Electronic states in spherical GaN nanocrystals embedded in various dielectric matrices: The k ⋅ p-calculations
TL;DR: In this article, the single-particle states of spherical GaN nanocrystals embedded in different amorphous dielectric matrices (SiO2, Al2O3, HfO2 and Si3N4) have been calculated using the isotropic approximation of the k ⋅ p -Hamiltonian.
Abstract: Using the envelope-function approximation, the single-particle states of electrons and holes in spherical GaN nanocrystals embedded in different amorphous dielectric matrices (SiO2, Al2O3, HfO2 and Si3N4) have been calculated. Ground state energies of electrons and holes in GaN nanocrystals are determined using the isotropic approximation of the k ⋅ p -Hamiltonian. All the ground state energies are found to increase with lowering the nanocrystal size and are proportional to the R−n, where R is the nanocrystal radius, n =1.5-1.9 for electrons and 1.7-2.0 for holes. The optical gap of GaN nanocrystals changes from 3.8 to 5 eV for the nanocrystal radius ranging from 3 to 1 nm.
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TL;DR: In this article, the energy eigenvalues, linear, nonlinear and total dielectric functions for GaN/AlxGa1-xN core/shell quantum dot (CSQD) encapsulated with three different matrices (PVA, PMMA and SiO2) were computed.
Abstract: In this research, the effective mass approximation (E.M.A) and the compact density matrix approach have been used to compute the energy eigenvalues, linear, nonlinear and total dielectric functions for GaN/AlxGa1-xN core/shell quantum dot (CSQD) encapsulated with three different matrices (PVA, PMMA and SiO2). The influence of the geometrical factor (core to shell radii ratio) on the electron spectrum and transition energy has been analyzed. Our theoretical investigation indicated that with the appropriate dielectric environment, peaks of the real and imaginary parts of the linear, nonlinear and total dielectric functions can be spectacularly enhanced and experience a red or a blue shift. These findings suggest the possibility of tuning the resonant peaks by using the combined effect of the spatial confinement and dielectric discontinuity between the dot and the surrounding medium which can be beneficial in many fields especially for optoelectronic device applications.
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TL;DR: In this paper, 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 is presented.
Abstract: 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...
2,525 citations
TL;DR: In this paper, a new method of developing an "effective-mass" equation for electrons moving in a perturbed periodic structure is discussed, particularly adapted to such problems as arise in connection with impurity states and cyclotron resonance in semiconductors such as Si and Ge.
Abstract: A new method of developing an "effective-mass" equation for electrons moving in a perturbed periodic structure is discussed. This method is particularly adapted to such problems as arise in connection with impurity states and cyclotron resonance in semiconductors such as Si and Ge. The resulting theory generalizes the usual effective-mass treatment to the case where a band minimum is not at the center of the Brillouin zone, and also to the case where the band is degenerate. The latter is particularly striking, the usual Wannier equation being replaced by a set of coupled differential equations.
2,260 citations
TL;DR: The observed shortening of the luminescence decay time in CdSe nanoncrystals in a magnetic field is in excellent agreement with the theory, giving further support to the validity of the model.
Abstract: We present a theoretical analysis of the band-edge exciton structure in nanometer-size crystallites of direct semiconductors with a cubic lattice structure or a hexagonal lattice structure which can be described within the framework of a quasicubic model. The lowest energy exciton, eightfold degenerate in spherically symmetric dots, is split into five levels by the crystal shape asymmetry, the intrinsic crystal field (in hexagonal lattice structures), and the electron-hole exchange interaction. Transition oscillator strengths and the size dependence of the splittings have been calculated. Two of the five states, including the ground state, are optically passive (dark excitons). The oscillator strengths of the other three levels (bright excitons) depend strongly on crystal size, shape, and energy band parameters. The relative ordering of the energy levels is also heavily influenced by these parameters. The distance between the first optically active state and the optically forbidden ground exciton state increases with decreasing size, leading to an increase of the Stokes shift in the luminescence. Our results are in good agreement with the size dependence of Stokes shifts obtained in fluorescence line narrowing and photoluminescence experiments in CdSe nanocrystals. Mixing of the dark and bright excitons in an external magnetic field allows the direct optical recombination of the dark exciton ground state. The observed shortening of the luminescence decay time in CdSe nanoncrystals in a magnetic field is also in excellent agreement with the theory, giving further support to the validity of our model. \textcopyright{} 1996 The American Physical Society.
1,180 citations
TL;DR: In this article, the band offsets of various gate dielectrics including HfO2, Al2O3, Gd2O 3, Si3N4, and SiO2 on III-V semiconductors such as GaAs, InAs, GaSb, and GaN have been calculated using the method of charge neutrality levels.
Abstract: III-V semiconductors have high mobility and will be used in field effect transistors with the appropriate gate dielectric. The dielectrics must have band offsets over 1eV to inhibit leakage. The band offsets of various gate dielectrics including HfO2, Al2O3, Gd2O3, Si3N4, and SiO2 on III-V semiconductors such as GaAs, InAs, GaSb, and GaN have been calculated using the method of charge neutrality levels. Generally, the conduction band offsets are found to be over 1eV, so they should inhibit leakage for these dielectrics. On the other hand, SrTiO3 has minimal conduction band offset. The valence band offsets are also reasonably large, except for Si nitride on GaN and Sc2O3 on GaN which are 0.6–0.8eV. There is reasonable agreement with experiment where it exists, although the GaAs:SrTiO3 case is even worse in experiment.
632 citations
TL;DR: In this article, the electronic properties of the wurtzite-type AlN and GaN were analyzed on the basis of the effective-mass Hamiltonian, where the hexagonal symmetry was considered.
Abstract: The electronic band structures of the wurtzite-type AlN and GaN are calculated by using a self-consistent full-potential linearized augmented plane-wave method within the local-density-functional approximation. In order to clarify the electronic properties near the Brillouin-zone (BZ) center and to give an important guideline on the material designs for short-wavelength optical devices, we link the first-principles band calculations with the effective-mass approximation. The electronic properties are analytically studied on the basis of the effective-mass Hamiltonian, where we consider the hexagonal symmetry of the wurtzite structure. The effective-mass parameters, such as electron effective mass, hole effective masses, or, equivalently, the Luttinger-like parameters, crystal-field splitting and spin-orbit splitting, are determined by reproducing the calculated band structures near the BZ center. The obtained results show that the cubic approximation is fairly successful in the analysis for the valence-band structures of the wurtzite-type nitrides. Further, the calculated parameters for GaN are consistent with the observed ones.
520 citations