Simplified Coherent Potential Approximation Research Articles

The band gap energy of BexMgyZn1−x−yO calculated by modified simplified coherent potential approximation

The band gap energy of BexMgyZn1−x−yO is estimated by modifying simplified coherent potential approximation. It is found that the model can give a good description for the band gap energy. The deviation between the results in this work and the experimental values is due to the phase separation and clusters. It is also found that the band gap energy of BexMgyZn1−x−yO is enlarged as the Mg content or Be content increases. The reason is that either increasing Be content or increasing Mg content can lead to the downward movement of the Г VBM of BexMgyZn1−x−yO and the upward movement of the Г CBM of BexMgyZn1−x−yO. The downward movement of the Г VBM of BexMgyZn1−x−yO is owing to two factors. One is that the p-p couping effect becomes strong. The other one is that the p-d coupling effect becomes weak. For the upward movement of the Г CBM of BexMgyZn1−x−yO, it is due to that the s-s coupling effect becomes strong.

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.

A Band-Gap Energy Model of the Quaternary Alloy InxGayAl1−x−yN using Modified Simplified Coherent Potential Approximation

Based on modification of the simplified coherent potential approximation, a model for the band-gap energy of InxGayAl1−x−yN is developed. The parameters of the model are obtained by fitting the experimental band-gap energy of their ternary alloys. It is found that the results agree with the experimental values better than those reported by others, and that the band-gap reduction of InxGayAl1−x−yN with increasing In or Ga content is mainly due to enhanced intraband coupling within the conduction band, and separately within the valence band.

Influence of pressure on exciton states and interband optical transitions in wurtzite InGaN/GaN coupled quantum dot nanowire heterostructures with polarization and dielectric mismatch

Considering the hydrostatic pressure, the spontaneous and piezoelectric polarization, the dielectric mismatch, and 3D confinement of the electron and hole, the exciton states and interband optical transitions in [0001]-oriented wurtzite InxGa1−xN/GaN strained coupled quantum dot (QD) nanowire heterostructures (NWHETs) have been investigated by using the effective mass approximation, the simplified coherent potential approximation, and a variational approach. Our results show that the hydrostatic pressure, the strong built-in electric field (BEF), and the dielectric mismatch have a significant influence on the exciton states and interband optical transitions. The exciton binding energy increases almost linearly with the hydrostatic pressure for a given QD NWHET. The emission wavelength has a blue-shift (red-shift) if the hydrostatic pressure (QD height or the potential barrier thickness) increases. Our calculations also indicate that the radiative decay time has a quick increase with increasing of the QD height and the barrier thickness. The radiative decay time decreases if the hydrostatic pressure increases. The BEF (dielectric mismatch) dramatically decreases (increases) the exciton binding energy. The physical reason has been analyzed in depth.

A modified simplified coherent potential approximation model of band gap energy of III–V ternary alloys

Based on the modification of the simplified coherent potential approximation (SCPA), a model is developed to calculate the composition dependence of the band gap energy of III-V ternary alloys with the same anion. The derived equation is used to fit the experimental band gap energy of InxAl1−xN, InxGa1−xN and AlxGa1−xN with x from 0 to 1. It is found that the fitting results are better than those done by using SCPA. The fitting results are also better than those obtained by using the formula with a small bowing coefficient, especially for InxAl1−xN. In addition, our model can also be used to describe the composition dependence of band gap energy of other III-V ternary alloys.

Exciton states and interband optical transitions in wurtzite InGaN/GaN quantum dot nanowire heterostructures: Effects of hydrostatic pressure

Considering the hydrostatic pressure, the strong built-in electric field as well as the three-dimensional confinements of the electrons and holes, we solve the confined exciton states and investigate the interband optical transitions in wurtzite In x Ga 1− x N/GaN strained quantum dot (QD) nanowire heterostructures (NWHETs) using a variational method under the effective mass approximation and the simplified coherent potential approximation. In our calculations, the effective masses of the electron and hole, dielectric constants, phonon frequencies, energy gaps, radius and height of QDs and piezoelectic polarizations are taken into account as a function of hydrostatic pressure. Our results show that the hydrostatic pressure has a significant influence on the exciton states and interband optical transitions. The exciton binding energy increases with the hydrostatic pressure. The emission wavelength has a blue-shift (red-shift) if the hydrostatic pressure (QD height) increases. For the small radius or the large height QDs, the hydrostatic pressure dependence of the exciton binding energy is more obvious. The hydrostatic pressure can effectively enhance the exciton oscillator strength and improve the light emission efficiency of In x Ga 1− x N/GaN QD NWHETs. The physical reason has been analyzed in depth.

Pressure influence on bound polarons in a strained wurtzite GaN/AlxGa1−xN heterojunction under an electric field

The binding energies of bound polarons near the interface of a strained wurtzite GaN/AlxGa1−xN heterojunction are studied by using a modified LLP variational method and a simplified coherent potential approximation under hydrostatic pressure and an external electric field. Considering the biaxial strain due to lattice mismatch or epitaxial growth, the uniaxial strain effects and the influences of the electron–phonon interaction as well as impurity–phonon interaction including the effects of interface-optical phonon modes and half-space phonon modes, the binding energies as functions of pressure, the impurity position, areal electron density and the phonon effect on the Stark energy shift are investigated. The numerical result shows that the contributions from the interface optical phonon mode with higher frequency and the LO-like half space mode to the binding energy and the Stark energy shift are important and obviously increase with increasing hydrostatic pressure, whereas the interface optical phonon mode with lower frequency and the TO-like half space mode are extremely small and are insensitive to the impurity position and hydrostatic pressure. It is also shown that the conductive band bending should not be neglected.

Effect of ternary mixed crystals on optical phonon modes in wurtzite nitride quantum well

Firstly, some results about the frequencies of phonons in wurtzite ternary mixed crystals (TMCs) fitted by several methods (modified random-element-isodiplacement model (MREI), virtual crystal approximation, and simplified coherent potential approximation, etc.) are compared. Then, combined with the continuous dielectric model and uniaxial crystal model, a fitting method available to experimental data is adopted to derive the dispersion relations of different kinds of optical phonon modes in TMC InxGa1－xN and AlxGa1－xN quantum wells. Furthermore, the variation of phonon modes dependent on the composition is analyzed. The results show that the fitting by the MREI for phonon frequencies of wurtzite TMCs with one-mode property agrees better with the experimental data. It can be also found that the optical phonon modes in quantum wells vary with the composition. The phonon modes, such as localized modes, interface modes, half-space modes, and propagating modes, exist in certain composition regions and frequency regions due to the anisotropy of phonon dispersion of wurtzite nitrides. Moreover, the shape of the same kind of phonon modes also varies with the composition.

Screening influence on the Stark effect of impurity states in strained wurtzite GaN/AlxGa1−xN heterojunctions under pressure

The screening effect of the random-phase-approximation on the states of shallow donor impurities in free strained wurtzite GaN/AlxGa1–xN heterojunctions under hydrostatic pressure and an external electric field is investigated by using a variational method and a simplified coherent potential approximation. The variations of Stark energy shift with electric field, impurity position, Al component and areal electron density are discussed. Our results show that the screening dramatically reduces both the blue and red shifts as well as the binding energies of impurity states. For a given impurity position, the change in binding energy is more sensitive to the increase in hydrostatic pressure in the presence of the screening effect than that in the absence of the screening effect. The weakening of the blue and red shifts, induced by the screening effect, strengthens gradually with the increase of electric field. Furthermore, the screening effect weakens the mixture crystal effect, thereby influencing the Stark effect. The screening effect strengthens the influence of energy band bending on binding energy due to the areal electron density.

Pressure influence on the Stark effect of impurity states in a strained wurtzite GaN/AlxGa1-xN heterojunction

A variational method is adopted to investigate the properties of shallow impurity states near the interface in a free strained wurtzite GaN/AlxGa1-xN heterojunction under hydrostatic pressure and external electric field by using a simplified coherent potential approximation. Considering the biaxial strain due to lattice mismatch or epitaxial growth and the uniaxial strains effects, we investigated the Stark energy shift led by an external electric field for impurity states as functions of pressure as well as the impurity position, Al component and areal electron density. The numerical result shows that the binding energy near linearly increases with pressure from 0 to 10 GPa. It is also found that the binding energy as a function of the electric field perpendicular to the interface shows an un-linear red shift or a blue shift for different impurity positions. The effect of increasing x on blue shift is more significant than that on the red shift for the impurity in the channel near the interface. The pressure influence on the Stark shift is more obvious with increase of electric field and the distance between an impurity and the interface. The increase of pressure decreases the blue shift but increases the red shift.

Temperature effects on interface polarons in a strained (111)-oriented zinc-blende GaN/AlGaN heterojunction under pressure

The properties of interface polarons in a strained (111)-oriented zinc-blende GaN/AlxGa1−xN heterojunction at finite temperature under hydrostatic pressure are investigated by adopting a modified LLP variational method and a simplified coherent potential approximation. Considering the effect of hydrostatic pressure on the bulk longitudinal optical phonon mode, two branches interface-optical phonon modes and strain, respectively, we calculated the polaronic self-trapping energy and effective mass as functions of temperature, pressure and areal electron density. The numerical result shows that both of them near linearly increase with pressure but the self-trapping energies are nonlinear monotone increasing with increasing of the areal electron density. They are near constants below a range of temperature whereas decrease dramatically with increasing temperature beyond the range. The contributions from the bulk longitudinal optical phonon mode and one branch of interface optical phonon mode with higher frequency are important whereas the contribution from another branch of interface optical phonon mode with lower frequency is extremely small so that it can be neglected in the further discussion.

Binding energies of excitons in a strained wurtzite GaN/AlGaN quantum well influenced byscreening and hydrostatic pressure

In the framework of effective mass and single-band approximations, avariational method combined with a self-consistent procedure is adopted todiscuss the binding energies of heavy-hole excitons in a strained wurtziteGaN/Al0.3Ga0.7N quantum well by considering the hydrostatic pressure effect and screeningdue to the electron–hole gas. The built-in electric field in such a structureproduced by spontaneous polarization and strain-induced piezoelectricpolarization is considered in our calculation. A simplified coherent potentialapproximation is extended to calculate the energy gaps of the ternary mixed crystalAlxGa1−xN. The result indicates that the binding energies of excitons increase nearly linearly withpressure even when taking into consideration the modification of strain. It is also foundthat the percentage increase of the binding energy with pressure is influenced by theelectron–hole density due to the influence of pressure on the screening and exclusion effects.The excitonic binding energies increase obviously with decreasing barrier thickness due tothe built-in electric field.

Stark effect of donor impurity states in strained heterojunctions under pressure

A modified variational method is adopted to investigate the binding energies of the shallow impurity states near the interface of a strained GaN/AlxGa1-xN heterojunction by using a simplified coherent potential approximation. The relations between the impurity binding energies and pressure, the impurity position, electric field strength and the Al components are calculated for strained zinc-blende GaN/AlxGa1-xN heterojunctions with (001) and (111) orientations respectively. The result indicates that the binding energy of impurity state nearly linearly increases with pressure. The Stark effect on the binding energy as a function of electric field shows blue or red shift in the spectra for different impurity positions. The results corresponding to (001) and (111) orientations are compared. It is found that the effect on the binding energy of Al component is obvious. For an impurity located in the channel side and comparatively far from the interface, a monotonic increase of the binding energies will appear with increasing Al content due to the stronger two-dimensional properties of the electrons, and pressure enhances the increase of amplitude. Whereas for an impurity located in the barrier side, the increase of Al content will weaken the bound between the impurity and the electron to decrease the binding energy.

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn1-xCdxSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models.

Scattering Mechanisms in Heavily Doped Semiconductors. II. Effect of Mass Anisotropy and Multiple Scattering

Resistivities and Hall coefficients of unstressed and uniaxially saturation-stressed samples of heavily antimony-doped germanium in the metallic concentration range are investigated by the degenerate electron gas model with impurity scattering. The effect of anisotropic effective mass is investigated, firstly by the variational method, and secondly by solving the Boltzmann equation directly in a numerical method. The anisotropy of screened impurity potential is fully taken into account within the linear screening theory. The effect of finite electron life time is studied by a simplified coherent potential approximation. By these effects, in addition to the effect of the nonlinear screening and many-body interaction investigated in the authors' previous paper, the agreement with experiments on the unstressed samples is much improved and a good agreement is obtained on the saturation-stressed samples.