Δ-doped Quantum Wells Research Articles

Modulation of nonlinear optical rectification, second, and third harmonic generation coefficients in n-type quadruple δ-doped GaAs quantum wells under external fields

The paper theoretically explores the variations in nonlinear optical rectification (NOR), second (SHG), and third harmonic generation (THG) coefficients of an n-type quadruple δ-doped GaAs quantum well in the presence of electric, magnetic, and THz laser fields. The energies of subbands and associated wave functions are derived through the solution of the Schrödinger equation, utilizing effective mass and parabolic band approximations. The findings indicate that the applied external electric and magnetic fields significantly influence both the magnitudes and the positions of the peaks in NOR, SHG, and THG concerning the incident photon energies. In addition to the influences of electric and magnetic fields, subjecting the system to an intense laser field results in noticeable changes in the THG, SHG, and NOR coefficients. These numerical findings regarding the optical properties of quadruple δ-doped quantum wells in the presence of external fields could offer valuable guidance for experimental studies.

Optical properties of n-type asymmetric triple δ-doped quantum well under external fields

We present a theoretical investigation about the the influence of external electric, magnetic and non-resonant intense laser fields on intersubband-related second harmonics generation (SHG) and the nonlinear optical rectification (NOR) coefficients in n-type asymmetric triple δ-doped quantum wells (QWs). A particular design of asymmetric triple δ-doped QW with Lw = 200 Å width and, respectively, in the left side, central and right side, and doping concentrations is taken into account. For QWs under the combined effect of the external electric, magnetic and laser fields, the time-dependent wave equation is modified by using Kramers-Henneberger transformation and the dipole approximation. The subband energy spectra and the electronic wave functions are obtained by solving numerically the wave equation. The originality of this work can be presented as; (i) The results explain NOR and SHG characteristics of triple QW depending on external field effects in detail. The effects of the electric, magnetic and laser field on transition energies and NOR, SHG characteristics are presented detail. (ii) In addition to, the alternativeness to each other of the external fields is discussed by probing the features of SHG and NOR under the strong and weak regimes of external fields. (iii) These nonlinear optical responses to the external fields are compared, researching the optimum cases for these optical specifications. (iv) The control of SHG through the external fields in triple δ-doped QWs reveals to be easier and more precise.

Model of n-type quadruple δ-doped GaAs quantum wells

Thomas Fermi (TF) approach was used to represent a model for the n-type quadruple δ-doped (QDD) system in GaAs. This is the first physical model in the literature for the QDD system. The energies, the wave functions and the Fermi energy (EF) were calculated. These calculations were performed for different density of impurities in the doped layer (N2D) and for different separation distances (d) between the doped layers. Preliminary results show that the value of the Fermi level for the first proposed model is well below its expected value. This observation is exploited for a second model consistent with the expected values of the EF. Our results indicate that there is a limit at the bottom of the potential profile for a multilayered doped delta system. This has a great importance for calculations in optoelectronic and transport properties.

Nonlinear optical properties of triple δ-doped quantum wells: The impact of the applied external fields

In the present paper, we theoretically investigate the effect of applied external fields, such as electric, magnetic, and intense terahertz laser fields on the optical absorption and the relative refractive index change coefficients of triple δ-doped quantum well structures. To investigate the applied external field effects, we perform the calculation of the allowed subband energy levels and their corresponding eigen-functions using the diagonalization method within the framework of the effective-mass approximation. The effects of the applied external fields on the nonlinear optical properties of the quantum well structure are treated within the compact-density-matrix approach via the iterative method. The numerical results obtained are presented for two different values of electric, magnetic, and intense terahertz laser fields. These results show that changing the intensity of the external electric, magnetic, and intense terahertz laser field. It is concluded that the nonlinear optical response of the triple δ-doped structure can be significantly changed through the changes in the configuration of the external probes.

Electron-related optical responses in triple δ-doped quantum wells

ABSTRACTA detailed theoretical study on the electron-related optical responses in triple δ-doped GaAs quantum wells in the presence of non-resonant, monochromatic intense laser field is presented. For this purpose, we first obtained the bound subband energy levels and their corresponding envelope wave functions of the structure for different central doping concentrations within the effective-mass approximation. Then, we calculate the effect of the non-resonant intense laser field on the optical properties of this structure using the compact-density-matrix approach via the iterative method. We found that the optical absorption coefficients and refractive index changes in the triple δ-doped GaAs quantum well can be modulated by changing the central doping concentration and the intensity of the non-resonant, monochromatic laser field. In addition, it is shown that a sufficiently intense laser field suppresses the multiple quantum well configuration towards a single potential well one and the optical response becomes practically independent of the δ-doping concentration.

Asymmetric GaAs n-type double δ-doped quantum wells as a source of intersubband-related nonlinear optical response: Effects of an applied electric field

In this work, the conduction band electron states and the associated intersubband-related linear and nonlinear optical absorption coefficient and relative refractive index change are calculated for an asymmetric double n-type δ-doped quantum well in a GaAs-matrix. The effects of an external applied static electric field are included. Values of the two-dimensional impurities density (N2d) of each single δ-doped quantum well are taken to vary within the range of 1.0×1012 to 7.0×1012cm−2, consistent with the experimental data growth regime. The optical responses are reported as a function of the δ-doped impurities density and the applied electric field. It is shown that single electron states and the related optical quantities are significantly affected by the structural asymmetry of the double δ-doped quantum well system. In addition, a brief comparison with the free-carrier-related optical response is presented.

Nonlinear absorption coefficient and relative refraction index change for an asymmetrical double [formula omitted]-doped quantum well in GaAs with a Schottky barrier potential

In this work we are reporting the energy level spectrum for a quantum system consisting of an n-type double δ-doped quantum well with a Schottky barrier potential in a Gallium Arsenide matrix. The calculated states are taken as the basis for the evaluation of the linear and third-order nonlinear contributions to the optical absorption coefficient and to the relative refractive index change, making particular use of the asymmetry of the potential profile. These optical properties are then reported as a function of the Schottky barrier height (SBH) and the separation distance between the δ-doped quantum wells. Also, the effects of the application of hydrostatic pressure are studied. The results show that the amplitudes of the resonant peaks are of the same order of magnitude of those obtained in the case of single δ-doped field effect transistors; but tailoring the asymmetry of the confining potential profile allows the control the resonant peak positions.

Exciton states in GaAs [formula omitted] systems under magnetic fields and hydrostatic pressure

Excitons in GaAs n-type δ-doped quantum wells are studied taking into account the effects of externally applied magnetic fields as well as of hydrostatic pressure. The one-dimensional potential profile in both the conduction and valence bands is described including Hartree effects via a Thomas–Fermi-based local density approximation. The allowed uncorrelated energy levels are calculated within the effective mass and envelope function approximations by means of an expansion over an orthogonal set of infinite well eigenfunctions and a variational method is used to obtain the exciton states. The results are presented as functions of the two-dimensional doping concentration and the magnetic field strength for zero and finite values of the hydrostatic pressure. In general, it is found that the exciton binding energy is a decreasing function of the doping-density and an increasing function of the magnetic field intensity. A comparison with recent experiments on exciton-related photoluminescence in n-type δ-doped GaAs is made.

Transport properties of InGaAs/GaAs Heterostructures with δ-doped quantum wells

The lateral transport of electrons in single- and double-well pseudomorphic GaAs/n-InGaAs/GaAs heterostructures with quantum wells 50–100 meV deep and impurity δ-layers in the wells, with concentrations in the range 1011 < N s < 1012 cm−2, has been investigated. Single-well structures with a doped well at the center exhibit a nonmonotonic temperature dependence of the Hall coefficient and an increase in low-temperature electron mobility with an increase in the impurity concentration. The results obtained indicate that the impurity-band electron states play an important role in the conductivity of these structures. Involvement of the impurity band also allows to explain adequately the characteristics of the conductivity of double-well structures; in contrast to single-well structures, band bending caused by asymmetric doping is of great importance. The numerical calculations of conductivity within the model under consideration confirm these suggestions.

Boron Delta-Doping Dependence on Si/SiGe Resonant Interband Tunneling Diodes Grown by Chemical Vapor Deposition

Si/SiGe resonant interband tunnel diodes (RITD) were fabricated using CVD on 200-mm silicon wafers. The RITD devices consist of a p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -i-n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> structure with δ-doped quantum wells providing resonant interband tunneling through a nominally intrinsic Si/SiGe region. The vapor-phase doping technique was used to obtain abrupt degenerate doping profiles. The boron doping in the δ-doped region was varied, and its effect on peak current density <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jp</i> and peak-to-valley current ratio (PVCR) was studied. As the flow rate is reduced, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jp</i> was found to reduce while the PVCR initially increases and then decreases. Device simulations were performed using the ATLAS simulator developed by SILVACO to interpret the results. A maximum PVCR of 2.95 was obtained, and the highest <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jp</i> recorded was 600 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This is the highest reported PVCR for any CVD-grown Si/SiGe RITD.

Electron spectrum of δ-doped quantum wells by the Thomas–Fermi method at finite temperatures

The electron spectrum of δ-doped quantum wells i n n-GaAs is investigated by means of the Thomas–Fermi (TF) method at finite temperatures. This method shows rapid convergence and good accuracy. Under two-dimensional (2D) doping concentrations 10 13…2×10 13 cm −2, the simplest TF method ( T=0 K) can be used to calculate the profiles of the potential well up to T≈200 K. The simplest TF method yields correct results for the electron concentrations and the differences of the electron energy sublevels in the quantum well up to room temperature ( T∼300 K).

A cascade laser on shallow-donor transitions in δ-Doped GaAs/AlGaAs superlattices

The possibility of amplification of terahertz-range electromagnetic waves due to optical transitions between a two-dimensional continuum and shallow-level donor states in GaAs/AlGaAs superlattices with selectively δ-doped quantum wells is analyzed theoretically. The population inversion required for the gain is attained under the conditions of vertical transport in the superlattice due to the hybridization of states in neighboring quantum wells coupled via electron tunneling through the barrier. It is shown that, at a doping level of 5 × 1010 cm−2 per period, the gain can be as high as 50 cm−1 at wavelengths 100–120 μm. The current density under operating conditions is ∼50 A/cm2.

Formula omitted] calculations of p-type δ-doped quantum wells in Si

We present the hole subband structure calculation in single and double p-type δ-doped quantum wells in Si based on the 4×4 Luttinger–Kohn Hamiltonian. The valence band bending and the Γ hole states are calculated within the lines of the Thomas–Fermi–Dirac approximation and the effective mass theory at the Brillouin zone center. The obtained zone center eigenstates are then used to diagonalize the k·p Hamiltonian for non-zero k. The hole subband structure is analyzed as a function of the impurity density and the distance between δ wells. It is shown that the application of a 4×4 model to describe the hole ground state in single p-type δ-doped in Si can be misleading.

Subband and transport calculations in double n-type δ-doped quantum wells in Si

The Thomas-Fermi approximation is implemented in two coupled n-type δ-doped quantum wells in Si. An analytical expression for the Hartree-Fock potential is obtained in order to compute the subband level structure. The longitudinal and transverse levels are obtained as a function of the impurity density and the interlayer distance. The exchange-correlation effects are analyzed from an impurity density of 8×1012to6.5×1013cm−2. The transport calculations are based on a formula for the mobility, which allows us to discern the optimum distance between wells for maximum mobility.

Thomas‐Fermi‐Dirac calculations of valence band states of double p‐type d‐doped quantum wells in Si

We present the hole subband structure calculation in double δ-doped (DDD) quantum wells in Si. We have used an analytical expression for the Hartre-Fock potential previously obtained within the lines of the Thomas-Fermi-Dirac (TFD) approximation. We have analysed the hole levels as a function of the interlayer distance as well as for different densities of impurities. It is found a difference of 60 Å in the degeneration distance of the system with and without exchange effects in the low impurity density regime (p2D = 1 × 1012 cm–2), while in the high impurity density such difference is about 5 Å. We also present the mobility ratio between DDD and simple δ-doped (SDD) quantum wells. We have found the interlayer distance for the maximum mobility for the whole range of impurities. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Resonant states in n ‐type δ‐doped GaAs quantum wells

We calculate the electron structure of δ-doped GaAs quantum wells within a realistic sp3s* tight-binding formalism, including spin. The results reveal the existence of a series of many quasi-bound states with a very strong spatial and energetic localization. For a donor impurity concentration of n2D = 1 × 1013 cm–2 the full width at half maxima (FWHM) of the first quasi-bound state is 1.5 × 10–3 meV and the corresponding mean-life time is about 4 ns. This value is 103 times greater that the mean lifetime reported for Bragg's reflectors based on quantum wells. We find many similar features of the symmetry, spatial and energetic characteristics between quasi-bound and bound states. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Thomas–Fermi approximation of double n-type delta-doped GaAs quantum wells: sub-band and transport calculations

We present the electronic structure calculation of two closely n-type δ-doped quantum wells within the lines of the Thomas–Fermi (TF) theory. The distance between the impurity planes as well as the impurity density of the δ-doped planes is varied. The exchange effects are also analyzed in the present study. We have found a degeneration distance for the ground state of 360 and 400Å with and without exchange effects, respectively (n2D=3.0×1012cm−2). We also calculate the mobility ratio of double δ-doped (DDD) GaAs quantum wells respect to a single δ-doped (SDD), finding the optimum distance between wells for the maximum mobility. Our results are in a good agreement with respect to the optical and transport measurements available.

Calculation of electronic properties in AlxGa1−x delta-doped systems

The calculation of the electronic energy levels of n-type δ-doped quantum wells in a AlGaAs matrix is presented. Many-body effects in the two-dimensional electron gas are taken into account by using a local-density Thomas-Fermi approach. Special consideration is taken into when the values of the Al molar fraction x≥0.45, and the ternary alloy becomes an indirect gap material. The results suggest that in this case the AlxGa1−xAs can support two-dimensional conduction channels associated to the delta-doping, with carrier densities exceeding 1013cm−2.

Exchange Energy of a Hole Gas and the Thomas-Fermi-Dirac Approximation in p-Type ?-Doped Quantum Wells in Si and GaAs

We present the electronic structure of p-type δ-doped quantum wells in Si and GaAs including exchange effects in the Thomas-Fermi-Dirac approximation. We also carry out Schrodinger-Poisson self-consistent calculations considering the particularities the exchange potential has in the Local Density Approximation in the case of a hole gas. Using the Thomas-Fermi-Dirac approximation, we present an analytical expression for the Hartree-Fock potential. We compare the results obtained from this model with those obtained through Schrodinger-Poisson self-consistent calculations. As a result of this comparison, we saw that the model presented, in spite of its simplicity, gives very good results. In particular, it practically fixes the energy differences between the occupied levels of the well. There is agreement between the results of our two calculations (self-consistent and with Thomas-Fermi-Dirac model) with the experimental results in the three systems (B δ-doped quantum wells in Si, Be δ-doped quantum wells in GaAs, and p-type Si δ-doped quantum wells in GaAs).

Trionic Gain in δ-Doped ZnSe Quantum Wells

Trionic Gain in δ-Doped ZnSe Quantum Wells