Full Band Structure Calculation Research Articles

Tl7]7- Clusters in Mixed Alkali Metal Thallides Cs7.29K5.71Tl13 and Cs3.45K3.55Tl7.

Investigations in the ternary system Cs-K-Tl resulted in the unexpected formation of new ternary thallides Cs7.29K5.71Tl13 and Cs3.45K3.55Tl7. Single crystal X-ray structure analyses of both compounds reveal the presence of isolated Tl cluster units. Cs7.29K5.71Tl13 crystallizes in the monoclinic space group C2/c (a = 30.7792(9) Å, b = 11.000(2) Å, c = 14.0291(4) Å, β = 112.676(4)°, Z = 4) and contains [Tl6]6- and [Tl7]7- clusters as thallium subunits. Cs3.45K3.55Tl7 crystallizes in the tetragonal space group I41/a (a = 13.6177(2) Å, c = 25.5573(8) Å, Z = 8) and contains [Tl7]7- clusters exclusively. The formation of Cs7.29K5.71Tl13 is obtained after slow cooling in addition to that of Cs3.45K3.55Tl7 and can be suppressed by quenching the stoichiometric mixture. First dissolution experiments in liquid ammonia suggest thallium and amide as final oxidation products. Full relativistic band structure calculations of Cs4K3Tl7 and Cs8K5Tl13 showed a (pseudo) band gap around EF for both compounds.

Dielectric Relaxation Processes, Electronic Structure, and Band Gap Engineering of MFU‐4‐type Metal‐Organic Frameworks: Towards a Rational Design of Semiconducting Microporous Materials

The electronic structures and band gaps of MFU‐4‐type metal‐organic frameworks can be systematically engineered leading to a family of isostructural microporous solids. Electrical properties of the microcrystalline samples are investigated by temperature‐dependent broad‐band dielectric and optical spectroscopy, which are corroborated by full band structure calculations performed for framework and cluster model compounds at multiple levels of density functional theory. The combined results glean a detailed picture of relative shifts and dispersion of molecular orbitals when going from zero‐dimensional clusters to three‐dimensional periodic solids, thus allowing to develop guidelines for tailoring the electronic properties of this class of semiconducting microporous solids via a versatile building block approach. Thus, engineering of the band gap in MFU‐4 type compounds can be achieved by adjusting the degree of conjugation of the organic ligand or by choosing an appropriate metal whose partially occupied d‐orbitals generate bands below the LUMO energy of the ligand which, for example, is accomplished by octahedral Co(II) ions in Co‐MFU‐4.

Electrical design of InAs-Sb/GaSb superlattices for optical detectors using full bandstructure sp3s* tight-binding method and Bloch boundary conditions

InAs-Sb/GaSb type-II strain compensated superlattices (SLS) are currently being used in mid-wave and long-wave infrared photodetectors. The electronic bandstructure of InSb and GaSb shows very strong anisotropy and non-parabolicity close to the Γ-point for the conduction band (CB) minimum and the valence band (VB) maximum. Particularly around the energy range of 45–80 meV from band-edge we observe strong non-parabolicity in the CB and light hole VB. The band-edge dispersion determines the electrical properties of a material. When the bulk materials are combined to form a superlattice we need a model of bandstructure which takes into account the full bandstructure details of the constituents and also the strong interaction between the conduction band of InAs and valence bands of GaSb. There can also be contact potentials near the interface between two dissimilar superlattices which will not be captured unless a full bandstructure calculation is done. In this study, we have done a calculation using second nearest neighbor tight binding model in order to accurately reproduce the effective masses. The calculation of mini-band structure is done by finding the wavefunctions within one SL period subject to Bloch boundary conditions ψ(L)=ψ(0)eikL. We demonstrate in this paper how a calculation of carrier concentration as a function of the position of the Fermi level (EF) within bandgap(Eg) should be done in order to take into account the full bandstructure of broken-bandgap material systems. This calculation is key for determining electron transport particularly when we have an interface between two dissimilar superlattices.

Analysis of plasmonic properties of heavily doped semiconductors using full band structure calculations

Surface plasmon polaritons (SPPs) and localized surface plasmon (LSP) resonances are not limited to noble metals. Any material with a substantial amount of free carriers will support surface plasma oscillations which, when coupled to an electromagnetic field, will result in surface plasmon polaritons and localized surface plasmon resonances in confined systems. Utilizing a full band structure approach, we analyze the plasmonic properties of several heavily doped semiconductors. We present rigorous quantum mechanical calculations of the plasma frequency, and study in detail its dependence on impurity doping concentration. Results are presented for silicon, germanium, gallium arsenide, zinc oxide, and gallium nitride. For silicon and zinc oxide, the surface plasmon resonance frequency is calculated for a large range of doping concentrations and we study the dispersion of surface plasmon polaritons on thin films. The investigated properties of heavily doped semiconductors hold promises for several interesting applications within plasmonics.

Full band structure calculation of two-photon indirect absorption in bulk silicon

Degenerate two-photon indirect absorption in silicon is an important limiting effect on the use of silicon structures for all-optical information processing at telecommunication wavelengths. We perform a full band structure calculation to investigate two-photon indirect absorption in bulk silicon, using a pseudopotential description of the energy bands and an adiabatic bond charge model to describe phonon dispersion and polarization. Our results agree well with some recent experimental results. The transverse acoustic/optical phonon-assisted processes dominate.

Temperature- and wavelength-dependent two-photon and free-carrier absorption in GaAs, InP, GaInAs, and InAsP

We present full-band structure calculations of temperature- and wavelength-dependent two-photon absorption coefficients and free-carrier absorption cross sections in GaAs, InP, and 0.92 eV-band gap Ga64In36As and InP60As40 alloys. The calculated coefficient decreases with increasing wavelength and band gap but increases with temperature. Using detailed band structure analysis, we identify various contributions to the free-carrier absorption in GaAs and InP. Although the free-carrier absorption is found to arise predominantly from hole absorption, we show that direct absorption by excited electrons is possible, leading to an enhanced free-carrier absorption coefficient. This excited state absorption could be exploited to modulate the transmission of light at communication wavelengths (of 1.33 or 1.55 μm) with, for example, the more commonly available 0.8 μm diode laser. We further show that the high-intensity transmission calculated with our values of nonlinear parameters in GaAs agrees very well with the measured values.

Optical rectification and current injection in unbiased semiconductors

We present a full band-structure calculation of the electronic contribution to the second-order susceptibility in the limit of a sum frequency that vanishes. We give a sum-over-states expression for the optical rectification coefficient ${\ensuremath{\chi}}_{\text{rect}}(\ensuremath{\omega})\ensuremath{\equiv}{\ensuremath{\chi}}_{\text{rect}}(0;\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega})$, which includes intraband contributions. Intraband transitions additionally lead to shift and injection currents, which we identify in the total response and separate from the optical rectification. The approach applies to all crystal classes and over a wide range of applied optical frequencies. We apply our results to a full band-structure calculation of the optical rectification, shift current, and injection current susceptibilities for wurtzite CdS and CdSe.

Magnetic and structural transitions in layered iron arsenide systems:AFe2As2versusRFeAsO

Resistivity, specific-heat, and magnetic-susceptibility measurements performed on ${\text{SrFe}}_{2}{\text{As}}_{2}$ samples evidence a behavior very similar to that observed in LaFeAsO and ${\text{BaFe}}_{2}{\text{As}}_{2}$, with the difference being that the formation of the spin-density wave and the lattice deformation occur in a pronounced first-order transition at ${T}_{0}=205\text{ }\text{K}$. Comparing further data evidences that the Fe magnetism is stronger in ${\text{SrFe}}_{2}{\text{As}}_{2}$ and in ${\text{EuFe}}_{2}{\text{As}}_{2}$ than in the other layered FeAs systems investigated up to now. Full potential local-density approximation band-structure calculations confirm the large similarity between the compounds, especially for the relevant low energy $\text{Fe}\text{ }3d$ states. The relation between structural details and magnetic order is analyzed.

Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures

We present a full acoustic band structure calculation for periodic elastomeric solids at different levels of deformation. We demonstrate the ability to use deformation to transform phononic band gaps. Periodic elastomeric structures are subjected to axial compression and are found to undergo a transformation in their patterned structure upon reaching a critical value of applied load. During the initial linear regime of the nominal stress-strain behavior, the band gaps evolve in an affine and marginal manner. Upon reaching the critical load, the pattern transformation is found to strongly affect the in-plane phononic band gaps, resulting in the closure of existing band gaps and in the opening of new ones. The elastomeric nature of the material makes the transformation in both structural pattern and phononic band gap a reversible and repeatable process, creating a phononic band gap switch.

Electronic and magnetic interfacial states of Ag in anNi81Fe19 /Ag coupled multilayer

Studies of the Ag induced magnetic moments at the interfaces in an[Ni81Fe19(29 Å)/Ag(11 Å)]135 multilayer by x-ray magnetic circular dichroism (XMCD) and x-ray resonant magnetic scattering (XRMS)at the Ag L2,3 edges are reported. This allows us to quantify the interfacial magnetic moments as well as theextension through the silver layer. From the experimental XMCD spectra and thanks tothe use of full relativistic band structure calculations, we succeed in extracting quantitativespin and orbital magnetic moments held by the 4d states of silver. Moreover, we show that,although silver has an almost full 4d band, magneto-optical sum rules can be safely appliedin the case of the noble metal L edges. We find from XMCD that Ag is polarized byNi81Fe19 and has a total magneticmoment of 0.0136 μB spatiallyaveraged over the 11 Å layer thickness. XRMS analysis indicates that this induced polarization is enhanced at theinterface but remains present inside the whole Ag layer, demonstrating the existence ofan indirect coupling between the NiFe layers through the non-magnetic spacer.

Accurate evaluation of nonlinear absorption coefficients in InAs, InSb, and HgCdTe alloys

We present a full band structure calculation of temperature- and wavelength-dependent two-photon absorption (TPA) coefficients and free carrier absorption (FCA) cross sections in InAs, InSb, and Hg1−xCdxTe alloys. The wavelength dependence of the TPA coefficients agrees well with a widely used analytical expression. However, the magnitudes of the TPA coefficients obtained here are smaller by a factor of 1.2–2.5 than the analytical values. In addition, the TPA coefficient is found to depend sensitively on the photoexcited carrier density in small gap materials. The FCA is found to arise predominantly from hole absorption. The FCA cross section is found to be independent of the carrier density, but is strongly dependent on the temperature. The calculated TPA, FCA coefficients, and lifetimes are fitted to closed-form expressions and are used in solving the rate equations to obtain the transmitted pump and probe intensities as functions of incident intensity and sample thickness. The calculated pump transmission and time-dependent probe transmission in InAs agree very well with the measured values.

Valence and conduction intersubband transitions in SiGe, Ge-rich, quantum wells on [001] Si0.5Ge0.5 substrates: A tight-binding approach

Electronic and optical properties of germanium-rich Si∕SiGe quantum wells grown on Si0.5Ge0.5 substrates are investigated by a nearest neighbor tight-binding Hamiltonian. The basis set includes spds* orbitals with both spin states. Appropriate scaling laws account for strain effects. We present full electronic band structure calculations both for valence and conduction bands. Confinement effects on the electronic states are considered in detail. Optical spectra related to hole and electron intersubband transitions are derived. Our results for optical absorption due to valence intersubband transitions show excellent agreement with experimental spectra and previous k∙p calculations. For the same quantum well samples, spectra due to conduction intersubband absorption are provided here.

Accurate measurement of composition, carrier concentration, and photoconductive lifetime in Hg1−xCdxTe grown by molecular beam epitaxy

Variable magnetic field Hall and transient photoconductance lifetime measurements were performed on a series of undoped, In-doped, and As-doped HgCdTe samples grown by molecular beam epitaxy and metalorganic chemical vapor deposition. Temperature variation and, in the case of Hall, magnetic-field variation are needed to give a more complete picture of the mechanisms that control lifetimes in HgCdTe samples. Recent predictions of recombination lifetimes from full band structure calculations were compared to experimental lifetimes at various doping levels at long-wave infrared (LWIR) and mid-wave infrared (MWIR) compositions. For n-type material, lifetimes from low doping levels fall well below the predictions, implying that Shockley-Read-Hall (SRH) recombination is still dominant. MWIR samples have a lifetime that increases somewhat with carrier concentration, suggesting that In doping passivates the SRH defects for that composition. Lifetimes in p-type MWIR material appear to be well-explained by recent theoretical calculations. In p-type material, trapping states may be introduced during the incorporation and activation of As, since some samples with unusually long lifetimes had a distinctly different type of temperature dependence.

Minority carrier lifetimes in HgCdTe alloys

We present the results of full band structure calculations of Fermi levels, intrinsic carrier densities, and one-photon absorption coefficients in undoped HgCdTe alloys. The full band structure is used in the calculation of majority and minority carrier densities and the minority carrier lifetimes limited by radiative, Auger-1, and Auger-7 mechanisms in both n- and p-doped alloys. The lifetimes we predicted differ substantially from those calculated with widely used analytical expressions, except in cases where the hole density is small. This difference originates from the significantly non-parabolic and anisotropic valence bands, which are of increasing significance as the hole density increases. From a comparison of the calculated and measured lifetimes, we deduce that the lifetimes at low temperatures are limited by the Shockley-Read-Hall (SRH) recombination. We have generalized the SRH expression to include Fermi-Dirac statistics, but we still treat the density, energy level, and cross section as adjustable parameters. We find that the calculated radiative and Auger recombination lifetimes, as well as SRH lifetimes, can fit the measured lifetimes using traps located (a) near the conduction band edge in n-HgCdTe and (b) near the valence band edge for p-HgCdTe. In addition, the movement of Fermi level with respect to the trap level explains the observed temperature-dependence of the lifetimes. We conclude that there is considerable room for improvement in HgCdTe material quality.

Analytic expression of the average energy of the field electrons from the n-type semiconductors

We have derived an analytic expression of the average energy of field electrons emitted from n-type semiconductors, for the first time. The average energy is obtained in terms of the hypergeometric and the Lerch transcendental functions. The analytic expression exhibits the apparent dependence of the average energy on the applied field, carrier concentration, and temperature. It also gives numerical values of the average energy in excellent agreement with those calculated using the full band structure calculation.

Systematic study of type II Ga1-xInxSb/InAssuperlattices for infra-red detection in the 10-12 µmwavelength range

We perform a systematic study of the factors governing the opticalproperties of type II Ga1-xInxSb/InAs superlatticestructures. We map the parameter space corresponding to the layer widths,alloy concentrations and interface bonding types, and identify thosestructures for which the fundamental gap lies in the desired range fordevice application. In addition, we examine the higher lying minibandenergies to assess the structures for favourable Auger recombinationlimits. The microscopic interface bonding configuration is shown to havea significant impact upon the magnitude of the fundamental gap, and confirmsthe requirement for full-bandstructure calculations in the evaluation ofpossible structures. We study the features of the optical spectra forthose structures whose bandstructuresare recognized as most suitable for detector applications.

Implementation of the Cyclic Cluster Model in Hartree-Fock LCAO Calculations of Crystalline Systems

The cyclic cluster model combines advantages of periodic and molecular cluster models for the quantum chemical treatment of perfect and defective crystalline solids. Implementations of this model into molecular codes have so far been realized for semiempirical and local density functional methods only. Due to the occurrence of four-center integrals in ab initio Hartree-Fock methods, the cyclic cluster model is difficult to realize for this case. This study presents a simple procedure for the extraction of cyclic cluster models from periodic Hartree-Fock calculations, based on the idempotency relations of the density matrix. The dependence of calculated results for bulk properties of defect-free titanium dioxide (rutile) from the size and shape of the cyclic clusters is investigated. It is demonstrated that by a proper choice of cyclic clusters where full spheres of nearest neighbor atoms are taken into account, relatively small cyclic clusters can reproduce results for total energies and one-electron energies obtained with full band structure calculations.

Role of occupieddstates in the relaxation of hot electrons in Au

We present first-principles calculations of electron-electron scattering rates of low-energy electrons in Au. Our full band-structure calculations indicate that a major contribution from occupied $d$ states participating in the screening of electron-electron interactions yields lifetimes of electrons in Au with energies of $1.0--3.0 \mathrm{eV}$ above the Fermi level that are larger than those of electrons in a free-electron gas by a factor of $\ensuremath{\sim}4.5.$ This prediction is in agreement with a recent experimental study of ultrafast electron dynamics in Au(111) films [J. Cao et al., Phys. Rev. B 58, 10 948 (1998)], where electron transport has been shown to play a minor role in the measured lifetimes of hot electrons in this material.

Measurement of the anisotropy of the two-photon absorption coefficient in ZnSe near half the band gap

The dispersion of the degenerate two-photon absorption coefficient is measured in ZnSe near half the band gap for different orientations of the light polarisation to the crystal axes. The anisotropy and dichroism parameters clearly show a sizeable dispersion just above the two-photon absorption edge in agreement with ab initio full band structure calculation.

Second-order optical response in semiconductors

We present a new general formalism for investigating the second-order optical response of solids, and illustrate it by deriving expressions for the second-order susceptibility tensor ${\ensuremath{\chi}}_{2}(\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\Sigma}};{\ensuremath{\omega}}_{\ensuremath{\beta}},{\ensuremath{\omega}}_{\ensuremath{\gamma}}),$ where ${\ensuremath{\omega}}_{\ensuremath{\Sigma}}={\ensuremath{\omega}}_{\ensuremath{\beta}}+{\ensuremath{\omega}}_{\ensuremath{\gamma}},$ for clean, cold semiconductors in the independent particle approximation. Based on the identification of a polarization operator $\mathbf{P}$ that would be valid even in a more complicated many-body treatment, the approach avoids apparent, unphysical divergences of the nonlinear optical response at zero frequency that sometimes plague such calculations. As a result, it allows for a careful examination of $\mathit{actual}$ divergences associated with physical phenomena that have been studied before, but not in the context of nonlinear optics. These are (i) a coherent current control effect called ``injection current,'' or ``circular photocurrent,'' and (ii) photocurrent due to the shift of the center of electron charge in noncentrosymmetric materials in the process of optical excitation, called ``shift current.'' The expressions we present are amenable for numerical calculations, and we demonstrate this by performing a full band-structure calculation of the shift current coefficient for GaAs.