Existence Of Surface States Research Articles

The diversity of isofrequency surface topologies in a hypercrystal composed of ferrite- and semiconductor-based metamaterials

Recent studies have centered on the potential for effectively controlling the topology state of iso-frequency surfaces in artificial photonic structures using external fields. This paper delves into the topological transitions and singularity states of the isofrequency surface of a highly anisotropic superlattice. This superlattice is composed of alternating layers of ferrite-dielectric and semiconductor-dielectric metamaterials. The superlattice is placed in an external magnetic field in the Voigt geometry that is parallel to the boundaries of the structure layers and perpendicular to the periodicity axis. Material properties of both constituent metamaterials are described in terms of effective components of permittivity and permeability in the long-wave approximation. An external magnetic field influences the properties of transverse electric (TE) waves in the ferrite-dielectric metamaterial, and the properties of transverse magnetic (TM) waves in the semiconductor-dielectric metamaterial. This results in the iso-frequency surface transition from a closed ellipsoid to an open hyperboloid for both TE and TM waves in various configurations. Furthermore, the superlattice can be identified as a hypercrystal under certain conditions, specifically when the constituent metamaterials possess a hyperbolic isofrequency surface state. This research demonstrates that the isofrequency surface properties of the studied hypercrystal can be effectively controlled by altering the external magnetic field, the fill factors of metamaterials, and frequency. Special attention is devoted to investigating the topological singularities that take place when iso-frequency surfaces of TE and TM polarized waves intersect. This intersection leads to the degeneracy of the hypercrystal’s isofrequency surface and the potential observation of unique phenomena such as conical refraction or the existence of surface states.

Experimental Investigation of Long-term Ageing Effect on the Structural and Electrochemical Behaviour of Self-organized TiO2 Array Nanotubes on Ti-6Al-4V Alloy

Background: The correlation between anodization conditions and the ageing effect on TiO2 nanotubes (TNT) surface has been widely studied in different media and conditions (physiological solutions, mechanical stresses in water, etc.) for the prediction of their behaviour over a long period of time. In the present study, the synthesized TiO2 nanotubes (TNT) from Ti-6Al-4V alloy, which were left unattended and exposed to environmental conditions (i.e., humidity and ambient temperature) for more than 4 years, were investigated to underline any important alteration/changes and ageing effects, on the surface morphology, the surface composition, and the electrochemical behaviour. The nanotubes were made in 2018 by anodization in different potentials (20V, 40V, 50V, and 60V) for different times (30 min, 60 min, 90 min, 150 min and 180 min) in an Ethylene Glycol solution for other purposes. Methods: For the surface morphology characterisation, electronic microscopy (SEM) was performed to depict any tendency with anodization conditions: potential and time. The comparison study between the obtained results and the SEM pictures taken on similar samples made and characterized under the same conditions in 2018, reveals a noticeable alteration in the morphology and a change in the TNT’s external diameter. Surface composition was checked using energy dispersive spectrometry (EDXS). The EDXS spectra analysis was realised to investigate the storage time impact on structure surface stability. A drastic decrease in the amount of oxygen was noticed on all of the surfaces where wettability measurements by contact angle were performed to confirm the latter. The verification of the hydrophobicity of TNT surfaces attested that all aged samples are hydrophobic in concordance with EDXS analysis and X-ray photoelectron spectroscopy (XPS). To affirm the surface modification during the storage duration and its impact on the electrical behaviour: cyclic voltammetry (CV), open circuit potential (OCP) measurements, and Tafel plots are undergone on the aged samples and compared with the freshly synthesised samples [1],[2]. The plotted CV curved as a function of the scan rate and the composition of the electrolyte showed a correlation between the different samples electrochemical behaviour and their surface morphologies as well as the existence of surface states for all samples. Results: From the previous characterisation, it was obvious that the sample prepared at 40V over 3 hours showed a remarkable electrochemical behaviour. The ageing effect is closely related to the anodization conditions. It was also noticed that the amount of water in the electrolyte solution EG played a contributing factor in the onset of ageing. High water content causes the formation of nanograss which have a non-negligible influence on the morphology. Conclusion: These results can open a new way for the optimization of the storage conditions according to anodization conditions (electrolyte, voltage, time, and temperature annealing) of this material as well as for the study of the life cycle of products made from TiO2 nanotubes. : Exposing nanotube surfaces to ambient conditions without taking any precautionary measures and without knowing their historical anodization conditions can cause drastic changes in the electrochemical behaviour of TNT. These changes affect considerably their function for different applications.

Effect of gallium doping on structural and transport properties of the topological insulator Bi2Se3 grown by molecular beam epitaxy

Topological insulators possess non-conductive bulk and present surface states, henceforth, they are electrically conductive along their boundaries. Bismuth selenide (Bi2Se3) is one of the most promising topological insulators. However, a major drawback is its n-type nature arising from its natural doping, which makes the transport in the bulk dominant. This effect can be overcome by shifting the chemical potential into the bandgap, turning the transport of the surface states to be more pronounced than the bulk counterpart. In this work, Bi2Se3 was grown by molecular beam epitaxy and doped with 0.8, 2, 7, and 14 at. % of Ga, with the aim of shifting the chemical potential into the bandgap. The structural, morphological, and electronic properties of the Ga doped Bi2Se3 are studied. Raman and x-ray diffraction measurements confirmed the incorporation of the dopants into the crystal structure. Transport and magnetoresistance measurements in the temperature range of 1.5–300 K show that Ga-doped Bi2Se3 is n-type with a bulk charge carrier concentration of 1019 cm−3. Remarkably, magnetotransport of the weak antilocalization effect measurements confirms the existence of surface states up to a doping percentage of 2 at. % of Ga and coherence length values between 50 and 800 nm, which envisages the possibility of topological superconductivity in this material.

Plasmonic Tamm states in periodic stubbed MIM waveguides: analytical and numerical study

We investigate both analytically and numerically the existence of localized surface modes, the so-called plasmonic Tamm states (PTSs), in a new and versatile platform based on a periodic array of metal-insulator-metal (MIM) stubs grafted along a MIM waveguide. By considering a semi-infinite structure in which we modify the length of the segment at the surface, we show the existence of surface states inside the bandgaps of the periodic structure and investigate the dependence of the localized modes as a function of the geometrical parameters and the boundary conditions applied at the surface. Three types of surface boundary conditions are considered, namely, two limiting cases of zero surface impedance (or perfect electric conductor), infinite surface impedance (or perfect magnetic conductor), and a third case where the structure is in contact with a real metal. In the latter case, we show that the existence of the interface state can be demonstrated based on topological arguments using the Zak phase. We also demonstrate that if a finite size comb-crystal is vertically grafted along a horizontal waveguide, the PTSs can be detected from the dips in the amplitudes of transmission and reflection coefficients as well as from the peaks in their delay times and the local density of states (LDOS). Our theoretical study is first performed analytically with the help of a Green’s function method, which allows the calculation of the dispersion relations of the bulk and surface modes and the LDOS, as well as the transmission and reflection coefficients of the plasmonic comb-like structure. Then, these results are confirmed by a numerical simulation utilizing a 2D finite element method. Besides providing a deep physical analysis of the PTSs, our work demonstrates the capability of the analytical method as a predictive approach in more complex structures. The proposed designs in this paper can be useful to realize highly sensitive plasmonic nanosensors.

Invariants of disordered semimetals via the spectral localizer

The spectral localizer consists in placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this technique is extended to disordered semimetals and allows to access the number of Dirac or Weyl points as well as weak invariants. These latter invariants imply the existence of surface states.

Tuning Surface States of Metal/Polymer Contacts Toward Highly Insulating Polymer-Based Dielectrics.

Metal-polymer interface plays a crucial role in controlling the dielectric performance in all flexible electronics. Ideally, the formation of the Schottky barrier due to the large band offset of the electron affinity of the polymer over the work function of the electrode should sufficiently impede the charge injection. Arguably, however, such an injection barrier has hardly been indisputably verified in polymer-metal junctions due to the ever-existing surface states, which dramatically compromise the barrier thus leading to undesired high electrical conduction. Here, we demonstrate experimentally a clear negative correlation between the breakdown strength and the density of surface states in polymer dielectrics. The existence of surface states reduces the effective barrier height for charge injection, as further revealed by density functional theory calculations and photoinjection current measurements. Based on these findings, we present a surface engineering method to enhance the breakdown strength with the application of nanocoatings on polymer films to eliminate surface states. The density of surface states is reduced by 2 orders of magnitude when the polymer is coated with a layer of two-dimensional hexagonal boron nitride nanosheets, leading to about 100% enhancement of breakdown strength. This work reveals the critical role played by surface states on electrical breakdown and provides a versatile surface engineering strategy to curtail surface states, broadly applicable for all polymer dielectrics.

Selective branching and converting of topological modes

The existence of surface states is a salient feature of topological phases and many of the widely studied physical properties are directly tied to it. Although less explored, a variety of topological phases can be similarly distinguished by their response to localized flux defects, resulting in the binding of modes whose stability can be traced back to that of conventional edge states. The reduced dimensionality of these objects offers the possibility of arranging them in distinct geometries, such as arrays that branch or terminate in the bulk. We show that the prospect of hybridizing the modes in these kinds of channels results in new opportunities in a dynamical context. In particular, we find that certain branches of junctions of such extended defect arrays can be actively biased by manipulating initial conditions. Discussing these physical effects within a generally applicable framework that relates to a variety of established artificial topological materials, such as spring-mass setups and LC circuits, our results offer an avenue to explore and manipulate new transport effects that are rooted in the topological characterization of the underlying system.Received 25 March 2021Revised 8 July 2021Accepted 8 July 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L032035Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasSymmetry protected topological statesTopological phases of matterPhysical SystemsHoneycomb latticeTechniquesTight-binding modelCondensed Matter, Materials & Applied Physics

Investigation of parameters of Schottky diodes based on chromium silicides

In this work, the parameters of Schottky diodes obtained by sputtering chromium on silicon and annealed at 900÷1100°C. were investigated. Experimental studies of Schottky contacts based on silicides have an all-microscopic analysis of the physical and chemical properties of the layers and an analysis of the electrical behavior of the system. The Schottky model assumes that surface states are located on the border between the transition layer and silicon. Using measurements of direct and inverse volt-amperage characteristics (VAC), values of the height of the effective Schottky barrier, the rate of change in the height of the barrier, as well as the value of the density of surface states, the thickness of the transition layer were obtained and the tunneling process was considered. The temperature dependencies of electrical conductivity are given and the course of the curve is analyzed. The obtained VAC is explained by the model of thermionic emission of the Schottky theory. Height of a barrier to contact chrome-silicon silicide which is equal to 0.65 eV is determined, and the factor of ideality was close to unit. The number of steps required by the charge carriers to overcome the potential barrier is determined. It is described that the current transfer mechanism is associated with the presence of surface states at the interface, as well as the occurrence of lattice mismatch and the difference in thermal coefficients. Diode illumination by LED confirms the effect of surface states on VAC. An increase in the surface states of photogenerated holes is shown. It has been shown that the existence of surface states affects the change in the height of the potential barrier, the amount of bending of the zones, and also determines that the predominant transfer mechanism is a tunneling multistage mechanism.

Weyl points and topological surface states in a three-dimensional sandwich-type elastic lattice

Following the realization of Weyl semimetals in quantum electronic materials, classical wave analogues of Weyl materials have also been theorized and experimentally demonstrated in photonics and acoustics. Weyl points in elastic systems, however, have been a much more recent discovery. In this study, we report on the design of an elastic fully-continuum three-dimensional material that, while offering structural and load-bearing functionalities, is also capable of Weyl degeneracies and surface topologically-protected modes in a way completely analogous to its quantum mechanical counterpart. The topological characteristics of the lattice are obtained by ab initio numerical calculations without employing any further simplifications. The results clearly characterize the topological structure of the Weyl points and are in full agreement with the expectations of surface topological modes. Finally, full field numerical simulations are used to confirm the existence of surface states and to illustrate their extreme robustness towards lattice disorder and defects.

Anomalous Hall effect in Cu doped Bi2Te3 topological insulator

The angle resolved photo-emission spectroscopy (ARPES) study and magneto-transport properties of Bi2CuxTe3−x have been investigated. ARPES study indicates the clear existence of surface states in the as-prepared samples. The estimated bandgap from ARPES is found to be ∼5 meV and 16 meV respectively for x = 0.03 and x = 0.15 samples. Presence of larger Cu concentration (x = 0.15) introduces magnetic ordering. Observed non-linearity in the Hall data is due to the existence of anomalous Hall effect which can be attributed to the 2D transport. The observed magneto-transport features might be related to the surface carriers which is confirmed by ARPES study.

Emergent dual topology in the three-dimensional Kane-Mele Pt2HgSe3

Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt$_2$HgSe$_3$), a naturally-occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a van-der-Waals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angle-resolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone of jacutingaite single crystals. The 001-surface states have been shown to be topologically protected by a mirror Chern number $C_M=-2$, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally-localized Wannier functions, we identify a large non-trivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.

Frequency and Voltage Dependence of the Dielectric Properties of Ni/SiO2/P-Si (MOS) Structure

The frequency (10 - 107 Hz), temperature (303-363 K) or /and bias voltage (−2 to 2 V) dependence of the dielectric properties of Ni/SiO2/p-Si (MOS), have been investigated using the broadband dielectric spectrometer (BDS). Molecular structure and microstructure have been characterized using X - ray diffraction (XRD) and scanning electron microscope (SEM), respectively. From the experimental results, the capacitance–frequency (C-f) characteristics for MOS structure described as a series capacitance (Cs) in the oxide layer (SiO2) and a depletion layer in the semiconductor (p-Si). Interestingly, the capacitance over the whole frequency range for all temperatures are hardly distinguished particularly in the accumulation region, exploring enhancements of the electrical performance for MOS structure. Value of the flat band voltage (VFB) separating the accumulation and depletion regions was determinate at −0.5 V. Furthermore, thickness of the interfacial layer (SiO2) found to be ~580 A. Both C and e' found to be strongly temperature and frequency dependent particularly at high temperatures and low frequencies due to creation of an inhomogeneous layer at the SiO2/p-Si interface, exploring Maxwell-Wagner or interfacial polarization. Variation of e' and e'' with frequency revealed to the existence of surface states or traps (Nss) located at interfacial layer (SiO2), dipole or/and surface polarization. The average conductivity value of MOS structure found to be 1.2 × 10−7 S/cm, exploring semiconducting feature.

Nonlinear Planar Hall Effect.

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

The fabrication of Al/p-Si (MS) type photodiode with (%2 ZnO-doped CuO) interfacial layer by sol gel method and their electrical characteristics

In this study, Al/p-Si (MS) type photodiodes with (%2 ZnO-doped CuO) interlayer were fabricated to investigate the effects of this interlayer on the electrical characteristics. Besides, the structural properties of this interlayer were also investigated using AFM. The forward and reverse bias current voltage (I-V) measurements were carried out both in dark and various illumination intensities (10–100 mW cm−2) whereas the capacitance/conductance-voltage (C/G-V) measurements were carried out at various frequencies (10 kHz-1 MHz) in dark at room temperature. Experimental results show that the values of current increase with increasing illumination intensity especially in the reverse bias region due to high electric field. Furthermore, the observed good response to the illumination indicated that the fabricated structures can be used as a photo-detector/diode in the electric and optic applications. The slope (m) was obtained from the log(IPH)-log(P) plot as 0.821 which is lower than unity which suggested that the photoconduction mechanism exhibited a linear behavior. The observed increase in the C and G values with decreasing frequency was attributed to the existence of surface states (Nss) which are located between interlayer and semiconductor and their relaxation times. The obtained frequency dependent Rs values show that it is more effective both on the C-V and G/w-V characteristics especially at accumulation region at high frequencies.

The study on negative dielectric properties of Al/PVA (Zn-doped)/p-Si (MPS) capacitors

In this research, PVA (doped with 7% Zn) was sandwiched between Al and p-Si as a polymer interfacial layer. Voltage and frequency effect on the real and imaginary components of complex dielectric constant (e′ and e″), electric modulus (M′ and M″), loss tangent (tan δ) and electrical conductivity (σ) of the MPS-type capacitor has been studied. Impedance spectroscopy method was used between 5 and 5000 kHz at room temperature. Almost all frequency-related parameters were found as quite susceptible, especially in the accumulation and depletion regions. These changes in real and imaginary components of dielectric properties in depletion region were attributed to the interface layer and dipole polarization, the existence of surface states (Nss) and their relaxation time (τ), especially at low frequencies. But these changes in the accumulation region were attributed to the existence of interfacial layer and series resistance (Rs) of the capacitor owing to the voltage divided between them and capacitor. As a result, frequency, applied biases, interfacial polymer layer, polarization processes, Nss and Rs of the capacitor are more effective on the values of e′, e″, tan δ, M′, M″ and σ. Therefore, the effects of them must be considered in determining the dielectric parameters, electric modulus, conductivity and conduction mechanisms in the capacitors with and without an interfacial layer such as insulator/oxide, polymer, ferroelectric materials.

Unraveling the Structural and Electronic Properties of Graphene/Ge(110)

The direct growth of graphene on a semiconducting substrate opens a new avenue for future graphene-based applications. Understanding the structural and electronic properties of the graphene on a semiconducting surface is key for realizing such structures; however, these properties are poorly understood thus far. Here, we provide insight into the structural and electronic properties of graphene grown directly on a Ge(110) substrate. Our scanning tunneling microscopy (STM) study reveals that overlaying graphene on Ge(110) promotes the formation of a new Ge surface reconstruction, i.e., a (6 × 2) superstructure, which has been never observed for a bare Ge(110) surface. The electronic properties of the system exhibit the characteristics of both graphene and Ge. The differential conductance (d I/d V) spectrum from a scanning tunneling spectroscopy (STS) study bears a parabolic structure, corresponding to a reduction in the graphene Fermi velocity, exhibiting additional peaks stemming from the p-orbitals of Ge. The density functional theory (DFT) calculations confirm the existence of surface states due to the p-orbitals of Ge.

Surface states of gapped electron systems and semi-metals

With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of scattering states is obtained. From the scattering states, we derive the criterion for the existence of surface states. The wave functions and the energy of the surface states are then determined. We obtain a connection between the wave functions of the bulk states and the surface states. For electrons in a system with time-reversal symmetry, with this connection, we rigorously prove the correspondence between the change of Kramers degeneracy of the surface states and the bulk time-reversal Z2 invariant. The theory is applicable to systems of (topological) insulators, superconductors, and semi-metals. Examples for solving the edge states of electrons with/without the spin–orbit interactions in graphene with a hard zigzag edge and that in a two-dimensional d-wave superconductor with a () edge are given in appendices.

Investigation of temperature dependent negative capacitance in the forward bias C-V characteristics of (Au/Ti)/Al2O3/n-GaAs Schottky barrier diodes (SBDs)

In this study, a metal-insulator-semiconductor (MIS) type Schottky barrier diodes (SBDs) were fabricated by growing a thin Al2O3 insulator layer between Au/Ti and n-GaAs using atomic layer deposition (ALD) method. The effect of temperature and voltage on interface states (Nss) and series resistance (Rs) of the (Au/Ti)/Al2O3/n-GaAs (MIS) type Schottky barrier diodes (SBDs) was investigated using the capacitance/conductance-voltage (C/(G/ω)-V) data measured in wide range of temperature (200–380 K) and voltage ( ± 5 V). It was found that C and G/ω are strongly dependent on temperature and voltage. The value of C in the forward bias region reaches to maximum and then becomes negative. This negative capacitance (NC) behavior of this SBD is observed for each temperature level. Also, capacitance-current (C-I) and conductance-current (G/ω-I) plots were drawn to explain the NC behavior. The negative value of C in the accumulation region corresponds to the maximum value of G/ω. Such behavior of C can be explained by the loss of interface charges located at (Al2O3)/n-GaAs interface because of impact ionization process, the existence of surface states (Nss), series resistance (Rs) and interfacial of (Al2O3) oxide layer.Therefore, the voltage dependent profiles of Rs and Nss were obtained using Nicollian-Brews and Hill-Colleman methods for enough high forward biases as a function of temperature at various positive bias voltages. The changes in Rs and Nss values were attributed to restructure and reordering of the carriers under temperature and voltage effects.

Electron microscopy and ultraviolet photoemission spectroscopy studies of native oxides on GaN(0001)

We investigated native oxides on GaN(0001) using high-resolution scanning transmission electron microscopy (STEM) and ultraviolet photoemission spectroscopy (UPS). As a result, it was confirmed that the native oxides on both n-type and p-type GaN(0001) with a thickness of ∼1 nm were not amorphous but crystalline with lattice-matched structures to GaN, as we reported previously [Y. Irokawa et al., Jpn J. Appl. Phys. 56, 128004 (2017)]. Moreover, the UPS spectra of native oxides on n-type GaN(0001), which were similar to the reported clean GaN(0001) spectra, showed the existence of surface states at the valence band maximum (VBM), reflecting the defective quality of the native oxides.

Effects of Frequency and Bias Voltage on Dielectric Properties and Electric Modulus of Au/Bi4Ti3O12/n-Si (MFS) Capacitors

In this work, a metal-ferroelectric-semiconductor (MFS) type capacitor was fabricated and admittance measurements were held in a wide frequency range of 1 kHz-5 MHz at room temperature for the investigation of frequency and voltage dependence of complex dielectric constant, complex electric modulus and electrical conductivity of the MFS capacitor . Bismuth titanate (Bi 4 Ti 3 O 12 ) with high dielectric constant was used as interfacial ferroelectric material and the structure of MFS capacitor was obtained as Au/Bi 4 Ti 3 O 12 /n-Si. Experimental results showed that dielectric, modulus and conductivity parameters are strong functions of frequency and voltage especially in depletion and accumulation regions due to the existence of surface states (N ss ), series resistance (R s ), interfacial polarization and interfacial layer. It was found that R s of the structure and interfacial ferroelectric layer are efective in accumulation region whereas surface states (N ss ) and interfacial polarization are efective in depletion region. Also the changes in dielectric, modulus and conductivity parameters become considerably high particularly at low frequencies due to high values of R s and N ss . The observed anomalous peak in voltage dependent plots of capacitance and dielectric constant was atributed to the particular density distribution of N ss , R s and minority carrier injection. Moreover, the value of conductivity at low and intermediate frequencies is almost independent of frequency thus low frequency data was used to extract d.c. conductivity. This work showed that the use of high-dielectric Bi 4 Ti 3 O 12 as ferroelectric interfacial layer in a MFS capacitor is preferable due to high values of its dielectric constant compared with traditional insulator layer materials such as SiO 2 and SnO 2 . Therefore, a MFS capacitor with Bi 4 Ti 3 O 12 interfacial layer can store more energy thanks to its high dielectric constant.