Parabolic Band Research Articles

Solution of Self-Consistent Kohn–Sham and Poisson Equations for Quasi Two-Dimensional Electron Gas in the Accumulation Layer of Semiconductor with Nonparabolic Conduction Band

We generalize the method proposed previously for a self-consistent solution of the system of the Kohn–Sham and Poisson equations to the case of high density of electrons localized near the surface of a semiconductor due to size quantization of the electron spectrum in a potential well in the band banding region. We obtain a completely self-consistent iterative solution for a quasi two-dimensional electron gas in the accumulation layer at the surface of a semiconductor with a degenerate electron gas in the bulk. Both parabolic and non-parabolic energy spectra of conduction electrons are considered. For a parabolic conduction band, we obtain the spatial distributions of the electron density and electrostatic potential, as well as the energies of size-quantized levels and their dependence on the depth of the near-surface potential well. A significant decrease in the density of three-dimensional electrons was revealed in the region where the quasi two-dimensional electron gas occupied the accumulation layer. We calculated the dependencies of the excess electron surface density and the capacitance of the structure on the surface potential. The results are presented in dimensionless form that can be used to semi-quantitatively evaluate the parameters of accumulation layers by the known level of doping and the value of band bending. In the case of the nonparabolic conduction band, due to the finite bandgap width, the spectrum of quasi two-dimensional electron gas is obtained in the two-band Franz–Kane approximation by solving the eigenvalue problem for the new single-band equation of the effective-mass method. The density of states and the effective mass of electrons in the 2D subbands is found to increase linearly with energy. We have derived the expression that analytically approximates the calculated energy spectrum. The position of levels, the dispersion of energy spectrum, and the dependence of effective mass on energy, which were found for the size-quantized sub-bands, are in agreement with the published results for characteristics of quasi two-dimensional electrons at n-InAs surface that were directly measured by angle resolved photoelectron spectroscopy and magnetotunneling spectroscopy. Conditions are considered when the nonparabolicity of the conduction band enables quasi two-dimensional electrons to absorb the normally incident radiation due to intersubband transitions.

Excitons in spherical quantum dots revisited: analysis of colloidal nanocrystals

The problem of exciton states in spherical semiconductor quantum dots is revisited, employing the finite element method to numerically solve the system of differential equations for the center of mass and relative motion of the interacting electron-hole pair. This process is performed within the effective mass and parabolic bands approximations. The use of a finite confinement together with a parabolic description of the conduction and valence band profiles prevents the two equations from uncoupling. The allowed energies are reported as functions of the quantum dot radius. A comparison of theoretically determined fundamental photoluminescence peak energies with available experimental reports in the cases of CdS, CdSe and CdTe is presented and discussed, showing a good agreement between calculated and measured results.

Heavy and light exciton states in c-AlGaN/GaN asymmetric double quantum wells

Abstract This work presents a theoretical study of the lowest heavy- and light-exciton energy states in a c-AlGaN/GaN asymmetric double quantum well. It makes use of the variational method to determine the eigenstates of the corresponding Schrodinger equation, within the effective mass and parabolic band approximations. We studied the behavior of the exciton energy, the corresponding binding energy as well as the photoluminescence energy peak as a function of the left quantum well width and the central barrier height. Direct and indirect exciton states can be obtained depending on the quantum well configuration. The motivation for this study comes from the experimental reports by T. Wecker et al., in which they measure the photoluminescence energy peak in similar systems with different aluminum concentrations. The comparison of our results with the experimental outputs shows good agreement.

Exact Green's function approach to RKKY interactions

The Green's function~(GF) of two localized magnetic moments embedded in the electron gas is calculated exactly. The electrons are treated in the effective mass approximation and the magnetic moments are coupled with electrons by a delta-like~$s-d$ interaction. The resulting GF is obtained by the exact summation of the Born series using a generalization of the method developed by Slater-Koster and Ziman to non-commuting spin operators with the use of the Woodbury identities. The exact GF crucially depends on the value of the one-electron GF at the origin, denoted as~$g_0$. The Born series is convergent only if~$g_0$ is finite, which holds for electrons in parabolic energy bands in~$1D$, but not in~$2D$ and~$3D$. In the general case, the exact GF includes nonlinear combination of localized spins operators. A method of calculating matrix elements of these operators is given. For spins~$S_a=S_b = 1/2$ the exact GF is expressed as a linear combination of components of~$\hS_a, \hS_b$, and the exact range function~${\cal J}(r)$ is obtained as a double integral over analytical expression. For electron energy~$E=0$ and~$J g_0/2 = 2$ or~$J g_0/2=-2/3$ the range function and GF are singular. Poles of GF occur in the vicinities of singularity points and the resulting energies of bound states are calculated. There are three regimes of~$J$. For small $J$ the range function resembles RKKY one: it has the same period~$\pi/k_F$, the same decay character and a slightly different amplitude, usually within a few percent. This regime occurs for most frequently in the nature. For~$|J|$ comparable to~$|g_0|^{-1}$ the exact range function differs qualitatively from RKKY one,. For large $|J|$ the exact range function oscillates with the same period and power-like decay as the usual RKKY function but it has much lower amplitude decaying with growing~$|J|$.

Enhancement on carrier mobility in amorphous indium tin oxynitride (ITON) thin films

Indium tin oxynitride (ITON) thin films were deposited by reactive DC magnetron sputtering technique. The samples were deposited onto glass and silicon (100) substrates at room temperature. For this purpose, the sputtering reactive atmosphere was composed of different argon and nitrogen concentrations, to modify the structural, optical and electrical properties of obtained ITON thin films. Energy dispersive spectroscopy (EDS) was used in order to know the chemical composition of the different deposited samples, the nitrogen incorporation in the indium tin oxide structure was verified in all ITON analyzed samples. Additionally, through an infrared absorption spectroscopy study of the deposited films, it was possible to confirm the nitrogen incorporation in the ITO structure for the samples deposited under nitrogen presence. Several absorption bands corresponding to In–N, N–N, In–O, and Sn–O bonds were detected. As the effect of nitrogen incorporation, both crystalline structure and surface morphology are widely affected. On the other hand, the nitrogen presence in the structure leads to increase the carrier mobility reaching a value above 1100 cm2/Vs for the sample deposited in a higher nitrogen flux concentration, this result of high mobility raises ITON thin films a promising candidate to be used as an active layer in thin film transistors. The band gap values were calculated using the Tauc parabolic band model from the absorption spectra and it resulted in values near to 4.0 eV. Finally, the obtained transmission values were in the order of 75–80% in the visible region.

Nonlinear optical properties of n-type asymmetric double $$\delta $$-doped quantum wells: role of high-frequency laser radiation, doping concentration and well width

A numerical investigation on the nonlinear optical rectification, second and third harmonic generation coefficients in asymmetric double n-type $$\delta $$ -doped GaAs quantum well is performed in order to identify the influence of non-resonant intense laser radiation, doping concentration and the change in well widths. The energy eigenvalues and the corresponding eigenfunctions are determined by using effective-mass and parabolic band approximations. The working analytical expressions for the optical coefficients are derived from the iterative solving of compact-density matrix description of dielectric susceptibility. The obtained results reveal that the position and amplitude of the nonlinear optical rectification, second and third harmonic generation coefficients can be altered by modifying the external field as well as the compositional and geometrical setups.

Non-Rigid Band Structure in Mg2Ge for Improved Thermoelectric Performance.

Magnesium silicide and its solid solutions are among the most attractive materials for thermoelectric generators in the temperature range of 500–800 K. However, while n‐type Mg2(Si,Ge,Sn) materials show excellent thermoelectric performance, the corresponding p‐type solid solutions are still inferior, mainly due to less favorable properties of the valence bands compared to the conduction bands. Here, Li doped Mg2Ge with a thermoelectric figure of merit zT of 0.5 at 700 K is reported, which is four times higher than that of p‐type Mg2Si and double than that of p‐type Mg2Sn. The reason for the excellent properties is an unusual temperature dependence of Seebeck coefficient and electrical conductivity compared to a standard highly doped semiconductor. The properties cannot be captured assuming a rigid band structure but well reproduced assuming two parabolic valence bands with a strong temperature dependent interband separation. According to the analysis, the difference in energy between the two bands decrease with temperature, leading to a band convergence at around 650 K and finally to an inversion of the band positions. The finding of a combination of a light and a heavy band that are non‐rigid with temperature can pave the way for further optimization of p‐type Mg2(Si,Ge,Sn).

Theory of electron energy-loss spectroscopy in atomically thin metallic films

We study strongly confined plasmons in ultrathin gold and silver films by simulating electron energy-loss spectroscopy (EELS). Plasmon dispersion relations are directly retrieved from the energy- and momentum-resolved loss probability under normal incidence conditions, whereas they can also be inferred for aloof parallel beam trajectories from the evolution of the plasmon features in the resulting loss spectra as we vary the impinging electron energy. We find good agreement between nonlocal quantum-mechanical simulations based on the random-phase approximation and a local classical dielectric description for silver films of different thicknesses down to a few atomic layers. We further observe only a minor dependence of quantum simulations for these films on the confining out-of-plane electron potential when comparing density-functional theory within the jellium model with a phenomenological experimentally-fitted potential incorporating atomic layer periodicity and in-plane parabolic bands of energy-dependent effective mass. The latter shows also a small dependence on the crystallographic orientation of silver films, while the unphysical assumption of energy-independent electron mass leads to spurious features in the predicted spectra. Interestingly, we find electron band effects to be more relevant in gold films, giving rise to blue shifts when compared to classical or jellium model simulations. In contrast to the strong nonlocal effects found in few-nanometer metal nanoparticles, our study reveals that a local classical description provides excellent quantitative results in both plasmon strength and dispersion when compared to quantum-mechanical simulations down to silver films consisting of only a few atomic layers, thus emphasizing the in-plane nearly-free conduction-electron motion associated with plasmons in these structures.

Synergistically promoted thermoelectric performance of SnTe by alloying with NaBiTe2

SnTe, as a lead-free analog of PbTe, shows limited thermoelectric performance because of the high hole concentration arising from intrinsic Sn vacancies and its high thermal conductivity. Herein, we show a significantly improved thermoelectric performance in p-type SnTe through NaBiTe2 alloying, by which carrier concentration optimization, band structure engineering, and thermal conductivity reduction are simultaneously realized. Band modification is confirmed by transport coefficient analysis based on the single parabolic band model. The low lattice thermal conductivity of SnTe−NaBiTe2 solid solutions is ascribed to point defect scattering. As a result, a zT value of ∼1.1 at 834 K is achieved in the sample with the nominal composition of (SnTe)0.96(NaBiTe2)0.04.

Thermoelectric modulation by intrinsic defects in superionic conductor AgxCrSe2

AgCrSe2 materials have shown the potential to be the promising thermoelectric materials due to the intrinsic ultralow lattice thermal conductivity enabled by the fluid-like motion of Ag ions in crystal structures. However, what important role the Ag point defects can play in promoting liquid-like conduction still remains a mystery. Moreover, understanding the electronic transport properties, specifically for clarifying the contribution of various impurity states, is of critical importance for improving the thermoelectric performance of AgCrSe2. Here, the thermoelectric properties of AgCrSe2 with various Ag content have been systematically investigated. It is found that the carrier concentration can be modulated in a broad range by inducing deep level impurity states, enabling a transition from degenerate semiconductor to nondegenerate one and a reliable evaluation on the thermoelectric transport properties. The single parabolic band model gives a good clarification regarding the increased electronic performance. Furthermore, the enhancement of the liquid-like effect triggered by the Ag vacancies contributes to the ultralow lattice thermal conductivity (∼0.25 W m−1 K−1). Eventually, a maximum figure of merit zT of ∼0.6 is realized in Ag0.97CrSe2 at 750 K. The present findings may shed light on the improvement of thermoelectric performance in AgCrSe2 materials.

Quasilinear dispersion in electronic band structure and high Seebeck coefficient in CuFeS2 -based thermoelectric materials

The earth-abundant natural mineral chalcopyrite $\mathrm{CuFe}{\mathrm{S}}_{2}$ is a potential $n$-type thermoelectric material because of its large Seebeck coefficient at high carrier concentrations. For a long time, the large Seebeck coefficient of $\mathrm{CuFe}{\mathrm{S}}_{2}$ has been attributed to a large electron effective mass, but the reasons for this and the unusual carrier concentration dependent behavior have rarely been discussed. Here, we systematically investigated the special transport behavior of $\mathrm{CuFe}{\mathrm{S}}_{2}$ and found the classical parabolic band model to be inadequate in explaining it. Our experimental and theoretical studies indicate that there are two flat electronic pockets at the \ensuremath{\Gamma} and $Z$ points of the Brillouin zone near the conduction band edge of $\mathrm{CuFe}{\mathrm{S}}_{2}$ that dominate the charge transport. These electronic pockets result from nonparabolic quasilinearly dispersing bands that give rise to a linear wave vector dependent energy ($E\ensuremath{\sim}k$) and a carrier density dependent effective mass (${m}^{*}\ensuremath{\sim}{m}_{0}{n}^{1/3}$). Such a strong carrier concentration dependent carrier effective mass results in the high Seebeck coefficient of $\mathrm{CuFe}{\mathrm{S}}_{2}$ compound under a large carrier density. The work demonstrates that quasilinearly dispersing bands can give strongly enhanced Seebeck coefficient, and could be useful in optimizing the properties of thermoelectric materials.

Analysis of simple scattering models on the thermoelectric performance of analytical electron dispersions

Recent first-principles electron–phonon scattering calculations of heavily doped semiconductors suggest that a simple DOS scattering model, wherein the electronic scattering rates are assumed to be proportional to the density-of-states, better approximates the rigorous scattering characteristics compared to the commonly used constant relaxation-time and constant mean-free-path approximations. This work investigates how the thermoelectric properties predicted with the DOS model compare to the other two scattering models, using three analytical electron dispersions (parabolic band in 3D/2D/1D, Kane band in 3D/2D/1D, and ring-shaped quartic band in 2D). Our findings show that the scattering models can lead to significant differences and can disagree about whether certain band structures can provide benefits. A constant relaxation-time is found to be always optimistic compared to a constant mean-free-path, while the DOS scattering model shows no such clear trend. Notably, the 1D parabolic band and 2D quartic band exhibit the highest power factors with the DOS model, resulting from a rapid decrease in density-of-states, and thus scattering—suggesting a possible strategy for improved thermoelectrics based on engineering band structures with sharp/discontinuous drops in density-of-states. The DOS scattering approximation also suggests that searches for materials with a delta function-like DOS (as a proxy to the transport distribution) or converged bands may yield limited benefits, due to the increase in scattering. This work highlights the importance of simple and accurate scattering models when rigorous ab initio scattering calculations are not feasible.

Signatures of Sixfold Degenerate Exotic Fermions in a Superconducting Metal PdSb2.

Multifold degenerate points in the electronic structure of metals lead to exotic behaviors. These range from twofold and fourfold degenerate Weyl and Dirac points, respectively, to sixfold and eightfold degenerate points that are predicted to give rise, under modest magnetic fields or strain, to topological semimetallic behaviors. The present study shows that the nonsymmorphic compound PdSb2 hosts six-component fermions or sextuplets. Using angle-resolved photoemission spectroscopy, crossing points formed by three twofold degenerate parabolic bands are directly observed at the corner of the Brillouin zone. The group theory analysis proves that under weak spin-orbit interaction, a band inversion occurs.

Large effective mass and low lattice thermal conductivity contributing to high thermoelectric performance of Zn-doped Cu5Sn2Se7

Cu5Sn2Se7 is a new family member of ternary Cu-based chalcogenides that consists of abundant and environmental friendly elements. It shows a great potential for thermoelectric application, but its metal-like electronic transport behavior leads to overall low thermoelectric performance. In this work, we successfully lower the intrinsically high hole concentration of Cu5Sn2Se7 via an aliovalent doping approach, i.e. replacing the monovalent Cu by divalent Zn. It is shown that one single parabolic band model reasonably fits the room temperature carrier concentration dependent Seebeck coefficients of Cu5−xZnxSn2Se7 (x = 0–1) samples with a large effective mass of 2.5 m0, and their power factors are significantly optimized by charge carrier concentration regulation. Moreover, these materials display ultralow lattice thermal conductivity close to the theoretical minimum (0.55 Wm−1K−1) at high temperatures because of its large Grüneisen parameter of ∼2 estimated by sound velocity data. Altogether, a maximum ZT of 0.51 is achieved at 750 K for Cu4.1Zn0.9Sn2Se7, which is 325% higher over the control sample Cu5Sn2Se7 (ZT = 0.12 @ 750 K).

Electron-phonon coupling in the ordered phase of Rb on monolayer graphene

In the mechanism of two-dimensional (2D) superconductivity in doped graphene, it was predicted that the presence of dopant bands plays a key role. However, it has been challenging to fabricate an ordered phase of alkali metals on graphene owing to its van-der-Waals nature. We systematically study the phase formation of Rb on graphene epitaxially grown on H-passivated SiC(0001). We found a range of control parameters that stabilize the well-ordered 2 × 2 phase (RbC8), as confirmed by in-situ low-energy electron diffraction. Angle-resolved photoemission (ARPES) spectra taken from the 2 × 2 phase show a folded band of graphene and a parabolic band of Rb. In the vicinity of the Fermi level, the self-energy extracted from ARPES data reveals a clear signature of electronic coupling to the in-plane and out-of-plane phonon modes of C and Rb atoms. The electronic coupling of graphene to the in-plane vibration mode of Rb atoms is identified as a key factor for the enhancement of electron-phonon coupling.

Coexistence of parabolic and linear band crossings and electron-doped spin-gapless properties in rhombohedral type YbBO3

Very recently, a novel Dirac half-metal has been investigated in the perovskite-type lanthanum manganite (LaMnO3) by Ma et al. [1] and the half metallicity with 100% spin polarization is discovered. More remarkably, multiple linear Dirac crossings are observed around the Fermi energy level in the spin-up direction. Inspired by this work, another perovskite-type material YbBO3, which has been synthesized before, is investigated by first principles calculation. Results confirm the presence of half metallicity in this material with also multiple Dirac-like linear and parabolic band crossings around the Fermi level. The estimated Curie temperature is 469.4 K and the mechanic and dynamic stabilities have been verified. Besides, the elastic anisotropy is revealed with the directional dependent Young’s modulus and shear modulus, together with the acoustic wave properties. The effect of the uniform strain, electron doping and spin-orbital coupling on the electronic structures have been also accessed. In particular, nearly spin-gapless semiconducting behavior with linear or parabolic energy dispersions is obtained by electron doping. Moreover, several thermodynamic properties have been examined under temperature from 0 to 500 K and pressure from 0 to 5 GPa. In combination, we expect YbBO3 can attract more research attention and even facilitate the spintronic application.

ZnAl2O4 decorated Al-doped ZnO tetrapodal 3D networks: microstructure, Raman and detailed temperature dependent photoluminescence analysis.

3D networks of Al-doped ZnO tetrapods decorated with ZnAl2O4 particles synthesised by the flame transport method were investigated in detail using optical techniques combined with morphological/structural characterisation. Low temperature photoluminescence (PL) measurements revealed spectra dominated by near band edge (NBE) recombination in the UV region, together with broad visible bands whose peak positions shift depending on the ZnO : Al mixing ratios. A close inspection of the NBE region evidences the effective doping of the ZnO structures with Al, as corroborated by the broadening and shift of its peak position towards the expected energy associated with the exciton bound to Al. Both temperature and excitation density-dependent PL results pointed to an overlap of multiple optical centres contributing to the broad visible band, with the peak position dependent on the Al content. While in the reference sample the wavelength of the green band remained unchanged with temperature, in the case of the composites, the deep level emission showed a blue shift with increasing temperature, likely due to distinct thermal quenching of the overlapping emitting centres. This assumption was further validated by the time-resolved PL data, which clearly exposed the presence of more than one optical centre in this spectral region. PL excitation analysis demonstrated that the luminescence features of the Al-doped ZnO/ZnAl2O4 composites revealed noticeable changes not only in deep level recombination, but also in the material's bandgap when compared with the ZnO reference sample. At room temperature, the ZnO reference sample exhibited free exciton resonance at ∼3.29 eV, whereas the peak position for the Al-doped ZnO/ZnAl2O4 samples occurred at ∼3.38 eV due to the Burstein–Moss shift, commonly observed in heavily doped semiconductors. Considering the energy shift observed and assuming a parabolic conduction band, a carrier concentration of ∼1.82 ×1019 cm−3 was estimated for the Al-doped ZnO/ZnAl2O4 samples.

ELECTRON ENERGY SPECTRA IN QUANTIZED STRUCTURES

In this paper we study the Electron Energy Spectra (EES) in quantum wells (QWs) of heavily doped (HD) non-linear optical, III-V, II-VI, IV-VI and stressed Kane type compounds by formulating HDEES in each case respectively considering all the specialties of the energy band constants of the said materials. It is noted that the complex EES in many cases in HDS, instead of real one, occurs from the existence of the essential poles in the corresponding EES in the absence of band tails. The EES in QWs is Quantized 2D closed surfaces. As a collateral study we have also investigated the effective mass (EM), Density-of-states (DOS) function and the electron statistics in this context for the purpose of comprehensive understanding. The EM exists in the forbidden zone, which is impossible without the effect of band tailing. In the absence of band tails, the EM in the band gap of semiconductors is infinity. Besides, depending on the type of unperturbed carrier energy spectrum, the new forbidden zone will appear within the normal energy band gap for HDS. Under certain limiting conditions all the results for all the models get simplified the well-known results of an isotropic parabolic energy bands which exhibit the mathematical compatibility of our present generalized analysis.

Impact of QW coupling on the binding energy in InGaN/GaN under the effects of the size, the impurity and the internal composition

In the present paper, the binding energy of hydrogenic shallow-donor impurity in simple and double coupled quantum wells based on unstrained wurtzite (In,Ga)N/GaN is investigated. Considering the effective-mass and dielectric mismatches between the well and its surrounding matrix, the numerical calculations are performed within the framework of the parabolic band and the single band effective-mass approximations under the finite potential barrier using finite element method (FEM). According to our results, it appears that the main effect of the wells coupling is to enhance the binding energy. It is also obtained that the binding energy is strongly sensitive to the internal and external parameters and can be adjusted by the quantum well/barrier width, the impurity position and the internal Indium composition. Our results are in good agreement with the finding especially for those obtained by the variational approach.

Comparative studies on the electronic transport in magnetically quantized low band gap semiconductor system

The Q1D system formed by magnetically confined system is attracting attention of researchers in device application because it is capable of over-looking the various techniques of fabrication difficulties and defects created by such fabrication techniques. In the presence of a high magnetic field, the transverse component of the energy dispersion relation gets quantized into various equally spaced energy levels called Landau levels and the motion of the carriers is completely restricted. However, the longitudinal component along the field is still free to move. The mobility of such system is enhanced when a low effective mass semiconductors n-HgCdTe (Mercury Cadmium Telluride) is used. The band structure of n-HgCdTe is found to be nonparabolic due to its low band gap according to Kane [Phadke and Sharma, 1975]. Recent publications, based on experimental verifications of transport coefficient of n-HgCdTe of Chen and Sher [Chen and Sher, 1982] show that the band structure of Mercury Cadmium Telluride (MCT) is more hyperbolic in nature rather than nonparabolic. The author has compared the effect of band structures on the various transport properties of MCT such as mobility, Seebeck coefficient, thermal conductivity, figure of merit (Z) etc. The figure of merit is a very important property of a material to be used in thermoelectric devices, such as cooler, refrigerator etc. The product of Z and temperature i.e. (ZT), a dimensionless quantity is found to be maximum for parabolic band structure and is followed by nonparabolic and hyperbolic band structures for all ranges of variation of temperature as well as magnetic field. Taking the hyperbolic band structure of MCT, the effect of high and low temperature scattering mechanisms on ZT is also observed.
 BIBECHANA 17 (2020) 34-41