Hydrostatic Deformation Potentials Research Articles

Hydrostatic deformation potentials of narrow-gap HgCdTe

Close to the semimetal-to-semiconductor topological phase transition, the band structure of HgCdTe is represented by massive Kane fermions that, in a semirelativistic approach, are characterized by two parameters: rest mass and velocity. Using terahertz magneto-optical spectroscopy, we explore the band structure evolution of HgCdTe films with hydrostatic pressure in the vicinity of the band-gap collapse. By analyzing the energies of interband optical transitions as a function of magnetic field, we have determined the rest mass of Kane fermions at different hydrostatic pressures. The pressure dependence of the rest mass allows us to obtain the hydrostatic deformation potential ${a}_{c}\ensuremath{-}{a}_{v}$ at low temperature, where ${a}_{c}$ and ${a}_{v}$ are the deformation potentials of the conduction and valence bands, respectively.

Indium Gallium Oxide Alloys: Electronic Structure, Optical Gap, Surface Space Charge, and Chemical Trends within Common-Cation Semiconductors.

The electronic and optical properties of (InxGa1-x)2O3 alloys are highly tunable, giving rise to a myriad of applications including transparent conductors, transparent electronics, and solar-blind ultraviolet photodetectors. Here, we investigate these properties for a high quality pulsed laser deposited film which possesses a lateral cation composition gradient (0.01 ≤ x ≤ 0.82) and three crystallographic phases (monoclinic, hexagonal, and bixbyite). The optical gaps over this composition range are determined, and only a weak optical gap bowing is found (b = 0.36 eV). The valence band edge evolution along with the change in the fundamental band gap over the composition gradient enables the surface space-charge properties to be probed. This is an important property when considering metal contact formation and heterojunctions for devices. A transition from surface electron accumulation to depletion occurs at x ∼ 0.35 as the film goes from the bixbyite In2O3 phase to the monoclinic β-Ga2O3 phase. The electronic structure of the different phases is investigated by using density functional theory calculations and compared to the valence band X-ray photoemission spectra. Finally, the properties of these alloys, such as the n-type dopability of In2O3 and use of Ga2O3 as a solar-blind UV detector, are understood with respect to other common-cation compound semiconductors in terms of simple chemical trends of the band edge positions and the hydrostatic volume deformation potential.

Excitons in Solids from Periodic Equation-of-Motion Coupled-Cluster Theory.

We present an ab initio study of electronically excited states of three-dimensional solids using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The explicit use of translational symmetry, as implemented via Brillouin zone sampling and momentum conservation, is responsible for a large reduction in cost. Our largest system studied, which samples the Brillouin zone using 64 k-points (a 4 × 4 × 4 mesh), corresponds to a canonical EOM-CCSD calculation of 768 electrons in 640 orbitals. We study eight simple main-group semiconductors and insulators, with direct singlet excitation energies in the range of 3 to 15 eV. Our predicted excitation energies exhibit a mean signed error of 0.24 eV and a mean absolute error of 0.27 eV when compared to experimental values. Although this error is similar to that found for EOM-CCSD applied to molecules, it may also reflect the role of vibrational effects, which are neglected in the calculations. Our results support recently proposed revisions of experimental optical gaps for AlP and cubic BN. We furthermore calculate the energy of excitons with nonzero momentum and compare the exciton dispersion of LiF with experimental data from inelastic X-ray scattering. By calculating excitation energies under strain, we extract hydrostatic deformation potentials to quantify the strength of interactions between excitons and acoustic phonons. Our results indicate that coupled-cluster theory is a promising method for the accurate study of a variety of exciton phenomena in solids.

Acoustically modulated optical emission of hexagonal boron nitride layers

We investigate the effect of surface acoustic waves on the atomic-like optical emission from defect centers in hexagonal boron nitride layers deposited on the surface of a LiNbO3 substrate. The dynamic strain field of the surface acoustic waves modulates the emission lines resulting in intensity variations as large as 50% and oscillations of the emission energy with an amplitude of almost 1 meV. From a systematic study of the dependence of the modulation on the acoustic wave power, we determine a hydrostatic deformation potential of about 40 meV/% for defect centers in this two-dimensional material. Furthermore, we show that the dynamic piezoelectric field of the acoustic wave could contribute to the stabilization of the optical properties of these emission centers. Our results show that surface acoustic waves are a powerful tool to modulate and control the electronic states of two-dimensional materials.

Nanoscale measurements of phosphorous-induced lattice expansion in nanosecond laser annealed germanium

Laser Thermal Annealing (LTA) at various energy densities was used to recrystallize and activate amorphized germanium doped with phosphorous by ion implantation. The structural modifications induced during the recrystallization and the related dopant diffusion were first investigated. After LTA at low energy densities, the P electrical activation was poor while the dopant distribution was mainly localized in the polycrystalline Ge resulting from the anneal. Conversely, full dopant activation (up to 1 × 1020 cm−3) in a perfectly recrystallized material was observed after annealing at higher energy densities. Measurements of lattice parameters performed on the fully activated structures show that P doping results in a lattice expansion, with a perpendicular lattice strain per atom βPs = +0.7 ± 0.1 Å3. This clearly indicates that, despite the small atomic radius of P compared to Ge, the “electronic contribution” to the lattice parameter modification (due to the increased hydrostatic deformation potential in the conduction band of P doped Ge) is larger than the “size mismatch contribution” associated with the atomic radii. Such behavior, predicted by theory, is observed experimentally for the first time, thanks to the high sensitivity of the measurement techniques used in this work.

Germanium under High Tensile Stress: Nonlinear Dependence of Direct Band Gap vs Strain

Germanium is a strong candidate as a laser source for silicon photonics. It is widely accepted that the band structure of germanium can be altered by tensile strain so as to reduce the energy difference between its direct and indirect band gaps. However, the conventional gap deformation potential model most widely adopted to describe this transition happens to have been investigated only up to 1% uniaxially loaded strains. In this work, we use a microbridge geometry to uniaxially stress germanium along [100] up to e100 = 3.3% longitudinal strain and then perform electroabsorption spectroscopy. We accurately measure the energy gap between the conduction band at the Γ point and the light- and heavy-hole valence bands and calculate the theoretical dependency using a tight-binding model. We measure the hydrostatic and tetragonal shear deformation potential of germanium to be a = −9.1 ± 0.3 eV and b = −2.32 ± 0.06 eV and introduce a second-order deformation potential that provides a better fit for both experim...

Electromodulation spectroscopy of direct optical transitions in Ge1−xSnx layers under hydrostatic pressure and built-in strain

Unstrained Ge1−xSnx layers of various Sn concentration (1.5%, 3%, 6% Sn) and Ge0.97Sn0.03 layers with built-in compressive (ε = −0.5%) and tensile (ε = 0.3%) strain are grown by molecular beam epitaxy and studied by electromodulation spectroscopy (i.e., contactless electroreflectance and photoreflectance (PR)). In order to obtain unstrained GeSn layers and layers with different built-in in-plane strains, virtual InGaAs substrates of different compositions are grown prior to the deposition of GeSn layers. For unstrained Ge1−xSnx layers, the pressure coefficient for the direct band gap transition is determined from PR measurements at various hydrostatic pressures to be 12.2 ± 0.2 meV/kbar, which is very close to the pressure coefficient for the direct band gap transition in Ge (12.9 meV/kbar). This suggests that the hydrostatic deformation potentials typical of Ge can be applied to describe the pressure-induced changes in the electronic band structure of Ge1−xSnx alloys with low Sn concentrations. The same conclusion is derived for the uniaxial deformation potential, which describes the splitting between heavy-hole (HH) and light-hole (LH) bands as well as the strain-related shift of the spin-orbit (SO) split-off band. It is observed that the HH, LH, and SO related transitions shift due to compressive and tensile strain according to the Bir-Pikus theory. The dispersions of HH, LH, and SO bands are calculated for compressive and tensile strained Ge0.97Sn0.03 with the 8-band kp Hamiltonian including strain effects, and the mixing of HH and LH bands is discussed. In addition, the dispersion of the electronic band structure is calculated for unstrained Ge1−xSnx layers (3% and 6% Sn) at high hydrostatic pressure with the 8-band kp Hamiltonian, and the pressure-induced changes in the electronic band structure are discussed.

Pressure-Dependent Photoluminescence Study of Wurtzite InP Nanowires.

The elastic properties of InP nanowires are investigated by photoluminescence measurements under hydrostatic pressure at room temperature and experimentally deduced values of the linear pressure coefficients are obtained. The pressure-induced energy shift of the A and B transitions yields a linear pressure coefficient of αA = 88.2 ± 0.5 meV/GPa and αB = 89.3 ± 0.5 meV/GPa with a small sublinear term of βA = βB = -2.7 ± 0.2 meV/GPa(2). Effective hydrostatic deformation potentials of -6.12 ± 0.04 and -6.2 ± 0.04 eV are derived from the results for the A and B transitions, respectively. A decrease of the integrated intensity is observed above 0.5 GPa and is interpreted as a carrier transfer from the first to the second conduction band of the wurtzite InP.

Study of confined coherent acoustic phonon modes in a free-standing cubic GaN membrane by femtosecond spectroscopy

Confined longitudinal coherent acoustic phonon modes are excited and detected in a sub-μm-thick free-standing cubic GaN membrane by femtosecond pump-probe spectroscopy. After fs laser excitation, Brillouin oscillation and thickness oscillation with frequencies up to 100 GHz are observed and studied in the time domain. We found an initial expansion of the membrane upon optical excitation at 400 nm. Our experimental results confirmed earlier existing theoretical predictions and experimental observations that the hydrostatic deformation potential of cubic GaN is positive.

Photoreflectance study of GaN grown on SiN treated sapphire substrate by MOVPE

GaN films were grown on silicon nitride (SiN) treated c-plane sapphire substrates in a home-made vertical reactor by atmospheric pressure metalorganic vapor phase epitaxy (MOVPE). In order to obtain different thickness layers, the growth procedure was interrupted at diverse stages using in-situ laser reflectometry. The structural and optical properties of obtained samples were investigated by high resolution X-ray diffraction (HRXRD) and photoreflectance (PR). In the 0.7–2μm epilayer thickness range, the dislocation density decreases and remains roughly constant above this range. For fully coalesced layers, PR measurements at 11K reveal the presence of well resolved excitonic transitions related to A, B and C excitons. A strong correlation between dislocation density and exciton linewidths is observed. Based on theoretical approaches and experimental results, the electronic band structure modification of GaN films due to isotropic biaxial strain was investigated. The valence band deformation potentials D3 and D4, interband hydrostatic deformation potentials a1 and a2, spin–orbit Δso and crystal field Δcr parameters were re-examined and found to be 8.2eV, −4.1eV, −3.8eV, −12eV, 15.6meV and 16.5meV, respectively.

Coherent acoustic phonon generation in GaAs1−xBix

We have used femtosecond laser pulses to generate coherent acoustic phonons in the dilute Bismide alloy, GaAs1−xBix. The observed oscillation periods match well with the oscillation periods calculated using the propagating strain pulse model. We attribute the generation process predominantly to electronic stress due to the absorption of the laser pulse at the surface of the GaAs1−xBix layer. Our initial estimates suggest that the incorporation of Bi in GaAs causes an enhancement of the hydrostatic deformation potential because of the resonant state in the valence band due to isolated Bi impurities.

Above-bandgap optical properties of biaxially strained GeSn alloys grown by molecular beam epitaxy

The complex dielectric function of biaxially strained Ge1−xSnx (0 ≤ x ≤ 0.17) alloys grown on Ge (100) has been determined by spectroscopic ellipsometry from 1.2 to 4.7 eV. The effect of substitutional Sn incorporation and the epitaxial strain on the energy transitions E1, E1 + Δ1, E0′, and E2 of GeSn alloys is investigated. Our results indicate that the strained GeSn alloys show Ge-like electronic bandstructure with all the transitions shifted downward due to the alloying of Sn. The strain dependence of E1 and E1 + Δ1 transitions is explained using the deformation potential theory, and values of −5.4 ± 0.4 eV and 3.8 ± 0.5 eV are obtained for the hydrostatic and shear deformation potentials, respectively.

Band engineering in nanowires:Ab initiomodel of band edges modified by (111) biaxial strain in group IIIA-VA semiconductors

Quantum dots in nanowires grow on a (111) substrate and it is expected that the modifications of the band structure due to a biaxial strain in the (111) crystallographic plane will determine the confinement of charge carriers in these systems. In this work, we develop an ab initio methodology for the determination of biaxial strain-modified band energies on an absolute energy scale due to a strain in an arbitrary crystallographic plane and apply it to calculate the evolution of band edges in group IIIA-VA zinc-blende semiconductors (InP, InAs, and GaAs) under the (111) biaxial strain. The absolute hydrostatic deformation potentials, a prerequisite for the accurate calculation of the strain-modified band energies within our scheme, are determined. The strain tensor for an InAs dot grown on a (111) GaAs substrate is calculated and the importance of the (111) biaxial strain is demonstrated. The strained band offsets in InAs under a compressive biaxial strain in the (001) and (111) crystallographic planes as well as the local band structure in a InAs/GaAs dot indicates a stronger confinement of holes in the (111) case.

Strain dependence of the direct energy bandgap in thin silicon on insulator layers

Photoreflectance spectroscopy is applied on tensilely strained silicon on insulator (sSOI) thin layers in order to evaluate the biaxial strain effect on the Si direct bandgap. The measured redshift of the E′0 transition (i.e. direct bandgap) with strain (∼ − 100 meV/%) corresponds to theoretical predictions. The hydrostatic and valence band deformation potential constants for E1 (i.e. transition close to the L point along the Λ-direction) are also measured: and .

Hydrostatic deformation potentials and the question of exciton binding energies and splittings in aluminium nitride

By comparing a series of optical experiments performed on bulk aluminum nitride crystals and heteroepitaxial films, we determine the hydrostatic excitonic deformation potentials of AlN. The agreement between the whole available experimental data and our analysis consolidates this determination. Using the previously determined values of the valence-band deformation potentials which account for the strain-induced variation in the crystal-field splitting: ${d}_{3}=\ensuremath{-}8.19\text{ }\text{eV}$ and ${d}_{4}=4.10\text{ }\text{eV}$ we obtain values of $\ensuremath{-}6.04$ and 2.15 eV for the hydrostatic excitonic deformation potentials ${a}_{1}$ and ${a}_{2}$ in the context of the quasicubic approximation. This constitutes the first series of values coherent with the whole set of experimental data. The experimental value of $1s\text{\ensuremath{-}}2s$ splitting disagrees with the theory of excitons in anisotropic semiconductors. This disagreement, we attribute it to our poor knowledge of the valence-band dispersion relations of AlN and to the difficulty we face for including in the calculation plausible values for the anisotropic hole effective mass, dielectric constant.

Practical B and P doping via SixSnyGe1−x−y−zMz quaternaries lattice matched to Ge: Structural, electrical, and strain behavior

We describe the fabrication of B and P doped SiGeSn ternaries, lattice-matched to Ge, with compositions adjusted to independently tune the band gap. These are deposited at 320–350 °C with superior crystallinity and morphology via in situ reactions of diborane (p-type) and designer P(SiH3)3 and P(GeH3)3 precursors (n-type). Device-level carrier concentrations in the 1019–1020/cm3 range are produced yielding film resistivities and carrier mobilities comparable to those of Ge indicating negligible alloy scattering. High boron levels induce a significant and systematic contraction of the host lattice, which is compensated by an adjustment of the Sn/Si ratio in accord with a simple model based on Vegard’s law, the mismatch of covalent radii of the constituents, and the absolute hydrostatic deformation potentials for the band edges.

Modification of the valence band structures of polar and nonpolar plane wurtzite-GaN by anisotropic strain

The influence of anisotropic strain on the valence band structure and related properties, including excitonic transition energies, transition polarization selection rules, band-edge hole effective masses, and exciton reduced effective masses, of polar and nonpolar plane GaN are systematically investigated using the well-known k⋅p Hamiltonian approach. We re-examine the band deformation potentials D3 and D4, and interband hydrostatic deformation potentials a1 and a2, and find that they take the values 9.4, −4.7, −3.0, and −12.4 eV, respectively. In order to correctly interpret the optical properties of GaN, the spin-orbit coupling effect cannot be neglected. Our numerical calculations show that pure linear polarization light emissions and absorptions can be obtained. In addition, the two topmost valence subbands can be effectively separated to reduce the band-edge density of state by manipulating the strain states in GaN epilayers, which is favorable for laser diode design. Furthermore, the band-edge hole effective masses exhibit significant in-plane anisotropy and are sensitive to the residual strain, while the influence of the residual strain on the exciton reduced effective masses is relatively weak.

Structural, thermodynamic and electronic properties of zinc-blende AlN from first-principles calculations

Structural, thermodynamic and electronic properties of zinc-blende AlN under pressure are investigated by first-principles calculations based on the plane-wave basis set. Through the analysis of enthalpy variation of AlN in the zinc-blende (ZB) and the rock-salt (RS) structures with pressure, we find the phase transition of AlN from ZB to RS structure occurs at 6.7 GPa. By using the quasi-harmonic Debye model, we obtain the heat capacity CV, Debye temperature ΘD, Grüneisen parameter γ and thermal expansion coefficient α. The electronic properties including fundamental energy gaps and hydrostatic deformation potentials are investigated and the dependence of energy gaps on pressure is analysed.

Calculations for the band lineup of strained InxGa1−xN/GaN quantum wells: Effects of strain on the band offsets

Band lineup is one of the most important parameters associated with carrier confinement in heterostructures. Relations for computing the band lineups of InxGa1−xN based heterostructures have been developed. The band positions for InxGa1−xN/GaN heterointerfaces are calculated from the equations developed, which directly corelate the positions of the bands with the band gap of InN and strain at the interface. The strains are calculated from the In mole fractions and lattice constants. The parameters implicitly involved are the elastic stiffness constants (C11 and C12), the hydrostatic deformation potential of the conduction band (a′), and the hydrostatic deformation potential (a) and shear deformation potential (b) for the valence band. Computations have been carried out for different reported band gaps of InN. The effects of strain become prominent as the mole fraction of In increases, changing the band offset ratio.

Mechanical stability and deformation potential in beryllium chalcogenides

The pressure dependence of the elastic constants associated with the fundamental band gap of beryllium chalcogenides has been studied by the state-of-the-art of Density Functional Theory. The resulting values of C i j were found to be strongly dependent on pressure. The fundamental band gap transition which occurs between Γ and X directions was found to shift linearly towards lower energy with increasing pressure, and yields a linear pressure coefficient of −22.7 (−25.85,−35.4) meV/GPa for BeS (BeSe, BeTe). The study is completed by the calculation of the effective hydrostatic deformation potential, which corresponds to 2.22 eV, 2.20 eV and 2.41 eV for BeS, BeSe and BeTe respectively.