Parabolic Energy Dispersion Research Articles

Perspectives of Silicon for Future Spintronic Applications From the Peculiarities of the Subband Structure in Thin Films

The two-band <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k·p</b> model for the conduction band is used to analyze the subband structure in (001) thin silicon films. In contrast to the usually assumed parabolic energy dispersion, the two-band <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</b> · <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</b> model is able to describe the conduction band structure in the presence of shear strain. It is demonstrated that the unprimed subbands are degenerate only in relatively thick relaxed films. In thin films, the subbands develop different in-plane effective masses. In orthogonal magnetic fields, this leads to a subband splitting linear in the field strength. It also results in a large subband splitting that is observed in [110]-oriented point contacts. With shear strain, the degeneracy between the unprimed subbands in (001) films is lifted. This splitting depends strongly on the film thickness and becomes large in ultrathin films. Strain-induced valley splitting results in reduced scattering and increased spin coherent time, which makes silicon attractive for future spintronic applications.

Seebeck Coefficient in Nonparabolic Bulk Materials

We address a simplified formulation of the Seebeck coefficient (S) in degenerate bulk III–V and skutterudite materials within the framework of the k·p formalism, the conduction-band electrons of which obey Kane’s second-order energy dispersion relation. Incorporation of longitudinal acoustic phonon, screened ionized impurity, and polar optical phonon scatterings explains the origin of the experimentally determined change of sign of S in a skutterudite material such as CoSb3. The use of an overlap function due to band nonparabolicity significantly affects the carrier relaxation time when compared with the corresponding parabolic energy dispersion relation. The well-known expression of S for nondegenerate wide-band-gap materials is obtained as a special case, and this compatibility is an indirect test of the generalized theoretical analysis. The present model of S also agrees well with the available experimental data on such materials over a wide range of temperatures and can be carried forward for accurate analysis of the thermoelectric figure of merit.

Large out-of-plane spin polarization in a spin-splitting one-dimensional metallic surface state on Si(557)-Au

We report unprecedented evidence of a spin split one-dimensional metallic surface state for the system of Si(557)-Au obtained by means of high-resolution spin- and angle-resolved photoelectron spectroscopy combined with first principles calculations. The surface state shows double parabolic energy dispersions along the Au chain structure together with a reversal of the spin polarization with respect to the time-reversal symmetry point as is characteristic from the Rashba effect. Moreover, we have observed a considerably large out-of-plane spin polarization which we attribute to the highly anisotropic wave function of the gold chains.

London penetration depth in the tight binding approximation: orthorhombic distortion andoxygen isotope effects in cuprates

We present a simple derivation of an expression for the superfluid density in superconductors with the tight binding energy dispersion. The derived expression isdiscussed in detail because of its distinction from the known expressions for ordinarysuperconductors with parabolic energy dispersion. We apply this expression for theexperimental data analysis of the isotope effect in London penetration depth parameterλ in the BiSrCuO and YBaCuO family compounds near optimal doping, taking intoaccount the orthorhombic distortion of crystal structure, and estimate the isotopicchange of hopping parameters from the experimental data. We point out that1/λ2 temperature behaviour is very sensitive to the ratio2Δm(T = 0)/kBTc and estimate this quantity for a number of compounds.

One-dimensional ring with Kronig–Penney periodic potential: Persistent currents at full filling

We study the persistent electron current in a one-dimensional conducting GaAs ring with the Kronig–Penney periodic potential applied along the ring circumference ( L). The periodic potential disturbs the free electron motion and changes the parabolic energy dispersion to a series of cosine-like energy bands separated by gaps. However, these cosine-like bands differ from the perfect cosine-shaped bands encountered in the lattice model with nearest-neighbor hopping or in the tight-binding model. Owing to this difference, in our model a non-zero persistent current exists when the energy band is completely filled by electrons. This current decays with increasing L exponentially, but we see measurable values for the properly chosen sample parameters. In contrast, in the tight-binding model the persistent current at full filling is zero which is a known result.

Scattering Anisotropy Effect on Layered Thermoelectric Materials

The effect of scattering anisotropy caused by mass anisotropy on the thermoelectric figure of merit is investigated. The simplest electron transport model is considered assuming a single-band, parabolic energy dispersion relation and ionized impurity scattering, which is assumed to be elastic. The wave-vector dependence of the relaxation time is fully considered within the relaxation-time approximation. Transport coefficients are calculated using the anisotropic relaxation time at finite temperatures. The figure of merit perpendicular to the axis with the largest effective mass is shown to decrease as the effective mass ratio increases. This result indicates that the weak confinement of electrons into layers of bulk materials cannot be the direct cause of the enhancement of the figure of merit along the layers.

Normal and Dirac fermions in graphene multilayers: Tight-binding description of the electronic structure

Within a tight-binding approach we show that around the $K$ point of the energy spectrum Dirac fermions are present in $AB$ stacked graphene multilayers if they have mirror plane symmetry. In other words, Dirac fermions are present in graphene stacks with an odd number of layers. For an even number of stacked graphene layers, only normal fermions with a parabolic energy dispersion are found near the $K$ point.

Surface states of a Pd monolayer formed on a Au(111) surface studied by angle-resolved photoemission spectroscopy

Electronic states of a Pd-deposited ($l1$ ML) Au(111) surface have been studied using angle-resolved ultraviolet photoemission spectroscopy. A shoulder induced by Pd deposition was observed on a peak assigned to the Shockley surface states of the Au(111) substrate in the spectra measured around the surface normal direction. The photoemission study revealed that the Pd-induced states have parabolic energy dispersion with an effective mass identical to that of the substrate states while its binding energy is $0.17\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ smaller than the substrate state. It is also found that the binding energy of the Au substrate surface states decreases with Pd deposition. The spectroscopic properties of the Pd-induced states indicate that the states originate from the Au(111) surface states and are modified by the presence of monolayer Pd islands on the substrate.

Negatively charged donors in semiconductor quantum wells in the presence of longitudinal magnetic and electric fields

We present variational calculations of the binding energy for negatively charged donors in GaAs/Al0.3Ga0.7As quantum wells. We show that the electronic quantum well ground state and parabolic energy dispersions are enough to obtain accurate results compared with previous Monte Carlo calculations. The configuration interaction method is used with a physically meaningful basis set. We study the charged donor binding energy dependence on the quantum well width and donor position in the presence of external electric and magnetic fields.

Binding energy of charged excitons in semiconductor quantum wells in the presence of longitudinal electric fields

We present variational calculations of the binding energy for positively and negatively charged excitons (trions) in idealized ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum wells with parabolic electrons and holes energy dispersions. The configuration interaction method is used with a physically meaningful single-particle basis set. We have shown that the inclusion of more than one electron quantum-well solution in the basis is important to obtain accurate values for the binding energies. The effects of longitudinal electric-field and quantum-well confinement on the charged excitons bound states are studied in the absence of magnetic field and the conditions for the trion ionization are discussed.

Analytic expressions for impact ionization rates and secondary particle energy distributions in semiconductors

Analytic expressions are obtained for the energy dependent impact ionization rate and secondary particle energy distribution functions in semiconductors based on the random-k technique. By approximating the conduction and valence band structure by a simple parabolic energy dispersion the impact ionization rate in semiconductors is found to have the form ∝(E−ET)7/2. The analytic expressions obtained for the secondary particle energy distribution functions are found to give excellent agreement with results obtained from a rigorous full band structure analysis for the case of silicon. By extending the model to multiple parabolic bands which emulate the true density of states a good agreement with results obtained on the basis of the full band structure is obtained for a range of semiconductor materials.

High-energy electron–electron interactions in silicon and their effect on hot carrier energy distributions

This paper presents results from the calculation of the high-energy electron–electron scattering rate in silicon based on a full energy-band structure obtained by the pseudopotential technique. The effects on the scattering rate of the overlap integrals, wave-vector-dependent dielectric function and umklapp processes are described and the transition rate is compared with that obtained using a semiclassical analysis based on a parabolic energy dispersion. A hybrid Monte Carlo/iterative technique for solving the Boltzmann transport equation is used to obtain the electron energy distribution function generated by binary particle interactions in a one-dimensional system.

Intervalence-band absorption spectra and hole effective masses in CuGaTe 2

The intervalence-band absorption spectra of CuGaTe 2 single crystals are measured at 92 and 300 K. Assuming spherical parabolic energy dispersion relations for all the three valence bands the effective masses of the heavy-hole, light-hole and split-off bands are determined to be m hh = 1.3 m 0, m lh = 0.13 m 0 and m sh = 0.16 m 0. The energetic distance between the split-off band and the heavy-hole band at the centre of the Brillouin zone is 0.58 eV at 300 K and 0.63 eV at 92 K.

Hole Effective Masses in CuInSe2

AbstractOptical transmittance and reflectance spectra are measured in p‐type CuInSeZ single crystals at 100 and 300 K in the photon energy range from 0.03 to about 1.0 eV. At hv = 0.07 to 0.70 eV the absorption is governed by intervalence band transitions. Assuming spherical parabolic energy dispersion relations for all the three valence bands, the effective masses of the heavy hole, light hole, and split‐off bands are determined to mhh = 0.71m0, m1h = 0.092m0, and msh = 0.085m0, respectively.

On the quantum limit behaviour of the magnetoresistance in non-parabolic semiconductors

The quantum limit behaviour of the magnetoresistance in narrow-gap semiconductors is investigated. The non-parabolicity of the energy dispersion is taken into account in the density of states. Assuming constant level broadening, both the longitudinal and the transverse magnetoresistance obey asymptotic power laws. The exponents in these power laws are found to be larger than in the case of parabolic energy dispersion.