Piezoelectric semiconductor shells, as a new type of multifunctional material structure, have shown broad application prospects in the fields of intelligent sensing, energy harvesting, and flexible electronic devices in recent years. Understanding the distributions of charge carriers under loading is crucial for the design and performance optimization of piezotronic devices. However, the distributions of charge carriers are also influenced by the form and magnitude of external loads, owing to the nonlinear interaction between electromechanical fields and charge carriers, which has usually been ignored in previous studies. Hence, in this study, a bending n-type piezoelectric semiconductor thin shell model taking account of this nonlinear effect is established on the basis of first-order shear deformation theory. The principle of virtual work is used to derive the governing equations and boundary conditions. The accuracy and effectiveness of the nonlinear model are validated through comparisons with a linearization under the condition of a small external load and with a three-dimensional pure piezoelectric model. Numerical results show that the linear model fails to accurately describe the distribution behaviors of charge carriers as the external load increases. The distributions of charge carriers in the plane and along the thickness direction are revealed for different magnitude of uniform loads. An interesting phenomenon is found in which the electron distribution is not confined to the loading region on the middle surface, regardless of whether the loading direction is along or against the c axis. In the former case, electrons are redistributed toward the outer boundary of the loading zone within the plane, while in the latter case, the redistribution is mostly toward the upper and lower surfaces in the thickness direction. The results of this study will provide guidance for designing new shell-based piezotronic devices.

Under intense optical illumination, piezoelectric semiconductors (PSs) undergo non-uniform temperature rise due to radiative heat transfer, which generates polarized charges and modifies the device barrier structures. This study develops a nonlinear multiphysics coupling model for piezoelectric semiconductor double-barrier structures (PS-DBSs), incorporating energy conversion processes under opto-thermoelectric coupled loading. Results show that the base current in PS-DBSs is primarily governed by the equivalent photoelectromotive force (E-PEMF) induced by optical loads, while the collector current is mainly controlled by the equivalent thermoelectromotive force (E-TEMF) from thermal loads. This finding reveals that quantitative decoupling of opto-thermal coupled excitation can be achieved via dual-electrode signals, a mechanism that remains valid over a wide operating voltage range. Further analysis indicates that the underlying mechanism originates from the competitive interplay between E-PEMF and E-TEMF in modulating carrier transport, suggesting that rational structural design enables PS devices to self-regulate under external excitation. Overall, this work provides new insights for developing space-borne optoelectronic sensors and high-performance solar cells.

In this study, we compare four electrode models, i.e., solid model, added mass model, thin-film model, and a combining model of thin-film with added mass, for a 76.8 MHz AT-cut quartz resonator. Relative to the high-fidelity solid electrode benchmark, the combining model accurately captures the thickness-shear mode but overestimates displacement confinement due to mass loading and boundary effects. The thin-film model fails to replicate practical device states by ignoring mechanical mass and stiffness. In contrast, the added mass model optimally balances fidelity and efficiency, matching the benchmark’s frequency and resistance predictions with a 43% reduction in computation time. Parametric studies further indicate that cut angle deviations (33°~37°) alter equivalent shear stiffness, while electrode mass variations (mass coefficient 0.99~1.02) modify vibrational inertia. Both of them are critical for frequency tuning. Our findings clarify the scope and limitations of these strategies, guiding high-precision simulations and designs for high-frequency resonators.

Achieving both non-volatility and efficient readability is a key challenge for memory devices. Herein, we innovatively realize their compatibility by constructing an independent mechanical potential well in a piezoelectric semiconductor (PS) PIN rod. A nonlinear multi-field coupling model (integrating piezoelectric effects, carrier transport, and mechanical loading) is established, and the governing equations are solved with high precision via the Finite Volume Method (FVM) combined with the Scharfetter-Gummel (S-G) discretization scheme. Results show that compressive loading induces an independent mechanical potential well in the I region of the PS-PIN rod, originating from the synergistic effect of weak polarization electric field screening by low doping in the I region and strong screening by high doping in P regions, as well as the interaction between the polarization electric field and non-uniform carrier distribution. The potential well efficiently traps holes injected from the P region for information storage in the on-phase, and exhibits slow carrier release in the cut-off phase via the synergistic regulation of the polarization electric field and applied bias field. This study provides a theoretical basis and technical support for developing low-power piezoelectric semiconductor memory devices integrated with sensing and storage functionalities.

The mechanical regulation of piezoelectric semiconductor interfaces represents an emerging research frontier that integrates interactions among multiple physical fields, such as electrical, mechanical, thermal, and optical fields, with charge carriers. This review examines the fundamental operating mechanisms and potential applications of piezoelectric PN junctions. We chronicle the evolution of multi-physics modeling frameworks, tracing the shift from classical depletion-layer approximations toward advanced non-depletion paradigms. Subsequently, we elaborate on the principles of mechanical tuning of electrical properties mediated by artificial potential barriers, linking these mechanisms to prospective applications in sensors, energy harvesters, and solar cells. Finally, we outline future directions and challenges for interface innovation, with an emphasis on the precision modeling. Besides, these insights provide a roadmap for harnessing artificial potential barriers to surpass conventional performance limits in adaptive electronics and the energy-information sector.

The performance of piezotronic devices is primarily governed by the interaction between elastic waves and charge carriers. Therefore, understanding the underlying mechanisms of this interaction in piezoelectric semiconductors is crucial for the research and development of piezotronic devices. Unlike in purely elastic or piezoelectric media, an elastic wave propagating in a piezoelectric semiconductor involves two interdependent physical processes: the evolution process of thermodynamic state, and the vibration state of elastic wave-front. The former is from the evolution of carrier behavior and the latter is related to the dynamic characteristics of polarization electric field. The mutual competition between two dynamic processes stimulates the interaction between electric field and charge carriers, i.e., appearing a field-particle coupling wave (FPCW). This coupling wave is useful in remaking elastic wave-front characteristics to develop new acoustoelectric devices or to prompt performance of piezoelectric semiconductor devices. Thus, a multi-field coupling dynamic model is established to analyze the relationship between polarized electric field and charge carriers at the elastic wave-front. Furthermore, the distinct coupling mechanisms of these processes at varying vibration frequencies are examined. It is found that a vibration state of an elastic wave-front was altered by the corresponding thermodynamic state most severely at a low-frequency situation, significantly at a medium-frequency one and almost none at a highfrequency one. Correspondingly, a FPCW becomes most pronounced due to strong competition between two dynamic processes in a medium-frequency situation, and very weak in the other two ones. Furthermore, it is revealed in the paper that the nonlinear behavior in drift current is to transfer energy to higher order vibration modes instead of being consumed as claimed from the harmonic analysis technique. These findings are of great significance for designing passive delay line filters, amplifiers, and circulators, etc.

When an elastic wave propagates in piezoelectric semiconductors, the interaction between charge carriers and electric fields on the elastic wave-front (EWF) generates a coupled wave, termed the field-particle coupling wave (FPCW). The propagation speed of FPCW is usually greater than that of the corresponding elastic wave, causing that a preceding EWF is undoubtedly overtaken and influenced by those FPCWs emitted from the trailing EWF. Hence, the effect of FPCW on EWF is systematically investigated in this paper. Our numerical results indicate that the nonlinear feature of drift current causes the stronger dispersion behavior on EWF, while the dissipation behavior of EWF is only caused by the Joule heating effect. Furthermore, loading configuration significantly affects the dynamic characteristics of EWF via different behavior of EPCW. Under a sine-typed loading, the dispersion effect is confined to act on EWF itself with very tiny effects ahead of it. In contrast, a cosine-typed loading induces dispersion not only at the EWF itself but also in front of it. Thus, an interesting phenomenon shows a moving reversal barrier or a moving barrier layer just ahead of the EWF under a cosine-typed loading. We particularly note that the above two moving layers of barriers cannot leave from the leading end of EWF, which is similar as that of the Greek hero Antaeus who had to constantly draw energy from the Earth Mother. The study of dispersion and dissipation in elastic waves propagating in piezoelectric semiconductors is crucial for the R&D and performance enhancement of piezoelectric electronic devices.

Molybdenum disulfide (MoS2) is considered a potential material for next-generation optoelectronic devices owing to its tunable bandgap and high carrier mobility. A pulsed laser-induced technology can rapidly synthesize centimeter-scale MoS2 films with high crystal quality at room temperature, making them compatible with complementary metal-oxide-semiconductor (CMOS) processes. Usually, the MoS2 thin films that are prepared belong to n-type. However, to promote the application of pulsed laser-induced technology in two-dimensional material devices and circuits, achieving effective and uniform p-type doping is crucial. In this study, a novel in situ doping technique was proposed, wherein copper (Cu) was successfully doped into MoS2 thin films as a p-type doping acceptor using pulsed laser-induced technology. The growth and doping processes were simultaneously completed. Raman spectra, high-resolution transmission electron microscopy (HRTEM) images and X-ray photoelectron spectroscopy (XPS) tests showed that Cu was successfully doped into the MoS2 thin film with a uniform and effective doping effect. To further verify the p-type doping effect, back-gate field-effect transistors (FETs) were fabricated. Compared with the undoped one, the current on/off ratio of FET improved from 5 x 102 to 105, and the field-effect mobility increased from 0.093 cm2 V-1 s-1 to 16.05 cm2 V-1 s-1. This indicated that the Cu doping of MoS2 thin films effectively enhanced their conductivity and field-effect mobility. These findings demonstrate that pulsed laser-induced technology can achieve growth and in situ doping of MoS2, improving both crystal quality and device performance, and it has the potential to be used in other element doping and two-dimensional (2D) materials.

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.

Piezoelectric semiconductor (PS) materials are widely used in the modern flexible, self-powered and wearable devices due to both of piezo-effect and semiconduction property. As well known, the interfacial properties play a key role in these devices and can be effectively tuned by the strain engineering (SE). However, many interesting phenomena of interfacial properties are still unrevealed due to the unopened potential barrier zone, such as the revolution laws of the interfacial barrier configuration corresponding to applied strains. In this study, a composite structure composed of a thin piezoelectric PN junction locally pasting over an electrically insulating wafer, such that the deformation will be transferred to the junction after the wafer subjecting to the external loads. Then, the matching laws between the non-uniform electromechanical fields and carriers are revealed by clarifying the interaction mechanisms among the deformation, electric polarization, and carriers in a piezoelectric PN junction. Based on a non-depletion-layer model, it is observed that the interfacial potential barrier configurations are effectively reconstructed by the surface-polarized charges at loading boundaries induced by discontinuous electric polarizations and piezoelectric charges in the volume induced by non-uniform strains. It is also found that the limitation of further optimization of the output performance of piezoelectric PN junctions is the carrier-type inversion. Thus, the optimization of the distribution of piezoelectric charges is carried out to suppress the excessive carrier-type inversion for a greater current density amplification factor. Besides, it is also found that the maximum current density amplification factor is commonly not shown with an optimal Gauge factor simultaneously. Obviously, the present study possesses referential significance to design high-performance piezotronic devices.

A refined nonlocal zigzag model for thermal buckling analysis of nano composite laminated and sandwich beams is proposed in this study based on a refined zigzag theory and Eringen's nonlocal theory. Firstly, present model satisfies the stress-free and continuity conditions a priori by introducing the piecewise-linear zigzag functions and a preprocessing, such that the transverse shear correction factors are not needed. In the preprocessing, accurate and continuous transverse shear stresses are obtained with the aid of the general mixed variational principle, which can be solved simultaneously with other stresses in the governing equations. This is quite different from the previous post-processing. Subsequently, thermal buckling problems of nano composite laminated and sandwich beams are analytically solved in simply supported boundary conditions. The degenerated results without small effect indicate that the non-dimensional critical loads and critical temperatures have a good agreement with the 3D elasticity solutions and previous results, which demonstrate the accuracy and reliability of present model. Moreover, it is observed that the small effect of the critical temperatures can be effectively captured by Eringen's differential constitutive law (EDCL), which shows the small effect decreases the critical temperature by weakening the stiffness of the beam. Finally, the effects of different thermal expansion coefficients, laminations, geometric sizes and beam theories are discussed. The results show that present model is robust in the arbitrary layouts for both of composite and sandwich structures, which may have some referential significance to Micro-Electro-Mechanical Systems (MEMS) sensors and actuators.

In this paper, the barrier region of a mixed hetero-junction consisting of a p-type Si and an n-type ZnO was fully opened by abandoning the depletion layer approximation in advance. The barrier configuration was reconstructed by the artificial potential barrier based on a new fully coupled model in which the interaction between physical fields and charge carriers was taken into account. Then, we put forward an interesting design idea of elevating the mechanical regulation performance of a PN junction by manufacturing it with a third-generation piezoelectric semiconductor and a narrow bandgap semiconductor. It is through the deformation of the third-generation piezoelectric semiconductor on one side under mechanical loadings to excite polarization charges at the PN interface such that the movement of charge carriers in the narrow bandgap semiconductor on the other side is able to be tuned by the interface polarization charges. Besides, it is found a specific current-stress characteristic for such a mixed hetero-junction, which will present three stages, i.e., rising stage, platform stage and falling stage. The rising stage is caused by the improving recombination rate, which can be used as a high sensitivity stress sensor (output current improved by more than 10 times in a small stress). Oppositely, the falling stage is caused by the weakened recombination rate due to carrier type-inversion, which can be used to determine overload (output current reduced dramatically when the stress increased to a specific value). Finally, the platform stage is caused by the competition of the above two cases. At this stage, the device operates very stable and can resist the external perturbation. Obviously, the study possesses referential significance to the design and mechanical tuning on performance of piezotronic devices.

By measuring the changes in the piezoelectric coefficient d33 of ZnO bulk single crystals before and after annealing, dependence of piezoelectric coefficient d33 on annealing temperature was obtained experimentally. After annealing, the piezoelectric coefficient d33 of the ZnO bulk single crystals with [0001] or [0001¯] orientation increases with increase of annealing temperature. Comparing the XPS and PL spectra before and after annealing, we found in this paper that the oxygen vacancy concentration on the Zn-terminated surface and O-terminated surface of ZnO bulk showed an opposite trend. This caused the redistribution of electrical domains within the entire bulk and achieved spontaneous polarization. As the annealing temperature increases, the gradual increase followed by stabilization in the oxygen vacancy concentration. Therefore, the relationship between the piezoelectric coefficient and annealing temperature satisfies the Boltzmann distribution.

Flexotronics induced by the strain gradient and flexoelectricity in a semiconductor with symmetric or asymmetric crystal structures have attracted considerable attention as a promising approach for tunable electronic processes. However, the electric nonlinear properties between the carriers and electric field are ignored in most of related studies. In this study, a new size-dependent nonlinear model is developed to investigate the interaction among the size effects (caused by strain gradient and flexoelectricity), piezo-effects and semiconducting properties in a piezoelectric semiconductor (PS) nanofiber with asymmetric crystal structures. In addition, the Von-Kármán's nonlinear strain is also considered to check the effect of geometric nonlinearity. It is found that the piezo-effect can be enhanced (reduced) by the effect of flexoelectricity (strain gradient) due to a new positive (negative) superimposed increment of electric field under a pair of tensile stress. Besides, the size effect will be weakened by the semiconducting property. The studies will provide guidance for theoretical analysis of size effect in nano PSs and design of flexotronic devices.

In this study, a new mixed-field zigzag shell model is proposed in terms of Reissner's Mixed Variational Theorem (RMVT) for the composite laminates with curvature. In this model, refined zigzag theory (RZT) is employed to improve the accuracy and efficiency by introducing through-the-thickness piecewise linear warping functions. Moreover, the shear correction factors are eliminated. It is also different from the published models for composite laminated shells, the continuity conditions of interlaminar transverse shear stresses (TSSs) are satisfied a priori based on RMVT. The equilibrium equations and related boundary conditions are also derived from RMVT. Subsequently, the static performance, natural frequencies, and critical loads of composite laminates with curvature are verified by comparing them with the 3D elastic solutions and other existing ones. It is observed that the present model accounts for not only the efficiency of the low-order models but also the accuracy of the high-order models. Finally, it is shown that the ply stacking, side-to-thickness ratios, and side-to-radius ratios play an important role in percentage errors between the present model and the previous ones.

Coupling of piezoelectric and semiconducting properties can stimulate a field-particle coupling wave (FPCW) between electric field and charge carriers on an elastic wave-front (EWF) propagating in a piezoelectric semiconductor. The wave velocity of a FPCW is usually greater than the EWF as vibration frequency rises such that carrier behavior on and in front of the EWF will be disturbed in advance. This interaction between two waves can stimulate a few novel dynamic features which are of obvious significance for the research and development of innovative piezoelectric electronic devices. Hence, we firstly established a dynamic model on the propagation processes of elastic waves in piezoelectric semiconductors and developed an alternately iterative algorithm between piezoelectric and semiconducting properties in this paper. Then, the propagation behavior of an elastic wave in an n-type ZnO rod was taken as an example to elucidate the dispersion and dissipation arising from the coupling between electric field and charge carriers. It was found that the action of a FPCW on the EWF can stir up previously undiscovered bizarre features in the following two aspects. One is the energy transfer between different frequency wave components from low-order to high-order vibration modes implemented by the flow of charge carriers, where the transfer process bears a resemblance story to the ‘vacated room’ operation in Hilbert's paradox of the Grand Hotel. The other more intriguing one is that when a tensile/compressive deformation signal is input, an opposite phase signal will be induced at the leading edge of the EWF by the FPCW through the inverse piezoelectric effect, meaning the appearance of a compressive/tensile signal in front of the input tensile/compressive one. The reason to appear such a phenomenon is that the electric field phase of the FPCW is precisely opposite to the one on the corresponding EWF. Evidently, the present studies will advance the integration and development of elastic dynamics and semiconductor physics, thereby providing valuable guidance for the research and development of new electronic devices.

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 EW-fronts. 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 low-frequency 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.

A coupling model is established on piezoelectric semiconductor bipolar junction transistors (PS-BJT) subjected to mechanical loadings by abandoning depletion layer approximation and low injection assumption. Effect of base region on device performance and interaction between emitter/base junction (E/B) and base/collector junction (B/C) are investigated. It is found that too small a base width will cause B/C to extract electrons directly from emitter region, implying that an electron passageway will be excited to link from collector- to emitter-region by striding over base-region (abbreviated as "EP-CE" hereafter). We particularly clarify that the current produced by electrons flowing across EP-CE is independent of electron-hole recombination in E/B, which means that this current has not yet been bestowed on the information of base current. "Information of base current" refers to dispatching information of base current on the electrons in emitter region. Thus, a current from EP-EC cannot be reckoned in the amplification effect of base current. Our investigations show that base width should not be designed too small to avoid EP-CE, which has not been revealed before. As regards to tuning PS-BJT performance by mechanical loadings, we revealed the mechanism as follows: 1) raising electron-hole recombination rate inside E/B to reduce resistivity such that more electrons can be driven from emitter- to base-region; 2) elevating electron conductivity in base-region for easier pass of electrons; 3) promoting attractive ability of B/C on electrons such that more electrons cross the interface. Numerical results show that transmission characteristics can be greatly increased as expected by mechanical tuning.