We report on a new type of quantum wells with the width as thin as 10Å, which are composed of SiC only, and consequently have ideal interfaces. These quantum wells are actually stacking faults in SiC. Certain types of stacking faults in SiC polytypes create small 3C-like regions, where the stacking sequences along the c-axis become locally cubic in the hexagonal host crystals. Since the conduction band offsets between the cubic and hexagonal polytypes are very large with the conduction band minima of 3C-SiC lower than that of the other polytypes, such thin 3C inclusions can introduce locally lower conduction bands, thus acting as quantum films perpendicular to the c-axis. One mechanism for the occurrence of stacking faults in the perfect SiC single crystals is the motion of partial dislocations in the basal planes, the partial dislocations leaving behind stacking fault regions. © 2003 Elsevier Science Ltd. All rights reserved.
The multiple stacking faults in 4H-SiC, leading to narrow 3C polytype inclusions along the hexagonal c direction, were discussed. The stacking fault energies for successive stacking faults were calculated. The analysis showed that the stacking fault energy for the two stacking faults in adjacent basal planes was reduced by approximately a factor of 4 relative to that of one isolated stacking fault.
A first-principles calculation of the effective mass of electrons in quantum-well-like gap states induced by stacking faults and cubic inclusions in 4H- and 6H-SiC is performed, based on the density functional theory in the local density approximation. Our calculated effective electron masses for perfect crystals are in very good agreement with those previously determined both theoretically and experimentally. It has been found that electrons confined in the thin 3C-like regions have clearly heavier effective masses than that in perfect 3C-SiC.
First-principles band structure calculations of all the structurally different stacking faults that can be introduced by glide along the (0001) basal plane in 3C-, 4H-, and 6H-SiC are performed, based on the local-density approximation within the density-functional theory. Our calculations, using supercells containing 96 atoms, have revealed that both types of stacking faults in 4H-SiC and two of the three different SFs in 6H-SiC give rise to quasi-2D energy band states in the band gap at around 0.2 eV below the lowest conduction band, and are electrically active. The corresponding wave functions are strongly localized around the stacking fault plane. These results imply that stacking faults in these SiC polytypes are efficient planar traps for electron capture and responsible for subsequent electron-hole recombination. This can therefore have a profound influence on bipolar SiC technology.
A first-principles calculation of stacking faults in 15R-SiC is reported. All the geometrically distinguishable stacking faults which can be introduced by the glide of partial dislocations in (0001)-basal planes are investigated: there exist as many as five different stacking faults in 15R-SiC. Electronic properties and stacking fault energies of these extended defects are studied based on the density functional theory in the local density approximation. Stacking fault energies are also calculated using the axial next nearest neighbor Ising (ANNNI) model.
We report on a first-principles band structure calculation of twin boundaries in 3C-SiC, Si, and diamond, based on the density functional theory in the local density approximation. It is found that the electron wave functions belonging to the conduction and valence band edge states in 3C-SiC tend to be localized almost exclusively on different sides of the boundaries, while there is no such feature in Si and diamond. We have interpreted these localization and segregation phenomena as a consequence of the electrostatic field caused by the spontaneous polarization due to the hexagonal symmetry around twin boundaries. A mechanism for the creation of twin boundaries, i.e., propagation of partial dislocations in neighboring basal planes, has been investigated using total energy calculations, and it has been realized that the double-intrinsic-stacking-fault structure in 3C-SiC, coinciding with the extrinsic stacking faults, is much energetically favored.
We report on a first-principles study of all the structurally different stacking faults that can be introduced by elide along the (0001) basal plane in 3C-, 4H-, and 6H-SiC based on the local-density approximation within the density-functional theory. Our band-structure calculations have revealed that both types of stacking faults in 4H-SiC and two of the three different types of stacking faults in 6H-SiC give rise to quasi-two-dimensional energy band states in the band gap at around 0.2 eV below the lowest conduction band, thus being electrically active in n-type material. Although stacking faults, unlike point defects and surfaces, are not associated with broken or chemically perturbed bonds, we find a strong localization, within roughly 10-15 Angstrom perpendicular to the stacking fault plane, of the stacking fault gap state wave functions. We find that this quantum-well-like feature of certain stacking faults in SiC can be understood in terms of the large conduction-band offsets between the cubic and hexagonal polytypes. Recent experimental results give qualitative support to our results.
We report on a first-principles supercell calculation of cubic inclusions in 6H-SiC. Motions of successive partial dislocations having the same Burgers vector in the basal planes can lead to a 3C-like region in the perfect 6H-SiC crystal, which corresponds to multiple stacking faults. We have calculated the electronic structures and the total energies of 6H-SiC crystals containing in stacking faults (m=1-4) in the adjacent basal planes, based on the density functional theory in the local density approximation. It has been found that 3C-like sequences in the 6H-host crystals can act as planar quantum wells, in which conduction band electrons can be confined. The total energy calculations using both the supercell method and the axial next nearest neighbor Ising model (ANNNI) have revealed that the 2nd stacking fault energy in 6H-SiC is about 6 times larger than that of an isolated stacking fault.
A first-principles calculation of stacking fault energies in 3C-, 4H-, and 6H-SiC, based on the local-density approximation within the density-functional theory, is reported. All the structurally different stacking faults which can be introduced by glide along the (0001) basal plane are considered. The number of such stacking faults in these polytypes is one, two, and three, respectively. The stacking fault energies are also calculated using the simpler generalized axial next-nearest-neighbor Ising (ANNNI) model. Our calculations confirm that the stacking fault energy of 3C-SiC is negative, and we also find that one of the three types of stacking faults in 6H-SiC has a considerably higher stacking fault energy than the other two types.
First-principles density-functional calculations of the band structure and wave functions around narrow X-like inclusions in 4H-SiC have been performed. X-like inclusions of various thicknesses, corresponding to two, three, and four stacking faults in neighbouring basal planes, have been investigated. The results for the number of bound states in the inclusion, their energies, and wave functions are well described by a simple one-dimensional quantum-well square potential. The quantum-well property of these inclusions suggests that X-like regions in 4H-SiC are efficient planar traps for conduction band electrons.
We report on a theoretical investigation of extended planar defects in 3C-, 4H-, 6H-, and 15R-SiC which can be formed without breaking any bonds, covering a wide range of planar defects: twin boundaries, stacking faults, and polytype inclusions. Their electronic structures have been intensively studied using an ab initio supercell approach based on the density functional theory. Stacking fault energies are also calculated using both the supercell method and the axial next-nearest-neighbour Ising model. We discuss the electronic properties and energies of these defects in terms of the geometrical differences of stacking patterns.
A ab initio study of 3 C inclusions and stacking fault-stacking fault interactions in 6H-SiC was presented. The electronic structures and the total energies of 6H-SiC single crystals that contain one, two, three and four stacking faults were studied. The possibility of local hexagonal to cubic polytypic transformations was discussed in light of the formation energy and quantum-well action.
The main purpose of this article is to determine the two-dimensional effective mass tensors of electrons confined in thin 3C wells in hexagonal SiC, which is a first step in the understanding of in-plane electron motion in the novel quantum structures. We have performed ab initio band structure calculations, based on the density functional theory in the local density approximation, for single and multiple stacking faults leading to thin 3C-like regions in 4H- and 6H-SiC and deduced electron effective masses for two-dimensional electron gases around the cubic inclusions. We have found that electrons confined in the thin 3C-like layers have clearly heavier effective masses than in the perfect bulk 3C-SiC single crystal.
First-principles calculations of twin boundaries in 3C-SiC, Si, and diamond are performed, based on the density-functional theory in the local density approximation. We have investigated the formation energies and electronic properties of isolated and interacting twin boundaries. It is found that in 3C-SiC, interacting twin boundaries which are separated by more than two Si-C bilayers are actually energetically more favorable, implying a relatively frequent appearance of these defects. The effect of the spontaneous polarization associated with the hexagonal symmetry around twin boundaries is also studied, and we have observed that the wave functions belonging to the conduction- and valence-band edge states in 3C-SiC tend to be localized almost exclusively on different sides of the faulted layers, while there is no such feature in Si or diamond.
We review of our theoretical work on various stacking faults in SiC polytypes. Since the discovery of the electronic degradation phenomenon in 4H-SiC p-i-n diodes, stacking faults in SiC have become a subject of intensive study around the globe. At the beginning of our research project, the aim was to find the culprit for the degradation phenomenon, but in the course of this work we uncovered a wealth of information for the general properties of stacking faults in SiC. An intuitive perspective to the diverse nature of stacking faults in SiC will be given in this conference report. (C) 2003 Published by Elsevier B.V.
Stress in epitaxial layers due to crystal lattice mismatch directly influences the growth, structure, and basic electrophysical parameters of epitaxial films and also to a large extent the degradation processes in semiconductor devices. In this letter, we present a theoretical model for calculating the induced lattice compression due to N doping and the critical thickness concerning formation of misfit dislocations in homoepitaxial 4H–SiC layers with different N-doping levels. For example: The model predicts that substrates with a N concentration of 3×10^{19} cm^{-3} induce misfit dislocations when the epilayer thickness reaches ∼10 μm. Also, the N-doping concentration in the 1×10^{18}–1×10^{19} cm^{-3} range yields a strain that not will cause misfit dislocactions at the substrate and epilayer interface until an epilayer thickness of 200–300 μm is reached. Supporting evidence of the induced lattice compression due to N doping have been done by synchrotron white-beam x-ray topography on samples with different N-doping levels and are compared with the predicted results from the model
Stress in epitaxial layers due to crystal lattice mismatch directly influences growth, structure, and basic electro-physical parameters of epitaxial films and also to a large extent the degradation processes in semiconductor devices. In this paper we present a theoretical model for calculating the induced lattice compression due to N doping and the critical thickness concerning formation of misfit dislocations in homoepitaxial 4H-SiC layers with different N doping levels. For example: The model predicts that substrates with N concentration of 3E19 induce misfit dislocations when the epilayer thickness reaches similar to10 mum. Also, N doping concentration in the 1E18-1E19 range yields a strain that not will cause misfit dislocactions at the substrate and epilayer interface until an epilayer thickness of 200-300 mum is reached. Supporting evidence of the induced lattice compression due to N doping have been done by synchrotron white-beam x-ray topography on samples with different N doping level and are compared with the predicted results from the model.
Soon after the discovery of the problem with electrical degradation of bipolar SiC devices, we started to perform ab initio calculations in order to evaluate the hypothesis that the degradation is caused by the expansion of stacking faults (SF) created by the propagation of partial dislocations in the (0001) basal plane. These investigations have created a wealth of important information, and constitutes a major part of our present understanding of the degradation phenomenon. Salient features are: (1) In 3C-, 4H-, 6H-, and 15R-SiC there are one, two, three, and five structurally different SFs, respectively, with different properties. (2) In 4H-, 6H- and 15R-SiC two of the different types of SFs give rise to states with energies around 0.2 eV (0.1-0.15 eV in 15R) below the conduction band. These states extend along the SF plane but are strongly localized to within around 10 A in the direction perpendicular to the SF plane. (3) These states and their one-dimensional confinement can be interpreted in terms of a quantum-well whose depth is determined by the conduction band offset between the relevant polytype and 3C-SiC. (4) Very shallow, localized (gap) states appear in some cases and can be related to the change in electronic polarization induced by the SF. (5) Calculated SF energies (SFE) are very close to both measured values and to the predictions of the simpler ANNNI (axial next nearest neighbour Ising) model. (6) The SFE in 3C-SiC is negative. (7) In 6H-SiC, the SFE for one of the SFs is considerably larger than for the other two. (8) In 15R-SiC, the SFEs for two of the SFs are almost zero. (9) The localized states described in item 2 are, beyond reasonable doubt, responsible for the electrical degradation. We have also investigated the electronic properties of two (2SF), three (3SF), and four SFs (4SF) in neighbouring planes in 4H-SiC, leading to thin 3C-like inclusions. Especially double SFs (2SF) have been observed, and may also be present in degraded devices. For these systems, some salient features are: (1) Like in the case of an isolated SF, localized gap states in the upper part of the band gap appear. The number of bound states, their energies and wave function localizations are well described by a quantum-well model. (2) The electronic polarization of the host crystal gives rise to a clear displacement of the wave functions for the localized gap states. (3) The SFE for a second SF in the presence of an already existing one (i.e., the change in total energy in going from ISF to 2SF) is around a factor four less than the SFE for the first SF. This is compatible with recent experimental observations.
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-, 4H- and 6H-SiC. It was found [Phys. Rev. B 65, 033203 (2002)] that both types of stacking faults in 4H-SiC and two types of stacking faults in 6H-SiC give rise to band states, which are strongly localized (confined within around 10 Angstrom) 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-SiC and the only stacking fault in 3C-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.
We present a theoretical investigation of how n- and p-type doping affect the band structure around the band gap of 3C-, 2H-, 4H-, and 6H-SiC. For comparison we also consider Si. We have calculated for various values of the dopant concentration (i) the shift in energy of the bottom (top) of the conduction (valence) band, (ii) the band gap narrowing, (iii) the shift of the optical band gap, and (iv) the doping-induced changes in conduction band curvature, i.e., changes in effective electron masses in n-type materials. In addition we have also (v) estimated the critical concentration for Mott transitions and (vi) calculated the shifts in conduction- and valence bands caused, not by doping, but by injection of an electron-hole plasma of various concentrations. To study the effects of doping we have considered a system consisting of impurity ions immersed in a (high-density) gas of majority carriers and a low-density gas of minority carriers. The changes in the bands relative to the idealised crystal are then regarded as being due to interparticle Coulomb interactions and associated particle correlation in and between the gases, as well as to electron and hole interactions with the randomly distributed ions. We have considered two models. The simplest model for band edge displacements is analytical and based on relatively simple assumptions like parabolic energy bands and simple modelling of electron correlation effects. The second model is numerical and includes full band non-parabolicity, and the electron and hole gas interactions are treated in the random-phase approximation.
Since the 1997 publication of Silicon Carbide - A Review of Fundamental Questions and Applications to Current Device Technology edited by Choyke, et al., there has been impressive progress in both the fundamental and developmental aspects of the SiC field. So there is a growing need to update the scientific community on the important events in research and development since then. The editors have again gathered an outstanding team of the world's leading SiC researchers and design engineers to write on the most recent developments in SiC. The book is divided into five main categories: theory, crystal growth, characterization, processing and devices. Every attempt has been made to make the articles as up-to-date as possible and assure the highest standards of accuracy. As was the case for earlier SiC books, many of the articles will be relevant a decade from now so that this book will take its place next to the earlier work as a permanent and essential reference volume.
Doping-induced energy shifts of the lowest conduction band and the uppermost valence band have been calculated for n-type 3 C-, 2H-, 4H-, 6H-SiC, and Si. We present the resulting narrowing of the fundamental band gap and of the optical band gap as functions of donor concentration. The effects on the curvature of the lowest conduction band have been investigated in detail for 3C- and 6H-SiC and, moreover, the effective electron masses in the vicinity of the conduction-band minimum have been calculated for,all five materials. The calculations go beyond the common parabolic treatments of the ground-state energy dispersion by using energy dispersion and overlap integrals from band structure calculations. The nonparabolic valence-band curvatures especially strongly influence the self-energies, but also the double-well minimum of 6H-SiC has effects on the self-energies and the resulting band curvatures. By comparing the total energy of the electron gas with the total energy of electrons in a nonmetal phase, we estimate the critical Mott concentration for the metal-nonmetal transition. The utilized method is based on a zero-temperature formalism within the random phase approximation with local field correction according to Hubbard. [S0163-1829(99)12647-X].
Plasma-induced energy shifts of the conduction band minimum and of the valence band maximum have been calculated for 3C-, 2H-, 4H-, 6H-, 6H-SiC and Si. The resulting narrowing of the fundamental band gap and of the optical band gap are presented. The method utilized is based on a zero-temperature formalism within the random phase approximation. Electron-electron, hole-hole, electron-hole, electron-optical phonon and hole-optical phonon interactions have been taken into account. The calculations are based on band structure data from a relativistic, full-potential band structure calculation.