Electronic structure and optical gain saturation of InAs1-xNx/GaAs quantum dots

The electronic band structures and optical gains of InAs1-xNx/GaAs pyramid quantum dots (QDs) are calculated using the ten-band k . p model and the valence force field method. The optical gains are calculated using the zero-dimensional optical gain formula with taking into consideration of both homogeneous and inhomogeneous broadenings due to the size fluctuation of quantum dots which follows a normal distribution. With the variation of QD sizes and nitrogen composition, it can be shown that the nitrogen composition and the strains can significantly affect the energy levels especially the conduction band which has repulsion interaction with nitrogen resonant state due to the band anticrossing interaction. It facilitates to achieve emission of longer wavelength (1.33 or 1.55 mu m) lasers for optical fiber communication system. For QD with higher nitrogen composition, it has longer emission wavelength and less detrimental effect of higher excited state transition, but nitrogen composition can affect the maximum gain depending on the factors of transition matrix element and the Fermi-Dirac distributions for electrons in the conduction bands and holes in the valence bands respectively. For larger QD, its maximum optical gain is greater at lower carrier density, but it is slowly surpassed by smaller QD as carrier concentration increases. Larger QD can reach its saturation gain faster, but this saturation gain is smaller than that of smaller QD. So the trade-off between longer wavelength, maximum optical, saturation gain, and differential gain must be considered to select the appropriate QD size according to the specific application requirement. (C) 2009 American Institute of Physics. [DOI 10.1063/1.3143025]

Electronic structure and optical gain saturation of InAs1-xNx/GaAs quantum dots

The electronic band structures and optical gains of InAs1-xNx/GaAs pyramid quantum dots (QDs) are calculated using the ten-band k . p model and the valence force field method. The optical gains are calculated using the zero-dimensional optical gain formula with taking into consideration of both homogeneous and inhomogeneous broadenings due to the size fluctuation of quantum dots which follows a normal distribution. With the variation of QD sizes and nitrogen composition, it can be shown that the nitrogen composition and the strains can significantly affect the energy levels especially the conduction band which has repulsion interaction with nitrogen resonant state due to the band anticrossing interaction. It facilitates to achieve emission of longer wavelength (1.33 or 1.55 mu m) lasers for optical fiber communication system. For QD with higher nitrogen composition, it has longer emission wavelength and less detrimental effect of higher excited state transition, but nitrogen composition can affect the maximum gain depending on the factors of transition matrix element and the Fermi-Dirac distributions for electrons in the conduction bands and holes in the valence bands respectively. For larger QD, its maximum optical gain is greater at lower carrier density, but it is slowly surpassed by smaller QD as carrier concentration increases. Larger QD can reach its saturation gain faster, but this saturation gain is smaller than that of smaller QD. So the trade-off between longer wavelength, maximum optical, saturation gain, and differential gain must be considered to select the appropriate QD size according to the specific application requirement. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3143025]

Existence of the transverse relaxation time in optically excited bulk semiconductors

Two basic types of depolarization mechanisms, carrier-carrier (CC) and carrier-phonon (CP) scattering, are investigated in optically excited bulk semiconductors (3D), in which the existence of the transverse relaxation time is proven based on the vector property of the interband transition matrix elements. The dephasing rates for both CC and CP scattering are determined to be equal to one half of the total scattering-rate-integrals weighted by the factors (1 - cos chi), where chi are the scattering angles. Analytical expressions of the polarization dephasing due to CC scattering are established by using an uncertainty broadening approach, and analytical ones due to both the polar optical-phonon and non-polar deformation potential scattering (including inter-valley scattering) are also presented by using the sharp spectral functions in the dephasing rate calculations. These formulas, which reveal the trivial role of the Coulomb screening effect in the depolarization processes, are used to explain the experimental results at hand and provide a clear physical picture that is difficult to extract from numerical treatments.

The origin of the transverse relaxation time in optically excited semiconductor quantum wells

The origin of the transverse relaxation time in optically excited semiconductor quantum wells is investigated based on the vector property of the interband transition matrix elements. The dephasing rate due to carrier-carrier (CC) scattering is found to be equal to half of the common momentum relaxation rate. The analytical expression of the polarization dephasing due to CC scattering in two-dimension is established and the dependence of the dephasing rate Gamma(cc) on the carrier density N is determined to be Gamma(cc) = constant (.) N-1/2, which is used to explain the experimental results and provides a promising physical picture. (C) 2004 Elsevier B.V. All rights reserved.

Effects of Yb3+ in Er3+/Yb3+ codoped fluorophosphate glasses

For the Er3+/Yb3+ codoped fluorophosphate glasses, Judd-Ofelt theory is used to analyse the influence of YbF3 as not a sensitizer but an average component on the spectroscopic properties around 1530 nm emission. The double roles of Yb3+, as a sensitizer and as an average component, are discussed. It is found that Yb3+ as an average component contributes to the increase of fluorescence lifetime, and Yb3+ as a sensitizer has the best sensitization when its concentration is 2.4 mol%.

Electronic structure and optical gain of truncated InAs1-xNx/GaAs quantum dots

The shape of truncated square-based pyramid quantum dots (QDs) is similar to that of real QDs in experiments. The electronic band structures and optical gain of InAs1-xNx/GaAs QDs are calculated by using the 10-band k.p model, and the strain is calculated by the valence force field (VFF) method. When the top part of the QD is truncated, greater truncation corresponds to a flatter shape of the QD. The truncation changes the strain distribution and the confinement in the z direction. A flatter QD has a greater C1-HH1 transition energy, greater transition matrix element, less detrimental effect of higher excited transition, and higher saturation gain and differential gain. The trade-off between these properties must be considered. From our results, a truncated QD with half of its top part removed has better overall performance. This can provide guidance to growing QDs in experiments in which the proper growing conditions can be controlled to achieve required properties. (C) 2009 Elsevier Ltd. All rights reserved.

Electronic structure and optical properties of quantum rods with wurtzite structure

The Hamiltonian of the wurtzite quantum rods with an ellipsoidal boundary is given after a coordinate transformation. The energies, wave functions, and transition possibilities are obtained as functions of the aspect ratio e with the same method we used on spherical dots. With an overall consideration of both the transition matrix element and the Boltzmann distribution we explained why the polarization factor increases with increasing e and approaches a saturation value, which tallies quite well with the experimental result. When e increases more and more S-z states are mixed into the ground, second, and third states of J(z)=1/2, resulting in an increase of the emission of z polarization. It is just the linear terms of the momentum operator in the hole Hamiltonian that cause the mixing of S and P states in the hole ground state. The effects of the crystal field splitting energy, temperature, and transverse radius to the polarization are also considered. We also calculated the band gap variation with the size and shape of the quantum rods.

Electronic structures of cubic lattice quantum dots

In this article, we give the electronic structure and optical transition matrix elements of coupled quantum dots (QDs) arranged as different cubic lattices: simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) superlattices. The results indicate that electron and hole energies of bcc, sc, and fcc superlattices are the lowest, the highest, and the middle, respectively, for the same subband under the same QD density or under the same superlattice constant. For a fixed QD density, the confinement effects in sc, fcc, and bcc superlattices are the strongest, the middle, and the weakest, respectively. There are only one, two, and four confined energy bands, with energies lower than the potential barrier for sc, bcc, and fcc QD superlattices, respectively. The results have great significance for researching and making semiconductor quantum dot devices. (C) 1998 American Institute of Physics. [S0021-8979(98)02119-7]

Quantum confinement effect in silicon quantum-well layers

The electronic states and optical transition properties of silicon quantum-well layers embedded by SiO2 layers are studied by the empirical pseudopotential homojunction model. The energy bands, wave functions, and the optical transition matrix elements are obtained for layers of thickness from 1 to 6 nm, and three oriented directions (001), (110), and (111). It is found that for Si layers in the (001) direction the energy gap is pseudodirect, for these in the (111) direction the energy gap is indirect, while for those in the (110) direction the energy gap is pseudodirect or indirect for a thickness smaller or larger than 3 nm, respectively. The optical transition matrix elements are smaller than that of diner transition, and increase with decreasing layer thickness. When the thickness of a layer is smaller than 2 nm, the Si QW layers have larger transition matrix elements. It is caused by mixing of bulk X states with the Gamma(1) state. The calculated results are compared with experimental results.

EFFECTIVE-MASS THEORY FOR GAAS/GA1-XALXAS QUANTUM WIRES AND CORRUGATED SUPERLATTICES GROWN ON (311)-ORIENTED SUBSTRATES

The electronic structures of GaAs/Ga1-xAlxAs quantum wires (corrugated superlattices) grown on (311)-oriented substrates are studied in the framework of the effective-mass envelope-function method. The electron and hole subband structure and optical transition matrix elements are calculated. When x=1, the results are compared with experiments, and it is found that the direct transition becomes an indirect transition as the widths of well and barrier become smaller.

THEORY OF THE ELECTRONIC-STRUCTURE OF POROUS SI

A theoretical model for the electronic structure of porous Si is presented. Three geometries of porous Si (wire with square cross section, pore with square cross section, and pore with circular cross section) along both the [001] and [110] directions are considered. It is found that the confinement geometry affects decisively the ordering of conduction-band states. Due to the quantum confinement effect, there is a mixing between the bulk X and GAMMA states, resulting in finite optical transition matrix elements, but smaller than the usual direct transition matrix elements by a factor of 10(-3). We found that the strengths of optical transitions are sensitive to the geometry of the structure. For (001) porous Si the structure with circular pores has much stronger optical transitions compared to the other two structures and it may play an important role in the observed luminescence. For this structure the energy difference between the direct and the indirect conduction-band minima is very small. Thus it is possible to observe photoluminescence from the indirect minimum at room temperature. For (110) porous Si of similar size of cross section the energy gap is smaller than that of (001) porous Si. The optical transitions for all three structures of (110) porous Si tend to be much stronger along the axis than perpendicular to the axis.

ELECTRONIC-STRUCTURES OF QUANTUM WIRES FORMED BY LATERAL STRAIN

The electronic structures of quantum wires formed by lateral strain are studied in the framework of the effective-mass envelope-function method. The hole energy levels, wave functions, and optical transition matrix elements are calculated for the real quantum-wire structure, and the results are compared with experiment. It is found that one-dimensional confinement effects exist for both electronic and hole states related to the n (001) = 1 state. The lateral strained confinement causes luminescence-peak redshifts and polarization anisotropy, and the anisotropy is more noticeable than that in the unstrained case. The variation of hole energy levels with well widths in the [110] and [001] directions and wave vector along the [110BAR] direction are also obtained.

EFFECTIVE-MASS THEORY FOR SUPERLATTICES GROWN ON (11N)-ORIENTED SUBSTRATES

An effective-mass formulation for superlattices grown on (11N)-oriented substrates is given. It is found that, for GaAs/AlxGa1-xAs superlattices, the hole subband structure and related properties are sensitive to the orientation because of the large anisotropy of the valence band. The energy-level positions for the heavy hole and the optical transition matrix elements for the light hole apparently change with orientation. The heavy- and light-hole energy levels at k parallel-to = 0 can be calculated separately by taking the classical effective mass in the growth direction. Under a uniaxial stress along the growth direction, the energy levels of the heavy and light holes shift down and up, respectively; at a critical stress, the first heavy- and light-hole energy levels cross over. The energy shifts caused by the uniaxial stress are largest for the (111) case and smallest for the (001) case. The optical transition matrix elements change substantially after the crossover of the first heavy- and light-hole energy has occurred.

Effective-mass theory for InAs/GaAs strained superlattices

By using the recently developed exact effective-mass envelope-function theory, the electronic structures of InAs/GaAs strained superlattices grown on GaAs (100) oriented substrates are studied. The electron and hole subband structures, distribution of electrons and holes along the growth direction, optical transition matrix elements, exciton states, and absorption spectra are calculated. In our calculations, the effects due to the different effective masses of electrons and holes in different materials and the strain are included. Our theoretical results are in agreement with the available experimental data.

Quantum confinement effect in thin quantum wires

The electronic states and optical transition properties of three semiconductor wires Si? GaAs, and ZnSe are studied by the empirical pseudopotential homojunction model. The energy levels, wave functions, optical transition matrix elements, and lifetimes are obtained for wires of square cross section with width from 2 to 5 (root 2a/2), where a is the lattice constant. It is found that these three kinds of wires have different quantum confinement properties. For Si wires, the energy gap is pseudodirect, and the wave function of the electronic ground state consists mainly of four bulk Delta states. The optical transition matrix elements are much smaller than that of a direct transition, and increase with decreasing wire width. Where the width of wire is 7.7 Angstrom, the Si wire changes from an indirect energy gap to a direct energy gap due to mixing of the bulk Gamma(15) state. For GaAs wires. the energy gap is also pseudodirect in the width range considered, but the optical transition matrix elements are larger than those of Si wires by two orders of magnitude for the same width. However, there is no transfer to a direct energy gap as the wire width decreases. For ZnSe wires, the energy gap is always direct, and the optical transition matrix elements are comparable to those of the direct energy gap bulk semiconductors. They decrease with decreasing wire width due to mixing of the bulk Gamma(1) state with other states. All quantum confinement properties are discussed and explained by our theoretical model and the semiconductor energy band structures derived. The calculated lifetimes of the Si wire, and the positions of photoluminescence peaks, are in good agreement with experimental results.