Deformation Potential Constants Research Articles

Raman scattering owing to magneto-polaron states in monolayer transition metal dichalcogenides

Magneto-optical measurements are fundamental research tools that allow for studying the hitherto unexplored optical transitions and the related applications of topological two-dimensional (2D) transition metal dichalcogenides (TMDs). A theoretical model is developed for the first-order magneto-resonant Raman scattering in a monolayer of TMD. A significant number of avoided crossing points involving optical phonons in the magneto-polaron (MP) spectrum, a superposition of the electron and hole states in the excitation branches, and their manifestations in optical transitions at various light scattering configurations are unique features for these 2D structures. The Raman intensity reveals three resonant splittings of double avoided-crossing levels. The three excitation branches are present in the MP spectrum provoked by the coupling of the Landau levels in the conduction and valence bands via an out-of-plane A1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_1$$\\end{document}-optical phonon mode. The energy gaps at the anticrossing points in the MP scattering spectrum are revealed as a function of the electron and hole optical deformation potential constants. The resonant MP Raman scattering efficiency profile allows for quantifying the relative contribution of the conduction and valence bands in the formation of MPs. The results obtained are a guideline for controlling MP effects on the magneto-optical properties of TMD semiconductors, which open pathways to novel optoelectronic devices based on 2D TMDs.

Robust in-plane ferroelectricity, high hole mobility, and low thermal conductivity in GeO monolayer: A first-principles study

Motivated by the experimental advancements in 2D crystalline germanium oxides, we investigated the electronic and transport properties of GeO and GeO2 monolayers (MLs) using first-principles calculations. GeO ML exhibits an in-plane ferroelectricity until the melting point of 1100 K. Compressive strain facilitates polarization reversion by lowering the ferroelectric transition barrier. The band edges meet the requirements for photocatalytic water splitting across a wide variety of strains. Meanwhile, GeO ML has a high hole mobility of 4854 cm2/V⋅s along the y-axis, owing to its low deformation potential constant. The large difference in hole and electron mobility promotes electron–hole separation. In addition, GeO ML has a low thermal conductivity of κx = 3.37 W/mK and κy = 12.53 W/mK at 300 K, due to the strong anharmonicity caused by lone-pair electrons. In contrast, GeO2 ML has an isotropic electron mobility of 382 cm2/V⋅s and an κ of 22.60 W/mK at 300 K. At last, we discussed the probable reaction to grow 2D GeO crystal and calculated the Raman intensity to distinguish it in future experiments. Our results show that 2D GeO has potential applications in ferroelectrics, thermoelectrics, and water splitting.

Re-understanding of the deformation potential constant in the single crystal silicon

The mobility formula based on deformation potential (DP) theory is of great importance in semiconductor physics. However, the related calculations for the DP constant are controversial. It is necessary to redo in-depth and comprehensive research on the mobility of single crystal silicon and the related parameters such as the effective mass and the DP constant. In this work the mobility effective mass is defined and a method based on the first principles is presented to evaluate the correction of the DP constant. It is found that the effective mass is closer to experimental data and the correction of the DP is a negligible value of about 0.3 eV being far lower than ∼10 eV calculated by other methods. Using these parameters, we obtain the mobilities of the single crystal silicon in reasonable agreement with the experimental values.

Carrier mobility in doped Sb<sub>2</sub>Se<sub>3</sub> based on deformation potential theory

Antimony selenide (Sb<sub>2</sub>Se<sub>3</sub>) is an element-rich, cost-effective, and non-toxic material used as an absorber layer in solar cells. The performance of solar cells is significantly influenced by the transport characteristics of charge carriers. However, these characteristics in Sb<sub>2</sub>Se<sub>3</sub> have not been well understood. In this work, through density functional theory and deformation potential theory, we investigate the hole transport properties of pure Sb<sub>2</sub>Se<sub>3</sub> and As-, Bi-doped Sb<sub>2</sub>Se<sub>3</sub>. The incorporation of as element and Bi element does not introduce additional impurity levels within the band gap. However, the band gaps are reduced in both As-Sb<sub>2</sub>Se3 and Bi-Sb<sub>2</sub>Se<sub>3</sub> due to the band shifts of energy levels. This phenomenon is primarily attributed to the interactions between the unoccupied 4p and 6p states of the doping atoms and the unoccupied 4p states of Se atoms, as well as the unoccupied 5p states of Sb atoms. In this study, we calculate and analyze three key parameters affecting mobility: effective mass, deformation potential, and elastic constants. The results indicate that effective mass has the greatest influence on mobility, with Bi-Sb<sub>2</sub>Se<sub>3</sub> exhibiting the highest average mobility. The average effective mass is highest in As-Sb<sub>2</sub>Se<sub>3</sub> and lowest in Bi-Sb<sub>2</sub>Se<sub>3</sub>. The elastic constants of the As- and Bi-doped Sb<sub>2</sub>Se<sub>3</sub> structures show minimal differences compared with that of the intrinsic Sb<sub>2</sub>Se<sub>3</sub> structure. By comparing the intrinsic, As-doped, and Bi-doped Sb<sub>2</sub>Se<sub>3</sub>, it is evident that doping has a minor influence on deformation potential energy along various directions. The study reveals that the hole mobility in Sb<sub>2</sub>Se<sub>3</sub> displays significant anisotropy, with higher mobilities observed in the <i>x</i>-direction and the <i>y</i>-direction than in the <i>z</i>-direction. This discrepancy is attributed to stronger covalent bonding primarily in the <i>x</i>- and <i>y</i>-direction, while in the <i>z</i>-direction weaker van der Waals forces is dominant. The directions with enhanced charge carrier transport capability contribute to efficient transfer and collection of photo-generated charge carriers. Therefore, our research theoretically underscores the significance of controlling the growth of antimony selenide along specific directions.

High-mobility transport symmetry and effect of strain on electronic and optical properties in few-layer blue phosphorus

As a new type of 2D semiconductor, blue phosphorus (BP) is an ideal material for new electronic devices, whose performance can be compared with that of black phosphorus. The first principles method of DFT is applied to calculate electronic and optical properties of few-layer BP. By applying uniaxial strain, the deformation potential constant is calculated, and the value obtained is very small (∼0.36 eV in a monolayer), which is the main reason for the extremely high carrier mobility (up to 47.9 × 103cm2V−1s−1). By the partial charge analysis of band edge, the small deformation potential constant is attributed to the fact that wave function is very isolated along the lattice vector direction in valence band. From monolayer to four-layer BP, conductivity type changes from p to n, the band gap decreases and the position of the first absorbance peak red shifts. When biaxial strain is applied, band gap peak appears at the position where the compression is greater with the increase of layers. Tension or compression can cause the absorbance peak red shift or blue shift. In the visible light range, the value of the first peak performs well (3.6 %–7.9 %). 8 % compressive strain will increase the absorbance peak by 50 %–60 %. These results can provide theoretical support for few-layer BP as low power-consumption devices or photosensitive devices in the future.

Electronic and elastic properties of BN, AlN and GaN

We have carried out first-principles total energy calculations to investigate electronic and elastic properties of both zinc-blende and wurtzite BN, AlN, and GaN. We have calculated lattice parameters, elastic constants, deformation potential constants, phonon frequencies at r point, Born effective charges, and piezoelectric constants. Lattice parameters are fully relaxed by using the first-principles molecular dynamics method with variable cell shape. The internal strain in a strained crystal is also relaxed by the first-principles molecular dynamics method. The internal strain influences the elastic constants, the deformation potential constants, and the piezoelectric constants effectively. We have calculated the wurtzite deformation potential constants D1 – D5 considering the internal strain correction. The piezoelectric constants of wurtzite and also zinc-blende crystals have been calculated using the Berry phase approach and we have found from first principles that those of BN have an inverse sign in contrast to AlN and GaN. Discussions will be given in comparison with results obtained herein with the previous ones. © 1998 American Institute of Physics. [S0021-8979(98)07921-3]

Metal-cation-mixed lead-less two-dimensional hybrid perovskites with high carrier mobility and promoted light adsorption

The metal cation mixing in hybrid perovskite has been suggested as an effective strategy not only to promote the performance and stability but also to reduce the content of toxic lead element for environmental and health concerns. However, such a strategy has yet been well demonstrated in two-dimensional (2D) hybrid perovskites with multilayered thickness (n > 1). Here, we theoretically investigated the lead-less and lead-free 2D hybrid perovskites with tin-lead (Sn–Pb) and germanium-tin (Ge–Sn) mixed metal cations, namely, the BA2MAn-1Snn/2Pbn/2I3n+1 and BA2MAn-1Gen/2Snn/2I3n+1 (BA: C4H9NH3+; n = 1–4), by means of first-principle calculations. It is found that the electronic structure and light absorption properties of the 2D hybrid perovskites can be efficiently tuned to the optimal range for solar cells by combining the metal cations mixing and the layer thickness (n) adjustment. Markedly, due to the enhanced in-plane elastic modulus but greatly reduced deformation potential constant, both the Ge–Sn and Sn–Pb mixed 2D perovskites show high carrier mobility (∼103−104 cm2V–1S−1), which are superior to that of their 3D analogues. Moreover, the Sn–Pb mixed 2D perovskites expose much stronger visible light absorption than the non-mixed Sn- or Pb-based 2D perovskites. In addition, the in-air stability of metal-cation-mixed 2D hybrid perovskites are greatly improved compared to the 3D halide perovskites. This work suggests the great potential of the metal-cation-mixed 2D hybrid perovskite for photovoltaic and optoelectronic applications with largely reduced lead content.

Interface modulated electron mobility enhancement in core–shell nanowires

The transport properties of core–shell nanowires (CSNWs) under interface modulation and confinement are investigated based on the atomic-bond-relaxation (ABR) correlation mechanism and Fermi’s golden rule. An analytical expression for the relationship between carrier mobility and interface mismatch strain is derived and the influence of size, shell thickness and alloyed layer on effective mass, band structures, and deformation potential constant are studied. It is found that interface modulation can not only reduce the lattice mismatch to optimize the band alignment, but also participate in the carrier transport for enhancing mobility. Moreover, the underlying mechanism regarding the interface shape dependence of transport properties in CSNWs is clarified. The great enhancement of electron mobility suggests that the interface modulation may become a potential pathway to improving the performance of nanoelectronic devices.

Electronic and elastic properties of BN, AlN and GaN

We have carried out first-principles total energy calculations to investigate electronic and elastic properties of both zinc-blende and wurtzite BN, AlN, and GaN. We have calculated lattice parameters, elastic constants, deformation potential constants, phonon frequencies at r point, Born effective charges, and piezoelectric constants. Lattice parameters are fully relaxed by using the first-principles molecular dynamics method with variable cell shape. The internal strain in a strained crystal is also relaxed by the first-principles molecular dynamics method. The internal strain influences the elastic constants, the deformation potential constants, and the piezoelectric constants effectively. We have calculated the wurtzite deformation potential constants D1 – D5 considering the internal strain correction. The piezoelectric constants of wurtzite and also zinc-blende crystals have been calculated using the Berry phase approach and we have found from first principles that those of BN have an inverse sign in contrast to AlN and GaN. Discussions will be given in comparison with results obtained herein with the previous ones. © 1998 American Institute of Physics. [S0021-8979(98)07921-3]

Investigating the high field transport properties of Janus WSSe and MoSSe by DFT analysis and Monte Carlo simulations

Janus transition metal dichalcogenides with out-of-plane structural asymmetry have attracted increasing attention due to their exceptional potential in electronic and optical applications. In this study, we systematically investigated the electron–phonon interactions and related transport properties in monolayer Janus MoSSe and WSSe using the density-functional formalism. The electron–phonon scattering rates were obtained using Fermi’s golden rule and extended to the extraction of the effective deformation potential constants for further Monte Carlo treatment. From the results of the Monte Carlo analysis, we found that WSSe provides better performance with higher low-field mobility, while MoSSe shows a higher peak velocity at higher fields. In our results, both MoSSe and WSSe seem to be competitive with other previously studied 2D materials. These predictions provide a systematic perspective on the potential of Janus WSSe and MoSSe for electronic applications.

Structural, electronic, and transport properties of quintuple atomic Janus monolayers Ga2SX2 ( X= O, S, Se, Te): First-principles predictions

Two-dimensional Janus structures with vertical intrinsic electric fields exhibit many interesting physical properties that are not possible with symmetric materials. We systematically investigate the structural, electronic, and transport properties of quintuple-layer atomic Janus ${\mathrm{Ga}}_{2}\mathrm{S}{X}_{2}$ ($X=$ O, S, Se, Te) monolayers using the first-principles calculations. The stability of the Janus structures is evaluated via the analysis of their phonon dispersion curves, cohesive and formation energies, and elastic constants. The existence of a vertical internal electric field due to the lack of mirror symmetry has resulted in a vacuum level difference between the two sides of the investigated Janus structures. At the ground state, while the Janus ${\mathrm{Ga}}_{2}\mathrm{S}{\mathrm{O}}_{2}$ is metallic, the other three configurations (${\mathrm{Ga}}_{2}{\mathrm{S}}_{3}, {\mathrm{Ga}}_{2}\mathrm{S}{\mathrm{Se}}_{2}$, and ${\mathrm{Ga}}_{2}\mathrm{S}{\mathrm{Te}}_{2}$) are semiconductors with indirect band gaps. The electronic properties of ${\mathrm{Ga}}_{2}\mathrm{S}{X}_{2}$ monolayers can be altered by strain engineering. In particular, the indirect--direct band gap and semiconductor-metal phase transitions were observed when the biaxial strain was introduced. The carrier mobilities of the semiconducting Janus monolayers are directional anisotropic due to their anisotropy of the deformation potential constant. It is found that all three semiconducting Janus monolayers have high electron mobility, up to 930.34 ${\mathrm{cm}}^{2}$/V s, which is suitable for applications in next-generation electronic devices.

Temperature frequency stability study of extensional mode N-doped silicon MEMS resonator

Analytical and numerical modeling techniques are presented to predict n-type-doped silicon resonators’ temperature coefficient frequencies for the extensional mode of vibration by modeling of single-crystal silicon ([100] and [110]) directions. We utilized a previously reported empirical exponential expression for the uniaxial deformation potential that allows us to determine the deformation potential constant. It was observed that by using the empirical model of exponential expression for the uniaxial deformation potential, our result shows that the frequency variation with temperature is closely dependent on the direction and the variation of the different doping levels. We apply our analytical model to the [100] and [110] length extensional modes of a Microelectromechanical Systems (MEMS) resonator. We calculated the resonance frequency with temperature dependence and found that the first-order temperature coefficient frequency shows zero values at doping concentration levels of 0.5 and 1 × 1019 cm−3, which indicates the existence of frequency turnover at room temperature. We also extended our study by finite element analysis of MEMS resonators to investigate the mode shapes and resonant frequency for different aspect ratios in the extensional mode of vibration. It is observed that the mode shapes are more stressed with higher aspect ratios, and the frequency variation (ppm) of the resonance frequency between the [100] and [110] crystal directions of the MEMS resonator increases with increasing aspect ratios.

Novel Janus group III chalcogenide monolayers Al2XY2 (X/Y = S, Se, Te): first-principles insight onto the structural, electronic, and transport properties

Motivated by the recent successful synthesis of 2D quintuple-layer atomic materials, for the first time, we design and investigate the electronic and transport properties of Janus Al2XY2 (X/Y = S, Se, Te; X ≠ Y) monolayers by using the density functional theory. Our calculations demonstrate that most of the models of Al2XY2 (except for Al2STe2 monolayer) are dynamically and mechanically stable. By using the hybrid functional, all models of Al2XY2 are semiconductors with an indirect bandgap. Meanwhile, Al2TeS2 monolayer is found to be metal at the Perdew–Burke–Ernzerhof level. Due to the vertical asymmetry structure, an intrinsic built-in electric field exists in the Al2XY2 and leads to a difference in the vacuum levels between the two sides of the monolayers. Carrier mobilities of Al2XY2 monolayers are high directional anisotropic due to the anisotropy of their deformation potential constant. Al2XY2 monolayers exhibit high electron mobility, particularly, the electron mobility of Al2SeS2 exceeds 1 × 104 cm2 V−1 s−1, suggesting that they are suitable for applications in nanometer-sized electronic devices.

Highly Strain-Tunable Interlayer Excitons in MoS2/WSe2 Heterobilayers

Interlayer excitons in heterobilayers of transition-metal dichalcogenides (TMDCs) have generated enormous interest due to their permanent vertical dipole moments and long lifetimes. However, the effects of mechanical strain on the optoelectronic properties of interlayer excitons in heterobilayers remain relatively uncharacterized. Here, we experimentally demonstrate strain tuning of Γ-K interlayer excitons in molybdenum disulfide and tungsten diselenide (MoS2/WSe2) wrinkled heterobilayers and obtain a deformation potential constant of ∼107 meV/% uniaxial strain, which is approximately twice that of the intralayer excitons in the constituent monolayers. We further observe a nonmonotonic dependence of the interlayer exciton photoluminescence intensity with strain, which we interpret as being due to the sensitivity of the Γ point to band hybridization arising from the competition between in-plane strain and out-of-plane interlayer coupling. Strain engineering with interlayer excitons in TMDC heterobilayers offers higher strain tunability and new degrees of freedom compared to their monolayer counterparts.

Ion-beam induced quasi-dynamic continual disorder in Bi-implanted Hongan silica glass

We have studied optical properties of glassy silicon dioxide (Hongan Silica Glass Store, China) irradiated with 30 keV bismuth ions. A broadening with a low-energy shift of absorption edge was found for the samples treated with 1 × 1016 – 3 × 1017 сm–2 ion fluences. The dose dependences of characteristic Urbach energy and width of the optical gap for direct interband transitions were determined and plotted. Based on the linear-type correlation between Urbach energy and optical gap width, the D/K ratio of deformation potential constants was established as well. The constancy of the D/K ratio for silicon dioxide at different fluences of bismuth ions indicates the proportionality between the values of the optical gap and band tails length, which are associated with the static atomic disorder of SiO2 host-matrix. An explanation of the obtained regularities was given using the quasi-dynamic (thermodynamic) approach. It was postulated that structural damage caused by ion-beam treatment determines Boltzmann entropy's magnitude as a combination of system various microstates. The functional dependence of σ-parameter (disordering effective cross-section) on the ion fluence has been established and proved experimentally.

Thermal conductivity and enhanced thermoelectric performance of SnTe bilayer

Tin chalcogenides (SnS, SnSe, and SnTe) are found to have improved thermoelectric properties upon the reduction of their dimensionality. Here we found the tilted AA + s stacked two-dimensional (2D) SnTe bilayer as the most stable phase among several stackings as predicted by the structural optimization and phonon transport properties. The carrier mobility and relaxation time are evaluated using the deformation potential theory, which is found to be relatively high due to the high 2D elastic modulus, low deformation potential constant, and moderate effective masses. The SnTe bilayer shows a high Seebeck coefficient, high electrical conductivity, and ultralow lattice thermal conductivity. High TE figure of merit (ZT) values, as high as 4.61 along the zigzag direction, are predicted for the SnTe bilayer. These ZT values are much enhanced as compared to the bulk as well as monolayer SnTe and other 2D compounds.

Comparative study of elastic, thermodynamic properties and carrier mobility of InX (X = O, S, Se, Te) monolayers via first-principles

With the generalized gradient approximation, our work presents a comparative research for elastic properties, carrier mobility and thermodynamic properties of InX (X = O, S, Se, Te) monolayers using first principles computational density functional theory (DFT). Among the four indium compounds of the same main group, they all show isotropic Young's modulus and Poisson's ratio. Among them, the Young's modulus and Poisson's ratio of InO are the largest, reaching 79.1 Nm−1 and 0.44, respectively. At the same time, we also calculated the cohesive energy of each primitive cell to explain their relationship. For the sake of studying the thermodynamic properties, the Helmholtz free energy in various area, area change, two-dimension bulk moduli, heat capacity of constant pressure and constant volume in different temperature are analyzing in detail. The heat capacity of both constant pressure and constant volume and thermal expansion coefficient adhere to the trend of InTe > InSe > InS > InO in the same temperature. Moreover, InO, InS and InSe have the negative thermal expansion coefficient at the low temperature. Furthermore, we used the deformation potential theory to calculate the carrier mobility, analyzing their elastic constants, deformation potential constants, and the effective mass of electrons and holes, and found that the effective mass of electrons is isotropic.

Ultrahigh carrier mobility of penta-graphene: A first-principle study

Within the formalism of density functional theory and using the concept of effective mass approximation, the electron-acoustic phonon scattering principle along with the deformation potential theory of Bardeen and Shockley, we have investigated the intrinsic charge carrier mobility of penta-graphene. The electron mobility of penta-graphene is significantly large compared to hole mobility and it is reasonably higher than other novel two-dimensional materials e.g. penta-X 2 C (X = P, As, Sb), Si-based pentagonal monolayer (SiX, X = B, C, N), penta-stanene monolayer and CaP 3 which possess the highest carrier (electron) mobility among phosphorene derivatives. This high carrier mobility originates from the low effective mass, low deformation potential and high stiffness constant of this material. As our main focus is to investigate the carrier mobility which depends on band edges, a detailed study about orbital contribution to the electronic states in the vicinity of band edges has been carried out. The intrinsic wide band gap and ultrahigh carrier mobility show the possible signature of using it in the fabrication of microelectronic devices, mainly in FETs and logic circuits and in optoelectronic devices . • The electron mobility of PG is significantly large compared to hole mobility. • Ultrahigh mobility originates from low effective mass and high stiffness constant. • The electron mobility of unstrained PG is 22.74 × 10 3 cm 2 /V at 300 K. • The electron mobility of PG varies from 11.72 to 40.90 × 10 3 cm 2 /V for +4% to −4% strain at 300 K. • PG may be suitable for microelectronics applications.

Spin Seebeck effect in the 2D ferromagnetic CrPbTe3

Spin Seebeck effect has been mostly explored in bulk magnetic materials, but the efficiency is not large enough for device application. Recently, we have found that the 2D ferromagnetic CrPbTe3 layer has rather a high Curie temperature of 110 K. Thus, we have investigated the spin dependent Seebeck effect using the Boltzmann transport approach. We have found the largest carrier mobility and relaxation time in the minority spin electron carrier system due to the spin dependent effective mass and deformation potential constant. The onset energy of the electrical conductivity shows spin and carrier type dependency. Thus, both effective spin and effective charge Seebeck coefficients are originated from the majority spin carrier in the hole doped system whereas the minority spin carrier controls the effective spin and effective charge Seebeck coefficient in the electron doped system. We have obtained the maximum spin Seebeck coefficient of 1320 μV/K at 50 K. This value is suppressed at 100 K, but we still find a large spin Seebeck coefficient of 715 μV/K.

Symmetry Breaking Induced Anisotropic Carrier Transport and Remarkable Thermoelectric Performance in Mixed Halide Perovskites CsPb(I1–xBrx)3

We present a combination of first-principles calculations and the Boltzmann transport theory to understand the carrier transport and thermoelectric performance of mixed halide perovskite alloys CsPb(I1-xBrx)3 with different Br compositions. Our computational results correlate the conduction band splitting in CsPb(I1-xBrx)3 to the significant anisotropy in their carrier transport properties, such as effective masses and deformation potential constants. Such band splitting originates from the symmetry-broken crystal structures of CsPb(I1-xBrx)3 polymorphs: with residue stresses/strains in asymmetric CsPb(I1-xBrx)3, nondegenerate orbitals reconstruct the conduction band and reduce the Pb-halide antibonding character along certain directions. While the Seebeck coefficient (S) and the relaxation time-normalized electrical conductivity (σ/τ) show weak directional anisotropy, the carrier relaxation time (τ) is highly direction-dependent. The reconstruction of the conduction band finally leads to significantly anisotropic and enhanced thermoelectric power factors (PF = S2σ) in CsPb(I1-xBrx)3 compared to those in pure CsPbI3 and CsPbBr3, showing anomalous nonlinear alloy behavior. A delicate balance between S2σ and combined measurement of the carrier effective mass and deformation potential constant, m*EDP, is confirmed. The lattice thermal conductivities of CsPb(I1-xBrx)3 are significantly suppressed compared to those of their pure counterparts due to strong mass disordering and strain fields upon halogen substitution. As a result, symmetry breaking in CsPb(I1-xBrx)3 leads to anisotropy in carrier transport, high PF, and scattered phonon transport (ultralow thermal conductivity), concurrently contributing to their promising thermoelectric figures of merit (ZT) up to 1.7 at room temperature. The principles behind the asymmetry-induced factors would serve as new design concepts to tailor the thermoelectric properties of alloys, mixtures, superlattices, and low-dimensional materials.