Valence Band Ordering Research Articles

Inversion of absorption anisotropy and bowing of crystal field splitting in wurtzite MgZnO

The anisotropic optical properties of wurtzite MgxZn1−xO thin films (0≤x≤0.45) grown on m-plane ZnO substrates by plasma assisted molecular beam epitaxy are studied using spectroscopic ellipsometry at room temperature. The data analysis provides the dielectric functions for electric field polarizations perpendicular and parallel to the optical axis. The splitting between the absorption edges of the two polarization directions decreases between x = 0 and x = 0.24, while an inverted absorption anisotropy is found at higher Mg content, indicating a sign change of the crystal field splitting Δcr as for the spin orbit parameter. The characteristic energies such as exciton binding energies and band gaps are determined from the analysis of the imaginary parts of the dielectric functions. In particular, these data reveal a bowing parameter of b=−283 meV for describing the compositional dependence of the crystal field splitting and indicate Δcr=−327 meV for wurtzite MgO. The inverted valence band ordering of ZnO (Γ7-Γ9-Γ7) is found to be preserved with increasing Mg content, while the optical selection rules interchange.

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.

Optical gain characteristics in Al-rich AlGaN/AlN quantum wells

The optical gain characteristics of Al-rich AlGaN/AlN quantum wells (QWs) were assessed by the variable stripe length method at room temperature. An Al0.79Ga0.21N/AlN QW with a well width of 5 nm had a large optical gain of 140 cm−1. Increasing the excitation length induced a redshift due to the gain consumption and the consequent saturation of the amplified spontaneous emission. Moreover, a change in the dominant gain polarization with Al composition, which was attributed to switching of the valence band ordering of strained AlGaN/AlN QWs at Al compositions of ∼0.8, was experimentally demonstrated.

Signatures of Γ1–Γ5 mixed-mode polaritons in polarized reflectance spectra of ZnO

Theoretical and experimental studies were carried out on exciton-polaritons excited in ZnO. Polaritons in which both Γ1 and Γ5 excitons couple to electromagnetic waves simultaneously are shown to exist, and their signatures are observed in polarized reflectance spectra measured under k⊥a and E ∥ c configurations for an m-plane sample. Theoretical calculations reveal that the mixed-mode polaritons consist of one Γ1 transverse mode and two Γ5 longitudinal modes. It is also shown that the signatures are sensitive to the valence band ordering.

Valence-band-ordering of a strain-free bulk ZnO single crystal identified by four-wave-mixing spectroscopy technique

Spectroscopic and temporal four-wave-mixing (FWM) measurements are carried out on a strain-free bulk ZnO single crystal, in order to clarify the valence-band-ordering. Under the collinearly polarized lights with the electric-field component parallel to the c-axis, which can excite dipole-allowed Γ1-excitons, the FWM signal appears only in the energies corresponding to the B-exciton. Under the cross-linear polarization configuration exciting both Γ5- and Γ1-excitons, the FWM signal arising from the two-photon-coherence is absent in the energies corresponding to A-exciton. Both the results indicate that Γ1-exciton state belongs exclusively to B-exciton, meaning that the valence-band ordering is Γ9-Γ7-Γ7 in order of decreasing electron energy for the present strain-free ZnO single crystal.

Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations

A nonlocal semiempirical pseudopotential calculation of the electronic structure of wurtzite ZnO is proposed. The local and nonlocal components of the atomic effective potentials have been sequentially optimized and an excellent quantitative agreement has been achieved with a wide range of band features (energy gaps at high symmetry points, valence band ordering, in-plane and perpendicular components of the effective masses for electrons and holes at Γ), selected not only from available experimental and ab initio results, but also from new calculations performed with the code developed by the ABINIT project. The valence band description has been further improved through the inclusion of spin-orbit corrections. The complex dielectric function along the main crystallographic directions corresponding to the optimized electronic structure is also presented, along with extensive comparisons of all the computed quantities with the literature data.

Biexcitons and their dephasing processes in ZnO

We have investigated free excitons and biexcitons of bulk ZnO by time-integrated and spectrally-resolved four-wave mixing. The polarization- and wave-vector-dependent FWM signals for A and B excitons demonstrate clearly that the valence-band ordering is A–Γ9, B–Γ7, and C–Γ7. Next, we gave qualitative explanation of the FWM signals induced by excitons and biexcitons in ZnO. For negative delay times, bound and unbound AB-biexcitons (A exciton-B exciton correlation), which have been considered to play a minor role in GaAs heterostructures, was found to play an important role and give a significant qualitative impact to the optical response of ZnO. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Polarization and wave-vector-dependent measurements by four-wave mixing in ZnO: valence-band ordering and biexcitons

We have investigated free excitons and biexcitons of bulk ZnO by time-integrated and spectrally resolved four-wave mixing (FWM). The polarization- and wave-vector-dependent FWM signals for A and B excitons demonstrate clearly that the valence-band ordering is A– Γ 9 , B– Γ 7 , and C– Γ 7 . Also, we gave qualitative explanation of the FWM signals induced by excitons and biexcitons in ZnO. For negative delay times, bound and unbound AB-biexcitons (A exciton–B exciton correlation), which have been considered to play a minor role in GaAs heterostructures, was found to play an important role and give a significant qualitative impact to the optical response of ZnO.

Polarized photoreflectance spectra of excitonic polaritons in a ZnO single crystal

Exciton–polariton structures in a high-quality bulk ZnO single crystal were resolved at 8 K by means of polarized photoreflectance (PR) and photoluminescence measurements. The energies of the PR resonances corresponded to those of the upper and lower exciton–polariton branches, where A, B, and C excitons couple simultaneously to an electromagnetic wave. Longitudinal-transverse splitting of ground-state exciton polaritons and resonances due to the first excited states of respective excitons were observed due to the large oscillator strength. Photoluminescence peaks due to the corresponding polarion branches were clearly resolved. The valence-band ordering was confirmed to be A-Γ9v, B-Γ7vu, and C-Γ7vl.

Valence-band ordering and magneto-optic exciton fine structure in ZnO

Using first-principles linear muffin-tin orbital density functional band structure calculations, the ordering of the states in the wurtzite ZnO valence-band maximum, split by crystal-field and spin-orbit coupling effects, is found to be ${\ensuremath{\Gamma}}_{7(5)}g{\ensuremath{\Gamma}}_{9(5)}g{\ensuremath{\Gamma}}_{7(1)},$ in which the number in parentheses indicates the parent state without spin-orbit coupling. This results from the negative spin-orbit splitting, which in turn is due to the participation of the Zn $3d$ band. The result is found to be robust even when effects beyond the local density approximation on the Zn $3d$ band position are included. Using a Kohn-Luttinger model parametrized by our first-principles calculations, it is furthermore shown that the binding energies of the excitons primarily derived from each valence band differ by less than the valence-band splittings even when interband coupling effects are included. The binding energies of $n=2$ and $n=1$ excitons, however, are not in a simple $1/4$ ratio. Our results are shown to be in good agreement with the recent magneto-optical experimental data by Reynolds et al. [Phys. Rev. B 60, 2340 (1999)], in spite of the fact that on the basis of these data these authors claimed that the valence-band maximum would have ${\ensuremath{\Gamma}}_{9}$ symmetry. The differences between our and Reynolds' analysis of the data are discussed and arise from the sign of the Land\'e g factor for holes, which is here found to be negative for the upper ${\ensuremath{\Gamma}}_{7}$ band.

Band structure nonlocal pseudopotential calculation of the III-nitride wurtzite phase materials system. Part I. Binary compounds GaN, AlN, and InN

This work presents nonlocal pseudopotential calculations based on realistic, effective atomic potentials of the wurtzite phase of GaN, InN, and AlN. A formulation formulation for the model effective atomic potentials has been introduced. For each of the constitutive atoms in these materials, the form of the effective potentials is optimized through an iterative scheme in which the band structures are recursively calculated and selected features are compared to experimental and/or ab initio results. The optimized forms of the effective atomic potentials are used to calculate the band structures of the binary compounds, GaN, InN, and AlN. The calculated band structures are in excellent overall agreement with the experimental/ab initio values, i.e., the energy gaps at high-symmetry points, valence-band ordering, and effective masses for electrons match to within 3%, with a few values within 5%. The values of the energy separation, effective masses, and nonparabolicity coefficients for several secondary valleys are tabulated as well in order to facilitate analytical Monte Carlo transport simulations.

Fermi Surface ofMg2Pb

Experimental observations are reported of Landau quantum oscillations (LQO) in the electrical transport properties of the compound ${\mathrm{Mg}}_{2}$Pb in the range $H\ensuremath{\le}50$ kG and $T=1.2\ensuremath{-}4.2$ \ifmmode^\circ\else\textdegree\fi{}K. The results are associated with two bands of holes previously inferred in explaining the lowfield ($H\ensuremath{\le}5$ kG) field dependence of the Hall coefficient, confirming the earlier interpretation. The magnetoconductivity tensor elements derived from the nonoscillatory contributions to the Hall and transverse magnetoresistivity have been fitted with three bands of carriers labeled as light holes, heavy holes, and electrons. This establishes band overlap in ${\mathrm{Mg}}_{2}$Pb. The light-hole band (F = 0.27 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ G) is nearly spherical (\ifmmode\pm\else\textpm\fi{}2%) with ${m}^{*}\ensuremath{\simeq}0.04{m}_{e}$, $g\ensuremath{\simeq}11$, and contains 7.9 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ carriers/${\mathrm{cm}}^{3}$. The heavy-hole band [$F=(2.8\ensuremath{-}3.7)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ G] is a warped sphere, whose shape has been determined from experimental extremal cross sections using the Fermi-radius inversion method developed by Mueller. The heavy-hole cyclotron effective mass has been measured as 0.35 and 0.45 electron masses for orbits perpendicular to [100] and [111], respectively. This band contains 4.2 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ carriers/${\mathrm{cm}}^{3}$. These two valence bands are compared with similar valence bands in Ge via the model of Dresselhaus et al., The evidence for a Ge-like, rather than grey-Sn-like, valence-band ordering is consistent with the band calculation of Van Dyke and Herman. No LQO associated with the electron band were observed, although the analysis of classical magnetoconductivity data requires the presence of 4.1 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ electrons/${\mathrm{cm}}^{3}$ in order to explain the high-field value of $H{\ensuremath{\sigma}}_{12}$.