in flowfield solver.Two modules of this code were tested in this study:one is the burning rate module and the other is the nozzle erosion module.Results show that the burning rate influenced the solid rocket motor efficiency,and the velocity profile in the chamber was affected by the nozzle shape,and the nozzle erosion could influence the head⁃end pressure spike.

Effect of ballistic electrons on ultrafast thermomechanical responses of a thin metal film

The ultrafast thermomechanical coupling problem in a thin gold film irradiated by ultrashort laser pulses with different electron ballistic depths is investigated via the ultrafast thermoelasticity model. The solution of the problem is obtained by solving finite element governing equations. The comparison between the results of ultrafast thermomechanical coupling responses with different electron ballistic depths is made to show the ballistic electron effect. It is found that the ballistic electrons have a significant influence on the ultrafast thermomechanical coupling behaviors of the gold thin film and the best laser micromachining results can be achieved by choosing the specific laser technology（large or small ballistic range）.In addition, the influence of simplification of the ultrashort laser pulse source on the results is studied, and it is found that the simplification has a great influence on the thermomechanical responses, which implies that care should be taken when the simplified form of the laser source term is applied as the Gaussian heat source.

Effect of Randomness of Interfacial Properties on Fracture Behavior of Concrete Under Uniaxial Tension

Interfacial transition zones （ITZs） between aggregates and mortar are the weakest parts in concrete. The random aggregate generation and packing algorithm was utilized to create a two-phase concrete model, and the zero-thickness cohesive elements with different normal distribution parameters were used to model the ITZs with random mechanical properties. A number of uniaxial tension-induced fracture simulations were carried out, and the effects of the random parameters on the fracture behavior of concrete were statistically analyzed. The results show that, different from the dissipated fracture energy, the peak load of concrete does not always obey a normal distribution, when the elastic stiffness, tensile strength, or fracture energy of ITZs is normally distributed. The tensile strength of the ITZs has a significant effect on the fracture behavior of concrete, and its large standard deviation leads to obvious diversity of the fracture path in both location and shape.

New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics

Recent analytical solutions for peridynamic(PD)models of transient diffusion and elastodynamics allow us to revisit convergence of 1D PD models to their classical counterparts.We find and explain the reasons for some interesting differences between the convergence behavior for transient diffusion and elastodynamics models.Except for very early times,PD models for transient diffusion converge monotonically to the classical one.In contrast,for elastodynamic problems this convergence is more complex,with some periodic/almost-periodic characteristics present.These special features are investigated for sine waves used as initial conditions.The analysis indicates that the convergence behavior of PD solutions to the classical one can be understood in terms of convergence properties for models using the Fourier series expansion terms of a particular initial condition.The results obtained show new connections between PD models and their corresponding classical versions.

Effect of Hydrogen on Dislocation Nucleation and Motion:Nanoindentation Experiment and Discrete Dislocation Dynamics Simulation

The hydrogen effect on the nucleation and motion of dislocations in single-crystal bcc Fe with(110)surface was investigated by both nanoindentation experiments and discrete dislocation dynamics(DDD)simulation.The results of nanoindentation experiments showed that the pop-in load decreased evidently for the electrochemical hydrogen charging specimen,indicating that the dislocation nucleation strength might be reduced by hydrogen.In addition,the decrease of hardness due to hydrogen charging was also captured,implying that the dislocation motion might be promoted by hydrogen.By incorporating the effect of hydrogen on dislocation core energy,a DDD model was specifically proposed to investigate the influence of hydrogen on dislocation nucleation and motion.The results of DDD simulation revealed that under the effect of hydrogen,the dislocation nucleation strength is decreased and the motion of dislocation is promoted.

Heterogeneous Fracture Simulation of Three-point Bending Plain-concrete Beam with Double Notches

Plain concrete is regarded as a two-phase material comprising randomly distributed aggregates and mortar matrix. A series of three-point bending concrete beams with symmetric or asymmetric double notches are modeled using the modified random aggregate generation and packing algorithm. The cohesive zone model is used as the fracture criterion and the cohesive el- ements are inserted into both the mortar matrix and the aggregate-mortar interfaces as potential micro-cracking zones. The dead and alive crack phenomena are studied experimentally and nu- merically; and the influences of notch location, aggregate distribution and gradation on fracture are numerically evaluated. Some important conclusions are given.

On dissipative gradient effect in higher-order strain gradient plasticity: the modelling of surface passivation

The phenomenological flow theory of higher-order strain gradient plasticity proposed by Fleck and Hutchinson(J.Mech.Phys.Solids,2001)and then improved by Fleck and Willis(J.Mech.Phys.Solids,2009)is used to investigate the surface-passivation problem and micro-scale plasticity.An extremum principle is stated for the theory involving one material length scale.To solve the initial boundary value problem,a numerical scheme based on the framework of variational constitutive updates is developed for the strain gradient plasticity theory.The main idea is that,in each incremental time step,the value of the effective plastic strain is obtained through the variation of a functional in regard to effective plastic strain,provided the displacement or deformation gradient.Numerical results for elasto-plastic foils under tension and bending,thin wires under torsion,are given by using the minimum principle and the numerical scheme.Implications for the role of dissipative gradient effect are explored for three non-proportional loading conditions:(1)stretch-passivation problem,(2)bending-passivation problem,and(3)torsion-passivation problem.The results indicate that,within the Fleck-Hutchinson-Willis theory,the dissipative length scale controls the strengthening size effect,i.e.the increase of initial yielding strength,while the surface passivation gives rise to an increase of strain hardening rate.

Transient Bending Vibration of a Piezoelec trie Semiconductor Nanofiber Under a Suddenly Applied Shear Force

We study transient bending vibration of a ZnO piezoelec trie semiconduc tor nanofiber fixed at one end with a suddenly applied shear force at the other end.A one-dimensional model based on the phenomenological t heory of piezoelec trie semiconductors consisting of the equations of piezoelectricity coupled to the continuity equation of electrons is used.An approximate theoretical analysis is performed,accompanied by a finite element analysis using COMSOL.The evolutions of deflection,elec trie pot ential and elec tron dist ribution are calculated and examined.It is found that when the fiber reaches its largest deflection,the distributions of the electromechanical fields are qualitatively similar to those in the case of static loading under the same shear force,but the amplitudes of the fields are about twice as large roughly.

Application of focused laser differential interferometer to hypersonic boundary-layer instability study

Accurate prediction of hypersonic boundary-layer transition plays an important role in thermal protection system design of hypersonic vehicles.Restricted by the capability of spatial diagnostics for hypersonic boundary-layer study,quite a lot of problems of hypersonic boundary-layer transition,such as nonlinearity and receptivity,remain outstanding.This work reports the application of focused laser differential interferometer to instability wave development across hypersonic boundary-layer on a flared cone model.To begin with,the focused laser differential interferometer is designed and set up in a Mach number 6 hypersonic quiet wind tunnel with the focal point in the laminar boundary-layer of a 5 degree half-angle flared cone model.Afterwards,instability experiments are carried out by traversing the focal point throughout the hypersonic boundary-layer and the density fluctuation along the boundary-layer profile is measured and analyzed.The results show that three types of instability waves ranging from 10 k Hz to over 1 MHz are co-existing in the hypersonic boundary-layer,indicating the powerful capability of focused laser differential interferometer in dynamic response resolution for instability wave study in hypersonic flow regime;furthermore,quantitative analyses including spectra and bicoherence analysis of instability waves throughout the hypersonic boundary-layer for both cold and heated cone models are performed.