Band Anti-crossing Model Research Articles

Understanding the optical properties of ZnO1−xSx and ZnO1−xSex alloys

ZnO1−xYx with chalcogen element Y exhibits intriguing optoelectronic properties as the alloying strongly impacts the band-gap energy Eg(x). In this work, we analyze and compare the electronic structures and the dielectric responses of Zn(O,S) and Zn(O,Se) alloys by means of the density functional theory and the partially self-consistent GW approach. We model the crystalline stability from the total energies, and the results indicate that Zn(O,S) is more stable as alloy than Zn(O,Se). We demonstrate also that ion relaxation strongly affects total energies, and that the band-gap bowing depends primarily on local relaxation of the bonds. Moreover, we show that the composition dependent band-gap needs to be analyzed by the band anti-crossing model for small alloying concentration, while the alloying band-bowing model is accurate for strong alloying. We find that the Se-based alloys have a stronger change in the band-gap energy (for instance, ΔEg(0.50) = Eg(ZnO) – Eg(x = 0.50) ≈ 2.2 eV) compared with that of the S-based alloy (ΔEg(0.50) = 1.2 eV), mainly due to a stronger relaxation of the Zn–anion bonds that affects the electronic structure near the band edges. The optical properties of the alloys are discussed in terms of the complex dielectric function ε(ω) = ε1(ω) + iε2(ω) and the absorption coefficient α(ω). While the large band-gap bowing directly impacts the low-energy absorption spectra, the high-frequency dielectric constant ε∞ is correlated to the intensity of the dielectric response at energies above 4 eV. Therefore, the dielectric constant is only weakly affected by the non-linear band-gap variation. Despite strong structural relaxation, the high absorption coefficients of the alloys demonstrate that the alloys have well-behaved optoelectronic properties.

Determination of composition and energy gaps of GaInNAsSb layers grown by MBE

We present a method to accurately determine the composition of GaInNAsSb heterostructures and a modified band anti-crossing model to calculate the corresponding bandgaps. The composition determination method is based on combining x-ray diffractometry and energy dispersive x-ray spectroscopy measurements. The modified band anti-crossing model was derived from the model known for GaInNAs and using band-gap composition relations for GaInAs, GaInSb, InAsSb and GaAsSb. The model parameters were defined by fitting with experimental bandgap data retrieved from photoluminescence. For validation and data fitting we used experimental samples with N composition in the range of 0–0.06, In composition from 0 to 0.17, and Sb composition in the range of 0–0.08. All samples were thermally annealed to minimize the band gap shift caused by the short range ordering effects in GaInNAsSb crystal. The modified model yields an excellent fit to the experimental band gap data with an accuracy of ~20meV, and is a practical tool for designing, fabricating and analyzing optoelectronics devices.

Estimation of Bi induced changes in the direct E0 band gap of III–V-Bi alloys and comparison with experimental data

Quantum dielectric Theory (QDT) is used to explain the band gap bowing effect observed in III–V-Bismides such as InSb1−xBix, InAs1−xBix, InP1−xBix, GaSb1−xBix, GaAs1−xBix and GaP1−xBix. The dependence of the direct E0 band gap for these alloys on Bi mole fraction is calculated using QDT which requires the evaluation of the bowing parameter c. The bowing parameter gives the deviation of the direct E0 band gap from the linear relationship of E0 with Bi mole fraction. The band gap reduction values obtained using QDT are compared with those calculated using Virtual Crystal approximation (VCA) and Valence Band Anticrossing (VBAC) model as well as with the reported experimental data and the results of the comparison shows excellent agreement.

Strongly nonparabolic variation of the band gap in InxAl1−xN with low indium content

80–120 nm thick InxAl1−xN epitaxial layers with 0 < x < 0.224 were grown by metalorganic vapour phase epitaxy on AlN/Al2O3-templates. The composition was varied through control of the growth temperature. The composition dependence of the band gap was estimated from the photoluminescence excitation absorption edge for 0 < x < 0.11 as the material with higher In content showed no luminescence under low excitation. A very rapid decrease in band gap was observed in this range, dropping down below 5.2 eV at x = 0.05, confirming previous theoretical work that used a band-anticrossing model to describe the strongly x-dependent bowing parameter, which in this case exceeds 25 eV in the x → 0 limit. A double absorption edge observed for InAlN with x < 0.01 was attributed to crystal-field splitting of the highest valence band states. Our results indicate also that the ordering of the valence bands is changed at much lower In contents than one would expect from linear interpolation of the valence band parameters. These findings on band gap bowing and valence band ordering are of direct relevance for the design of InAlN-containing optoelectronic devices.

Simulation and optimization of current and lattice matching double-junction GaNAsP/Si solar cells

This paper deals with theoretical investigation of the performance of current and lattice matched GaNxAsyP1−x−y/Si double-junction solar cells. The nitrogen and arsenic concentrations ensuring lattice matching to Si are determined. The band gap of GaNAsP is calculated using the band anti-crossing model. Calculations were performed under 1-sun AM1.5 using the one diode ideal model. Impact of minor carrier lifetime and surface recombination in the top sub-cell on the cell performances is analyzed. Optimum compositions of the top sub-cell have been identified (x = 4.5%, y = 11.5% and Eg = 1.68 eV). The simulation results predict, for the optimized GaNAsP/Si double-junction solar cell, a short circuit current Jsc = 20 mA/cm2, an open circuit voltage Voc = 1.95 V, and a conversion efficiency η = 37.5%.

Influence of Bi-related impurity states on the bandgap and spin–orbit splitting energy of dilute III–V-Bi alloys: InP1−xBix, InAs1−xBix, InSb1−xBix and GaSb1−xBix

Valence Band Anticrossing (VBAC) Model is used to calculate the changes in band structure of Bi containing alloys such as InP1−xBix, InAs1−xBix, InSb1−xBix and GaSb1−xBix due to the incorporation of dilute concentrations of bismuth. The coupling parameter CBi which gives the magnitude of interaction of Bi impurity states with the LH, HH and SO sub bands in VBAC depends on the increase in the HH/LH related energy level EHH/LH+, location of the Bi related impurity level EBi and valence band offset ΔEVBM between the endpoint compounds in the corresponding III–V-Bi. The reduction in band gap as well as the enhancement of the spin–orbit splitting energy is well explained using this model and the calculated results are compared with the results of Virtual Crystal Approximation (VCA) and Density Functional Theory (DFT) calculations, as well as with the available experimental data and are found to have good agreement. The incorporation of Bi mainly perturbs the valence band due to the interaction of the Bi impurity states with the HH, LH and SO bands. The lowering of the conduction band minimum (CBM) due to VCA is added with the upward movement of the HH/LH bands to get the total reduction in band gap for the bismides. The valence band shifts of 31.9, 32.5, 20.8 and 12.4 meV/at%Bi for InP1−xBix, InAs1−xBix, InSb1−xBix and GaSb1−xBix respectively constitute 65, 76, 59 and 31% of the total band gap reduction and the rest is the contribution of the conduction band shift. The spin–orbit splitting energy also shows significant increase with the maximum change in InPBi and the minimum in InSbBi. The same is true for Ga containing bismides if we make a comparison with the available values for GaAsBi and GaPBi with that of GaSbBi. It has also been observed that the increase in splitting energy is greater in case of the bismides such as InAsBi, InPBi and GaAsBi than the bismides such as InSbBi and GaSbBi with the parent substrates having higher values of splitting energy. This may be due to the proximity of the Bi related impurity level EBi with the SO bands of InAs, InP and GaAs.

Compositional dependence of the band gap in Ga(NAsP) quantum well heterostructures

We present experimental and theoretical studies of the composition dependence of the direct band gap energy in Ga(NAsP)/GaP quantum well heterostructures grown on either (001) GaP- or Si-substrates. The theoretical description takes into account the band anti-crossing model for the conduction band as well as the modification of the valence subband structure due to the strain resulting from the pseudomorphic epitaxial growth on the respective substrate. The composition dependence of the direct band gap of Ga(NAsP) is obtained for a wide range of nitrogen and phosphorus contents relevant for laser applications on Si-substrate.

The study of electronic structure and absorption coefficient of ZnTe:O alloys: A GGA+U method

In this study the electronic structures and absorption coefficient for highly mismatched ZnTe1−xOx alloys have been investigated on the basis of the GGA+U approximation. It is found that an isolated intermediate band (E−) is formed within the band gap of ZnTe by the incorporation of low content of O (x<0.0625) into ZnTe. In the range of the low O content, the variation of E− and E+ is in agreement with the theoretical prediction by the well-known band anti-crossing model. As the O content x exceeds 0.0625, the E+ energy position decreases and intermediate band (E−) cannot exist in isolation states, which is consistent with the experimental results but in contrast to the band anti-crossing model. The chemical bonding pictures show that the intermediate band states are mainly caused by the antibonding states that are formed through the hybridization of a localized O 2s state and some localized Zn 3d4s4p states. The calculated absorption coefficient exhibits an obvious enhancement within the ZnTe:O bandgap, which indicates the formation of intermediate states can effectively make use of low energy photons to improve the conversion efficiency of final solar cell based on ZnTe:O materials.

Valence band anticrossing model for GaSb1−xBix and GaP1−xBix using k.p method

The reduction in band gap as well as the increase in spin–orbit splitting energy in GaSb1−xBix and GaP1−xBix are explained by the Valence Band Anticrossing (VBAC) model. This restructuring of the valence band is due to the interaction of the Bi related impurity levels with the extended states of the valence band of the host semiconductor. The band gap reduction in GaSb1−xBix and GaP1−xBix calculated using VBAC model are respectively 40.2meV and 206meV/at% Bi. A comparison of the theoretical and experimentally obtained values of band gap in GaSbBi shows good agreement. Valence band structure for GaPBi is obtained by the extrapolation of the parameters used for modeling of the GaSbBi system. The upward movement of the spin–orbit split-off E+ energy level in GaSbBi by 19.2meV/at% Bi is also responsible for the suppression of Auger recombination processes making it a potential candidate for near and mid-infrared optoelectronic applications.

Effects of the d-donor level of vanadium on the properties of Zn1−xVxO films

We report the effect of d-levels of vanadium atoms on the electronic band structure of ZnO. Polycrystalline layers of Zn1−xVxO with 0 ≤ x ≤ 0.08 were synthesized using magnetron sputtering technique. Electrical measurements show that electron concentration increases with vanadium up to x = 0.04 and then decreases and films become insulating for x &amp;gt; 0.06. Optical characterization reveals that the absorption edge shifts to higher energy, while the photoluminescence (PL) peak shows a shift to lower energy with increasing vanadium content. This unusual optical behavior can be explained by an anticrossing interaction between the vanadium d-levels and the conduction band (CB) of ZnO. The interaction results in an upward shift of unoccupied CB (E+) and the downward shift of the fully occupied E− band derived from the vanadium d-levels. The composition dependence of optical absorption edge (E+) and PL peak (E−) can be fitted using the Band Anticrossing model with the vanadium d-level located at 0.13 eV below CB of ZnO and a coupling constant of 0.65 eV.

SAFSIZLIK DÜZEYLERİ ARASINDAKİ KIZILÖTESİ GEÇİŞLER ÜZERİNE ELEKTRİK ALAN ETKİSİ

Abstract .In this study, the effects of electric fields, the concentrations of nitrogen and indium on infrared transitions between 1s, 2s ve 2p± donor impurity energy levels at the single GaInNAs/GaAs quantum well are investigated using the variational method in the framework of the effective mass approximation. Key Words: Single quantum well, band anti-crossing (BAC) model, Impurity binding energy, Dilute III-N-V semiconductors

Exploration of the growth parameter space for MBE-grown GaN1−xSbx highly mismatched alloys

Highly mismatched GaN1−xSbx alloys were grown under N-rich conditions at low substrate temperatures (325–550°C) at a growth rates of ~0.09μm/hr on sapphire. The alloys ranged in Sb composition from 0% to 16%, with the bandgap shifting from 3.3 to 1.6eV in accordance with the band anticrossing (BAC) model. We compare these results to growths from another chamber, having a different N source, and using a faster growth rate (~0.24μm/hr), much lower substrate temperatures (as low as 80°C), different III/V ratios and absolute fluxes. Despite the range of morphologies obtained, all alloys follow the predictions of the BAC model with the bandgap only depending on the Sb composition.

Analytic modeling of temperature dependence of 2D carrier mobility in as-grown and annealed GaInNAs/GaAs quantum well structures

Temperature and nitrogen dependence of 2D carrier mobility in as-grown and annealed Ga1−xInxNyAs1−y/GaAs quantum well (QW) structures (x = 0.32; y = 0, 0.009, and 0.012) are investigated. An analytical model that accounts for the most prominent scattering mechanisms is used to explain the characteristic of temperature dependence of the carrier mobility. An expression for alloy scattering-limited mobility in N-related alloys is developed to explain the behavior of hole mobility for N-containing p-type samples. Analytical modeling of temperature dependence of the electron mobility indicates that N-related alloy scattering and interface roughness scattering are the dominant mechanism at the entire temperature range of interest. The temperature insensitivity of the electron mobility is explained in terms of the overriding effect of N-related alloy scattering and high 2D electron density. A deviation between theoretical and experimental electron mobility at low temperatures is observed not to have any dependency on N concentration. We, therefore, suggest that CNM interaction parameter of the band anti-crossing (BAC) model must be defined as temperature dependent in order to explain the observed low temperature characteristics of electron mobility. The hole mobility is mainly restricted by interface roughness and alloy scatterings at temperatures lower than 100 K, whilst high temperature hole mobility is drastically affected from optical phonon scattering. Moreover, the hole mobility at high temperatures exhibits an N-independent characteristic and hole density starts to increase at temperatures above 70 K, which is explained using the concept of parallel conduction. Extraction of the hole density in each transport channel (QW and barrier) by using a simple parallel conduction extraction method (SPCEM) shows that, in p-type samples, low temperature hole mobility takes place in quantum well, while as temperature increases barrier channel also contribute to the hole mobility and becomes dominant at high temperatures. The experimental and calculated Hall mobility results reveal that thermal annealing has decreased interface roughness and alloy scatterings.

First principles study of structural, electronic and optical properties of indium gallium nitride arsenide lattice matched to gallium arsenide

First principles calculations in the framework of the full-potential linearized augmented plane wave (FP-LAPW) scheme have been carried out. The dilute-nitride zinc blende (InxGa1−xNyAs1−y) was modeled at selected nitrogen compositions of y=3.125%, 6.25% and 9.375% lattice matched to gallium arsenide (GaAs). We pay attention to the InxGa1−xNyAs1−y alloy which can be perfectly lattice matched to the GaAs over its entire compositional range. In our study, this is achieved when a condition y~2.7x is maintained. The band structure calculations were performed with and without relaxation by using the generalized gradient approximation of Engel and Vosko (EV-GGA) as well as by the modified Becke–Johnson potential exchange (TB-mBJ). The action of the localized potential of subsisted nitrogen atoms was attributed to effect of relaxation. Increasing both indium and nitrogen compositions leads to decreasing energy band gap. In addition a band anti-crossing model (BAC) was also adopted to study the composition dependence of the direct band gap of quaternary alloys, building a bridge between their electronic and linear optical properties.

Theoretical study of optoelectronic properties of GaAs1−xBix alloys using valence band anticrossing model

The (12×12) and (14×14) valence band anticrossing (V-BAC) models were applied to calculate the electronic band structure of GaAs1−xBix dilute alloys along Δ-, Λ- and Σ-directions at room temperature. A comparative study based on these models was performed in terms of energy levels, optical transitions, spin–orbit splitting and effective mass. We found a significant reduction of the band-gap energy Eg by roughly 81meV/%Bi accompanied by an increase in the spin–orbit splitting Δso+ by about 56meV/%Bi. Furthermore, Δso+ does come into resonance with Eg at ∼12%Bi for resonance energy equal to 0.73eV. An excellent agreement has occurred between the (14×14) V-BAC model predictions and experimental results reported in the literature. In addition, we have investigated the Bi composition and k-directions dependence of the effective mass at Γ point. A slight increase of the holes effective mass with x can affect the holes transport properties of GaAsBi. The intrinsic carrier density increases with both x and the temperature T, but it remains below 1010cm−3 for x⩽5% and T⩽300K.

Exciton-related nonlinear optical response and photoluminescence in dilute nitrogen [formula omitted] cylindrically shaped quantum dots

An investigation of the effects of the dilute nitrogen contents in the exciton states of cylindrical InxGa1−xNyAs1−y/GaAs quantum dots is presented. The exciton states in the system are obtained within the effective mass theory and the band anti-crossing model. Exciton-related nonlinear optical absorption and refractive index change, as well as excitonic photoluminescence are studied with the help of the calculated exciton states.

A model for the bandgap energy of the dilute nitride InGaNAs alloys by modifying simplified coherent potential approximation

In this paper, a model describing the bandgap energy of the dilute nitride alloy In x Ga 1-x N y As 1-y is developed based on the modification of simplified coherent potential approximation (MSCPA) and the band anti-crossing model (BAC). The parameters in the model are obtained by fitting the experimental bandgap energies of the ternary alloys InGaAs , InGaN , GaNAs and InNAs . It is found that the results agree well with the experimental data. We also find that although the bandgap energies of In x Ga 1-x N y As 1-y and In x Ga 1-x As can be calculated by using MSCPA, the physical mechanisms for the bandgap evolution of In x Ga 1-x N y As 1-y and In x Ga 1-x As are very different. In addition, it is found that the model in this work may be used in a larger composition range than the BAC model.

Optical absorption of dilute nitride alloys using self-consistent Green’s function method

We have calculated the optical absorption for InGaNAs and GaNSb using the band anticrossing (BAC) model and a self-consistent Green’s function (SCGF) method. In the BAC model, we include the interaction of isolated and pair N levels with the host matrix conduction and valence bands. In the SCGF approach, we include a full distribution of N states, with non-parabolic conduction and light-hole bands, and parabolic heavy-hole and spin-split-off bands. The comparison with experiments shows that the first model accounts for many features of the absorption spectrum in InGaNAs; including the full distribution of N states improves this agreement. Our calculated absorption spectra for GaNSb alloys predict the band edges correctly but show more features than are seen experimentally. This suggests the presence of more disorder in GaNSb alloys in comparison with InGaNAs.

Dependence of the hybridization parameter on nitrogen molar fraction in nitrogen-containing GaPN solid solutions

Heterostructures with GaP1 − xNx layers synthesized by molecular beam epitaxy on GaP(001) substrates have been studied by photoluminescence and X-ray diffraction measurement. The results are compared to parameters calculated using the band anticrossing (BAC) model. Results of this comparative study lead to the conclusion that the hybridization parameter of GaP1 − xNx depends on the molar fraction of nitrogen in the solid solution.

Modeling of the atomic structure and electronic properties of amorphous GaN1−xAsx

Chemically ordered 250-atom models for amorphous GaN1−xAsx alloys in the concentration range of 0.17<x<0.75 have been studied with density functional theory simulations, starting with initial continuous random network structures. The analysis of network topology has been achieved by examining partial-pair correlation functions, bond angle distributions, ring statistics and average coordination numbers. The electronic properties of amorphous GaN1−xAsx alloys have been estimated by means of electronic density states (EDOS) and inverse participation ratios (IPR). Our calculations indicate that the introduction of As into GaN reduces the bond angle disorder. According to our ring analysis the 250atom a-GaN1−xAsx model has a disordered tetrahedral characteristic confirming the fact that continuous random network (CRN) can provide an ideal initial structure. The study of EDOS and IPR proves that the bandgap of a-GaN1−xAsx gets narrower with increasing As concentration, which is in good agreement with the experimental results and the band anti-crossing model.