On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Intrinsic electrical properties of individual single-walled carbon nanotubes with small band gaps

Individual single-walled carbon nanotubes (SWNT) exhibiting small band gaps on the order of 10 meV are observed for the first time in electron transport measurements. Transport through the valence or conduction band of a small-gap semiconducting SWNT (SGS-SWNT) can be tuned by a nearby gate voltage. Intrinsic electrical properties of the Ohmically contacted SGS-SWNT are elucidated. An SGS-SWNT exhibits metal- or semiconductorlike characteristics depending on the Fermi level position in the band structure.     

A computational study of nonparabolic conduction band effect on quantum wire transport (e.g. GaN)

We studied the physics insight the GaN (example) quantum wire FET transistors. The model is based on the four $\mathbf{k}{\cdot } \mathbf{p}$ k · p Kane band model. We have introduced closed compact model for the Einstein relation of the diffusivity to mobility ratio (DMR) in quantum wires. The model can be applied for both wide and narrow band gaps of nonparabolic conduction band dispersion. The model is related to the optical matrix elements between conduction and valence bands. We have used 1D electrostatic to model the electron density over the maximum energy point. We have studied the effects of gate-to-source and drain-to-source voltages on the DMR by calculating the electron density using flux theory. We observed that above the threshold the non-parabolic dispersion increases the DMR. Additionally, we have studied the nonparabolic effects on the Fermi level and found that for low doping concentrations, the nonparabolic effect must be considered and an accurate calculation for the optical matrix elements is needed.     

Narrow band gap group III-nitride alloys

Recent results on the properties of narrow gap group III-nitrides and their alloys are reviewed. It is shown that InN with the energy gap of 0.7 eV exhibits classical characteristics of a narrow gap semiconductor with strongly nonparabolic conduction band and an energy dependent electron effective mass. With the new discovery, the direct band gaps of the group III-nitride alloys span an extremely wide energy range from near infrared in InN to deep ultraviolet in AlN offering possibilities for new device applications of these materials. We also discuss properties of dilute group III-N–V alloys in which incorporation of a small amount of nitrogen results in a dramatic band gap reduction. All the unusual properties of the alloys are well described by a band anticrossing model that considers an interaction between localized nitrogen states and the extended states of the conduction band.     

Numerical computation of potential profiles and energy spectrum in the space charge region of semiconductors at high electric field

Numerical computations of the potential profiles are performed for the space charge region of semiconductors with a spherical nonparabolic conduction band at a high electric field externally applied to the surface. For the obtained potential profiles, the energy spectrum in the surface region was calculated for an electron moving perpendicularly to the surface (field emitted electron). To perform this calculation, a special iterative procedure was developed to compute the complex eigenvalues of the Hamiltonian with an arbitrary potential.     

Electrons in dry DNA from density functional calculations

The electronic structure of an infinite polyguanine-polycytosine DNA molecule in its dry A-helix structure is studied by means of density functional calculations. An extensive study of 30 nucleic base pairs is performed to validate the method. The electronic energy bands of DNA close to the Fermi level are then analysed in order to clarify the electron transport properties in this particularly simple DNA realization, probably the best suited candidate for conduction. The energy scale found for the relevant band widths, as compared with the energy fluctuations of vibrational or genetic-sequence origin, makes highly implausible the coherent transport of electrons in this system. The possibility of diffusive transport with subnanometre mean free paths is, however, still open. Information for model Hamiltonians for conduction is provided.     

Electron-electron spin-flip scattering and spin relaxation in III–V and II–VI semiconductors

Spin relaxation time of conduction electrons resulting from electron-electron spin-flip collisions has been investigated in III–V and II–VI semiconductors with InSb-like energy band structure. Analytical expression has been obtained for non-degenerate electron gas. The proposed mechanism can be dominent in the experimental conditions of electron spin resonance in InSb at higher temperatures.     

Electronic band structure and Fermi surface of CaB6 studied by angle-resolved photoemission spectroscopy

We report high-resolution angle-resolved photoemission spectroscopy (ARPES) on CaB6. The band structure determined by ARPES shows a 1 eV energy gap at the X point between the valence and the conduction bands. We found a small electron pocket at the X point, whose carrier number is estimated to be (4-5) x 10(19) cm(-3), in good agreement with the Hall resistivity measurement with the same crystal. The experimental results are discussed in comparison with band structure calculations and theoretical models for the high-temperature ferromagnetism.     

Energy band structure of I–III–VI2 semiconductors

We review recent studies of the energy band structure of I-III-VI₂ semiconductors. The structure of the uppermost valence bands of a I-III-VI₂ compound is profoundly influenced by the proximity of noble metal d levels in the valence band. The direct energy gaps observed in I-III-VI₂ compounds are low relative to the energy gaps in the II–VI analogs by amounts up to 1.6eV, and the spin-orbit splittings observed in the ternaries are low relative to the values observed in the binary analogs, owing to a partial cancellation of the positive spin-orbit parameter for p levels and the negative spin-orbit parameter for d levels. The presence of the noble metal d levels in the valence band has been confirmed directly by the observation of electroreflectance structure due to transitions from the d levels themselves to the lowest conduction band minimum.     

Free-carrier absorption in quantum well structures for acoustic phonon scattering

Free-carrier absorption has been studied for quantum well structures fabricated from III-V semiconducting materials where the acoustic phonon scattering is important. The energy band of carriers is assumed to be nonparabolic. We discuss the effect of acoustic phonon scattering on the free-carrier absorption for both deformation-potential coupling and piezoelectric coupling. It is found that the free-carrier absorption coefficient depends upon the polarization of the electromagnetic radiation relative to the layer plane or quantum well, the photon frequency, and the temperature. When the deformation-potential coupling is dominant, the free-carrier absorption coefficient increases with increasing temperature for photons polarized in the layer plane or perpendicular to the layer plane. However, when the piezoelectric coupling is dominant, the free-carrier absorption coefficient increases with increasing temperature for photons polarized in the layer plane, but for photons polarized perpendicularly to the layer plane, the free-carrier absorption coefficient decreases with increasing temperature. Moreover, at high temperatures such as T = 300 K, the free-carrier absorption coefficient oscillates with the film thickness in a small quantum well region and then decreases monotonically with increasing the film thickness. This is different from the result for three-dimensional semiconducting solids.     

Influence of magnetic quantization on the effective electron mass in Kane-type semiconductors

Summary We study the effective electron mass at the Fermi level in Kane-type semiconductors on the basis of fourth order in effective mass theory and taking into account the interactions of the conduction electrons, heavy holes, light holes and split-off holes, respectively. The results obtained are then compared to those derived on the basis of the well-known three-band Kane model. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass at the Fermi level in accordance with fourth-order model depends on the Fermi energy, magnetic quantum number and the electron spin respectively due to the influence of band nonparabolicity only. The dependence of effective mass on electron spin is due to spin-orbit splitting parameter of the valence band in three-band Kane model and the Fermi energy due to band nonparabolicity in two-band Kane model. The same mass exhibits an oscillatory magnetic-field dependence for all the band models as expected since the origin of oscillations in the effective mass in nonparabolic compounds is the same as that of the Shubnikov-de Hass oscillations. In addition, the corresponding results for parabolic energy bands have been obtained from the generalized expressions under certain limiting conditions.     

Nonparabolic multivalley balance-equation approach to impact ionization: Application to wurtzite GaN

Extended nonparabolic multivalley balance equations including impact ionization (II) process are presented and are applied to study electron transport and impact ionization in wurtzite-phase GaN with a , L-M, and conduction band structure at high electric field up to 1000kV/cm. Hot-electron transport properties and impact ionization coefficient are calculated taking account of the scatterings from ionized impurity, polar optical, deformation potential, and intervalley interactions. It is shown that, for wurtzite GaN when the electric field approximately equals 530kV/cm, the II process begins to contribute to electron transport and results in an increase of the electron velocity and a decrease of the electron temperature, in comparison with the case without the II process. Similar calculations for GaAs are also carried out and quantitative agreement is obtained between the calculated II coefficients by this present approach and the experimental data. Relative to GaAs, GaN has a higher threshold electric field for II and a smaller II coefficient. Received: 27 April 1998 / Revised: 17 July 1998 / Accepted: 13 August 1998     

Subband states inn-inversion layers on small-gap semiconductors

Subband states inn-inversion layers on small-gap semiconductors are subject to the coupling between valence and conduction band (nonparabolicity effects). In order to account for this coupling we study different models: two of them are based on Kane's 6×6 and 8×8 bulk-Hamiltonians, the third one takes into account higher order terms of the electron momentum in a 2×2 conduction band Hamiltonian. We perform selfconsistent calculations for these models with parameters characteristic for InSb and HgCdTe and electron concentrationsN _S , for which up to two subbands are occupied. The calculated subband separations and Fermi energies are independent of the models only if the same energy band dispersion is used and depend strongly on the applied boundary conditions.Work supported in part by the Deutsche Forschungsgemeinschaft     

Energy bands in the presence of an external force field—II Anomalous velocities

The theory of field-modified energy bands is extended to include the effect of weak scattering forces on the energy band structure. The modified current operator is found to contain terms giving anomalous currents of a type previously treated by and (Phys. Rev. 95, 1154 (1954) in connection with electrical conduction in ferromagnets. The physical meaning of these currents is discussed, and they are shown to be analogous to spin-dependent currents in Dirac's theory of the electron. They may be regarded formally as resulting from a non-commutability of the components of the coördinates. It is shown that such currents, proportional to the acceleration, are caused by every accelerating mechanism, including scattering mechanisms. A classical transport theory including the anomalous currents is derived, valid for scattering mechanisms for which the momentum transfer per collision is small, and a very simple problem carried through by way of example. A formal theory including the anomalous transport currents is given for the general case of arbitrary scattering mechanism and overlapping bands. Finally, a critique is given of some recent theories of the spontaneous Hall effect in ferromagnetics.     

The electronic structure of lithium metagallate

Herein we present a study of the electronic structure of lithium metagallate (LiGaO(2)), a material of interest in the field of optoelectronics. We use soft x-ray spectroscopy to probe the electronic structure of both the valence and conduction bands and compare our measurements to ab initio density functional theory calculations. We use several different exchange-correlation functionals, but find that no single theoretical approach used herein accurately quantifies both the band gap and the Ga 3d(10) states in LiGaO(2). We derive a band gap of 5.6 eV, and characterize electron hybridization in both the valence and conduction bands. Our study of the x-ray spectra may prove useful in analysing spectra from more complicated LiGaO(2) heterostructures.