Bandgap Design Research Articles

Oxidation State Dependent Conjugation Controls Electrocatalytic Activity in a Two-Dimensional Di-Copper Metal–Organic Framework

Molecularly defined two-dimensional conjugated metal–organic frameworks combine properties of molecular and material based electrocatalyst, enabling tunable active site and bandgap design. The rational optimization of these systems requires an understanding of the complex interplay between the various metal sites and their influence on catalysis. For this purpose, copper-phthalocyanine-based two-dimensional conjugated metal–organic framework (CuPc-CuO4 2D c-MOF) films with an edge-on layer orientation were transferred to nickel-nitrilotiacetic acid (Ni-NTA)-functionalized graphite electrodes and analyzed via electrochemical resonance Raman spectroscopy. With the help of density functional theory (DFT) calculations for the first time a detailed assignment of the vibrational bands for different Cu oxidation states could be achieved and correlated to their electrocatalytic activity in respect to oxygen reduction (ORR). Potential dependent Raman spectroscopy made it furthermore possible to determine the redox potentials of the Cu in the CuPc moieties and the Cu-catecholate nodes individually with ECuPc = −0.04 V and ECuO4 = +0.33 V versus Ag|AgCl. Electrocatalytic ORR, however, was only observed below −0.2 V where both Cu units were present in their respective CuI state. DFT calculations of bandgaps and density of states (DOS) showed a significant decrease in bandgap and increase in π-conjugation upon transition from the inactive mixed CuII/CuI state to the active CuI/CuI state, suggesting that slow electron transfer in the mixed state limits ORR catalysis. Our results indicate that the coupling between metal oxidation changes and π-conjugation of the 2D c-MOF is a key parameter toward achieving electrocatalytic activity.

Research on the Design of Phononic Crystal Rod Band Gaps Based on Lumped Mass Method

Research on the Design of Phononic Crystal Rod Band Gaps Based on Lumped Mass Method

Research on the design of phononic crystal shaft bandgaps based on lumped mass method

Phononic crystals tend to mature in the research of forward problems due to their unique bandgap characteristics, but it is difficult to realize reasonable parameter design at specific bandgap frequencies in practical engineering applications. Thus, based on the lumped mass method, a research method for the inverse problem of phononic crystal shaft bandgaps is proposed in this paper. On the basis of the discretization model, the relationship between polynomials and the characteristic of bandgaps is discussed through derivation of the dispersive polynomial, and the feasible regions of the corresponding parameters are solved according to the bandgap existence criterion established by the characteristic rules for analytical verification. The results show that the bandgap existence criterion for frequency points and frequency bands can accurately and effectively invert the relevant parameters that meet the requirements, and the method is of great practical significance for promoting the development of phononic crystal shaft parameter design under the target bandgap in engineering applications.

Band Gap Design of Beam-Supported Phononic Crystal by Regulation and Control of Beam Bending Stiffness

Band Gap Design of Beam-Supported Phononic Crystal by Regulation and Control of Beam Bending Stiffness

Ultra-wide low-frequency bandgap design of acoustic metamaterial via multi-material topology optimization

Ultra-wide low-frequency bandgap design of acoustic metamaterial via multi-material topology optimization

Tunable thermal expansion and bandgap properties of the bi-material-directional honeycomb metamaterial

The excellent shape stability of thermally expanded metamaterials and the good bandgap properties of acoustic metamaterials have a wide range of promising applications in aerospace and sensors. Here, a bi-material-directional honeycomb metamaterial (BHM) with tunable coefficient of thermal expansion (CTE) and bandgap properties is proposed. The theoretical analysis and numerical simulations are employed to reveal the thermal deformation mechanism of the BHM. In addition, the analytical expression of the effective Young’s modulus is established by considering both tensile and bending deformation. Based on the Bloch theorem, the band structures of the BHM are calculated by the finite element method. Parameter analysis confirms that the CTE and bandgap of the BHM can be simultaneously regulated and drastically adjusted by changing the geometric parameters and material combinations. Meanwhile, the coupling relationship of the effective CTE, Young’s modulus, and total effective bandgap width are investigated. The results show that the BHM can have tunable CTE function and large total effective bandgap width by selecting suitable parameters while satisfying stiffness requirements. This study achieves a dual objective of specific CTE properties and bandgap design through rational material selection and shape design, which makes the metamaterials have better tunability and multifunctionality.

A Sub-1-V 8.5-ppm/°C Sampled Bandgap Voltage Reference

This brief proposes a novel sub-1V discrete-time CMOS bandgap reference circuit where a constant voltage is produced by summation of a CTAT and a PTAT voltage that are sampled onto a capacitor. By sampling the voltages onto a capacitor, we eliminate the need for an opamp in the bandgap core, which tends to be the dominant source of noise and offset concerns in low voltage bandgap designs in scaled technologies. A prototype was designed and fabricated in 28nm TSMC HPC+ technology with a nominal output voltage of 108mV. It demonstrates a temperature coefficient of 8.5ppm/°C between −40°C and 125°C, and occupies an area of 0.0075mm2 while consuming <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$11.6\mu \text{W}$ </tex-math></inline-formula> of power.

A Passive Vibration Control Method of Modular Space Structures Based on Band Gap Optimization

Modular space structure has become a research hotspot in the aerospace field. In the microgravity and weak damping space environment, modular space structures may continuously vibrate due to the transient excitation caused by satellite attitude adjustment or space debris impact, which will make the structure unstable. Therefore, a passive vibration control method based on band gap design is proposed for the modular space structures. Firstly, a modular spectral element model based on the super element is established, and the modular spectral element model is expanded into modular space structures. Then, band gap characteristics of the modular space structure are analyzed and optimized to improve the wave isolation ability. The numerical simulation shows that the elastic wave in the band gap can be effectively isolated and the band gap is significantly improved by optimizing structural parameters.

Band-gap design of reconfigurable phononic crystals with joint optimization

In this article, a joint topology optimization procedure is executed to design phononic crystals (PnCs) with a maximized band gap. First, the band gap of two-dimensional PnCs is calculated using a finite element model under the plane strain assumption for easy and efficient optimization. In the numerical computation of the band gaps, the band structures of in-plane and out-of-plane modes are analyzed and verified using COMSOL. Then, the density-based and feature-driven methods are sequentially used to design the unit cell of the PnCs with single-phase material. A stiffness constraint is added to ensure the continuity of the material inside the unit cell, and a boundary constraint guarantees continuity amongst the unit cells. The optimization problem is solved through the Method of Moving Asymptotes (MMA), and reconfigurable manufacturing PnC is obtained via joint topology optimization. Lastly, the band structures and vibration modes of the reconstructed model are analyzed. Research results show that the optimal PnCs generate broadband vibrations by localized resonance and have negative refraction characteristics. This research also confirms that the joint topology optimization is an efficient approach for designing novel elastic metamaterials.

Tunable Bandgap Design of Soft Phononic Crystals Using Topology Optimization (Adv. Theory Simul. 7/2022)

Tunable Bandgap Design of Soft Phononic Crystals Using Topology Optimization Tunable band gap designs of mechanism-driven soft PnCs composed of hyperelastic materials is reported in article number 2100620 by Yangjun Luo and Yan Li. The gradient-free MFSE topology optimization method provides an effective way to design soft PnCs with the maintenance, opening and closing of arbitrary order bang gaps using tensile deformation.

Omnidirectional nonreciprocal absorber realized by the magneto-optical hypercrystal.

Photonic bandgap design is one of the most basic ways to effectively control the interaction between light and matter. However, the traditional photonic bandgap is always dispersive (blueshift with the increase of the incident angle), which is disadvantageous to the construction of wide-angle optical devices. Hypercrystal, the photonic crystal with layered hyperbolic metamaterials (HMMs), can strongly modify the bandgap properties based on the anomalous wavevector dispersion of the HMM. Here, based on phase variation competition between HMM and isotropic dielectric layers, we propose for the first time to design nonreciprocal and flexible photonic bandgaps in one-dimensional photonic crystals containing magneto-optical HMMs. Especially the zero-shift cavity mode and the blueshift cavity mode are designed for the forward and backward propagations, respectively. Our results show maximum absorption about 0.99 (0.25) in an angle range of 20-75 degrees for the forward (backward) incident light at the wavelength of 367 nm. The nonreciprocal omnidirectional cavity mode not only facilitates the design of perfect unidirectional optical absorbers working in a wide-angle range, but also possesses significant applications for all-angle reflectors and filters.

Harmonic decomposition of the trace of 1D transfer matrices in layered media

The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be established via a matrix, termed (global) transfer matrix (product of “atomic” single-layer matrices). As a matter of convenience, we focus on 1D propagation of axial waves in rods, but our results extend to other fields where the formalism applies. When the layering corresponds to a representative repeated cell in an otherwise infinitely periodic medium, the trace of the cumulative multi-layer matrix is known to control the dispersion relation. It is proved that this trace has a discrete spectrum made up of distinct 2N−1 harmonics (not necessarily orthogonal to each other in any sense) which are exactly characterized in terms of both the period of their oscillations (each period being defined by N constituents) and their amplitudes; the phase shift among harmonics is either zero or π. This definite appraisal of the discrete spectrum of the trace opens new strategies for rational design of bandgaps, going beyond parametric or sensitivity studies.

Tunable Bandgap Design of Soft Phononic Crystals Using Topology Optimization

AbstractSoft phononic crystals (PnCs) have significant advantages for tuning bandgaps and undergoing reversible large deformations. However, the difficulty of the design arises from the presence of material and geometrical nonlinearities coupled with the energy band performance. This study presents an effective topological optimization method to realize tunable bandgap designs of mechanism‐driven soft PnCs composed of two hyperelastic materials. Based on the material‐field series‐expansion method, the topology optimization model with a small number of topological design variables is defined as maximizing the bandgaps of PnCs before and/or after stretching. The optimization problem is then solved by a gradient‐free algorithm, which eliminates the need for the complex sensitivity analysis. Numerical examples show that using tensile deformation to switch between different acoustic functions can achieve the maintenance, opening, and closing of arbitrary order bandgaps, and the proposed method provides an effective way to design soft PnCs with rapid tunability of bandgaps.

Topology optimization of magnetorheological smart materials included PnCs for tunable wide bandgap design

Topology optimization of magnetorheological smart materials included PnCs for tunable wide bandgap design

Cascaded band gap design for highly efficient electron transport layer-free perovskite solar cells.

The elimination of the electron transport layer (ETL) to fabricate ETL-free perovskite solar cells (PSCs) could save manufacturing cost and time. However, the direct contact of the perovskite and transparent conducting oxide (TCO) electrodes results in mismatched energy level alignment and current leakage. Therefore, ETL-free PSCs suffer from unsatisfactory photovoltaic performance. Herein, a special perovskite material with a cascaded band gap, called gradient homojunction perovskite (GHJP), is designed and synthesized by a large cation-assisted method. The inherent nature of GHJP was the type-II cascaded energy level alignment, which could block holes during the electron collection. This facilitated the dissociation of the excitons in the GHJP. Due to the excellent properties, ETL-free PSCs based on GHJP obtained 20.55% PCE, which was over 90% higher than that of ETL-free PSCs based on the control perovskite material.

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

Propagation Characteristics of Flexural Wave in One-Dimensional Phononic Crystals Based on Lattice Dynamics Model

In this paper, we establish discrete flexural lattice chain models of Bragg and locally resonant phononic crystals by setting mass defect atoms and local resonant elements on the flexural lattice chain. The bandgap characteristics of flexural wave in phononic crystals are studied by establishing the governing equations of the model. The results from models show that with the change of the mass ratio of defective atoms to normal atoms, the bandgap of the flexural wave produced by Bragg scattering shows a certain rule. When the local resonant bandgap and Bragg scattering bandgap are close to each other, the two bandgaps will be coupled to form a wider flexural wave bandgap. The effect of axial strain on bending wave propagation is only the shift of bandgap position. The effect of material damping on the propagation of a bending wave is only energy dissipation at high frequency. In addition, we use finite element simulation to calculate the bandgap of flexural wave in phononic crystals with mass defects, and the results are consistent with lattice chain model. This shows that lattice chain model can effectively guide the bandgap design of phononic crystals. This comprehensive study may help to elucidate the rule of bandgap generation of flexural wave in one-dimensional phononic crystals.

Study on Band Gap Characteristics of Boat-Shaped Phononic Crystal

In this paper, we analyze the two-dimensional Boat-shaped structure based on the finite element method. We calculated its energy band structure and vibration transmission properties and found that the structure has band gaps at both high and low frequencies. Compared with common traditional two- dimensional phononic crystals, the boat-shaped phononic crystal has the advantage of larger bandgap design and modulation parameter space due to their structural complexity. In order to obtain better bandgap characteristics, we studied the influence of four key parameters, such as the rod length and the angle between the rods, on the bandgap. The results show that: for low frequency band gaps, the width of the band gap can be effectively changed by changing the size of the angle between the rods while rod length greatly affects the bandgap position; for high band gaps, the length of rods has a large effect on the band gap position. These laws have guiding significance for the bandgap regulation of boat-shaped phononic crystal.

Band gap mechanism and vibration attenuation characteristics of the quasi-one-dimensional tetra-chiral metamaterial

In this paper, the quasi-one-dimensional tetra-chiral metamaterial is proposed for low-frequency broadband vibration attenuation, inspired by the 3D chiral compression-torsion coupling metamaterials. Different from the traditional metamaterials utilizing translational local resonators to induce reaction force to prevent vibration transmission, this paper can realize rotation and translation on a resonator by introducing chiral structure, which is more beneficial for vibration energy dissipation. The band gap mechanism and vibration attenuation characteristics of the proposed metamaterial are studied based on the discrete mass-spring model. The dependences of the band gap characteristics on the parameters are studied in detail as the bigger the chiral angle, the bigger the mass ratio, the smaller the stiffness ratio, the smaller the dimensionless rotational inertia, the wider the band gap. The analytical boundary equations for band gaps are derived to provide guidance for desired band gap design, and multiple and ultra-wide band gaps can be obtained by tuning the structural parameters. Through the investigation of eigenstate modes, the mode reversals at dispersion curves intersection and veering are observed, and the interchange mechanism for the boundary equations of dispersion curves is unveiled. The vibration transmission in finite unit cells validates the frequency ranges with high vibration attenuation predicted by band structure. The movement energy analysis and wave packet propagation in finite unit cells also demonstrate the vibration attenuation characteristics of the proposed metamaterial. This study can provide new ideas and theoretical guidance for metamaterial design.

Simulation Study on Novel GaN‐Based n−p−n Heterojunction Bipolar Transistors with a Quaternary AlGaInN Emitter and a Two‐Dimensionally Conductive Base

Herein, a simulation study on novel GaN‐based n−p−n heterojunction bipolar transistors (HBTs) with a quaternary n‐AlGaInN emitter and a thin GaInN quantum well (QW) layer inserted in its p‐GaN base is reported. The idea of the quaternary AlGaInN emitter facilitates the design and independent growth of the energy bandgaps and lattice strain. In addition, the p‐GaN base inserted with the thin GaInN QW is expected to be effective in enhancing its lateral conduction via 2D hole gases (2DHGs). The simulation results indicate that the designed GaInN QW definitely functions to generate and transport the 2DHGs and ultimately contributes to the improvement of the device performance. In other words, the lateral resistivity of the p‐GaN base is reduced from 1.8 × 10−1 to 7.0 × 10−2 Ω cm with the use of the GaInN QW insertion layer. Further, the simulation study focusing on the lateral distance between the n‐emitter and p‐base electrodes exhibits stable device characteristics for the HBT with the GaInN QW insertion layer compared with the conventional HBT structure. Dynamic analysis of the carrier concentration distribution indicates that the QW functions as a low‐resistance current path and it has the effect of avoiding the punch‐through phenomenon.