Interband Momentum Matrix Elements Research Articles

Non-parabolicity and anisotropy in the conduction band of GaAs

The spin-doublet splitting and effective-mass shift of the cyclotron resonance in n-GaAs has been studied in high static magnetic fields applied along the (001), (011) and (111) crystal directions. A clear anisotropy of the conduction band has been observed in the orientation dependence of the spin-doublet splitting. The experimental results are described using a five-level k·p model. Comparison between the experimental data and this theoretical model allowed the determination of important band-structure parameters for GaAs, such as the interband momentum matrix element Q .

Electronic structure models, bonding, and optical moments in amorphous and crystalline semiconductors

A deteiled comparison of moments of ε 2 for a variety of amorphous (a) semiconductors and closely related crystals (x) is presented as an example of a general methodology utilizing such moments as a probe of electronic structure and chemical bonding models. The moments 0 and 2 are found to be explicitly related within a one-electron approximation to average interband dipole and momentum matrix elements ( Q and P ). Although the scope of this study is limited by the availability of sufficiently extensive optical data, the present results strongly suggest that for nearly “ideal” amorphous samples Q a > Q x in simple tetrahedral semiconductors, Q a ≈ Q x in tetrahedral oxides, and Q a < Q x in chain-like or layered semiconductors. In the materials considered here the differences in Q values are typically less than 15%. The validity of the “independent band” model and a more general real space analog are discussed using these results. Differences between Q a and Q x are shown to result from short-range disorder. The effects of such disorder are examined qualitatively. The result Q a > Q x in tetrahedral semiconductors is attributed to bond angle and dihedral angle fluctuations and the result Q a < Q x in molecular semiconductors is attributed to reduced interactions between lone pair electrons.

Transport Properties of CdvHg1–vSe Crystals

AbstractHall coefficient and mobility of electrons are measured in CdvHg1–vSe in the temperature range 4.2 to 300 K and for compositions 0.035 ≦ v ≦ 0.05. The temperature and composition dependence of energy gaps and interband momentum matrix element is obtained by fitting the Hall coefficient data calculations based on Kane's full model. Numerical calculation of electron mobility is also performed with temperature and composition dependence of band parameters. The results of these calculations are in good agreement with the experiment.

Energy levels of A and B excitons in wurtzite‐type semiconductors with account of electron–hole exchange interaction effects

AbstractThe effect of both the complexity of the two upper valence bands as well as the electron–hole exchange interaction on the exciton binding energies in wurtzite‐type semiconductors is studied. The energy level scheme and explicit expressions for the lowest exciton states of both A and B series are given. Using recent very accurate experimental data on exciton energies in CdS, the averaged B band hole mass is estimated to 1.6mo, and the position of the n = 1 B(Γ2) exciton level to about 0.2 meV below the transverse B(γ5) level. The longitudinal–transverse splitting of γ5 excitons is calculated from a microscopic approach in excellent agreement with experimental data taking into account an interband momentum matrix element P = 21 eV screened by a background dielectric constant ε' = 8. The exchange parameters introduced by Cho are determined for CdS to 3j0 ≈ 1 meV and 9j1 ≈ 2.1 meV.

Calculation of momentum matrix elements using the Green's-function method

A method for calculating the interband momentum matrix elements in the Green's-function method has been obtained, which is applicable to the $l$- and $E$-dependent potentials. This method is convenient in that it requires only the knowledge of wave functions inside the muffin-tin spheres. Numerical results calculated from this method are used to study the dependence of the matrix elements on the number of angular momentum components included. It is found that $l&gt;2$ components are important for the matrix elements.

Oscillatory Magnetoresistance in Mercuric Selenide

The oscillatory magnetoresistance (Shubnikov-de Haas effect) in oriented single crystals of mercuric selenide was measured at 1.2 and 4.2\ifmmode^\circ\else\textdegree\fi{}K and in transverse magnetic fields up to 25 kG. Analysis of the periods of the oscillations for the magnetic field aligned with $〈110〉$, $〈111〉$, and $〈100〉$ crystallographic directions showed that the Fermi surface for conduction electrons in HgSe, although nearly spherical, has slight bulges in the $〈111〉$ directions of k space. From the temperature dependence of the amplitudes of the oscillations, it was determined that the cyclotron effective masses of conduction electrons at the Fermi surface ranged from 0.033 to 0.068 ${m}_{e}$ for samples having from 1.86\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 4.52\ifmmode\times\else\texttimes\fi{}${10}^{18}$ electrons/${\mathrm{cm}}^{3}$. This variation of effective mass with electron concentration is consistent with the nonparabolic conduction-band model developed for compounds that have the zincblende crystal structure. The band parameters derived are $p=7.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ eV cm and ${E}_{G}=0.24$ eV, where $P$ is an interband momentum matrix element and ${E}_{G}$ is the band gap at k=0; these values are in fair agreement with parameters deduced from reflectivity data by other investigators.