Valence Band Model Research Articles

Valence Band Dispersion in Bi-Doped (Ga,Mn)As Epitaxial Layers

The impact of incorporating Bi into (Ga,Mn)As layers on their electronic, band structure, magnetic, and structural properties has been studied. The low-temperature molecular beam epitaxy technique was employed to grow homogeneous (Ga,Mn)(Bi,As) layers with high structural perfection. Post-growth annealing treatment resulted in improved structural and magnetic properties, as well as an increase in the hole concentration in the layers. Modulation photoreflectance spectroscopy confirmed modifications to the valence and split-off band in the (Ga,Mn)(Bi,As) layers. The experimental results are consistent with the valence band model of hole-mediated ferromagnetism in the layers. The (Ga,Mn)(Bi,As) compound combines the properties of (Ga,Mn)As and Ga(Bi,As) ternary compounds, offering the possibility of tailoring the bandgap structure to the requirements of novel device functionalities for future spintronic and photonic applications.

Electrocatalytic activity of a β-Sb two-dimensional surface for the hydrogen evolution reaction.

Hydrogen energy is considered to be one of the most promising clean energy sources. The development of highly active, low-cost catalysts, and good stability is essential for hydrogen production. Herein, the catalytic activity of a two-dimensional β-Sb surface doped with main-group elements (N, P, As, O, S, Se, and Te) for the hydrogen evolution reaction (HER) was investigated by density functional theory, and the catalytic activity of the β-Sb monolayer can be improved by doping group VIA atoms. The catalytic activity of Se@Sb and O@Sb structures at the doping concentration of 2.78% and the S@Sb structure at the doping concentration of 5.56% may be as good as the Pt(111) surface, while keeping energetically stable. In addition, the catalytic performance could be optimized under biaxial strain. Further analysis suggests that the activity is caused by hole states in the lone pair electrons, which are created by the group VIA atom dopants. And our work also reveals that the density of states at the Fermi level could be an appropriate descriptor of the hydrogenation Gibbs free energy. This work not only proposes a novel non-platinum HER catalyst but also provides physical foundations for further application on antimonene-based catalysts.

Advancing thermoelectrics by vacancy engineering and band manipulation in Sb-doped SnTe–CdTe alloys

A decrease in valence band energy offset can considerably improve the thermoelectric performance of SnTe, and alloying CdTe in SnTe has been confirmed to be efficient for inducing band convergence. However, the low solubility of CdTe in SnTe severely limits the further decrease in the energy offset and the reduction of lattice thermal conductivity. Inspired by the high solubility of Sb in SnTe-based thermoelectric materials, the trivalent Sb is introduced into SnTe–CdTe alloys, aiming at manipulating the thermoelectric transport properties. Combined with the valence band model, it is demonstrated that high concentration of Sb in SnTe–CdTe enables a further optimization in valence band structures, resulting in an improvement in density-of-state effective mass, thus significantly reinforces the power factor in the whole temperature range. Meanwhile, we propose the solid solution mode of Sb in SnTe, which always generates vacancies to balance the valence state, and the introduction of vacancies explains the reduced lattice parameters and almost constant carrier concentration. Particularly, the Debye–Callaway model quantitatively compares the contribution of Sb substitutional defects and vacancy defects. As a result, an enhanced zT of ∼1.1 has been achieved for Sn0.83Cd0.05Sb0.12Te at 823 K. This work clearly shows the critical role of Sb for enhancing the thermoelectric performance of SnTe–CdTe materials.

Revisiting the Determination of the Valence Band Maximum and Defect Formation in Halide Perovskites for Solar Cells: Insights from Highly Sensitive Near-UV Photoemission Spectroscopy.

Using advanced near-UV photoemission spectroscopy (PES) in constant final state mode (CFSYS) with a very high dynamic range, we investigate the triple-cation lead halide perovskite Cs0.05(MA0.17FA0.83)0.95Pb(I0.83Br0.17)3 and gain detailed insights into the density of occupied states (DOS) in the valence band and band gap. A valence band model is established which includes the parabolic valence band edge and an exponentially decaying band tail in a single equation. This allows us to precisely determine two valence band maxima (VBM) at different k-vectors in the angle-integrated spectra, where the highest one, resulting from the VBM at the R-point in the Brillouin zone, is found between -1.50 to -1.37 eV relative to the Fermi energy EF. We investigate quantitatively the formation of defect states in the band gap up to EF upon decomposition of the perovskites during sample transfer, storage, and measurements: during near-UV-based PES, the density of defect states saturates at a value that is around 4 orders of magnitude below the density of states at the valence band edge. However, even short air exposure, or 3 h of X-ray illumination, increased their density by almost a factor of six and ∼40, respectively. Upon prolonged storage in vacuum, the formation of a distinct defect peak is observed. Thus, near-UV CFSYS with modeling as shown here is demonstrated as a powerful tool to characterize the valence band and quantify defect states in lead halide perovskites.

Band Alignments, Band Gap, Core Levels, and Valence Band States in Cu3BiS3 for Photovoltaics.

The earth-abundant semiconductor Cu3BiS3 (CBS) exhibits promising photovoltaic properties and is often considered analogous to the solar absorbers copper indium gallium diselenide (CIGS) and copper zinc tin sulfide (CZTS) despite few device reports. The extent to which this is justifiable is explored via a thorough X-ray photoemission spectroscopy (XPS) analysis: spanning core levels, ionization potential, work function, surface contamination, cleaning, band alignment, and valence-band density of states. The XPS analysis overcomes and addresses the shortcomings of prior XPS studies of this material. Temperature-dependent absorption spectra determine a 1.2 eV direct band gap at room temperature; the widely reported 1.4-1.5 eV band gap is attributed to weak transitions from the low density of states of the topmost valence band previously being undetected. Density functional theory HSE06 + SOC calculations determine the band structure, optical transitions, and well-fitted absorption and Raman spectra. Valence band XPS spectra and model calculations find the CBS bonding to be superficially similar to CIGS and CZTS, but the Bi3+ cations (and formally occupied Bi 6s orbital) have fundamental impacts: giving a low ionization potential (4.98 eV), suggesting that the CdS window layer favored for CIGS and CZTS gives detrimental band alignment and should be rejected in favor of a better aligned material in order for CBS devices to progress.

Heterointerface-Driven Band Alignment Engineering and its Impact on Macro-Performance in Semiconductor Multilayer Nanostructures.

Interfaces in semiconductor heterostructures is of continuously greater significance in the trend of scaling materials down to the atomic limit. Since atoms tend to behave more irregularly around interfaces than in internal materials, accurate energy band alignment becomes a major challenge, which determines the ultimate performance of devices. Therefore, a comprehensive understanding of the interplay between heterointerface, energy band, and macro-performance is desiderated. Here, such interplay is explored by investigating asymmetric heterointerfaces with identical fabrication parameters in multiple-quantum-well lasers. The unexpected asymmetry derives from the atomic discrepancy around heterointerfaces, which ultimately improves the optical property through altered valence band offsets. Strain and charge distribution around heterointerfaces are characterized via geometric phase analysis and in situ bias electron holography, respectively. Combining experiments with theories, arsenic-enrichment at one of the interfaces is considered the origin of asymmetry. To reveal actual band alignment, valence band model is modified focusing on the transition around heterojunctions. The enhanced photoluminescence intensity reflects the alleviation of hole confinement insufficiency and the enlargement of valence band offset. The results help to advance the understanding of the general problem of interface in nanostructures and provide guidance applicable to various scenarios for micro-macro correlation.

Magneto-optical spectroscopy of diluted magnetic semiconductors GaMnAs prepared by ion implantation and further impulse laser annealing

Ga1−xMnxAs layers prepared by ion implantation and subsequent pulsed laser annealing with the planned Mn concentrations of x = 0.01–0.08 have been studied using the magneto-optical transversal Kerr effect (TKE) and spectral ellipsometry. The spectral dependences of the diagonal and nondiagonal components of the permittivity tensor (PT), as well as the spectrum of magnetic circular dichroism (MCD) have been calculated for the layers. The obtained spectra of the diagonal PT components show that the layers under study maintain the zinc-blende crystal structure of the parent GaAs semiconductor. All studied samples reveal a strong TKE response at low temperatures with a dependence of an effective Curie temperature (at which TKE appears) on the Mn concentration. A number of extrema in the low-temperature TKE and MCD spectra are close to the energies of transitions in the Γ and L critical points of the parent semiconductor band structure that confirms the intrinsic ferromagnetism of the Ga1−xMnxAs layers. The MCD spectra shape and its change with Mn concentration increasing are discussed on a base of the valence-band model of ferromagnetism in DMS.

Insights from simple models for surface states in nanostructures

Surface passivation is of great technological importance due to the increasing miniaturisation of electronic devices. It has been known for many years that under certain conditions surface states can form; when they do so in a quantum well (QW) the result is an unbound (i.e., evanescent) state in the QW. Such surface states are generally undesirable, so a good physical understanding of them is important. A simple single-p-orbital valence band model is used with two types of surface passivation to examine surface states in a QW: (1) an energy upshift added to the terminal atoms; and (2) explicit passivation by an s-orbital on each end of the QW. These models show these unbound/evanescent QW states can occur in both models; that in them the wavefunction is bound to the terminal atoms; and that the existence of these states is connected to the effective valence-band offset between the terminal atoms and the bulk QW.

Precise tuning of the Curie temperature of (Ga,Mn)As-based magnetic semiconductors by hole compensation: Support for valence-band ferromagnetism

For the prototype diluted ferromagnetic semiconductor (Ga,Mn)As, there is a fundamental concern about the electronic states near the Fermi level, i.e., whether the Fermi level resides in a well-separated impurity band derived from Mn doping (impurity-band model) or in the valence band that is already merged with the Mn-derived impurity band (valence-band model). We investigate this question by carefully shifting the Fermi level by means of carrier compensation. We use helium-ion implantation, a standard industry technology, to precisely compensate the hole doping of GaAs-based diluted ferromagnetic semiconductors while keeping the Mn concentration constant. We monitor the change of Curie temperature ($T_C$) and conductivity. For a broad range of samples including (Ga,Mn)As and (Ga,Mn)(As,P) with various Mn and P concentrations, we observe a smooth decrease of $T_C$ with carrier compensation over a wide temperature range while the conduction is changed from metallic to insulating. The existence of $T_C$ below 10\,K is also confirmed in heavily compensated samples. Our experimental results are naturally explained within the valence-band picture.

The Influence of Electron-Hole Exchange Interaction of Colloidal CdSQuantum Dots on the Value of the Resonant Stokes Shift

On the basis of the model of the multiband valence band the exiton energy was calculated in the CdSnanocrystals as a function of quantum dot radius. The dependence of the resonance Stokes shift was analized and the comparison with the corresponding experimental data were provided.

Band-gap shrinkage calculations and analytic model for strained bulk InGaAsP

Band-gap shrinkage is an important effect in semiconductor lasers and optical amplifiers. In the former it leads to an increase in the lasing wavelength and in the latter an increase in the gain peak wavelength as the bias current is increased. The most common model used for carrier-density dependent band-gap shrinkage is a cube root dependency on carrier density, which is strictly only true for high carrier densities and low temperatures. This simple model, involves a material constant which is treated as a fitting parameter. Strained InGaAsP material is commonly used to fabricate polarization insensitive semiconductor optical amplifiers (SOAs). Most mathematical models for SOAs use the cube root bandgap shrinkage model. However, because SOAs are often operated over a wide range of drive currents and input optical powers leading to large variations in carrier density along the amplifier length, for improved model accuracy it is preferable to use band-gap shrinkage calculated from knowledge of the material bandstructure. In this letter the carrier density dependent band-gap shrinkage for strained InGaAsP is calculated by using detailed non-parabolic conduction and valence band models. The shrinkage dependency on temperature and both tensile and compressive strain is investigated and compared to the cube root model, for which it shows significant deviation. A simple power model, showing an almost square-root dependency, is derived for carrier densities in the range usually encountered in InGaAsP laser diodes and SOAs.

Hole scattering and mobility in compressively strained Ge/(001)Si1-xGex

Strained Ge attracts attention of researchers for its high mobility and compatibility with Si technology. Based on the valence band model for compressively strained Ge/(001)Si1-xGex, the relationships between hole scattering, mobility, and Ge content (x) are established in this paper, including ionized impurity, acoustic phonon, non-polar optical phonon, total scattering rates, and the averaged and directional mobility of holes. Our quantitative data gained within the models can provide valuable references for the research of modified Ge materials physics and the design of the related devices.

Ferromagnetism and the electronic band structure in (Ga,Mn)(Bi,As) epitaxial layers

Impact of Bi incorporation into (Ga,Mn)As layers on their electronic- and band-structures as well as their magnetic and structural properties has been studied. Homogenous (Ga,Mn)(Bi,As) layers of high structural perfection have been grown by the low-temperature molecular-beam epitaxy technique. Post-growth annealing treatment of the layers results in an improvement of their structural and magnetic properties and an increase in the hole concentration in the layers. The modulation photoreflectance spectroscopy results are consistent with the valence-band model of hole-mediated ferromagnetism in the layers. This material combines the properties of (Ga,Mn)As and Ga(Bi,As) ternary compounds and offers the possibility of tuning its electrical and magnetic properties by controlling the alloy composition.

Observation of a blue shift in the optical response at the fundamental band gap in Ga1−xMnxAs

We report the observation of a sharp band-edge response in spectrally resolved differential reflectivity experiments on GaMnAs, in contrast to linear optical experiments in which large band-tail effects are known to dominate. The differential reflectivity response exhibits a blue shift relative to results in GaAs and LT-GaAs, consistent with the valence-band model of ferromagnetism. Our results demonstrate the utility of nonlinear optical techniques for studying the electronic structure of III-Mn-V diluted magnetic semiconductors.

Exchange interaction and Curie temperature in Ge1−xMnxTe ferromagnetic semiconductors

We present the magnetotransport studies of Ge1−xMnxTe ferromagnetic semiconductor under hydrostatic pressure. The investigation of the normal and Hall resistivities provide an insight to the dependence of carrier concentration, mobility, and magnetic properties on pressure. Our results reveal that the application of pressure changes the band structure, which can be explained by a two valence band model. We observe the enhancement and reduction of Curie temperature within a pressure range of 0–24 kbar. Analysis within the framework of the Ruderman–Kittel–Kasuya–Yosida model allows us to identify the factors in controlling the Tc, in which the exchange interaction plays a predominant role in the formation of ferromagnetic phase.

Thermoelectric transport in the coupled valence-band model

The Boltzmann transport equation (BTE) is applied to the problem of thermoelectric transport in p-type semiconductors whose valence band-structure is describable in terms of two bands degenerate at the Γ point. The Seebeck coefficient and mobility are calculated from the solution to two coupled BTEs, one for each band, with interband scattering and scattering by inelastic mechanisms treated exactly by the application of an algorithm developed by the authors in an earlier work. Most treatments of this problem decouple the two bands by neglecting certain terms in the BTE, greatly simplifying the mathematics: the error in the Seebeck coefficient and mobility introduced by this approximation is quantified by comparing with the exact solution. Degenerate statistics has been assumed throughout, and the resulting formalism is therefore valid at high hole concentrations. Material parameters are used that have been deduced from optical, strain and other experiments often not directly related to hole transport. The formulations in this work thus do not use adjustable or fitting parameters. The transport coefficients of heavily doped gallium antimonide, a typical high-efficiency p-type thermoelectric material, are calculated and agreement to experimentally determined values is found to be satisfactory.

Microscopic Analysis of the Valence Band and Impurity Band Theories of (Ga,Mn)As

We analyze microscopically the valence and impurity band models of ferromagnetic (Ga,Mn)As. We find that the tight-binding Anderson approach with conventional parametrization and the full potential local-density approximation+U calculations give a very similar band structure whose microscopic spectral character is consistent with the physical premise of the k·p kinetic-exchange model. On the other hand, the various models with a band structure comprising an impurity band detached from the valence band assume mutually incompatible microscopic spectral character. By adapting the tight-binding Anderson calculations individually to each of the impurity band pictures in the single Mn impurity limit and then by exploring the entire doping range, we find that a detached impurity band does not persist in any of these models in ferromagnetic (Ga,Mn)As.

Investigation of Ga Substitution in ZnO Powder and Opto-Electronic Properties

Two sets of Ga-doped ZnO powders were synthesized via solid-state and Pechini routes with a substitution rate varying from 0 to 4 mol %. The gallium solubility limit is strongly dependent on the synthesis history. Indeed, a low temperature annealing allows incorporating about 1.5 mol % (X-ray diffraction (XRD), inductive coupled plasma spectroscopy (ICP), optical properties) whereas under 0.1% of dopant is introduced after thermal treatment at high temperature: 1500 degrees C (from XRD and pellets conductivity). The incorporation of gallium leads to an anisotropic distortion of the zincite crystal lattice (a and c parameters increase and decrease, respectively, versus the Ga content leading to a decrease of the c/a ratio) which can be explained from the valence bond model. XRD analysis, chemical titration by ICP, and conductivity measurements (on pellets obtained at high temperature) allow determining accurately the maximum Ga content in the zincite. The optical properties (IR absorption efficiency) linked to electron carriers are directly correlated to the gallium rate introduced in ZnO oxide; nevertheless, the non linear correlation between these two parameters tends to show that the concentration of charge carriers in the system is not equal to the amount of Ga(3+) atoms inserted per ZnO volume unit. A saturation regime is observed and was here explained once again on the basis of the valence band model by the increase of inhibiting p type defects with the increase of (n-type donors) Ga(3+) concentration.

Dispersion relation model of valence band in strained Si

There has been much interest lately in the strained Si CMOS technology used for carrier mobility enhancement. The dispersion relation of valence band in strained Si is the theoretical basis for understanding and enhancing hole mobility. With in the frame of K.P theory, the dispersion relation is derived by taking strained Hamiltonian perturbation into account. The corresponding model obtained can be applied to calculate the valence band structure and hole effective mass along arbitrarily K wavevector direction in strained Si grown on arbitrarily oriented relaxed Si1－xGex(0≤x≤0.6) substrates, and hence is valuable as reference for the design of devices.

A solution of the effective-mass Schrödinger equation in general isotropic and nonparabolic bands for the study of two-dimensional carrier gases

In this paper we develop a suitable method for solving the effective-mass Schrödinger equation for two-dimensional electron and hole gases in semiconductor structures such as quantum wells using a general nonparabolic band structure. We present two different ways to treat barriers, the first being the exact solution and the second a suitable option when the band structure is not determined inside the gap. As a first application, this procedure was implemented to solve the effective-mass Schrödinger equation for holes in Si and Ge using an analytical valence-band model. Analyzing the results obtained enabled us to demonstrate the importance of nonparabolicity in energy quantization in these systems and to discuss the suitability of each of these two procedures for dealing with barriers.