Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Electronic states of a hydrogenic donor impurity in semiconductor nano-structures

We propose a method for uniformly calculating the electronic states of a hydrogenic donor impurity in low-dimensional semiconductor nano-structures in the framework of effective-mass envelope-function theory, and we study the electronic structures of this systems. Compared to previous methods, our method has the following merits: (a) It can be widely applied in the calculation of the electronic states of hydrogenic donor impurities in nano-structures of various shapes; (b) It can easily be extended to study the effects of external fields and other complex cases; (c) The excited states are more easily calculated than with the variational method; (d) It is convenient to calculate the change of the electronic states with the position of a hydrogenic donor impurity in nano-structures; (e) The binding energy can be calculated explicitly. (c) 2007 Elsevier B.V. All rights reserved.

Self-assembling of submicrometer three-dimensional photonic crystals in concave microzones etched on silicon substrates

By vertical sedimentation and oblique titration, silica microspheres were grown in different shapes of concave microzones that were etched on a (100) p-silicon substrate. Through scanning electron microscope observation and optical reflective spectra measurement, sedimentation of microspheres in those microzones was compared. An index was introduced to judge the efficiency of sedimentation. The comparison demonstrates that regular hexagons and triangles facilitate the growth of photonic crystals the most. (c) 2006 Optical Society of America

Electronic structures of GaAs/AlxGa1-xAs quantum double

In the framework of effective mass envelope function theory, the electronic structures of GaAs/AlxGa1-xAs quantum double rings(QDRs) are studied. Our model can be used to calculate the electronic structures of quantum wells, wires, dots, and the single ring. In calculations, the effects due to the different effective masses of electrons and holes in GaAs and AlxGa1-xAs and the valence band mixing are considered. The energy levels of electrons and holes are calculated for different shapes of QDRs. The calculated results are useful in designing and fabricating the interrelated photoelectric devices. The single electron states presented here are useful for the study of the electron correlations and the effects of magnetic fields in QDRs.

Transport phenomena in radial flow MOCVD reactor with three concentric vertical inlets

Transport phenomena in radial flow metalorganic chemical vapor deposition (MOCVD) reactor with three concentric vertical inlets are studied by two-dimensional numerical modeling. By varying the parameters such as gas pressure, flow rates combination of multi-inlets, geometric shapes and sizes of reactor and flow distributor, temperatures of susceptor and ceiling, and susceptor rotation, the corresponding velocity, temperature, and concentration fields inside the reactor are obtained; the onset and change of flow recirculation cells under influences of those parameters are determined. It is found that recirculation cells, originated from flow separation near the bend of reactor inlets, are affected mainly by the reactor height and shape, the operating pressure, the flow rates combination of multi-inlets, and the mean temperature between susceptor and ceiling. By increasing the flow rate of mid-inlet and the mean temperature, decreasing the pressure, maintaining the reactor height below certain criteria, and trimming the bends of reactor wall and flow distributor to streamlined shape, the recirculation cells can be minimized so that smooth and rectilinear flow prevails in the susceptor region, which corresponds to smooth and rectilinear isotherms and larger reactant concentration near the susceptor. For the optimized reactor shape, the reactor size can be enlarged to diameter D = 40 cm and height H = 2 cm without flow recirculation. The susceptor rotation over a few hundred rpm around the reactor central axis will induce the recirculation cell near the exit and deflect the streamlines near the susceptor, which is not the case for vertical reactors. (c) 2006 Elsevier B.V. All rights reserved.

Micro-mould method for self-assembling three-dimensional opal photonic crystals

By vertical sedimentation, silica micro-spheres were grown in different shapes of concave micro-zones which were etched on a (100) p-silicon substrate. The following were found: this method can effectively raise the quality of films by avoiding cracks; the geometry of the micro-zones affects the sediment of the film; regular hexagons and triangles best facilitate the growth of photonic crystals. This method is practical for its ability to fabricate self-assembly photonic crystals in previously designed small areas.

Electron and hole transport through quantum dots

The transmission through quantum dots (QDs) is calculated using the recursion method. In our calculation, the effect of finite offset is taken into account. The results show that the shapes of the QDs determine the number of resonant tunneling peaks and the distances between the peaks decrease as the radii of the QDs increase. The intensities of the conductance are strongly dependent on the barrier widths. The conductance peaks are split when transmitting through two QDs. The theoretical results qualitatively agree with the available experimental data. Our calculated results should be useful for the application of QDs to photoelectric devices. (C) 2002 American Institute of Physics.

Nanofabrication of grid-patterned substrate by holographic lithography

The two-dimensional grid patterns on Si(001) in nanometer scale have been fabricated by holographic lithography and reactive ion etching, which can be used as a substrate for positioning Ge islands during self-assembled epitaxy to obtain an ordered Ge quantum dots matrix. By changing the configuration of the holographic lithography and the etching rate and time, we can control the grid period, the shape of the pattern cell, and the orientation of those shapes, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.

Valence band structures of the InAs/GaAs quantum ring

In the framework of effective-mass envelope function theory, the valence energy subbands and optical transitions of the InAs/GaAs quantum ring are calculated by using a four-band valence band model. Our model can be used to calculate the hole states of quantum wells, quantum wires, and quantum dots. The effect of finite offset and valence band mixing are taken into account. The energy levels of the hole are calculated in the different shapes of rings. Our calculations show that the effect of the difference between effective masses of holes in different materials on the valence subband structures is significant. Our theoretical results are consistent with the conclusion of the recent experimental measurements and should be useful for researching and making low-dimensional semiconductor optoelectronic devices. (C) 2002 American Institute of Physics.

Electronic states of InAs/GaAs quantum ring

In the framework of effective mass envelope function theory, the electronic states of the InAs/GaAs quantum ring are studied. Our model can be used to calculate the electronic states of quantum wells, quantum wires, and quantum dots. In calculations, the effects due to the different effective masses of electrons in rings and out rings are included. The energy levels of the electron are calculated in the different shapes of rings. The results indicate that the inner radius of rings sensitively changes the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. If decreasing the inner and outer radii simultaneously, one may increase the energy spacing between energy levels and keep the ground state energy level unchanged. If changing one of two radii (inner or outer radius), the ground state energy level and the energy spacing will change simultaneously. These results are useful for designing and fabricating the double colors detector by intraband and interband translations. The single electron states are useful for studying the electron correlations and the effects of magnetic fields in quantum rings. Our calculated results are consistent with the recent experimental data of nanoscopic semiconductor rings. (C) 2001 American Institute of Physics.

Theoretical analysis and experimental study of Fourier transformation of Franz-Keldysh oscillations in GaAs

Fourier transformation (FT) has been used in the theoretical line shape analysis of Franz-Keldysh oscillations (FKOs) in detail by numerical simulations. FKOs from the surface-intrinsic-n(+) GaAs structure were obtained in photoreflectance (PR) measurements with various modulation light intensities and with different strengths of bias light illumination, which were used to change the static electric field in the intrinsic layer of the sample. The FT spectra of the PR spectra, including the real part, imaginary part, and the modulus, were very consistent with the theoretical line shapes. The ratio of the square root of the reduced mass (root mu (L)/root mu (H)) and the ratio of transition strength of the electron heavy hole to the electron light hole were obtained from the PT spectra. In addition, the electric field in the intrinsic layer of the sample without and with bias illumination and the modulation field induced by photomodulation were also obtained. (C) 2000 American Institute of Physics. [S0021-8979(00)02123-X].

Influence of indium composition on the surface morphology of self-organized InxGa1-xAs quantum dots on GaAs substrates

InxGa1-xAs self-organized quantum dots with x=1.0, 0.5, and 0.35 have been grown by molecular beam epitaxy. The areal density, distribution, and shapes have been found to be dependent on x. The dot shape changes from a round shape for x=1.0 to an elliptical shape for x less than or equal to 0.5. The major axis and minor axis of the elliptical InxGa1-xAs dots are along the [(1) over bar 10] and [110] directions, respectively. The ordering phenomenon is also discussed. It is suggested that the dot-dot interaction may play important roles in the self-organization process. (C) 2000 American Institute of Physics. [S0021-8979(00)10701-7].

Structural and optical properties of self-assembled InAs quantum dots grown on GaAs (311) A substrate

We report the structural and optical characteristics of InAs quantum dots (QDs) grown on GaAs (311)A substrates. Atomic force microscopic result shows that QDs on (311)A surface exhibit a nonconventional, faceted, arrowhead-like shapes aligned in the [233] direction. The photoluminescence (PL) intensity, peak position and the full width at half maxinum (FWHM) are all closely related to the measurement temperature. The fast redshift of PL energy and monotonous decrease of linewidth with increasing temperature were observed and explained by carriers being thermally activated to the barrier produced by the wetting layer and then being retrapped and recombined in energetically lower-lying QDs states. This model explains our results well.

Structural and optical characteristics of self-organized InAs quantum dots grown on GaAs (3 1 1)A substrates

Structural and optical investigations of InAs QDs grown on GaAs (3 1 1)A by molecular beam epitaxy (MBE) were reported. InAs/GaAs (3 1 1)A QDs with nonconventional, faceted, arrowhead-like shapes aligned in the [ - 2 3 3] direction have been disclosed by AFM image. Low defect and dislocation density on the QDs interfaces were indicated by the linear dependence of photoluminescence (PL) intensity on the excitation power. The fast red shift of PL energy and the monotonic decrease of FWHM with increasing temperature were observed and explained by carriers being thermally activated to the energy barrier produced by the wetting layer and then retrapped and recombined in energetically low-lying QDs states. (C) 1999 Elsevier Science B.V. All rights reserved.

Degenerate four-wave-mixing signals from dc- and ac-driven semiconductor superlattice

Within the one-dimensional tight-binding model;rnd chi-3 approximation, we have calculated four-wave-mixing (FWM) signals for a semiconductor superlattice in the presence of both static and high-frequency electric fields. When the exciton effect is negligible, the time-periodic field dynamically delocalizes the otherwise localized Wannier-Stark states, and accordingly quasienergy band structures are formed, and manifest in the FWM spectra as a series of equally separated continua. The width of each continuum is proportional to the joint width of the valence and conduction minibands and is independent of the Wannier-Stark index. The realistic homogeneous broadening blurs the continua into broad peaks, whose line shapes, far from the Lorentzian, vary with the delay time in the FWM spectra. The swinging range of the peaks is just the quasienergy bandwidth. The dynamical delocalization (DDL) also induces significant FWM signals well beyond the excitation energy window. When the Coulomb interaction is taken into account, the unequal spacing between the excitonic Wannier-Stark levels weakens the DDL effect, and the FWM spectrum is transformed into groups of discrete lines. Strikingly, the groups are evenly spaced by the ac field frequency, reflecting the characteristic of the quasienergy states. The homogeneous broadening again smears out the line structures, leading to the excitonic FWM spectra quite similar to those without the exciton effect. However, all these features predicted by the dynamical theory do not appear in a recent experiment [Phys. Rev. Lett. 79, 301 (1997)], in which, by using the static approximation the observed Wannier-Stark ladder with delay-time-dependent spacing in the FWM spectra is attributed to a temporally periodic dipole field, produced by the Bloch oscillation of electrons in real space. The contradiction between the dynamical theory and the experiments is discussed. In addition, our calculation indicates that the dynamical localization coherently enhances the time-integrated FWM signals. The feasibility of using such a technique to study the dynamical localization phenomena is shown. [S0163-1829(99)10607-6].