Valence Band Extrema Research Articles

A First-Principles Calculation of Electronic Properties of LiNH2 and NaNH2

Band spectra, densities of states, total and deformation densities of α-LiNH2 and α-NaNH2 are calculated from the first principles using the density functional method in the all-electron approximation. The upper valence band is formed mostly by nitrogen p-states with a small admixture of metal states, the lower conduction bands are formed by the states of all atoms in α-LiNH2 and mainly by sodium and nitrogen states in α-NaNH2. The bottom of the conduction band appears in both crystals in the center of the Brillouin zone. α-LiNH2 exhibits indirect-gap transitions at the absorption edge and three valence band extrema at a short distance of ~0.15 eV from each other. The top of the valence band in α-NaNH2 appears in the center of the Brillouin zone with the competing maximum at the lateral point at a distance of ~0.06 eV. The electron density distributions testify that polar covalent bonding occur inside the amide anion and ionic bonding occurs between the metal and the amide ion.

Biaxial strain tuned electronic structures and power factor in Janus transition metal dichalchogenide monolayers

Tuning the physical properties of transition metal dichalcogenide (TMD) monolayers by strain engineering is an area that has been widely studied, and recently a Janus TMD monolayer MoSSe has been synthesized. In this work, we systematically study the biaxial strain dependence of the electronic structures and transport properties of Janus TMD MXY (M = Mo or W, X/Y = S, Se, or Te) monolayer by using generalized gradient approximation (GGA) and spin–orbit coupling (SOC). It is found that SOC has a noteworthy detrimental influence on power factor in p-type MoSSe, WSSe, n-type WSTe, p-type MoSeTe and WSeTe, and has a negligible influence on n-type MoSSe, MoSTe, p-type WSTe and n-type MoSeTe. This can be understood by considering SOC effects on their valence and conduction bands. For all six monolayers, the energy band gap firstly increases, and then decreases, when strain changes from a compressive one to a tensile one. It is found that strain can tune the strength of band convergence of both valence and conduction bands by changing the numbers and relative position of valence band extrema (VBE) or conduction band extrema (CBE), which can produce very important effects on their electronic transport properties. By applying appropriate compressive or tensile strain, both n- or p-type Seebeck coefficient can be enhanced by strain-induced band convergence, and then the power factor can be improved. Our works further enrich studies on the strain dependence of electronic structures and the transport properties of new-style TMD monolayers, and will motivate further experimental works.

Identifying defect-tolerant semiconductors with high minority-carrier lifetimes: beyond hybrid lead halide perovskites

Abstract

Intrinsic transport properties of electrons and holes in monolayer transition-metal dichalcogenides

Intrinsic electron- and hole-phonon interactions are investigated in monolayer transition metal dichalcogenides MX$_2$ (M=Mo,W; X=S,Se) based on a density functional theory formalism. Due to their structural similarities, all four materials exhibit qualitatively comparable scattering characteristics with the acoustic phonons playing a dominant role near the conduction and valence band extrema at the K point. However, substantial differences are observed quantitatively leading to disparate results in the transport properties. Of the considered, WS$_2$ provides the best performance for both electrons and holes with high mobilities and saturation velocities in the full-band Monte Carlo analysis of the Boltzmann transport equation. It is also found that monolayer MX$_2$ crystals with an exception of MoSe$_2$ generally show hole mobilities comparable to or even larger than the value for bulk silicon at room temperature, suggesting a potential opportunity in p-type devices. The analysis is extended to estimate the effective deformation potential constants for a simplified treatment as well.

Features of the energy spectrum and hole-scattering mechanisms in PbSb2Te4

The kinetic Hall Rikl, electrical-conduction σkk, thermopower αkk coefficients, and their anisotropy are investigated in the temperature range of 77–450 K for a series of copper-doped PbSb2Te4 crystals with various hole concentrations of (1.6–3.2) × 1020 cm−3. The thermopower anisotropy observed in all investigated crystals is indicative of a mixed hole-scattering mechanism. The main scattering mechanisms are scattering at acoustic phonons and at the Coulomb potential of impurities and defects. The experimental effective scattering parameters and partial mobilities are determined in the cleavage plane and along the trigonal axis. The theoretical estimates of mobility are in satisfactory agreement with the experiment. It is established that the character of the temperature dependence for the ratio αkk/T = f(T) depends on the hole concentration. It is shown that the physical properties can be described within the framework of the one-band model for a crystal with pmin = 1.6 × 1020 cm−3; the value of the effective mass density of the hole state in the main-valence band extremum is estimated as md ≈ 0.5m0. The energy gap between the valence-band extrema is estimated as ΔEv ≈ 0.23 eV.

Deep defect states in narrow band-gap semiconductors

The nature of defect states associated with group III impurities (Ga, In, and Tl) in PbTe, a narrow band-gap semiconductor, has been studied within density functional theory and supercell model. For all three impurities (both substitutional—at the Pb site and interstitial—at the tetrahedral site), there is a hyper-deep defect state which lies about 0.5–1.0 eV below the valence band. It is a highly localized bonding state between the impurity s-orbital and the surrounding p-orbitals of the Te atoms. The corresponding anti-bonding state, denoted as the deep defect state, lies in the band-gap region. Its precise position vis-à-vis the conduction- and valence-band extrema controls the unusual properties exhibited by these defects.

Electrophysical properties and electronic structure of tin-doped antimony telluride

The effect of Sn atoms on the electrophysical properties and x-ray photoelectron spectra of Czochralski-grown Sb2Te3 single crystals is studied. The character of the temperature dependences of the kinetic coefficients is shown to depend noticeably on the structure of the valence band, which consists of two valence subbands. Estimates of the effective density-of-states masses of holes and of the gap between the valence-band extrema in Sb2Te3: Sn agree with the data available for the Sb2Te3 not doped with tin. X-ray photoelectron spectra of Sb2Te3: Sn single crystals do not exhibit noticeable core-level shifts and electron density redistribution in the valence band.

Electronic Structure of Complex Bismuth Chalcogenides and Other Narrow-Gap Thermoelectric Materials

AbstractThere is considerable current effort to discover new thermoelectric materials with a high figure of merit Z. Some of these new materials are narrow-gap semiconductors with rather complex crystal structures. In this paper we discuss the results of electronic structure calculations in two classes of such systems. The first class consists of BaBiTe3, a structural and chemical derivative of the well-studied Bi2Te3. Similarities and differences in the band structures of these two systems are discussed. The second class consists of half-Heusler or “stuffed”-NaCl compounds MNiX, where M is Y, La, Lu, Yb, and X is a pnictogen; As, Sb, Bi. To understand the physical reason behind the energy gap formation, we compare the electronic structure of YNiSb with that of an isoelectronic system ZrNiSn, another isostructural compound of thermoelectric interest. These calculations were carried out within density functional theory (in generalized gradient approximation) using self-consistent full-potential LAPW method. Energy gaps and effective masses associated with the conduction band minimum and valence band maximum have been calculated and these quantities have been used to estimate transport properties. Large room temperature thermopower values in Bi2Te3 and BaBiTe3 can be understood in terms of multiple conduction and valence band extrema whereas similar large values in ZrNiSn and other half-Heusler compounds can be ascribed to large electron and hole effective mass.

Explicit incorporation of the energy-band structure into an analysis of the defect chemistry of PbTe and SnTe

A framework is established for the analysis of the defect chemistry of the entire (Pb1−xSnx)1−yTey system based upon statistical thermodynamic calculations and experimentally measured carrier-concentration and tellurium partial-pressure data. The energy-band structure, in which inversion of light-mass, non-parabolic, direct-gap bands occurs and a second, parabolic valence band is present, is explicity incorporated into the analysis for the first time and the usual non-degeneracy assumption is abandoned. The densities of states of the non-ellipsoidal bands and the Fermi levels are calculated numerically. The remaining intrinsic material parameters (the partial pressure of tellurium over intrinsic, pure material and the Schottky constant for doubly-ionized vacancies) are then determined by the fit to the carrier concentration-partial pressure-temperature data. The model established is applied to only PbTe and SnTe because of the lack of partial-pressure data for the ternary solid solutions and satisfactory fits are obtained. The Fermi level lies in the light-mass valence band of SnTe for all of the observed carrier concentrations so that previous analyses of SnTe, which assumed that the hole distribution is non-degenerate, were in error. The 1 at. % wide homogeneity range of SnTe is wide enough that a compositional variation in the sum of the chemical potentials of tin and tellurium has been detected experimentally. This variation is theoretically zero in the usual models for narrow homogeneity-range compounds, but is accounted for in this analysis. Quantitatively satisfactory fits are obtained for PbTe using 0.85mo for the density-of-states effective mass which characterizes the second, parabolic valence band extrema. Only slightly poorer fits are obtained with the roughly established value of 1.0mo. To obtain good fits for SnTe this mass must be increased from its rough value of 2.0mo to 2.8mo; otherwise the partial pressure-temperature curves for fixed compositions within the homogeneity range show too much curvature.

Impact ionisation rate and soft energy thresholds for anisotropic parabolic band structures

The effect of anisotropic parabolic energy bands and of indirect parabolic energy bands (conduction and valence band extrema at different points in wavevector space) on the transition probability per unit time for impact ionisation is investigated. The resulting direction-dependent threshold energy is described by introducing a threshold ellipsoid. It is found that for the 'lucky-drift' model for impact ionisation in an electric field the transition probability rate which is applicable increases from zero above the energy threshold with a cubic power for anisotropic or indirect parabolic bands, or, in special circumstances a 5/2 power compared with the more usual square law of the Keldysh result for direct isotropic parabolic band structures.

Optical properties of electron irradiation induced defects in InP

The optical properties of deep hole traps H 4 and H 5 in p type and of the deep electron trap E 11 in n type InP, introduced by electron irradiation, have been studied using deep level optical spectroscopy. Comparison of the optical threshold with the thermal activation energy of H 5 level shows that it is highly relaxed with a Frank-Condon shift d Fc = 0.45 eV. The electron level E 11 is weakly relaxed and its optical cross section σ 0 is well accounted for by transitions to the Γ 6c minimum. The optical absorption σ p 0 associated to level H 4 shows two successive onsets at hν = 0.5 and hν = 1.2 eV which can be attributed to hole transitions to the Γ 7–8 and to the L 4–5 valence band extrema, respectively. The deduced Frank-Condon shift, d Fc = 0.23 eV, agrees with the measured difference of 40 meV between its apparent activation energy E a and its thermal activation energy E T.

Self-consistent relativistic energy bands for tin telluride

The APW method has been considered and programmed in a form for which accurate self-consistent relativistic band structure calculations are both economic and easy to carry out. The first self-consistent relativistic energy band structure for tin telluride is presented, and results compared with experiment and with previous band calculations. Effective mass parameters near valence band extrema are also given.

Gain-frequency-current relation for Pb<inf>1-x</inf>Sn<inf>x</inf>Te double heterostructure lasers

The active region gain expression for Pb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Sn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Te lasers is obtained from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> model of the conduction and valence band extrema. Curves of gain versus frequency with current, temperature, and majority carrier concentration as parameters are calculated using published values of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> model parameters. In addition, threshold current versus temperature and threshold current versus majority carrier concentration curves are given. A simple expression is obtained for the conductivity effective mass for use in the equation for free-carrier absorption appropriate to the highly degenerate majority carrier concentrations typical of Pb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Sn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Te laser material.

Absorption edge and photoconductivity of CuPbAsS3 Single crystals

Absorption curves of CuPbAsS3 have been measured in the temperature range 90÷300 K. Their analysis leads to conclusion that the absorption edge of CuPbAsS3 is due to allowed indirect electronic transitions between the valence and conduction band extrema. The forbidden-gap width, its temperature dependence and energies of three interacting phonons have been determined. The temperature shift of the photoconductivity band is in agreement with that of the forbidden gap in CuPbAsS3.

Analysis of Cyclotron Absorption in Lead Telluride

Cyclotron absorptions in n - and p -type PbTe recently observed by Nii are analysed under classical skin effect conditions. When the values of d.c. magnetic field corresponding to peaks are plotted against the field directions, a close fit is obtained between the calculated and observed results on an assumption of a set of ellipsoids of revolution model for the both conduction and valence band extrema. From the best fit m t =0.024 m 0 and 0.031 m 0 for the transverse effective masses and K = m l / m t =9.8 and 12.2 for the anisotropic mass ratios are obtained for each band. The observed absorption curve shows weak structures at low magnetic field. They are supposed to be due to the second harmonics of Azbel'-Kaner cyclotron resonance. However it is unnecessary to introduce other bands to explain the experimental results. The applicability of the classical magneto-ionic theory is examined by calculating the power absorption coefficient and the penetration depth as a function of d.c. magnetic field.

Analysis of cyclotron absorption in lead telluride

Cyclotron absorptions in n - and p -type PbTe recently observed by Nii are analysed under classical skin effect conditions. When the values of d.c. magnetic field corresponding to peaks are plotted against the field directions, a close fit is obtained between the calculated and observed results on an assumption of a set of ellipsoids of revolution model for the both conduction and valence band extrema. From the best fit m t =0.024 m 0 and 0.031 m 0 for the transverse effective masses and K = m l / m t =9.8 and 12.2 for the anisotropic mass ratios are obtained for each band. The observed absorption curve shows weak structures at low magnetic field. They are supposed to be due to the second harmonics of Azbel'-Kaner cyclotron resonance. However it is unnecessary to introduce other bands to explain the experimental results. The applicability of the classical magneto-ionic theory is examined by calculating the power absorption coefficient and the penetration depth as a function of d.c. magnetic field.

Edge and Impurity Emission in Cadmium Sulfide

A model was recently proposed for the band structure of CdS which purports to explain much of the observed optical phenomena in terms of conduction and valence band extrema centered around k = 0. A set of observations is described which cannot be explained in terms of this simple structure. (W.D.M.)

Optical Absorption Band Edge in Anisotropic Crystals

The shape of the optical absorption band edge in insulating crystals is discussed for both direct and indirect electronic transitions. Selection rules are invoked to explain the apparent shift in the band edge with polarization observed in anisotropic crystals. The absorption coefficient obeys a law of the form $K\ensuremath{\propto}{(\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}E)}^{n}$, where $E$ is closely related to the minimum band gap and $n$ is \textonehalf{} for allowed direct transitions, $\frac{3}{2}$ for forbidden direct transitions, and 2 for indirect transitions. The experimental observations of the shift in CdS and Te are analyzed in terms of conduction and valence band extrema at k=0 with symmetry types such that the transition is allowed for light polarization perpendicular to the hexagonal axis and forbidden for the polarization parallel to this axis.

Band structure of indium antimonide

The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0. The small band gap requires an accurate treatment of conduction and valence band interactions while higher bands are treated by perturbation theory. A highly nonparabolic conduction band is found. The valence band is quite similar to germanium. Energy terms linear in k which cannot exist in germanium are estimated and found to be small, though possibly of importance at liquid-helium temperature. An absolute calculation of the fundamental optical absorption is made using the cyclotron resonance mass for n-type InSb. The agreement with experimental data for the fundamental absorption and its dependence on n-type impurity concentration is quite good. This evidence supports the assumptions made concerning the band structure.