Valence Band Mixing Research Articles

Impact of band structure and transition matrix elements on polarization properties of the photoluminescence of semipolar and nonpolar InGaN quantum wells

AbstractPartial or full linear polarization is characteristic for the spontaneous emission of light from semipolar and nonpolar InGaN quantum wells. This property is an implication of the crystalline anisotropy as a basic property of the wurtzite structure. The influence of this anisotropy on the band structure and the transition matrix elements was calculated by a ${\bf k}\cdot {\bf p}$‐method for arbitrary quantum well orientations with respect to the c‐axis; results are shown here in detail. Optical polarization is a direct consequence of a broken symmetry, mainly affecting the transition matrix elements from the conduction to the valence bands. Furthermore, the strain of the InGaN quantum well strongly depends on the crystal orientation of the substrate, resulting in a valence band mixing. The composition of the eigenfunctions has emerged to be most important for the polarization dependence of strained semipolar and nonpolar InGaN QW. The matrix elements, in combination with the thermal occupation of the bands, determine the polarization of the spontaneously emitted light. Our photoluminescence measurements of nonpolar QW match well with this model. However, in contrast to calculations with standard band parameters, the two topmost subbands show a larger separation in the emitted energy.

Barrier effects on the optoelectronic properties of GaN-based irregular multiple quantum wells for dichromatic white LEDs

The GaN-based irregular multiple quantum well (IMQW) structures for dichromatic white light-emitting diodes (LEDs) are assembled by two different types of QWs emitting complementary blue and yellow light. The electronic and optical properties of the designed GaN-based IMQW structures are investigated in details by fully considering the effects of strain, well-coupling, valence band-mixing and polarization effect by employing a newly modified theoretical model based on the k·p theory. The influences of the height and thickness of the barrier between blue QWs and yellow QWs together with the polarization effect on the optoelectronic properties of GaN-based IMQW structure are analyzed. Numerical results show that the ratio of the two color lights emmited from the IMQW structure for dichromatic white LED can be tuned by changing the height and thickness of the barrier between two types of QWs.

Electronic states in the valence band of a cylindrical ZnSe quantum dot

Electronic states in the valence band of a cylindrical ZnSe quantum dot are studied with allowance for the valence band mixing. Dependences of the wave functions and energy levels on the quantum dot radius are calculated. The influence of a magnetic field parallel to the quantum dot radius on the energy levels is also considered.

Strain effects on optical polarisation properties in (112̄2) plane GaN films

We present the theoretical results of the electronic band structure of wurtzite GaN films under biaxial strains in the (112̄2)-plane. The calculations are performed by the k · p perturbation theory approach through using the effectivemass Hamiltonian for an arbitrary direction. The results show that the transition energies decrease with the biaxial strains changing from −0.5% to 0.5%. For films of (112̄2)-plane, the strains are expected to be anisotropic in the growth plane. Such anisotropic strains give rise to valence band mixing which results in dramatic change in optical polarisation property. The strain can also result in optical polarisation switching phenomena. Finally, we discuss the applications of these properties to the (112̄2) plane GaN-based light-emitting diode and lase diode.

Design of columnar quantum dots for polarization-independent emission using 8–band k·p method

Control of the polarization of the emitted light can be highly beneficial for certain optoelectronic applications such as optical amplifiers. It has been recently demonstrated experimentally that semiconductor quantum dots with large height to base length aspect ratio are able to emit polarization-independent light from the edge of the wafer. However, analysis of the physics responsible for the observed polarization properties of such nano–objects (like columnar quantum dots or quantum rods) is still rather limited. In particular, the role of the material surrounding the columnar QD on the strain and thus on the polarization properties has not been considered previously. We report here, based on original software, the results of eight–band k·p calculations of the electronic and polarization properties of columnar InyGa1-yAs quantum dots (CQD) with high aspect ratio (up to 6) embedded in an InxGa1-xAs/GaAs quantum well. We calculate the relative intensities of transverse-magnetic (TM) and transverse-electric (TE) linear polarized light emitted from the edge of the semiconductor wafer as a function of the two main factors affecting the heavy hole – light hole valence band mixing and hence the polarization dependent selection rules for the optical transitions, namely i) the composition contrast y/x between the dot material and the surrounding well, and ii) the dot aspect ratio. Our numerical results show, in contrast to the previously reported expectations, that the former is the main driving parameter for tuning the polarization properties. This is explained analyzing the biaxial strain in the CQD, based on which it is possible to predict on the TM to TE intensity ratio.

Polarization sensitive lateral photoconductivity in GaAs/AlGaAs quantum well based structures on low-temperature grown GaAs(001)

Polarization-resolved lateral-photoconductivity measurements are reported on device structures made of GaAs/Al0.3Ga0.7As quantum wells sandwiched between low-temperature grown GaAs(001) layers. The mesa device structures have long length (3 mm∥y) and narrow width (10 and 20 μm∥x) in the (001) plane. For light incident along [001], the ground state light-hole exciton transition is much stronger for light polarization E∥x, compared to E∥y. The heavy-hole exciton transition shows a weaker polarization anisotropy of opposite sign, being stronger for E∥y. Through calculations based on the Bir–Pikus Hamiltonian, the observed in-plane optical polarization anisotropy is shown to arise from valence band mixing induced by anisotropic strain in the plane of quantum wells.

Optical gain characteristics of staggered InGaN quantum wells lasers

Staggered InGaN quantum wells (QWs) are analyzed as improved gain media for laser diodes (LDs) lasing at 440 and 500 nm. The calculation of band structure is based on a 6-band k⋅p method taking into account the valence band mixing, strain effect, and spontaneous and piezoelectric polarizations as well as the carrier screening effect. Staggered InGaN QWs with two-layer and three-layer step-function like In-content InGaN QWs structures are investigated to enhance the optical gain as well as to reduce the threshold current density for LDs emitting at 440 and 500 nm. Our analysis shows that the optical gain is enhanced by 1.5–2.1 times by utilizing the staggered InGaN QW active region emitting at 440 nm, which leads to a reduction of the threshold current density up to 24% as compared to that of the conventional InGaN QW laser. Staggered InGaN QWs with enhanced optical gain shows significantly reduced blue-shift as carrier density increases, which enables nitride QWs with high optical gain in the green spectral regime. The use of green-emitting three-layer staggered InGaN QW is also expected to lead to reduction in the threshold carrier density by 30%.

Reversal of Coherently Controlled Ultrafast Photocurrents by Band Mixing in Undoped GaAs Quantum Wells

It is demonstrated that valence-band mixing in GaAs quantum wells tremendously modifies electronic transport. A coherent control scheme in which ultrafast currents are optically injected into undoped GaAs quantum wells upon excitation with femtosecond laser pulses is employed. An oscillatory dependence of the injection current amplitude and direction on the excitation photon energy is observed. A microscopic theoretical analysis shows that this current reversal is caused by the coupling of the light- and heavy-hole bands and that the hole currents dominate the overall current response. These surprising consequences of band mixing illuminate fundamental physics as they are unique for experiments which are able to monitor electronic transport resulting from carriers with relatively large momenta.

Eight-band k⋅p calculations of the composition contrast effect on the linear polarization properties of columnar quantum dots

We present eight-band k⋅p calculations of the electronic and polarization properties of columnar InzGa1−zAs quantum dots (CQD) with high aspect ratio embedded in an InxGa1−xAs/GaAs quantum well. Our model accounts for the linear strain effects, linear piezoelectricity, and spin-orbit interaction. We calculate the relative intensities of transverse-magnetic (TM) and transverse-electric (TE) linear polarized light emitted from the edge of the semiconductor wafer as a function of the two main factors affecting the heavy hole—light hole valence band mixing and hence, the polarization dependent selection rules for the optical transitions, namely, (i) the composition contrast z/x between the dot material and the surrounding well and (ii) the dot aspect ratio. The numerical results show that the former is the main driving parameter for tuning the polarization properties. This is explained by analyzing the biaxial strain in the CQD, based on which it is possible to predict the TM to TE intensity ratio. The conclusions are supported by analytical considerations of the strain in the dots. Finally, we present the compositional and geometrical conditions to achieve polarization independent emission from InGaAs/GaAs CQDs.

Calculation of valence band structures of InAs/GaAs quantum ring and quantum dot: using numerical Fourier transform method

This article puts forward a new method in calculating the band structures of low-dimensional semiconductor structures. In this study, the valence band structures of InAs/GaAs quantum ring and lens-shaped quantum dot are calculated with four-band model, in the framework of effective-mass envelope function theory. To determine the Hamiltonian matrix elements, this article develops the numerical Fourier transform method instead of the widely used analytical integral method. The valence band mixing is considered. The hole energy levels change dramatically with the geometrical parameters of the quantum ring and quantum dot. It is demonstrated that numerical Fourier transform method can be adopted in low-dimensional structures with any shape. The results of Fourier transform method are consistent with the ones of analytical integral in literature; and they are helpful for studying and fabricating optoelectronic devices.

Exciton states and tunneling in semimagnetic asymmetric double quantum wells

Exciton level structure and interwell relaxation are studied in Cd(Mn,Mg)Te-based asymmetric double quantum wells (ADQWs) by a steady-state optical spectroscopy in magnetic fields up to B = 10 T. The as grown heterostructures with CdTe QWs and nonmagnetic interwell CdMgTe barrier were subjected to a rapid temperature annealing to introduce Mn and Mg atoms from opposite barriers inside the QWs which results in a formation of the ADQW with completely different magnetic field behavior of the intrawell excitons. The giant Zeeman effect in the QW with magnetic Mn ions gives rise to a crossing of the ground exciton levels in two QWs at BC ∼ 3–6 T which is accompanied by a reverse of the interwell tunneling direction. In a single-particle picture the exciton tunneling is forbidden at B < 1 T as supported by calculations. Experimentally, nevertheless, a very efficient interwell relaxation of excitons is found at resonant excitation in the whole magnetic field range, regardless of the tunneling direction, emphasizing importance of excitonic correlations in the interwell tunneling. At nonresonant excitation an unexpectedly slow relaxation of the σ−-polarized excitons from the nonmagnetic QW to the σ+-polarized ground state in the semimagnetic QW is observed at B > BC, giving rise to a nonequilibrium distribution of excitons in ADQW. A strong dependence of the total circular polarization degree on the hh–lh splitting Δhh–lh in the nonmagnetic QW is found and attributed to the spin dependent interwell tunneling controlled by an exciton spin relaxation. Different charge-transfer mechanisms are analyzed in details and an elastic scattering due to a strong disorder is suggested as the main tunneling mechanism with the underlying influence of the valence band-mixing.

Design of Phosphor-Free Single-Chip White Light-Emitting Diodes Using InAlGaN Irregular Multiple Quantum Well Structures

A novel approach for the design of phosphor-free single-chip white light-emitting diodes (LEDs) is proposed by employing InAlGaN irregular multiple quantum well (IMQW) structures. The electronic and optical properties of the designed InAlGaN IMQWs are analyzed in detail by fully considering the effects of strain, well-coupling, valence band-mixing, and quasi-bound states using the effective-mass Hamiltonian deduced from k · p theory. For comparison, three different types of InAlGaN IMQW structures with ultra-wide band spontaneous emission spectra are analyzed, and the results show that phosphor-free single-chip white light LEDs with more than 200 nm emission band can be obtained using properly designed InAlGaN IMQW structures.

Design Analysis of Staggered InGaN Quantum Wells Light-Emitting Diodes at 500–540 nm

Staggered InGaN quantum wells (QWs) are analyzed as improved active region for light-emitting diodes (LEDs) emitting at 500 nm and 540 nm, respectively. The calculation of band structure is based on a self-consistent 6-band kmiddotp formalism taking into account the valence band mixing, strain effect, and spontaneous and piezoelectric polarizations as well as the carrier screening effect. Both two-layer staggered InxGa1- xN/InyGa1- yN QW and three-layer staggered InyGa1- yN/InxGa1- xN/InyGa1- yN QW structures are investigated as active region to enhance the spontaneous emission radiative recombination rate (R sp) for LEDs emitting at 500 nm and 540 nm. Analysis of the spontaneous emission radiative recombination rate (R sp) shows significant enhancement for both two-layer staggered InGaN QW and three-layer staggered InGaN QW, in comparison to that of the conventional InzGa1- zN QW. The studies of the carrier lifetime indicate a significant reduction of the carrier lifetime for staggered InGaN QWs, which contribute to the enhancement of the radiative efficiency for both two-layer staggered InGaN QW and three-layer staggered InGaN QW LEDs emitting at 500 nm and 540 nm.

Are AlN and GaN substrates useful for the growth of non‐polar nitride films for UV emission? The oscillator strength perspective

AbstractThe authors present results of a perturbation theory study of the effect of strain on the oscillator strengths of interband transitions in wurtzite group‐III‐nitride films suitable for ultraviolet light emission applications. Ternary alloy films are investigated, which can be pseudomorphically grown on GaN and AlN substrates with nonpolar M ‐plane (1$ \bar 1 $00) and A ‐plane (11$ \bar 2 $0) orientations. Valence band mixing, induced by the anisotropic in‐plane strain that arises in these films, can have a dramatic influence on the optical polarization properties of the transitions. An increased efficiency of light emission in the 0.21 μm to 0.25 μm spectral range is best achieved using AlN substrates, on which both Al1–x Gax N and Al1–x Inx N films experience compressive strain. On GaN substrates, Al1–x Gax N films experience tensile strain and will exhibit poor light emission efficiency. However Al1–x Inx N films on GaN substrates can emit light efficiently in the 0.3 μm to 0.36 μm spectral range. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Design and numerical analysis of a polarization-insensitive quantum well optoelectronic integrated amplifier-switch

A quantum well optoelectronic integrated amplifier-switch is proposed, in which the device operation mode (amplification or switching) is independent of input light polarization. It is composed of a tensile-strained periodic coupled-double-quantum well heterojunction phototransistor and a compressive strained multi quantum wells laser diode. This structure shows unresolved heavy hole and light hole transitions due to applying tensile strain in absorption region of phototransistor. Hence, the absorption spectra for TE and TM polarizations are almost equal which provide polarization independent operation. A rigorous numerical analysis based on the device rate equations for dynamic response and relative intensity noise is presented, for which we calculate the laser diode gain and phototransistor electroabsorption coefficient. The Hamiltonian of strained quantum well structure is numerically solved by Transfer matrix method taking into accounts the valence band mixing between heavy hole and light hole. In order to calculate the electroabsorption coefficient, the exciton equation is solved numerically in momentum space using Gaussian Quadrature method. Langevin noise in laser part, phototransistor current noise, input power noise and noise due to the internal optical feedback from laser to phototransistor are considered as the device noise sources. It is shown that the higher gain of the phototransistor for TM polarization and lower threshold current of compressive strained laser diode lead to reduction of the RIN in amplification mode.

Self-Consistent Analysis of Strain-Compensated InGaN–AlGaN Quantum Wells for Lasers and Light-Emitting Diodes

Strain-compensated InGaN-AlGaN quantum wells (QW) are investigated as improved active regions for lasers and light emitting diodes. The strain-compensated QW structure consists of thin tensile-strained AlGaN barriers surrounding the InGaN QW. The band structure was calculated by using a self-consistent 6-band kmiddotp formalism, taking into account valence band mixing, strain effect, spontaneous and piezoelectric polarizations, as well as the carrier screening effect. The spontaneous emission and gain properties were analyzed for strain-compensated InGaN-AlGaN QW structures with indium contents of 28%, 22%, and 15% for lasers (light-emitting diodes) emitting at 480 (500), 440 (450), and 405 nm (415 nm) spectral regimes, respectively. The spontaneous emission spectra show significant improvement of the radiative emission for strain-compensated QW for all three structures compared to the corresponding conventional InGaN QW, which indicates the enhanced radiative efficiency for light emitting diodes. Our studies show the improvement of the optical gain and reduction of the threshold current density from the use of strain-compensated InGaN-AlGaN QW as active regions for diode lasers.

Optical polarization characteristics of m-oriented InGaN/GaN light-emitting diodes with various indium compositions in single-quantum-well structure

Spontaneously polarized light emission from m-plane InGaN/GaN light-emitting diodes was studied as a function of In composition in the InGaN single quantum-well layer. Emission wavelength was varied between 394 and 472 nm. A strong correlation was confirmed between optical polarization and In composition; the higher the In composition, the stronger the optical polarization. The photon-energy difference between the emission spectra associated with the two polarizations, ΔM, was evaluated as a function of current. ΔM exhibited a negative monotonic current dependence for the 394 nm emitting sample and the dependence was changed to positive monotonic as the wavelength became longer towards 472 nm. This change was tentatively attributed to the valence band mixing and the crystal momentum conservation that became relevant with the band filling. ΔM and optical polarization exhibited only a moderate correlation; the Fermi–Dirac function has been used to explain the weakened optical polarization under increased current injection.

Self-consistent gain analysis of type-II ‘W’ InGaN–GaNAs quantum well lasers

Type-II InGaN–GaNAs quantum wells (QWs) with thin dilute-As (∼3%) GaNAs layer are analyzed self-consistently as improved III-nitride gain media for diode lasers. The band structure is calculated by using a six-band k⋅p formalism, taking into account valence band mixing, strain effect, spontaneous and piezoelectric polarizations, as well as the carrier screening effect. The type-II InGaN–GaNAs QW structure allows large electron-hole wave function overlap by confining the hole wave function in the GaNAs layer of the QW. The findings based on self-consistent analysis indicate that type-II InGaN-GaNAs QW active region results in superior performance for laser diodes, in comparison to that of conventional InGaN QW. Both the spontaneous emission radiative recombination rate and optical gain of type-II InGaN–GaNAs QW structure are significantly enhanced. Reduction in the threshold current density of InGaN–GaNAs QW lasers is also predicted.

Optical polarization properties of interband transitions in strained group-III-nitride alloy films on GaN substrates with nonpolar orientation

The authors present results of a perturbation theory study of the combined effects of composition and anisotropic in-plane strain on the optical polarization properties of the three interband transitions in the vicinity of the fundamental energy gap of wurtzite group-III-nitride alloy films, pseudomorphically grown on GaN substrates with nonpolar orientation such as M-plane GaN(11¯00). Valence band mixing induced by the anisotropic in-plane strain is shown to have a dramatic influence on the optical polarization properties. The results indicate that an increased efficiency of light emission in the visible spectral range can be achieved with compressively strained InxGa1−xN active layers. While AlxGa1−xN layers under tensile strain will exhibit a very poor light emission efficiency in the ultraviolet (UV) spectral range, efficient emission in the UV range can instead be achieved with InxAl1−xN films. These results also hold for alloy films on A-plane GaN(112¯0) substrates.

Optical gain analysis of strain-compensated InGaN–AlGaN quantum well active regions for lasers emitting at 420–500 nm

Strain-compensated InGaN quantum wells with tensile AlGaN barriers are analyzed as improved gain media for laser diodes emitting at 420–500 nm. The band structure is calculated using the 6-band k ·p formalism, taking into account valence band mixing, strain effect, and spontaneous and piezoelectric polarizations. The optical gain analysis exhibits significant improvement in the peak optical gain and differential gain for the strain-compensated structures. The calculation also shows a significant reduction of threshold carrier density and current density for diode lasers employing the strain-compensated InGaN–AlGaN QW active regions.