Topmost Valence Band Research Articles

Pressure-Driven Reordering of Valence Band States in AlGaN/AlN Quantum Wells

We study theoretically the in uence of external hydrostatic pressure on the valence band structure in [0001]-oriented AlxGa1−xN/AlN quantum wells used in deep-ultraviolet light emitting devices. The calculations performed using the multi-band k·p method with excitonic e ects show that for AlxGa1−xN/AlN quantum wells with x = 0.7 and quantum well width of 1.5 nm, reordering of the topmost valence subbands having di erent symmetries occurs with increasing pressure. In these structures, at low pressure values the topmost valence level is of Γ9 symmetry whereas it changes to the Γ7 state for pressures about 2.5 GPa. We also nd that the excitonic e ects increase the critical value of pressure at which the change in the polarization of the emitted light occurs to 7 GPa. This behavior is opposite to the pressure-dependent reordering of the topmost valence band states in thin GaN/AlGaN quantum wells which occurs from Γ7 to Γ9 states. PACS: 78.55.Cr, 78.67.De, 62.50.−p

The contribution of quantum confinement to optical anisotropy of a-plane Cd0.06Zn0.94O/ZnO quantum wells

We investigated quantum size effects on polarized photoluminescence (PL) from a-plane Cd0.06Zn0.94O/ZnO quantum wells (QWs) with different well widths (LW). The degree of polarized PL at 300 K increased with a narrowing of LW, which obeyed the polarization selection rule based on a Boltzmann-like distribution. Furthermore, the narrowing of LW enhanced the anisotropic lattice distortions in well layers along the growing direction, which resulted in an increase of energy separation between the two topmost valence band levels. The effect of quantum confinement on polarized PL of QWs was accompanied by a change of structural symmetry of the well layers.

Large optical polarization anisotropy due to anisotropic in-plane strain in m-plane GaInN quantum well structures grown on m-plane 6H-SiC

We investigated the optical polarization anisotropy of m-plane GaInN/GaN quantum well structures on m-plane SiC and bulk GaN substrates. On bulk GaN, the degree of polarization increases with increasing indium content according to the larger strain-induced separation of the topmost valence bands. On m-plane SiC, however, we observe constantly large polarization ratios of around 90% and more. From an x-ray strain state analysis and calculations of the valence band energies, we find that an anisotropic strain of the GaN buffer layer leads to a very strong separation of the topmost valence bands resulting in a large degree of polarization.

Confinement effects on valence-subband character and polarization anisotropy in (112¯2) semipolar InGaN/GaN quantum wells

We perform self-consistent Schrödinger-Poisson simulations on (112¯2) In-GaN/GaN quantum wells (QW). By solving the 6 × 6 k·p Hamiltonian, including strain and polarization fields, we study the separation, ordering, and wavefunction character of the topmost valence bands in the QW and their dependence on In composition and QW width. Our results show that quantum confinement has only slight effects on the ordering and the character of the valence states and therefore cannot be the cause of the experimentally observed optical polarization switching. Instead, the switching may be due to the inhomogeneous strain distribution in (112¯2) InGaN films with high In composition.

Theory of non-polar and semi-polar nitride semiconductor quantum-well structures

We investigate the electronic and optical properties of non-polar a- and m-planes and semi-polar InGaN–GaN quantum-well structures using the multiband effective-mass theory taking into account the many-body effects. These results are compared with those of (0 0 0 1) oriented c-plane wurtzite InGaN–GaN quantum wells. We derive explicitly the valence-band Hamiltonian and interband optical matrix elements with polarization dependence for an arbitrary crystal polar angle θ and an azimuthal angle φ. The average hole effective masses of the topmost valence band along the wave vector perpendicular to the crystal orientation for the non-polar and semi-polar cases are substantially lower than that of the c-plane case. It is found that the azimuthal angle φ does not change the shape of the band structure but shifts the sub-band position. Thus the transition energy will be dependent on both the polar angle θ and the azimuthal angle φ. It is expected that the optical matrix elements are strongly anisotropic and optical gain would be larger for the non-polar and semi-polar cases because of the vanishing of the internal electric fields.

Dependence on composition of the optical polarization properties of m-plane InxGa1−xN commensurately grown on ZnO

We have grown m-plane InxGa1−xN (x = 0.24-0.43) commensurately on m-plane ZnO by the use of a low temperature epitaxial growth technique and investigated its optical properties. We found that the critical thickness for strain relaxation in the InGaN films prepared by the present technique is at least one order of magnitude larger than those reported by the other techniques. Polarized optical absorption measurements revealed that the allowed optical transition between the conduction band and the topmost valence band in m-plane InxGa1−xN (x = 0.24−0.43) on ZnO is for light polarized along c-axis. We found that the valence band splitting energy strongly depends upon the In composition. The values of the deformation potentials of InN were determined as D3 = 2.4 eV, D4 = −6.3 eV, and D5 = −1.2 eV, by fitting the experimental results with theoretical calculations based on the k·p approach.

Optical Gain Analysis of Graded InGaN/GaN Quantum-Well Lasers

Optical properties of graded InGaN/GaN quantum well (QW) lasers are analyzed as improved gain media for laser diodes emitting near 500 nm. These results are compared with those of conventional InGaN/GaN QW structures. The heavy-hole effective mass around the topmost valence band is found to nearly not be affected by the inclusion of the graded layer. The graded InGaN/GaN QW structure shows a much larger matrix element than the conventional InGaN/GaN QW structure. The radiative current density dependences of the optical gain are similar to each other. However, the graded QW structure is expected to have lower threshold current density than the conventional QW structure because the former has a lower threshold carrier density than the latter.

Optical Properties of Staggered InGaN/InGaN/GaN Quantum-Well Structures with Ga- and N-Faces

Optical properties of staggered InGaN/InGaN/GaN quantum-well (QW) light-emitting diodes with Ga- and N-faces were investigated using the multiband effective mass theory. The staggered QW structure shows that the carrier density dependence of the transition wavelength is largely reduced compared to the conventional QW structure. On the other hand, the heavy-hole effective mass around the topmost valence band is almost unaffected by the polarity. The N-face staggered InGaN/InGaN/GaN QW structure has a greater spontaneous emission peak than the Ga-face staggered InGaN/InGaN/GaN QW structure because the former has a larger matrix element than the latter. We expect the N-face staggered InGaN/InGaN/GaN QW structure to have improved characteristics compared with the Ga-face staggered InGaN/InGaN/GaN QW structure.

Polarization switching of the optical gain in semipolar InGaN quantum wells

AbstractWe investigate the influence of polarization switching on the optical gain of semipolar InGaN quantum wells (QWs) depending on indium content and charge carrier concentration using self‐consistent 6 × 6 k·p‐band structure calculations. The semipolar planes considered here are the $(11\bar {2}2)$‐ and the $(20\bar {2}1)$‐plane. In contrast to the $(20\bar {2}1)$‐plane, the dominant polarization of the optical gain in a QW on the $(11\bar {2}2)$‐plane can depend on both the indium content and the charge carrier concentration, as reported from experiments. These effects are explained by a detailed analysis of the wave function composition of the topmost valence bands in a semipolar QW.

Silicon concentration dependence of optical polarization in AlGaN epitaxial layers

The optical polarization of Si-doped AlxGa1−xN epitaxial layers (x=0.37–0.95) has been studied by means of photoluminescence (PL) spectroscopy. The predominant polarization component of the band-edge PL switched from E⊥c to E∥c at an Al composition between 0.68 and 0.81. This critical Al composition was much higher than in previous reports for AlGaN epitaxial layers. In addition, the predominant polarization in Al0.55Ga0.45N epitaxial layers switched from E⊥c to E∥c with increasing Si concentration. Therefore, the topmost valence band changed from the heavy-hole band to the crystal-field split-off-hole band with decreasing in-plane compressive strain induced by Si doping.

Role of strain in polarization switching in semipolar InGaN/GaN quantum wells

The effect of strain on the valence-band structure of (112¯2) semipolar InGaN grown on GaN substrates is studied. A k⋅p analysis reveals that anisotropic strain in the c-plane and shear strain are crucial for deciding the ordering of the two topmost valence bands. The shear-strain deformation potential D6 is calculated for GaN and InN using density functional theory with the Heyd–Scuseria–Ernzerhof hybrid functional [J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 124, 219906 (2006)]. Using our deformation potentials and assuming a pseudomorphically strained structure, no polarization switching is observed. We investigate the role of partial strain relaxation in the observed polarization switching.

Characterising the degree of polarisation anisotropy in an a ‐plane GaN film

AbstractWe have performed a thorough characterisation of an a ‐plane GaN film, using X‐ray diffraction reciprocal space mapping, k·p theory and polarised photoluminescence spectroscopy Within the plane of the film and along the growth direction, the strain was found to be compressive and tensile respectively. The relative oscillator strength of the transitions involving the topmost valence bands has been calculated as a function of strain. We find that using the experimentally determined strain values as input parameters to the theoretical model, results in good agreement between the predicted relative oscillator strengths and the degree of optical polarisation anisotropy measured in the low temperature photoluminescence spectroscopy. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electronic structure and optical properties of ZnSiO3 and Zn2SiO4

The electronic structure and optical properties of orthorhombic, monoclinic, and rhombohedral (corundum type) modifications of ZnSiO3, and of rhombohedral, tetragonal, and cubic (spinel type) modifications of Zn2SiO4 have been studied using ab initio density functional theory calculations. The calculated fundamental band gaps for the different polymorphs and compounds are in the range 2.22–4.18 eV. The lowest conduction band is well dispersive similar to that found for transparent conducting oxides such as ZnO. This band is mainly contributed by Zn 4s electrons. The carrier effective masses were calculated and compared with those for ZnO. The topmost valence band is much less dispersive and contributed by O 2p and Zn 3d electrons. From the analysis of charge density, charges residing in each site, and electron localization function, it is found that ionic bonding is mainly ruling in these compounds. The calculated optical dielectric tensors show that the optical properties of ZnSiO3 and Zn2SiO4 are almost isotropic in the visible part of the solar spectra and depend negligibly on the crystal structure. Within the 0–4 eV photon energy range, the calculated magnitude of the absorption coefficient, reflectivity, refractive index, and extinction coefficient are smaller than 103 cm−1, 0.15, 2.2, and 0.3, respectively, for all the ZnSiO3 and Zn2SiO4 phases considered in this work. This suggests that zinc silicates can be used as antireflection coatings.

Dip-shaped InGaN/GaN quantum-well light-emitting diodes with high efficiency

Optical properties of dip-shaped InGaN/GaN quantum well (QW) light-emitting diodes are investigated using the multiband effective-mass theory. These results are compared with those of conventional and staggered InGaN/GaN QW light-emitting diodes. In the case of a dip-shaped QW structure, the carrier density dependence of the transition wavelength is reduced due to a relatively small internal field effect. Also, we observe that the heavy-hole effective mass around the topmost valence band is greatly reduced with the inclusion of the dip-shaped layer. The spontaneous emission peak of a dip-shaped QW structure is shown to be larger than that of a staggered QW structure or a conventional QW structure. This is mainly due to the fact that a dip-shaped QW structure has larger optical matrix elements produced by Kane’s parameter.

Optical Anisotropy Control of Non-c-plane InGaN Quantum Wells

A method to control the optical polarization of non-c-plane InGaN quantum wells (QWs) is proposed. Firstly, it is described the numerical and analytical solutions of the valence band eigenenergies and eigenfunctions for non-c-plane nitride semiconductors. It is found that anisotropic strain dominates optical anisotropy due to the small spin–orbit interaction and the large lattice mismatch. Subsequently, it is introduced the InGaN/AlGaN QW structure instead of the InGaN/GaN QW in order to manipulate the eigenenergies of the two topmost valence bands. This resulted in optical polarization switching. We conclude with a discussion of relevant computational results.

Classification of hydrides according to features of band structure

Band structure of hydrides has been studied by density functional calculations. From analysis of band structures, it is found that, similar to semiconductors, some hydrides possess open fundamental band gap, and can be classified according to the following three characteristic features. The first is based on the value of the fundamental band gap and, therefore, the hydrides have been classified as narrow or wide band gap materials. The second feature is based on a comparison of the relative location in k space of the bottommost conduction band and topmost valence band (VB). Thus, hydrides can be classified as either direct or indirect band gap materials. The third feature is based on the origin of the topmost valence band and depends on the dominant contribution of s-, p-, and d-electrons to the topmost VB. According to this criterion, hydrides can be classified as type s, p, d or hybridised materials. This classification will be useful in the application of hydrides for the construction and processing of electronic devices within the framework of the recent innovations in ‘hydride electronics’.

Strain effect on polarized optical properties of c -plane GaN and m -plane GaN

The polarized optical property of c-plane and m-plane GaN with varying strain was discussed by analyzing the changes of relative oscillator strength (ROS) of the three transitions related to the top three valence bands. The ROS was calculated by applying the effective-mass Hamiltonian based on k · p perturbation theory. For c-plane GaN, it was found that ROS of X> -like state and Y>-like state were superposed with each other. Especially, they increased with compressive strain, while that of |Z> decreased in the second band. For m-plane GaN under compressive strain, the first three bands were dominated by |X>, |Z> and |Y>-like states, respectively, which led to nearly linearly-polarized light emissions. With compressive strain, the ROS of |X>-like state increased more rapidly than |Z>-like state in the topmost valence band. As a result, TE mode emissions from both c-plane and m-plane GaN increased more rapidly than TM mode emission with compressive strain, leading to larger polarization degree. Experimental results of luminescences from InGaN/GaN quantum wells showed good coincidence with our theoretical calculations.

Strain-induced modulation of band structure of silicon

This work presents ab initio study of strain-induced modulation of band structure of Si. It is shown that at straining pressures >12GPa, band structure of Si can be turned from indirect to direct. Both the bottommost conduction band and topmost valence band are located at the Γ point. The conduction band minimum at the Γ point of the strained Si is found to be much more dispersive than that at the X point of the unstressed Si. Consequently, electrical conductivity through the Γ valley is suggested to be more superior than the X point of the unstressed Si. Barrier height, which is needed to transfer electrons in the Γ point to X∕L points or from Γ point to X∕L to Γ point have been calculated. The results have been applied to explain peculiarities of electronic structure and light emission of Si based materials containing dislocations and voids.

Hydrides as materials for semiconductor electronics

Systematic studies using density functional theory have shown that some hydrides possess the features of semiconductors. These features include larger fundamental band gap, well dispersed bottom-most conduction band and/or top-most valence band, small electron/hole effective masses and small intrinsic carrier concentration. It is demonstrated that depending upon the composition, hydrides possess a wide range of band gap values and hence they can be regarded as materials for narrow to wide band gap semiconducting applications. The possibility of designing hydride-based p–n junctions, and also their advantages as well as deficiencies compared to existing oxide semiconductors, are discussed. Replacing oxide-based semiconductors by hydrides can help to avoid problems such as formation of an oxide layer, band offsets, large concentration of defect states at the interface between the oxide and semiconductor, etc. Moreover, hydrides can be regarded as an alternative to conventional semiconductors and hence can be used in future-generation electronic devices called “hydride electronics”.

Valence band engineering for remarkable enhancement of surface emission in AlGaN deep‐ultraviolet light emitting diodes

AbstractValence band engineering for remarkable enhancement of surface emission in AlGaN deep‐ultraviolet (UV) light emitting diodes (LEDs) has been theoretically investigated by the calculation using the 6×6 k·p Hamiltonian. It has already been pointed out that the topmost valence band in deep‐UV AlGaN material has a Z‐like character and this causes the c‐axis polarized emission unfavourable for light extraction from c‐plane based LEDs. We have found, in this study, that this unfavourable polarization can be switched into favourable in‐plane polarization by decreasing quantum well (QW) width and/or introducing in‐plane compressive strain, which cause band‐crossing and change the character of the topmost band. It is also shown that such polarization changes occur in the QWs on semipolar substrates although that does not take place in those on nonpolar substrates. Furthermore, we have derived the condition of the polarization switch as an approximate analytical expression which could be useful for device structural design. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)