Parabolic Band Approximation Research Articles

Donor impurity states and related optical responses in triangular quantum dots under applied electric field

The linear and nonlinear coefficients for the optical absorption and relative refractive index change associated with transitions between donor impurity states in a two-dimensional quantum dot of triangular shape under applied electric field are calculated for y-polarization of the incident light. Both the effective mass and parabolic band approximations have been considered. The results show that the application of a DC electric field strengthens the impurity-related optical absorption response, with particular relevance in the case of the nonlinear contribution to it. However, for a fixed donor atom position inside the triangular quantum dot, the calculations show that the in-plane orientation of the applied field can becomes a critical parameter that may lead to a strong quenching of the interstate light absorption.

Pressure-dependent of linear and nonlinear optical properties of (In,Ga)N/GaN spherical QD

Third-order nonlinear intra-conduction band optical properties of (In,Ga)N–GaN spherical quantum dot are investigated. Linear, third-order nonlinear and total absorption coefficients (ACs) of 1p–1d and 1d–1f transitions are computed using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock–Roothaan (HFR) method. Hydrostatic pressure effect is examined within the single band effective-mass and the one parabolic band approximations under finite potential barrier. The results show that the hydrostatic pressure has a great impact on the optical properties of QDs. A blue shift of the resonant peak is observed while the maximum of the amplitude of optical absorption coefficients decreases nonlinearly under hydrostatic pressure effect. Two competing parameters are suggested to explain our results. Compared with the finding results, a good agreement is shown.

Inter-band optoelectronic properties in quantum dot structure of low band gap III-V semiconductors

A generalized theory is developed to study inter-band optical absorption coefficient (IOAC) and material gain (MG) in quantum dot structures of narrow gap III-V compound semiconductor considering the wave-vector (k→) dependence of the optical transition matrix element. The band structures of these low band gap semiconducting materials with sufficiently separated split-off valance band are frequently described by the three energy band model of Kane. This has been adopted for analysis of the IOAC and MG taking InAs, InSb, Hg1−xCdxTe, and In1−xGaxAsyP1−y lattice matched to InP, as example of III–V compound semiconductors, having varied split-off energy band compared to their bulk band gap energy. It has been found that magnitude of the IOAC for quantum dots increases with increasing incident photon energy and the lines of absorption are more closely spaced in the three band model of Kane than those with parabolic energy band approximations reflecting the direct the influence of energy band parameters. The results show a significant deviation to the MG spectrum of narrow-gap materials having band nonparabolicity compared to the parabolic band model approximations. The results reflect the important role of valence band split-off energies in these narrow gap semiconductors.

Electron-related optical responses in triangular quantum dots

The linear and nonlinear coefficients for the optical absorption and relative refractive index change associated with intersubband transitions of electrons in the conduction band of a two-dimensional quantum dot of triangular shape are calculated for x-polarization and y-polarization of the incident light. Both the effective mass and parabolic band approximations have been considered. The results show that the increase in the size of the triangular quantum dot leads to the expected fall of the intersubband energy transition and that there is an increment in the values of the associated off-diagonal electric dipole moment matrix elements. All this reflects in the increase of the amplitude of the nonlinear optical absorption resonant peak, as well as in the growth of the total relative refractive index in the system.

Excited-states of hydrogenic-like impurities in InGaN–GaN spherical QD: Electric field effect

By means of a traditional Ritz variational method within the effective-mass and single parabolic band approximations, the excited-states energy with and without the existence of the impurity is performed. Externally applied electric field and system radius effects are considered in wurtzite (In,Ga)N–GaN spherical quantum dot with finite potential barrier. The normalized binding energy is also reported. Compared to the previous theoretical findings, a good agreement is shown.

Electric field effects on the electronic states in a triangular prism nanocrystal

The effect of applied electric fields on the binding energy and polarizability of a donor impurity in a prism-shaped GaAs quantum dot with triangular cross-section is theoretically investigated. Calculations have been made in the effective mass and parabolic band approximations by using a finite element method. The results are reported for the ground and the first excited states of an on-center donor when the electric field is applied along different directions of the quantum dot. We found that the variation of the binding energy reflects the spatial distributions of the electron wave functions, which significantly changes when the electric field is varied. In this low-symmetry system the impurity polarizability exhibits a strong dependence on the applied field direction.

Exciton states in CdSe/ZnS core–shell quantum dots under applied electric fields

Within the effective-mass and parabolic-band approximations, the effect of the applied electric field on the exciton states in CdSe/ZnS core–shell quantum dots is investigated. Electron and hole single-particle energies as functions of the electric field are obtained by using the finite element method. The Coulomb interaction is calculated in the first-order perturbation theory, and optical absorption wavelengths of the nanocrystals with a fixed outer radius and different shell thicknesses are compared. We found that the spatial distribution of the carrier wave functions inside the heterostructure and emission spectra of the excitons can be tuned by varying the core size and the electric field strength.

Electric field effect on the third-order nonlinear optical susceptibility in inverted core–shell nanodots with dielectric confinement

Third-order nonlinear optical processes associated with the interlevel transitions in ZnS/CdSe core–shell quantum dots under electric fields are theoretically investigated. Taking into account the dielectric mismatch with the surrounding matrix, the electronic structure of the dots is obtained within the effective mass and parabolic band approximations. It is shown that large applied electric fields break the symmetry of the confinement potential and lead to a significant blue-shift of the peak positions in the nonlinear optical spectrum. The size effect is also discussed and it is proved that large nonlinear susceptibility can be obtained by increasing the thickness of the nanocrystal shell. Our results suggest that external factors such as the applied electric field and orientation of the incident light polarization can be used – in addition to spatial confinement – to improve the performances of the optical devices.

Impact ionization threshold energy of trigonal selenium: An ab initio study

Impact ionization coefficient is a critical parameter that determines the multiplication gain in avalanche photodiodes. The impact ionization coefficient is closely related to the ionization threshold, Eth, which is determined by the band dispersion of the semiconducting material used in detectors. The ionization threshold energy is commonly calculated based on a parabolic band assumption, which provides only a crude approximation. Here we present a first principle study of the ionization threshold energy through an analysis of the electronic structure of trigonal selenium. It is shown that the excess energy of primary charge carriers required to initiate the impact ionization in trigonal selenium can be as low as the band gap, Eg, which is a sharp contrast to the parabolic band approximation that implies Eth = 3/2Eg. Such a low Eth value is a favourable factor for impact ionization.

A model for multiphoton absorption in dielectric materials induced by short laser pulses at moderate intensities

We present a semi-analytical model for free electron production induced by multiphoton ionization in dielectric materials for short laser pulses at moderate intensities. Within this approach, the laser-induced absorption is described through the Bloch–Volkov formalism, and the electronic structure of materials is evaluated through first-principles calculations. Results obtained for NaCl and KDP (KH2PO4) materials show that significant deviations from the parabolic band approximation may occur. When the laser intensity increases, high multiphotonic orders may become the predominant mechanisms outside the centre of the Brillouin zone.

Modeling of nanoscale devices with carriers obeying a three-dimensional density of states

While aggressively nanoscale field-effect transistors commonly used in CMOS technology exhibit strong quantum confinement of charge carriers in one or two dimensions, few devices have been recently proposed whose operation reminds that of vacuum tube triodes and bipolar transistors, since charge carriers are ballistically injected into a three-dimensional k-space. In this work we derive, under the parabolic band approximation, the analytical expressions of the first three directed ballistic moments of the Boltzmann transport equation (current density, carrier density, and average kinetic energy), suitable to describe ballistic and quasi-ballistic transport in such devices. The proposed equations are applied, as an example, to describe the ballistic transport in graphene-based variable-barrier transistors.

Nonlinear optical rectification associated to exciton states in asymmetric coupled double quantum wells

In this work the variational method is applied within the framework of the parabolic band and effective mass approximations, in order to study the 1s-like exciton energy spectrum in the GaAs–Ga 1−xAlxAs asymmetric coupled double quantum well configuration. The obtained states are then used to calculate the coefficient of nonlinear optical rectification associated to the transitions between the excitonic levels. It is shown that different exciton interstate transitions can lead to comparable optical rectification responses. With few exceptions, the increase of the system dimensions implies the appearance of a redshift in the resonant peak positions as well as the fall of their amplitudes.

Effect of band parameters on interband optical absorption in quantum wire structure of low band gap III–V semiconductors

A generalized theory is presented to study the effect of band parameters on inter band optical absorption in quantum wire structure of III---V compound semiconductors considering the wave-vector ( $\vec{k}$ ) dependence of the optical transition matrix element (OME). The band structures of these low band gap semiconducting materials with sufficiently separated split-off valance band are frequently described by the three energy band model of Kane. This has been adopted to calculate the inter band optical absorption coefficient (IOAC) for a wide range of III---V compound semiconductors like, InAs, InSb, Hg1?x Cd x Te and In1?x Ga x As y P1?y lattice matched to InP, having varied split-off energy band compared to their energy band gap. It has been found that IOAC for quantum wires (QWRs) increases in oscillatory manner with increasing incident photon energy and the positions of peaks of oscillation of the coefficient are more closely spaced in the three band model of Kane than those with parabolic energy band approximations reflecting the direct the influence of band energy constants. This effect of band parameters is better revealed from the study of light polarization dependence of the absorption coefficient.

Generalized optical gain analysis in nonparabolic semiconductor laser

SUMMARY A simple generalized theory is developed for optical gain of nonparabolic semiconductor lasers based on the three-band model of Kane, by taking into account the wave-vector () dependence of the optical matrix element. The gain in laser of nonparabolic semiconductors is demonstrated, by taking InAs, InSb, Hg1−xCdxTe and In1−xGaxAsyP1−y lattice matched to InP as examples, and it has been found that the peak of the gain spectra for a given carrier density is higher in the three-band model of Kane than those with parabolic energy band approximations in all the cases. The difference between the peak of gain spectra for three-band model and the parabolic band model is greater for laser of narrow band gap materials in comparisons with that of laser of wide band gap materials, thereby reveals the necessity for inclusion of the nonparabolicity in modeling lasers of small band gap materials. The well-known results for wide band gap materials having parabolic energy bands has also been obtained from our generalized formulation under certain limiting condition. Copyright © 2013 John Wiley & Sons, Ltd.

A study of photomodulated reflectance on staircase-like, n-doped GaAs/Al x Ga1−xAs quantum well structures

In this study, photomodulated reflectance (PR) technique was employed on two different quantum well infrared photodetector (QWIP) structures, which consist of n-doped GaAs quantum wells (QWs) between undoped AlxGa1−xAs barriers with three different x compositions. Therefore, the barrier profile is in the form of a staircase-like barrier. The main difference between the two structures is the doping profile and the doping concentration of the QWs. PR spectra were taken at room temperature using a He-Ne laser as a modulation source and a broadband tungsten halogen lamp as a probe light. The PR spectra were analyzed using Aspnes’ third derivative functional form.Since the barriers are staircase-like, the structure has different ground state energies; therefore, several optical transitions take place in the spectrum which cannot be resolved in a conventional photoluminescence technique at room temperature. To analyze the experimental results, all energy levels in the conduction and in the valance band were calculated using transfer matrix technique, taking into account the effective mass and the parabolic band approximations. A comparison of the PR results with the calculated optical transition energies showed an excellent agreement. Several optical transition energies of the QWIP structures were resolved from PR measurements. It is concluded that PR spectroscopy is a very useful experimental tool to characterize complicated structures with a high accuracy at room temperature.

Modeling the radiation ionization energy and energy resolution of trigonal and amorphous selenium from first principles

Advances in the development of amorphous selenium-based direct conversion photoconductors for high-energy radiation critically depend on the improvement of its sensitivity to ionizing radiation, which is directly related to the pair production energy. Traditionally, theories for the pair production energy have been based on the parabolic band approximation and do not provide a satisfactory agreement with experimental results for amorphous selenium. Here we present a calculation of the pair creation energy in trigonal and amorphous selenium based on its electronic structure. In indirect semiconductors, such as trigonal selenium, the ionization threshold energy can be as low as the energy gap, resulting in a lower pair creation energy, which is a favorable factor for sensitivity. Also, the statistics of photogenerated charge carriers is studied in order to evaluate the theoretical value of the Fano factor and its dependence on recombination processes. We show that recombination can significantly compromise the detector’s energy resolution as a result of an increase in the Fano factor.

Exciton-related nonlinear optical absorption and refractive index change in GaAs–Ga1−xAlxAs double quantum wells

In this work the variations of the exciton-related optical absorption and the change of the refractive index in a GaAs–(Ga,Al)As double quantum well as functions of the geometric parameters of the heterostructure are investigated. The variational method is applied within the framework of the parabolic band and effective mass approximations, in order to obtain the 1s-like exciton energy spectrum. The outcome for the related optical coefficients shows a quenched and redshifted light absorption as a result of the increment in the inner barrier and right-hand well widths, with the possibility of an enhancement of the excitonic contribution to the relative change in the refractive index.

Plasma frequency and dielectric function dependence on doping and temperature for p-type indium phosphide epitaxial films

The optical properties of p-type InP epitaxial films with different doping concentrations are investigated by infrared absorption measurements accompanied by reflection and transmission spectra taken from 25 to 300 K. A complete dielectric function (DF) model, including intervalence band (IVB) transitions, free-carrier and lattice absorption, is used to determine the optical constants with improved accuracy in the spectral range from 2 to 35 μm. The IVB transitions by free holes among the split-off, light-hole, and heavy-hole bands are studied using the DF model under the parabolic-band approximation. A good understanding of IVB transitions and the absorption coefficient is useful for designing high operating temperature and high detectivity infrared detectors and other optoelectronic devices. In addition, refractive index values reported here are useful for optoelectronic device designing, such as implementing p-InP waveguides in semiconductor quantum cascade lasers. The temperature dependence of hole effective mass and plasma frequency is also reported.

Schottky Current in Carbon Nanotube-Metal Contact

Silicon based technology has received its technical limitation because of its unstable structure at nano-level. Carbon nanotube as an alternative material has attracted significant scientific efforts. Fabrication of Schottky diode using carbon nanotube is an open area of research to overcome this limit. In this study, we model the current of CNT Schottky diode under applied voltage. Parabolic band approximation on CNT induces Fermi-Dirac integral of order zero on its current voltage which is similar to the conventional one dimensional material. This model shows that its current has a weak dependence on temperature corresponding to the small applied voltage. It is quite different in high bias voltages which are independent of temperature. Based on this model, incremental effect of the carbon nanotube diameter has been explained by increasing the current with the applied voltage. The model presented in this paper is in good agreement with the reported data from experiments. This device can be used in the integrated circuit miniaturization.

PHONON DRAG AND CARRIER DIFFUSION CONTRIBUTIONS IN THERMOELECTRIC POWER OF K3C60 FULLERIDES

The thermoelectric power (S) of K3C60 fullerides is theoretically analyzed. Mott expression within parabolic band approximation is used to reveal the electron diffusive thermoelectric power (Sc diff ) following Fermi energy as electron parameter, Sc diff show linear temperature dependence. S infers a change in slope above transition temperature and become almost linear above 70 K. The phonon drag thermoelectric power (S ph drag ) is computed within relaxation time approximation when thermoelectric power is limited by scattering of phonons from defects, grain boundaries, phonons and electrons as carriers. The S ph drag of K3C60 is anomalous and it is an artifact of strong phonon-electron and phonon scattering mechanism. The thermoelectric power within relaxation time approximation has been taken into account ignoring a possible energy dependence of the scattering rates. Behaviour of S(T) is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between carrier diffusion and phonon drag contributions.