We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

We present a comprehensive and up-to-date compilation of band parameters for all of the nitrogen-containing III–V semiconductors that have been investigated to date. The two main classes are: (1) “conventional” nitrides (wurtzite and zinc-blende GaN, InN, and AlN, along with their alloys) and (2) “dilute” nitrides (zinc-blende ternaries and quaternaries in which a relatively small fraction of N is added to a host III–V material, e.g., GaAsN and GaInAsN). As in our more general review of III–V semiconductor band parameters [I. Vurgaftman et al., J. Appl. Phys. 89, 5815 (2001)], complete and consistent parameter sets are recommended on the basis of a thorough and critical review of the existing literature. We tabulate the direct and indirect energy gaps, spin-orbit and crystal-field splittings, alloy bowing parameters, electron and hole effective masses, deformation potentials, elastic constants, piezoelectric and spontaneous polarization coefficients, as well as heterostructure band offsets. Temperature an...

Band parameters for nitrogen-containing semiconductors

White light emitting diodes (LEDs) based on III-nitride InGaN/GaN quantum wells currently offer the highest overall efficiency for solid state lighting applications. Although current phosphor-converted white LEDs have high electricity-to-light conversion efficiencies, it has been recently pointed out that the full potential of solid state lighting could be exploited only by color mixing approaches without employing phosphor-based wavelength conversion. Such an approach requires direct emitting LEDs of different colors, including, in particular, the green-yellow range of the visible spectrum. This range, however, suffers from a systematic drop in efficiency, known as the "green gap," whose physical origin has not been understood completely so far. In this work, we show by atomistic simulations that a consistent part of the green gap in c-plane InGaN/GaN-based light emitting diodes may be attributed to a decrease in the radiative recombination coefficient with increasing indium content due to random fluctuations of the indium concentration naturally present in any InGaN alloy.

Efficiency Drop in Green InGaN/GaN Light Emitting Diodes: The Role of Random Alloy Fluctuations.

We have derived consistent sets of band parameters band gaps, crystal field splittings, band-gap deformation potentials, effective masses, and Luttinger and EP parameters for AlN, GaN, and InN in the zinc-blende and wurtzite phases employing many-body perturbation theory in the G0W0 approximation. The G0W0 method has been combined with density-functional theory DFT calculations in the exact-exchange optimized effective potential approach to overcome the limitations of local-density or gradient-corrected DFT functionals. The band structures in the vicinity of the point have been used to directly parametrize a 44 k·p Hamiltonian to capture nonparabolicities in the conduction bands and the more complex valence-band structure of the wurtzite phases. We demonstrate that the band parameters derived in this fashion are in very good agreement with the available experimental data and provide reliable predictions for all parameters, which have not been determined experimentally so far.

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Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN

We study the carrier distribution in multi quantum well (multi-QW) InGaN light-emitting diodes. Conventional wisdom would assume that a large number of QWs lead to a smaller carrier density per QW, enabling efficient carrier recombination at high currents. We use angle-resolved far-field measurements to determine the location of spontaneous emission in a series of multi-QW samples. They reveal that, no matter how many QWs are grown, only the QW nearest the p layer emits light under electrical pumping, which can limit the performances of high-power devices.

Carrier distribution in (0001)InGaN∕GaN multiple quantum well light-emitting diodes

We derive the effective-mass Hamiltonian for wurtzite semiconductors, including the strain effects. This Hamiltonian provides a theoretical groundwork for calculating the electronic band structures and optical constants of bulk and quantum-well wurtzite semiconductors. We apply Kane's model to derive the band-edge energies and the optical momentum-matrix elements for strained wurtzite semiconductors. We then use the k\ensuremath{\cdot}p perturbation method to derive the effective-mass Hamiltonian, which is then checked with that derived using an invariant method based on the Pikus-Bir model. We obtain the band structure ${\mathit{A}}_{\mathit{i}}$ parameters in the group theoretical model explicitly in terms of the momentum-matrix elements. We also find the proper definitions of the important physical quantities used in both models and present analytical expressions for the valence-band dispersions, the effective masses, and the interband optical-transition momentum-matrix elements near the band edges, taking into account the strain effects. \textcopyright{} 1996 The American Physical Society.

k⋅p method for strained wurtzite semiconductors

We demonstrate ferroelectric switching in CeO<inf>2</inf> doped Hf<inf>0.5</inf>Zr<inf>0.5</inf>O<inf>2</inf> (HZCO) thin films and their applications for back-end-of-line (BEOL) compatible embedded memories. At low cerium oxide doping concentrations (2.0 - 5.6 mol%), the polar orthorhombic phase is stabilized after annealing at temperatures below 400°C. HZCO ferroelectrics show reliable switching characteristics beyond 10<sup>11</sup> cycles in TiN/HZCO/TiN (MFM) capacitors, several orders magnitude higher than the identically processed Hf<inf>0.5</inf>Zr<inf>0.5</inf>O<inf>2</inf> (HZO) capacitors, without sacrificing polarization and retention. We also report enhanced endurance (> 10<sup>10</sup> cycles) in HZCO metal-ferroelectric-insulator-semiconductor (MFIS) stacks, which is promising for ferroelectric FET memory applications.

C. S. Chang

Papers

k⋅p method for strained wurtzite semiconductors

CeO2-Doped Hf0.5Zr0.5O2 Ferroelectrics for High Endurance Embedded Memory Applications