Donors In Quantum Wells Research Articles

The temporal dynamics of impurity photoconductivity in quantum wells in GaAs

A theory of cascade capture at charged donors in quantum wells (QWs) is developed without using the Fokker-Planck approximation, which is not valid in QWs. The time dependences of impurity photoconductivity and photoelectron concentration in GaAs QWs are determined. The cascade capture time as a function of the charge donor concentration is calculated.

The diamagnetic susceptibilities of donors in quantum wells with anisotropic effective mass

The diamagnetic susceptibility of a hydrogenic donor placed in Si, Ge and GaAs quantum wells with infinite confinement potential which have different effective mass anisotropy parameters ( γ = m ⊥ / m ∥ ) has been investigated as a function of the well sizes. The binding energies of the donor have also been computed using a trial wave function with two parameters in the framework of the effective mass approximation. It has been observed that the diamagnetic susceptibility of the donor in the anisotropic materials converges rapidly to the bulk limit as the well size increases.

Calculation of the States of Shallow Donors in Quantum Wells in a Magnetic Field Using Plane Wave Expansion

A nonvariational method for calculating the states of shallow donors in quantum wells in a magnetic field is suggested. The method can be used in a wide range of magnetic fields, starting with zero. The method is based on the expansion of the electron-wave function in a basis of eigenfunctions of the Hamiltonian operator that describes a rectangular quantum well. The results obtained by this method are compared to the experimental data and to the results of calculations using different theoretical methods. The comparison shows that our method describes the observed spectrum of the shallow-donor states in quantum wells in a magnetic field with a higher accuracy than the methods used in the study by Chen et al.

Resonance Donor States in Quantum Wells

The energies and wave functions of the resonance states of shallow donors in quantum wells (QWs) are calculated. The calculations are performed in a model of an isolated impurity center using the example of a GaAs/AlGaAs heterostructure. A formula for the probability of a spontaneous emission of polar optical (LO) phonons is derived. It is shown that, in the vicinity of the resonance-state energies, polar electron-phonon interaction is modified. This modification is produced by a hybridization of confinement subbands. Generally, due to hybridization, an electron interacts with phonons simultaneously in two channels (subbands). The absorption cross section for infrared radiation is calculated, taking into account both homogeneous (in the mid-infrared range) and inhomogeneous broadening (in the far-infrared range). The absorption of radiation whose electric field is normal to the heterointerfaces is related to optical transitions to the states near the resonances. Homogeneous broadening of the absorption lines, as well as the LO-phonon scattering rate, depends on the width of the resonance states (the degree of subband hybridization).

Impurity absorption of light involving resonant states of shallow donors in quantum wells

The energy spectrum of localized and resonant states of shallow donors in heterostructures GaAs/AlxGa1−xAs with quantum wells is calculated. The widths of the resonant states belonging to the second size quantization subband are determined. It is shown that the width of a resonance level is mainly determined by the interaction with optical phonons. The spectrum of impurity absorption of light due to electron transitions from the ground state of the donor to the resonant states belonging to the second size quantization subband is calculated.

Binding energies of donors in quantum wells under hydrostatic pressure

The binding energies of donors in quantum wells are investigated with a variational method considering the influence of finite barriers under hydrostatic pressure. In the calculation, we take into account the electronic effective mass, dielectric constant, and conduction band offset between the well and barriers varying with pressure. The numerical result shows that the donor binding energy linearly increases with the pressure from 0 to 40 kbar. The pressure effect for GaAs/Al x Ga 1− x As quantum wells is more obvious than that for GaN/Al x Ga 1− x N quantum wells. We also calculate the binding energy as a function of the Al concentration, which can influences the barrier height. The result indicates that the donor binding energy monotonically increases with increasing the barrier height.

Off-Center Neutral and Negatively Charged Donor Impurities in Semiconductor Heterostructures: Fractal Dimension Method

We reduce the problems of the on- and off-center D0 and D— S-states in semiconductor heterostructures to the similar ones in an isotropic effective space with variable fractional dimension starting from the variational principle. The dimension of this space is defined as a scaling parameter that relates the radii of a set of spherical boxes to the charge densities within induced by the free electron ground state in the heterostructure. Explicit expressions for the effective space dimensionality in a quantum well (QW), quantum-well wire (QWW) and a quantum dot (QD) are found by using this definition. To solve the wave equations for the free electron ground state in the heterostructure and for the hydrogen-like atom S-states in the fractional-dimensional space, we use the numerical trigonometric sweep method. The three-parameter Hylleraas trial function is used to solve the similar problem for a negative-hydrogen-like ion in the effective space. Ground state binding energies for off-center neutral and negatively charged donors in QWs and spherical QDs are calculated. Our results are in a good agreement with those of the variational and Monte Carlo methods. In addition, novel results for the D— binding energy as a function of the cylindrical GaAs/Ga0.7Al0.3As QWW radius and the magnetic field intensity are presented. It is found that the D— binding energy in the wire increases from 0.055 Ry* up to about 1.230 Ry* as the radius decreases to 30 Å. It is also shown that the magnetic field produces a considerable enhancement of negative-donor binding energy in QWW only for radii greater than 100 Å.

Phonon resonances in optical spectra of donors in quantum wells

An influence of electron–phonon coupling and electron confinement on optical spectra is studied for donors in semiconductor quantum wells. A binding and 1s–2p transition energies have been calculated by the optimized canonical transformation method for GaAs/AlGaAs, CdTe/CdZnTe, and CdF2/CaF2 quantum wells. We have found that — in the quantum wells made from the ionic semiconductors — the 1s–2p transition energy exceeds the LO-phonon energy and the phonon resonances can appear in the optical spectra of donors. We have estimated the parameters of quantum wells, for which the phonon resonances can be detected in the absence of external magnetic field.

A simple model to study the effect of Γ- X hybridization on the binding energy of shallow donors in quantum wells of [formula omitted

In this work we perform a variational calculation of the electron binding energy in an AlAs GaAs quantum well. We take into account the fact that the minima of the conduction band in those materials occur in points of the Brillouin zone with different symmetries (Γ for GaAs and X for AlAs). Therefore, for thin quantum wells the first subband becomes a hybrid state of those Bloch states in the points Γ and X. The hybridization is included in the variational function by means of contour conditions for the first subband wave function. In the present model we are able to treat impurities anywhere inside the well. At well widths smaller than 37 Å the GaAs layer becomes a barrier for the electrons, so the model is no longer valid. We also compare the results obtained with the Γ- X hybridization with the results obtained by just taking the barrier at the interfaces as the energy differences between the Γ level inside the GaAs layer and the X level across the interface.

Far-infrared photoconductive magnetospectroscopy as a tool for studying shallow donor concentration profiles in wide GaAs/AlGaAs quantum wells

The feasibility of using far-infrared photoconductive magnetospectroscopy to accurately determine the positions of shallow donors in multiple quantum well samples grown by molecular-beam epitaxy has been investigated and the technique successfully applied to silicon donors in quantum wells at doping levels below 2×1016 cm−3. Theoretical spectra calculated using a combined segregation and diffusion model for predicting donor position along with a theory of mapping donor 1s→2p+1 transition energies to magnetic fields are in good agreement with experimental spectra. A new value for the segregation decay rate, 3.1 nm/decade, is indicated for Si donors in wide GaAs/AlGaAs quantum wells grown at a substrate temperature of 680 °C. This new tool which is effective in the doping range of 1×1014 to 2×1016 cm−3 complements capacitance–voltage (C–V) techniques and secondary ion mass spectrometry. The technique is also applicable to a variety of heterostructures.

Doping and magnetic field effects on the dielectric constant of shallow donors in quantum wells

We investigate the effects of magnetic field, compensation and impurity concentration on the dielectric constant of a GaAlAs/GaAs quantum well (QW) due to intraimpurity transitions.

Investigation of the effect of quantum well width on the binding energy of excitons to neutral donors

Observations of bound exciton states in some bulk semiconductor materials has shown the validity of Haynes' rule, namely that the binding energy of the exciton to a donor is a multiple 1/ξ (say) of the binding energy of the electron to the donor (i.e., the neutral donor binding energy E D ), although in other bulk materials more general linear dependencies are required. Quantum well structures (QWS) typically exhibit such donor hound exciton complexes. There are several points of difference however, E D is a function of donor position, the donor distribution is unknown and interface roughness could also influence the donor bound exciton emission. Hence in order to determine whether a generalised form of Haynes' rule can be applied to excitons bound to donors in quantum wells of varying width requires a careful combination of theory with experiment. The binding energies of the donors at various positions in each well region must be calculated with due allowance made for the effects of interface roughness. A presumed distribution of the donor concentration is then made and, on the assumed validity of Haynes' rule, the lineshape of the bound exciton emission calculated. Comparison with the observed emission spectra will then give insight into whether Haynes' rule is satisfied as a function of position and well width in QWS. This analysis has been carried out for a series of single quantum wells, all of different widths and all grown in the same sample by the technique of molecular beam epitaxy. A careful analysis of all the data showed that Haynes' rule is not applicable--i.e., the observed exciton energies are not a constant multiple of the donor binding energy for QWS of different well width. PACS: 71.55.Gs; 78.66.Hf.

Photoionization of impurities in quantum wells

The dependence of photoionization cross-section on photon energy is calculated for shallow donors in quantum wells. The resulting spectra is completely different for light polarized along and perpendicular to the growth direction.

Excited states of donors in quantum wells in a magnetic field.

Excited states of donors in quantum wells in a magnetic field.

Magneto-optical study of donor-level crossing in tipped GaAs/(Ga,Al)As quantum wells.

We present evidence for an anticrossing between the 2${\mathit{p}}_{+1}$ and 2${\mathit{p}}_{0}$ levels of Si donors situated near the center of a GaAs quantum well. This anticrossing, which does not appear for magnetic fields perpendicular to the plane of the sample, is induced by tipping the sample normal away from the direction of the applied magnetic field. All donor transitions were detected with photoconductivity, a method that is standard for GaAs bulk donors but has only recently been employed successfully for donors in quantum wells.

Polarizabilities of shallow donors in quantum wells.

Polarizabilities of shallow donors in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells are calculated with use of the Hasse variational method within the effective-mass approximation. The magnetic field dependence of polarizabilities is also studied.

Magneto-emission from shallow donors in quantum wells

Landau emission studies from intentionally doped GaAsGaAlAs multi-quantum-well structures are reported. Besides the usual cyclotron emission, impurity emission has been observed and identified as due to the 2p + → 1s (z i) transition for donors located at all the possible positions z i in the structure. The general features of this confined-impurity emission are discussed.

Theory of anisotropic donor states in quantum-well structures.

The s-, ${p}_{0}$-, and ${p}_{\ifmmode\pm\else\textpm\fi{}}$-like ground and excited states of anisotropic donors in quantum wells are calculated with a linear combination of Gaussian orbitals with different exponents in the z direction and xy plane. The energies and wave functions of the ground and excited states can be obtained simultaneously by this method. In the case of anisotropic donors in the bulk materials and isotropic donors in the quantum wells our results are in agreement with previous theoretical results. In some cases our results are better. Using this method we calculate the variation of the anisotropic donor energies with well widths, anisotropic factors \ensuremath{\gamma}, and impurity positions in the quantum well. The energies of s-like donor states related to the second subband are also calculated. Finally, the donors of the X band edge in Si/Si-Ge quantum wells are discussed.

SHALLOW IMPURITIES IN SEMICONDUCTOR QUANTUM WELLS

Energy spectra of shallow impurities (donors and acceptors) in quantum wells are studied within the effective mass approximation. New theoretical calculations on donor states in quantum wells are presented. A model potential which allows a simple and fairly accurate estimate of the entire spectrum of donors in quantum wells with intermediate width (20–300 A) is introduced. New developments for acceptors in strained-layer quantum wells (GaAs–Ga 1– x In x As) are reported. The effect of biaxial strain on the electronic structure of the strained-layer quantum well is properly included.

Shallow impurities in semiconductor quantum wells

Energy spectra of shallow impurities (donors and acceptors) in quantum wells are studied within the effective mass approximation. New theoretical calculations on donor states in quantum wells are presented. A model potential which allows a simple and fairly accurate estimate of the entire spectrum of donors in quantum wells with intermediate width (20–300 Å) is introduced. New developments for acceptors in strained-layer quantum wells (GaAsGa 1- x In x As) are reported. The effect of biaxial strain on the electronic structure of the strained-layer quantum well is properly included.