Gallium nitride (GaN) and its allied binaries InN and AIN as well as their ternary compounds have gained an unprecedented attention due to their wide-ranging applications encompassing green, blue, violet, and ultraviolet (UV) emitters and detectors (in photon ranges inaccessible by other semiconductors) and high-power amplifiers. However, even the best of the three binaries, GaN, contains many structural and point defects caused to a large extent by lattice and stacking mismatch with substrates. These defects notably affect the electrical and optical properties of the host material and can seriously degrade the performance and reliability of devices made based on these nitride semiconductors. Even though GaN broke the long-standing paradigm that high density of dislocations precludes acceptable device performance, point defects have taken the center stage as they exacerbate efforts to increase the efficiency of emitters, increase laser operation lifetime, and lead to anomalies in electronic devices. The p...

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Luminescence properties of defects in GaN

Silicon carbide (SiC), a material long known with potential for high-temperature, high-power, high-frequency, and radiation hardened applications, has emerged as the most mature of the wide-bandgap (2.0 eV ≲ Eg ≲ 7.0 eV) semiconductors since the release of commercial 6HSiC bulk substrates in 1991 and 4HSiC substrates in 1994. Following a brief introduction to SiC material properties, the status of SiC in terms of bulk crystal growth, unit device fabrication processes, device performance, circuits and sensors is discussed. Emphasis is placed upon demonstrated high-temperature applications, such as power transistors and rectifiers, turbine engine combustion monitoring, temperature sensors, analog and digital circuitry, flame detectors, and accelerometers. While individual device performances have been impressive (e.g. 4HSiC MESFETs with fmax of 42 GHz and over 2.8 W mm−1 power density; 4HSiC static induction transistors with 225 W power output at 600 MHz, 47% power added efficiency (PAE), and 200 V forward blocking voltage), material defects in SiC, in particular micropipe defects, remain the primary impediment to wide-spread application in commercial markets. Micropipe defect densities have been reduced from near the 1000 cm−2 order of magnitude in 1992 to 3.5 cm−2 at the research level in 1995.

Status of silicon carbide (SiC) as a wide-bandgap semiconductor for high-temperature applications: A review

Understanding energy dissipation and transport in nanoscale structures is of great importance for the design of energy-efficient circuits and energy-conversion systems. This is also a rich domain for fundamental discoveries at the intersection of electron, lattice (phonon), and optical (photon) interactions. This review presents recent progress in understanding and manipulation of energy dissipation and transport in nanoscale solid-state structures. First, the landscape of power usage from nanoscale transistors (∼10−8 W) to massive data centers (∼109 W) is surveyed. Then, focus is given to energy dissipation in nanoscale circuits, silicon transistors, carbon nanostructures, and semiconductor nanowires. Concepts of steady-state and transient thermal transport are also reviewed in the context of nanoscale devices with sub-nanosecond switching times. Finally, recent directions regarding energy transport are reviewed, including electrical and thermal conductivity of nanostructures, thermal rectification, and the role of ubiquitous material interfaces. 
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Energy dissipation and transport in nanoscale devices

Contemporary theories of defects and impurities in semiconductors rely to a large extent on supercell calculations within density-functional theory using the approximate local-density approximation (LDA) or generalized gradient approximation (GGA) functionals. Such calculations are, however, affected by considerable uncertainties associated with: (i) the ``band-gap problem,'' which occurs not only in the Kohn-Sham single-particle energies but also in the quasiparticle gap (LDA or GGA) calculated from total-energy differences, and (ii) supercell finite-size effects. In the case of the oxygen vacancy in ZnO, uncertainties (i) and (ii) have led to a large spread in the theoretical predictions, with some calculations suggesting negligible vacancy concentrations, even under Zn-rich conditions, and others predicting high concentrations. Here, we critically assess (i) the different methodologies to correct the band-gap problem. We discuss approaches based on the extrapolation of perturbations which open the band gap, and the self-consistent band-gap correction employing the $\text{LDA}+U$ method for $d$ and $s$ states simultaneously. From the comparison of the results of different gap-correction, including also recent results from other literature, we conclude that to date there is no universal scheme for band gap correction in general defect systems. Therefore, we turn instead to classification of different types of defect behavior to provide guidelines on how the physically correct situation in an LDA defect calculation can be recovered. (ii) Supercell finite-size effects: We performed test calculations in large supercells of up to 1728 atoms, resolving a long-standing debate pertaining to image charge corrections for charged defects. We show that once finite-size effects not related to electrostatic interactions are eliminated, the analytic form of the image charge correction as proposed by Makov and Payne leads to size-independent defect formation energies, thus allowing the calculation of well-converged energies in fairly small supercells. We find that the delocalized contribution to the defect charge (i.e., the defect-induced change of the charge distribution) is dominated by the dielectric screening response of the host, which leads to an unexpected effective $1/L$ scaling of the image charge energy, despite the nominal $1/{L}^{3}$ scaling of the third-order term. Based on this analysis, we suggest that a simple scaling of the first order term by a constant factor (approximately 2/3) yields a simple but accurate image-charge correction for common supercell geometries. Finally, we discuss the theoretical controversy pertaining to the formation energy of the O vacancy in ZnO in light of the assessment of different methodologies in the present work, and we review the present experimental situation on the topic.

Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs

Understanding energy dissipation and transport in nanoscale structures is of great importance for the design of energy-efficient circuits and energy-conversion systems. This is also a rich domain for fundamental discoveries at the intersection of electron, lattice (phonon), and optical (photon) interactions. This review presents recent progress in understanding and manipulation of energy dissipation and transport in nanoscale solid-state structures. First, the landscape of power usage from nanoscale transistors (~10^-8 W) to massive data centers (~10^9 W) is surveyed. Then, focus is given to energy dissipation in nanoscale circuits, silicon transistors, carbon nanostructures, and semiconductor nanowires. Concepts of steady-state and transient thermal transport are also reviewed in the context of nanoscale devices with sub-nanosecond switching times. Finally, recent directions regarding energy transport are reviewed, including electrical and thermal conductivity of nanostructures, thermal rectification, and the role of ubiquitous material interfaces.

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Energy Dissipation and Transport in Nanoscale Devices

Epitaxial p-n diodes in 4H SiC are fabricated showing a good uniformity of avalanche multiplication and breakdown. Peripheral breakdown is overcome using the positive angle beveling technique. Photomultiplication measurements were performed to determine electron and hole ionization rates. For the electric field parallel to the c-axis impact ionization is strongly dominated by holes. A hole to electron ionization coefficient ratio of up to 50 is observed. It is attributed to the discontinuity of the conduction band of 4H SiC for the direction along the c axis. Theoretical values of critical fields and breakdown voltages in 4H SiC are calculated using the ionization rates obtained.

Ionization rates and critical fields in 4H silicon carbide

Crystal Defects as Source of Anomalous Forward Voltage Increase of 4H-SiC Diodes

A full-potential band structure calculation, within the local density approximation to the density functional theory, has been performed for the polytypes 3C, 2H, 4H, and 6H of SiC. The calculated effective electron masses are found to be in very good agreement with experimental values. The electron-optical phonon coupling has been estimated and the polaron masses are calculated to be 3%–13% larger than the corresponding bare masses. The effective electron masses of the second lowest conduction band minima are also presented and the calculated energy difference between the two lowest minima in 4H–SiC is only 0.12 eV. The lowest conduction band in 6H–SiC is found to be very flat and to have a double-well-like minimum along the ML line. The top of the valence bands has been parametrized according to the k⋅p approximation, whereupon the effective hole masses have been determined. The spin-orbit interaction was found to have a strong influence on the value of the effective hole masses. Furthermore, total and partial densities of states are presented.

Relativistic band structure calculation of cubic and hexagonal SiC polytypes

Models for doping-induced band edge displacements and band gap narrowing in both n-type and p-type 3C–, 4H–, and 6H–SiC are presented for the first time. For comparison, Si has also been considered. The models constitute an extension of the theory of Jain and Roulston [Solid State Electron. 34, 453 (1991)] and take into account the three different electron effective mass components associated with hexagonal lattices. Furthermore, a more careful treatment of minority carrier correlation energy has been made, applying a two-band model for the dielectric function of a hole gas in the plasmon-pole approximation. The results for the band edge displacements are expressed in simple analytical form as functions of doping concentration.

Doping-induced band edge displacements and band gap narrowing in 3C-, 4H- 6H-SiC and Si

Recent attempts to make SiC diodes have revealed a problem with stacking fault expansion in the material, leading to unstable devices. In this paper, we present detailed results from a density-functional supercell calculation on the electronic structure of stacking faults which result from glide of Shockley partials in $3C\ensuremath{-}, 4H\ensuremath{-}$ and $6H\ensuremath{-}\mathrm{SiC}.$ It was found [Phys. Rev. B 65, 033203 (2002)] that both types of stacking faults in $4H\ensuremath{-}\mathrm{SiC}$ and two types of stacking faults in $6H\ensuremath{-}\mathrm{SiC}$ give rise to band states, which are strongly localized (confined within around 10 \AA{}) in the direction orthogonal to the stacking fault plane. Based on estimates of the band offsets between different polytypes and a simple quantum-well theory, we show that it is possible to interpret this one-dimensional localization as a quantum-well confinement effect. We also find that the third type of stacking fault in $6H\ensuremath{-}\mathrm{SiC}$ and the only stacking fault in $3C\ensuremath{-}\mathrm{SiC}$ do not give rise to states clearly separated from the band edges, but instead give rise to rather strongly localized band states with energies very close to the band edges. We argue that these localized near band edge states are created by stacking fault induced changes in the dipole moment associated with the hexagonal symmetry. In addition, we have also calculated the stacking fault energies, using both the supercell method and the simpler ANNNI (axial next nearest-neighbor Ising) model. Both theories agree well with the low stacking fault energies found experimentally.

Ulf Lindefelt

Papers

Ionization rates and critical fields in 4H silicon carbide

Crystal Defects as Source of Anomalous Forward Voltage Increase of 4H-SiC Diodes

Relativistic band structure calculation of cubic and hexagonal SiC polytypes

Doping-induced band edge displacements and band gap narrowing in 3C-, 4H- 6H-SiC and Si

Stacking faults in 3C-, 4H-, and 6H-SiC polytypes investigated by an ab initio supercell method