There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

First-principles calculations have evolved from mere aids in explaining and supporting experiments to powerful tools for predicting new materials and their properties. In the first part of this review we describe the state-of-the-art computational methodology for calculating the structure and energetics of point defects and impurities in semiconductors. We will pay particular attention to computational aspects which are unique to defects or impurities, such as how to deal with charge states and how to describe and interpret transition levels. In the second part of the review we will illustrate these capabilities with examples for defects and impurities in nitride semiconductors. Point defects have traditionally been considered to play a major role in wide-band-gap semiconductors, and first-principles calculations have been particularly helpful in elucidating the issues. Specifically, calculations have shown that the unintentional n-type conductivity that has often been observed in as-grown GaN cannot be a...

First-principles calculations for defects and impurities: Applications to III-nitrides

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

Status and future outlook of III-V compound semiconductor visible-spectrum light-emitting diodes (LEDs) are presented. Light extraction techniques are reviewed and extraction efficiencies are quantified in the 60%+ (AlGaInP) and ~80% (InGaN) regimes for state-of-the-art devices. The phosphor-based white LED concept is reviewed and recent performance discussed, showing that high-power white LEDs now approach the 100-lm/W regime. Devices employing multiple phosphors for "warm" white color temperatures (~3000-4000 K) and high color rendering (CRI>80), which provide properties critical for many illumination applications, are discussed. Recent developments in chip design, packaging, and high current performance lead to very high luminance devices (~50 Mcd/m2 white at 1 A forward current in 1times1 mm2 chip) that are suitable for application to automotive forward lighting. A prognosis for future LED performance levels is considered given further improvements in internal quantum efficiency, which to date lag achievements in light extraction efficiency for InGaN LEDs

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Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting

We have identified piezoelectric fields in strained GaInN/GaN quantum well p-i-n structures using the quantum-confined Stark effect. The photoluminescence peak of the quantum wells showed a blueshift with increasing applied reverse voltages. This blueshift is due to the cancellation of the piezoelectric field by the reverse bias field. We determined that the piezoelectric field points from the growth surface to the substrate and its magnitude is 1.2 MV/cm for Ga0.84In0.16N/GaN quantum wells on sapphire substrate. In addition, from the direction of the field, the growth orientation of our nitride epilayers can be determined to be (0001), corresponding to the Ga face.

Determination of piezoelectric fields in strained GaInN quantum wells using the quantum-confined Stark effect

Photoluminescence investigations on undoped n‐type GaN layers grown on 6H‐SiC and sapphire reveal the presence of residual acceptors with a binding energy of 230 meV. Their presence in high temperature vapor phase epitaxy grown layers is strongly correlated with the graphite susceptor containing the Ga. Mg as a contamination can be ruled out. In metal organic vapor phase epitaxially grown layers, the metal organic are probably the source of the carbon contamination. It is concluded that carbon on nitrogen sites introduces the most shallow acceptor in GaN. The experimental observations are supported by an estimate of the acceptor binding energy using effective‐mass‐theory.

https://www.rpi.edu/~wetzel/Preprints/APLFischerAppl.Phys.Lett.67,1298-300(1995).pdf

On p-type doping in GaN—acceptor binding energies

O and Si donors in GaN are studied by Raman spectroscopy under hydrostatic pressure p. The ground state of O is found to transfer from a shallow level to a deep gap state at p{gt}20 GPa reminiscent of {ital DX} centers in GaAs. Transferred to Al{sub x}Ga {sub 1-x}N we predict that O induces a deep gap state for x{gt}0.40. In GaN:Si no such state is induced up to the highest pressure obtained (p=25 GPa ) equivalent to x=0.56 in Al{sub x}Ga {sub 1-x}N and possibly higher. We attribute this distinction to the lattice sites of the dopants. O substituting for N is found to be the origin of high free electron concentration in bulk GaN crystals. {copyright} {ital 1997} {ital The American Physical Society}

https://www.rpi.edu/~wetzel/Preprints/PRLWetzelOxygeninGaN.Phys.Rev.Lett.78,3923-6(1997).pdf

Pressure induced deep gap state of oxygen in gan

Green GaInN/GaN quantum well light-emitting diode (LED) wafers were grown on nanopatterned c-plane sapphire substrate by metal-organic vapor phase epitaxy. Without roughening the chip surface, such LEDs show triple the light output over structures on planar sapphire. By quantitative analysis the enhancement was attributed to both, enhanced generation efficiency and extraction. The spectral interference and emission patterns reveal a 58% enhanced light extraction while photoluminescence reveals a doubling of the internal quantum efficiency. The latter was attributed to a 44% lower threading dislocation density as observed in transmission electron microscopy. The partial light output power measured from the sapphire side of the unencapsulated nanopatterned substrate LED die reaches 5.2 mW at 525 nm at 100 mA compared to 1.8 mW in the reference LED.

https://homepages.rpi.edu/~wetzel/Preprints/APL2011_Li_DefectReducedGreenLED_NanopatternedSapphire,Yufeng_Li_Appl.Phys.Lett,98(15),(2011).pdf

Defect-reduced green GaInN/GaN light-emitting diode on nanopatterned sapphire

The etch pit density of organometallic vapor phase epitaxy (OMVPE)-grown GaN on sapphire was discovered to reduce drastically by the insertion of either a low-temperature-deposited AlN buffer layer or GaN buffer layer between high-temperature-grown-GaN on sapphire.

https://homepages.rpi.edu/~wetzel/Preprints/JJAPIwayaInterlayerJpn.J.Appl.Phys.37,L316(1998).pdf

Reduction of Etch Pit Density in Organometallic Vapor Phase Epitaxy-Grown GaN on Sapphire by Insertion of a Low-Temperature-Deposited Buffer Layer between High-Temperature-Grown GaN

Christian Wetzel

Papers

Determination of piezoelectric fields in strained GaInN quantum wells using the quantum-confined Stark effect

On p-type doping in GaN—acceptor binding energies

Pressure induced deep gap state of oxygen in gan

Defect-reduced green GaInN/GaN light-emitting diode on nanopatterned sapphire

Reduction of Etch Pit Density in Organometallic Vapor Phase Epitaxy-Grown GaN on Sapphire by Insertion of a Low-Temperature-Deposited Buffer Layer between High-Temperature-Grown GaN