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 model, in an elementary way, the excited electronic states of semiconductor crystallites sufficiently small (∼50 A diam) that the electronic properties differ from those of bulk materials. In this limit the excited states and ionization processes assume a molecular‐like character. However, diffraction of bonding electrons by the periodic lattice potential remains of paramount importance in the crystallite electronic structure. Schrodinger’s equation is solved at the same level of approximation as used in the analysis of bulk crystalline electron‐hole states (Wannier excitons). Kinetic energy is treated by the effective mass approximation, and the potential energy is due to high frequency dielectric solvation by atomic core electrons. An approximate formula is given for the lowest excited electronic state energy. This expression is dependent upon bulk electronic properties, and contains no adjustable parameters. The optical f number for absorption and emission is also considered. The same model is applied to the problem of two conduction band electrons in a small crystallite, in order to understand how the redox potential of excess electrons depends upon crystallite size.

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Electron–electron and electron‐hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state

A quantized Hall plateau of ${\ensuremath{\rho}}_{\mathrm{xy}}=\frac{3h}{{e}^{2}}$, accompanied by a minimum in ${\ensuremath{\rho}}_{\mathrm{xx}}$, was observed at $Tl5$ K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is $\frac{1}{3}$ filled. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation.

https://link.aps.org/pdf/10.1103/PhysRevLett.48.1559

Two-Dimensional Magnetotransport in the Extreme Quantum Limit

Graphene, the single-atom-thick form of carbon, holds promise for many applications, notably in electronics where it can complement or be integrated with silicon-based devices. Intense efforts have been devoted to develop a key enabling device, a broadband, fast optical modulator with a small device footprint. Now Liu et al. demonstrate an exciting new possibility for graphene in the area of on-chip optical communication: a graphene-based optical modulator integrated with a silicon chip. This new device relies on the electrical tuning of the Fermi level of the graphene sheet, and achieves modulation of guided light at frequencies over 1 gigahertz, together with a broad operating spectrum. At just 25 square micrometres in area, it is one of the smallest of its type. Integrated optical modulators with high modulation speed, small footprint and large optical bandwidth are poised to be the enabling devices for on-chip optical interconnects1,2. Semiconductor modulators have therefore been heavily researched over the past few years. However, the device footprint of silicon-based modulators is of the order of millimetres, owing to its weak electro-optical properties3. Germanium and compound semiconductors, on the other hand, face the major challenge of integration with existing silicon electronics and photonics platforms4,5,6. Integrating silicon modulators with high-quality-factor optical resonators increases the modulation strength, but these devices suffer from intrinsic narrow bandwidth and require sophisticated optical design; they also have stringent fabrication requirements and limited temperature tolerances7. Finding a complementary metal-oxide-semiconductor (CMOS)-compatible material with adequate modulation speed and strength has therefore become a task of not only scientific interest, but also industrial importance. Here we experimentally demonstrate a broadband, high-speed, waveguide-integrated electroabsorption modulator based on monolayer graphene. By electrically tuning the Fermi level of the graphene sheet, we demonstrate modulation of the guided light at frequencies over 1 GHz, together with a broad operation spectrum that ranges from 1.35 to 1.6 µm under ambient conditions. The high modulation efficiency of graphene results in an active device area of merely 25 µm2, which is among the smallest to date. This graphene-based optical modulation mechanism, with combined advantages of compact footprint, low operation voltage and ultrafast modulation speed across a broad range of wavelengths, can enable novel architectures for on-chip optical communications.

/pdf/a-graphene-based-broadband-optical-modulator-rvjxppjsy5.pdf

A graphene-based broadband optical modulator

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

Electric field dependence of optical absorption near the band gap of quantum-well structures.

We present theory and extended experimental results for the large shift in optical absorption in GaAs-AlGaAs quantum well structures with electric field perpendicular to the layers. In contrast to the Stark effect on atoms or on excitons in bulk semiconductors, the exciton resonances remain resolved even for shifts much larger than the zero-field binding energy and fields g 50 times the classical ionization field. The model explains these results as a consequence of the quantum confinement of carriers.

Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect

GaAs‐AlxGa1−xAs superlattice structures in which electron mobilities exceed those of otherwise equivalent epitaxial GaAs as well as the Brooks‐Herring predictions near room temperature and at very low temperatures are reported. This new behavior is achieved via a modulation‐doping technique that spatially separates conduction electrons and their parent donor impurity atoms, thereby reducing the influence of ionized and neutral impurity scattering on the electron motion.

Electron mobilities in modulation‐doped semiconductor heterojunction superlattices

Quantum levels associated with the confinement of carriers in very thin, molecular-beam—grown AlxGa1−xAs−GaAs-Alx Ga1−xAs heterostructures result in pronounced structure in the GaAs optical absorption spectrum Up to eight resolved exciton transitions, associated with different bound-electron and bound-hole states, have been observed The heterostructure behaves as a simple rectangular potential well with a depth of ≈088ΔE g , for confining electrons and ≈012ΔE g for confining holes, where ΔE g is the difference in the semiconductor energy gaps

Quantum States of Confined Carriers in Very Thin Al x Ga 1 − x As -GaAs- Al x Ga 1 − x As Heterostructures

We report a new type of optoelectronic device, a self‐electro‐optic effect device (SEED), which uses the same GaAs/GaAlAs multiple quantum well material simultaneously as an optical detector and modulator. Using a series resistor and constant voltage bias supply the SEED shows optical bistabilty (OB) of the recently discovered type which relies on increasing absorption and requires no mirrors. OB is seen at room temperature from ∼850–860 nm, at powers as low as 670 nW or switching times as short as 400 ns (limited only by power restrictions) with ∼1‐nJ optical switching energy in a 600‐μm‐diam device. Total energies per unit area (∼18 fJ/μm2) are substantially lower than any previously reported for OB.We report a new type of optoelectronic device, a self‐electro‐optic effect device (SEED), which uses the same GaAs/GaAlAs multiple quantum well material simultaneously as an optical detector and modulator. Using a series resistor and constant voltage bias supply the SEED shows optical bistabilty (OB) of the recently discovered type which relies on increasing absorption and requires no mirrors. OB is seen at room temperature from ∼850–860 nm, at powers as low as 670 nW or switching times as short as 400 ns (limited only by power restrictions) with ∼1‐nJ optical switching energy in a 600‐μm‐diam device. Total energies per unit area (∼18 fJ/μm2) are substantially lower than any previously reported for OB.

W. Wiegmann

Papers

Electric field dependence of optical absorption near the band gap of quantum-well structures.

Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect

Electron mobilities in modulation‐doped semiconductor heterojunction superlattices

Quantum States of Confined Carriers in Very Thin Al x Ga 1 − x As -GaAs- Al x Ga 1 − x As Heterostructures

Novel hybrid optically bistable switch: The quantum well self‐electro‐optic effect device