Isotropic Effective Mass Research Articles

Theoretically Calculated Properties of a MOS Device on Gallium Oxide

The properties of a MOS device on (100) oriented β-Ga2O3 semiconductor are determined theoretically utilizing the concept of physics that the carrier effective masses in materials are related to the intrinsic Fermi energy levels in materials by the universal mass-energy equivalence equation given as dE/E = dm/m, where E is the energy and m is the free electron mass. The known parameters of isotropic electron effective mass of 0.27m and the bandgap of 4.8 eV for β-Ga2O3 semiconductor are utilized to determine the properties of the MOS device along with the parameter of threshold for electron heating in SiO2 as 2 MV/cm-eV.

Investigation of Aluminum Arsenide Honeycomb Monolayer via Density Functional Theory

First principle calculations are performed to theoretically predict the physical properties of hexagonal aluminium arsenide planar and buckled monolayers. The structural characteristics showed that the buckled parameter is about 0.32 A°. Cohesive energies have favourable values and it indicates the fabrication possibility. Phonon dispersion properties indicated that the planar aluminium arsenic monolayers are dynamically unstable, while the buckled is less dynamically unstable. The elastic constant parameters achieved the required characteristics of stable hexagonal monolayer structures. The study of electronic band structure prefers to indirect semiconductor band gaps, and the density of states showed strong orbital hybridization in the conduction band. Planar structure has isotropic light electron effective mass and anisotropic heavy hole effective mass. The buckled structure has isotropic light electron effective mass and isotropic heavy hole effective mass. The absorption spectra have high absorption coefficient in various visible and ultraviolet wavelength. The absorption coefficient levels off at about direct and indirect band gaps.

Confined Stark effect and statistical distribution of charge carriers in β-HgS cylindrical quantized layer

The spectrum of single-particle states of charge carriers in the β-HgS quantized layer of the β-CdS/β-HgS/β-CdS cylindrical nanoheterostructure is considered in the approximation of the isotropic effective mass. Consideration is carried out for the most interesting case, when only the first size quantization subband is filled. The cases of strong quantization of the carriers’ motion in both the transverse-radial and longitudinal directions are considered separately. The splitting of the valence band into subbands of heavy and light holes is also taken into account. The dependence of the position of the chemical potential of electrons and holes on the quantization energy of charge carriers is obtained. Explicit expressions are obtained for the dependence of the density, internal energy, and heat capacity of charge carriers in the β-HgSlayer on the geometric sizes of the system and its temperature, and the corresponding graphic illustrations are presented. The influence of a longitudinal external uniform electric field on the statistical distribution of carriers in the β-HgS layer is also considered. An explicit dependence of the chemical potential and other statistical characteristics of the sample on the magnitude of the perturbing field has been obtained.

Hybridization-Induced Image Potential States with Large Effective Mass in Lead Phthalocyanine Overlayers on Graphene

The structural and electronic properties of lead phthalocyanine (PbPc) adsorbed on graphene are studied theoretically using the van der Waals density functional method. It is revealed that an extended state analogous to an image potential state (IPS) emerges in a close-packed PbPc monolayer, hybridizing with the lowest IPS of graphene to form bonding and antibonding states at the PbPc–graphene interface. The impact of the PbPc adsorption manifests itself as increased effective masses of the hybrid IPSs as compared with those on pristine graphene. In particular, the bonding IPS exhibits a marked anisotropy in the effective mass, reflecting the uniaxially elongated unit cell adopted in the present calculations, whereas the antibonding one has an almost isotropic effective mass, which is comparable to experimental results obtained with two-photon photoemission spectroscopy of PbPc on highly oriented pyrolytic graphite and on single crystalline graphite. It is also shown that the increase in the effective masses is triggered by the hybridization with unoccupied molecular orbitals of PbPc that is localized at the Pb atom.

Aharonov-Bohm oscillations in phosphorene quantum rings: Mass anisotropy compensation by confinement potential

We consider the Aharonov-Bohm (AB) effect on a confined electron ground state in a quantum ring defined electrostatically within the phosphorene monolayer. The strong anisotropy of effective masses in phosphorene quenches ground-state oscillations for a circular ring because of interrupted persistent current circulation around the ring. An elliptic deformation of the confinement potential can compensate for the anisotropy of the effective masses and produce ground-state parity transformations with the AB periodicity. Moreover, a specific ratio of the semiaxes is determined for which the spectrum becomes identical to that of a circular quantum ring and an isotropic effective mass. We identify a generalized angular momentum operator which commutes with the continuum Hamiltonian for the chosen ratio of the semiaxes that closes the avoided crossings of energy levels for states of the same parity and spin. Ground-state oscillations for the two-electron ground state are also discussed.

Zinc gallate spinel dielectric function, band-to-band transitions, and Γ-point effective mass parameters

We determine the dielectric function of the emerging ultrawide bandgap semiconductor ZnGa2O4 from the near-infrared (0.75 eV) into the vacuum ultraviolet (8.5 eV) spectral regions using spectroscopic ellipsometry on high quality single crystal substrates. We perform density functional theory calculations and discuss the band structure and the Brillouin zone Γ-point band-to-band transition energies, their transition matrix elements, and effective band mass parameters. We find an isotropic effective mass parameter (0.24 me) at the bottom of the Γ-point conduction band, which equals the lowest valence band effective mass parameter at the top of the highly anisotropic and degenerate valence band (0.24 me). Our calculated band structure indicates the spinel ZnGa2O4 is indirect, with the lowest direct transition at the Γ-point. We analyze the measured dielectric function using critical-point line shape functions for a three-dimensional, M0-type van Hove singularity, and we determine the direct bandgap with an energy of 5.27(3) eV. In our model, we also consider contributions from Wannier–Mott type excitons with an effective Rydberg energy of 14.8 meV. We determine the near-infrared index of refraction from extrapolation (1.91) in very good agreement with results from recent infrared ellipsometry measurements (ε∞=1.94) [M. Stokey, Appl. Phys. Lett. 117, 052104 (2020)].

Deformation of the Fermi surface of a spinless two-dimensional electron gas in presence of an anisotropic Coulomb interaction potential

We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree–Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.

Electron mobility and mode analysis of scattering for β-Ga2O3 from first principles

The electrical transport properties of β-Ga2O3 are studied by first-principles calculations. The calculated intrinsic electron Hall mobilities agree well with experiments, with intrinsic Hall factor decreasing monotonically from 1.54 at 100 K to 1.14 at 800 K. The anisotropy of electron mobility is weak due to the almost isotropic electron effective mass, which also results in nearly isotropic Seebeck coefficient and electronic contribution to the thermal conductivity. The mode analysis of phonon scattering reveals that the optical phonon scattering is almost entirely determined by the long-range polar interactions, whereas the acoustic phonon scattering also plays an important role especially at low temperatures. The intrinsic electron mobility is significantly overestimated even above room temperature by only considering the polar optical phonon scattering, in contrast to previous predictions from fitting of phenomenological models.

Band structure, effective mass, and carrier mobility of few-layer h-AlN under layer and strain engineering

Wide bandgap two-dimensional semiconductors are of paramount importance for developing van der Waals heterostructure electronics. This work reports the use of layer and strain engineering to introduce the feasibility of two-dimensional hexagonal (h)-AlN to fill the scientific and application gap. We show that such one- to five-layer h-AlN has an indirect bandgap, tunable from 2.9 eV for a monolayer to ∼3.5 eV for multilayer structures, along with isotropic effective masses and carrier mobilities between zigzag and armchair directions. With an increase in the layer number to bulk AlN, the bandgap will experience a transition from an indirect gap to direct gap. Surprisingly, high room-temperature mobilities of electrons and holes (of the order of 1000 cm2 V−1 s−1) in a relaxed monolayer h-AlN system and widely adjustable effective masses and carrier mobilities in a different layer h-AlN are observed. In the presence of strain engineering, the bandgap decreases obviously with an increase in tensile strain; meanwhile, the isotropy and value of effective mass or carrier mobility in monolayer h-AlN can also be modulated effectively; the hole mobilities in the armchair direction, especially, will be enhanced dramatically. With a tunable bandgap, high carrier mobilities, and modifiable isotropy, our results indicate that few-layer h-AlN has potential applications in future mechano-electronic devices.

On the Two-Phonon Relaxation of Excited States of Boron Acceptors in Diamond

The relaxation of holes from excited states of boron acceptors in diamond with the emission of two optical phonons is studied theoretically. To describe the wave function of acceptor states, an electron-like Hamiltonian with an isotropic effective mass is used. The wave function of the ground state is determined by the quantum-defect method. The probability of the transition is calculated in the adiabatic approximation. It is assumed that the phonon dispersion law is isotropic and the phonon frequency is quadratically dependent on the wave-vector modulus, with the maximum and minimum frequencies ωmax and ωmin at the center and boundary of the Brillouin zone, respectively. A high sensitivity of the probability of the transition to the characteristic of phonon dispersion ωmax – ωmin is revealed, especially for the transition with the energy ET in the range 2ℏωmin ≤ ET 1012 s–1) in the “resonance” range ℏωmin + ℏωmax ≤ ET ≤ 2ℏωmax.

An efficient method for subband calculations of cylindrical nanowire transistors using a Fourier harmonics expansion

We propose an efficient method for subband calculations of cylindrical nanowire transistors with an arbitrary channel orientation. To perform the subband calculation efficiently, the wavefunctions are expanded using Fourier harmonics. It is confirmed that the use of an approximate isotropic effective mass introduces an error in the subband calculation due to the incorrectly calculated potential energy. A comparison with the results obtained in the Cartesian coordinate system confirms the accuracy of our method. Moreover, the simulation time required to obtain the self-consistent solution is significantly reduced.

Двухфононная релаксация возбужденных состояний акцепторов бора в алмазе

The relaxation of holes in the excited states of boron acceptors in diamond is theoretically investigated when two optical phonons are emitted. An electron-like Hamiltonian with an isotropic effective mass was used to describe the wave function of the acceptor states. The wave function of the ground state was found by the quantum defect method. The transition probability was calculated in adiabatic approximation. The dispersion law of phonons was considered isotropic, and the frequency of phonons is quadratically dependent on the wave vector module, with the maximum value, omegamax, achieved in the center of the Brillouin zone, and the minimum, omegamin, at the edge of the Brillouin zone. The high sensitivity of the rates to the characteristic of phonon dispersion, omegamax-omegamin, especially for the transition energy, ET, in the 2homegamin≤ ET<homegamin +homegamax interval was revealed. Depending on the transition energy and dispersion of phonons, the rate of two-phonon relaxation in the low-temperature limit varies from ultra-low values (less than 108 s-1) near the threshold, ET=2homegamin, to ultra-high values (more than 1012 s-1) in the "resonance" region homegamin+homegamax≤ ET≤2homegamax.

Interband Absorption and Photoluminescence in Nanospherical InP/InAs/InP Core/Shell/Shell Heterostructure

The single-particle states of charge carriers in the nanospherical InP/InAs/InP heterostructure are theoretically considered in the isotropic effective mass approximation and in the regime of strong size quantization. The results of numerical computations of the energy levels of charge carriers at various thicknesses of the quantizing of the InAs layer of the indicated heterophase structure are presented. It is shown that it is possible to achieve the desired value and position of the size quantization levels of charge carriers in the layer by an appropriate choice of the layer thickness. The interband optical transitions in the InAs layer are also considered. The values of the effective broadening of the band gap of the InAs layer as a function of the layer thickness are computed. By numerical computations, it is shown that the absorption has a resonant character and that the diagonal transitions dominate in the spectrum of the interband absorption. For several diagonal transitions involving both light and heavy holes, the values of threshold frequencies and absorption curves are given. In the spherical InP/InAs/InP nanoheterostructure, the photoluminescence spectra were also constructed for various temperatures close to room temperature.

Multiphonon Intracenter Relaxation of Boron Acceptor States in Diamond

The relaxation rates are calculated in the adiabatic approximation, in which the steady-state impurity states are taken to be electronic-vibrational (vibronic) states. The probabilities of transitions between these states with the emission (or absorption) of one or several phonons are calculated in first-order perturbation theory on the assumption that the transitions are a result of the violation of adiabaticity. The electron part of the wave function of the vibronic state is described by a simple Hamiltonian with an isotropic effective mass. The wave function of the ground state is determined by the quantum defect method. According to the calculations, a hole relaxes from the excited boron acceptor state, whose energy is 304 meV higher than the energy of the ground state, to the ground state with the emission of two optical phonons with a rate of ~1011 s–1. This value is an estimate from above, since the model of nondispersive optical phonons used in the study overestimates the number of phonon modes, whose participation in relaxation is allowed by the energy conservation law. However, despite the rough approximation, it can be concluded that the multiphonon relaxation of boron acceptor states in diamond is a fast process.

Многофононная внутрицентровая релаксация состояний акцепторов бора в алмазе

AbstractThe relaxation rates are calculated in the adiabatic approximation, in which the steady-state impurity states are taken to be electronic-vibrational (vibronic) states. The probabilities of transitions between these states with the emission (or absorption) of one or several phonons are calculated in first-order perturbation theory on the assumption that the transitions are a result of the violation of adiabaticity. The electron part of the wave function of the vibronic state is described by a simple Hamiltonian with an isotropic effective mass. The wave function of the ground state is determined by the quantum defect method. According to the calculations, a hole relaxes from the excited boron acceptor state, whose energy is 304 meV higher than the energy of the ground state, to the ground state with the emission of two optical phonons with a rate of ~10^11 s^–1. This value is an estimate from above, since the model of nondispersive optical phonons used in the study overestimates the number of phonon modes, whose participation in relaxation is allowed by the energy conservation law. However, despite the rough approximation, it can be concluded that the multiphonon relaxation of boron acceptor states in diamond is a fast process.

Electron effective mass in Sn-doped monoclinic single crystal β-gallium oxide determined by mid-infrared optical Hall effect

The isotropic average conduction band minimum electron effective mass in Sn-doped monoclinic single crystal β-Ga2O3 is experimentally determined by the mid-infrared optical Hall effect to be (0.284 ± 0.013)m0 combining investigations on (010) and (2¯01) surface cuts. This result falls within the broad range of values predicted by theoretical calculations for undoped β-Ga2O3. The result is also comparable to recent density functional calculations using the Gaussian-attenuation-Perdew-Burke-Ernzerhof hybrid density functional, which predict an average effective mass of 0.267m0. Within our uncertainty limits, we detect no anisotropy for the electron effective mass, which is consistent with most previous theoretical calculations. We discuss upper limits for possible anisotropy of the electron effective mass parameter from our experimental uncertainty limits, and we compare our findings with recent theoretical results.

Interband Absorption and Photoluminescence in the Cylindrical Layered CdS/HgS/CdS Heterostructure

Within the approximation of an isotropic effective mass, the one-particle states of charge carriers in the layered CdS/HgS/CdS heterostructure are considered. It is shown that under conditions in which the strong-quantization regime is realized in the HgS layer, the spatial localization of charge carriers is realized there with the maximum probability. The energy spectrum and envelopes of the wave functions of the electron and hole states are computed in the structure under consideration. The interband optical absorption is computed, when the system is a layered cylindrical quantum dot and when there is a free motion of the charge carriers along the symmetry axis. For the same cases, the photoluminescence spectrum is also considered.

Electronic structure and defect properties of B6O from hybrid functional and many-body perturbation theory calculations: A possible ambipolar transparent conductor

${\mathrm{B}}_{6}\mathrm{O}$ is a member of icosahedral boron-rich solids known for their physical hardness and stability under irradiation bombardment, but it has also recently emerged as a promising high mobility $p\ensuremath{-}$type transparent conducting oxide. Using a combination of hybrid functional and many-body perturbation theory calculations, we report on the electronic structure and defect properties of this material. Our calculations identify ${\mathrm{B}}_{6}\mathrm{O}$ has a direct band gap in excess of 3.0 eV and possesses largely isotropic and low effective masses for both holes and electrons. Of the native defects, we identify no intrinsic origin to the reported $p\ensuremath{-}$type conductivity and confirm that $p\ensuremath{-}$type doping is not prevented by intrinsic defects such as oxygen vacancies, which we find act exclusively as neutral defects rather than hole-killing donors. We also investigate a number of common impurities and plausible dopants, finding that isolated acceptor candidates tend to yield deep states within the band gap or act instead as donors, and cannot account for $p\ensuremath{-}$type conductivity. Our calculations identify the only shallow acceptor candidate to be a complex consisting of interstitial H bonded to C substituting on the O site ${(\mathrm{CH})}_{\mathrm{O}}$. We therefore attribute the origins of $p\ensuremath{-}$type conductivity to these complexes formed during growth or more likely via isolated ${\mathrm{C}}_{\mathrm{O}}$ which later binds with H within the crystal. Lastly, we identify Si as a plausible $n\ensuremath{-}$type dopant, as it favorably acts as a shallow donor and does not suffer from self-compensation as may the C-related defects. Thus, in addition to the observed $p\ensuremath{-}$type conductivity, ${\mathrm{B}}_{6}\mathrm{O}$ exhibits promise of $n\ensuremath{-}$type dopability if the stoichiometry and both native and extrinsic sources of compensation can be sufficiently controlled.

Electron–hole transition in a spherical quantum dot confined at the center of a cylindrical nano-wire: Comparison of isotropic and anisotropic effective mass

Electronic structure of an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire is investigated. The Schrodinger equation within the effective mass approximation is solved and the energy eigenvalues and transition energies are calculated as a function of quantum dot and nano-wire radii using the finite element method. The two types of heavy holes, hhI and hhII, with isotropic and anisotropic effective masses are considered, respectively. The effect of spherical and nano-wire confining potentials, the size of the dot and the nano-wire on ground and first excited state energies of the electron, heavy hole I and heavy hole II are investigated. The results show that the electron and heavy holes energies decrease as the dot and the nano-wire radii increase. The emitted wavelength of transitions between el-hhI and el-hhII are also calculated and compared. The results show that the anisotropy of the effective mass has great effect on the emitted wavelength.

Anisotropy and isotropy of hole effective mass of strained Ge

In this paper, the hole effective mass along arbitrarily k wavevector direction and the hole isotropic effective masses in strained Ge/(001)(101)(111)Si1-xGex are obtained with in the frame work of kp theory. It is found that the hole effective mass of the top valence band along [010] wave vector decreases obviously with stress increasing and its absolute value is smallest. The hole effective mass of the second valence band tends to gently decrease with stress increasing, and is not significant in magnitude. Compared with the existing isotropic effective quality, the result obtained in this paper is proved to be correct.