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physica status solidi (b)

Nonlinear intersubband optical absorption of Si δ‐doped GaAs under an electric field

Hasan Yıldırım, Mehmet Tomak

Published Jul 12, 2006• 16 citations
Publisher

Abstract

Abstract We study the nonlinear intersubband optical absorption of a single Si δ‐doped GaAs sheet placed in the middle of a GaAs quantum well and subjected to an electric field. The Schrödinger and Poisson equations are solved self‐consistently for various electric field strengths. The self‐consistent solutions provide us with the correct confining potential, the wave functions, the corresponding subband energies and the subband occupations. The nonlinear optical intersubband absorption spectra are discussed within the framework of the density matrix formulation for various electric field strengths, well widths, and sheet thicknesses in which Si atoms are distributed uniformly. We include both the depolarization and exciton shifts in calculations. The depolarization effect not only shifts the peak value but also makes the nonlinear absorption spectrum strongly asymmetric with the increasing intensity of the optical field. The blue‐shift associated with the depolarization shift is decreased when the intensity is increased. The absorption line shape becomes more asymmetric at smaller well widths and thicker doping layers. The electric field restores the symmetry of the absorption line shape at larger well widths and thinner doping layers, but it decreases the peak value of the line shape. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200642065

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Yarıiletken heteroyapıların lineer olmayan optik özellikleri.

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The nonlinear optical properties of semiconductor heterostructures, such as GaAsAl/GaAs alloys, are studied with analytic and numerical methods on the basis of quantum mechanics. Particularly, second and third-order nonlinear optical properties of quantum wells described by the various types of confining potentials are considered within the density matrix formalism. We consider a Pöschl-Teller type potential which has been rarely considered in this area. It has a tunable asymmetry parameter, making it a good candidate to investigate the effect of the asymmetry on the nonlinear optical properties. The calculated nonlinear quantities include nonlinear absorption coefficient, second-harmonic generation, optical rectification, third-harmonic generation and the intensity-dependent refractive index. The effects of the DC electric field on the corresponding nonlinearities are also studied. The results are in good agreement with the results obtained in other types of quantum wells, such as square and parabolic quantum wells. The effects of the Coulomb interaction among the electrons on the nonlinear intersubband absorption are considered within the rotating wave approximation. The result is applied to a Si-delta-doped, square quantum well in which the Coulomb interaction among the electrons are relatively important, since there has been no work on the nonlinear absorption spectrum of the Si-\delta-doped quantum well. The results are found to be new and interesting, especially when a DC electric field is included in the calculations.

•Jan 1, 2006•0 citations
Abstract We study the nonlinear intersubband optical absorption of a single Si δ‐doped GaAs sheet placed in the middle of a GaAs quantum well and subjected to an electric field. The Schrödinger and Poisson equations are solved self‐consistently for various electric field strengths. The self‐consistent solutions provide us with the correct confining potential, the wave functions, the corresponding subband energies and the subband occupations. The nonlinear optical intersubband absorption spectra are discussed within the framework of the density matrix formulation for various electric field strengths, well widths, and sheet thicknesses in which Si atoms are distributed uniformly. We include both the depolarization and exciton shifts in calculations. The depolarization effect not only shifts the peak value but also makes the nonlinear absorption spectrum strongly asymmetric with the increasing intensity of the optical field. The blue‐shift associated with the depolarization shift is decreased when the intensity is increased. The absorption line shape becomes more asymmetric at smaller well widths and thicker doping layers. The electric field restores the symmetry of the absorption line shape at larger well widths and thinner doping layers, but it decreases the peak value of the line shape. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The effect of the depolarization field on the nonlinear intersubband absorption spectrum of a rectangular quantum well (described by the two-subband model) is discussed. Calculations are performed in the framework of the density-matrix formulation with use of the relaxation-time approximation. Obtained results show that the depolarization effect not only shifts the peak by an amount depending on the intensity of the incident light but also leads to a significant distortion (asymmetry) of the line shape.
The effect of the electrostatic Coulomb interaction on the line shape related to the intensity-dependent intersubband optical processes in a Si δ-doped quantum well is studied using the density matrix formalism. The electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schrödinger–Poisson equations. The line shape function is considerably modified by the optical intensity and the electric and magnetic fields. Moreover, we demonstrate the existence of the optical bistability for appropriate values of the optical intensity and also the control of the optical bistability with the electric and magnetic fields. It is also found that the intersubband relaxation time plays an important role in determining the optical bistability region.
Abstract By using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive‐index changes (RICs) in a semiparabolic quantum well (QW) with an applied electric field have been investigated in detail. Simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The effect of the band nonparabolicity has been taken into account. Numerical calculations of typical GaAs semiparabolic QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequency of the confined potential of the semiparabolic quantum well, and the strength of the applied electric field were discussed under both conditions of considering and ignoring the band nonparabolicity. Results reveal that the RICs in the semiparabolic quantum‐well system sensitively depend on these factors. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Infrared intersubband optical absorption between the quantized subbands and the Stark effects is of considerable interest because of their potential applications in high-speed IR modulators and photodetectors. Recently, we calculated the linear1 and third-order nonlinear2 intersubband optical absorptions with an applied electric field for the infinite quantum-well model with an effective well width (which gives the same ground state energy of a given finite quantum well). The observed intersubband absorption has a large dipole strength suggesting large optical nonlinearities which are in good agreement with our calculation based on the simple model. Distinct features of the intersubband absorption are as follows: (a) The absorption peak for the intersubband absorption increases in energy with increasing electric field over a wide range of the electric field because the energy difference between the two lowest subbands increases with the electric field. (b) The absorption peak for the intersubband absorption may (1) increase in magnitude with an increasing electric field if the intrasubband relaxation time τin is assumed to be constant or (2) decrease with an increasing electric field if the field broadening of the linewidth is taken into account. The nonlinear optical absorption coefficient with the electric field dependence is discussed.
The effect of the electric field and intense laser field on the intersubband transition and optical absorption in an Al0.3Ga0.7As/GaAs asymmetric double quantum well is theoretically investigated by using the transfer matrix approach.The Hartree potential due to the electron-electron interaction is considered in our calculation.For intersubband transitions in an asymmetric double quantum well,the peaks of the absorption coefficient are found to be a blue or red shifted by tuning the intensity of the laser field and the applied electric field.It can be concluded that the intense laser field and external electric field have a considerable influence on the electronic and optical properties for an asymmetric double quantum well.
The nonlinear optical properties of semiconductor heterostructures, such as GaAsAl/GaAs alloys, are studied with analytic and numerical methods on the basis of quantum mechanics. Particularly, second and third-order nonlinear optical properties of quantum wells described by the various types of confining potentials are considered within the density matrix formalism. We consider a Pöschl-Teller type potential which has been rarely considered in this area. It has a tunable asymmetry parameter, making it a good candidate to investigate the effect of the asymmetry on the nonlinear optical properties. The calculated nonlinear quantities include nonlinear absorption coefficient, second-harmonic generation, optical rectification, third-harmonic generation and the intensity-dependent refractive index. The effects of the DC electric field on the corresponding nonlinearities are also studied. The results are in good agreement with the results obtained in other types of quantum wells, such as square and parabolic quantum wells. The effects of the Coulomb interaction among the electrons on the nonlinear intersubband absorption are considered within the rotating wave approximation. The result is applied to a Si-delta-doped, square quantum well in which the Coulomb interaction among the electrons are relatively important, since there has been no work on the nonlinear absorption spectrum of the Si-\delta-doped quantum well. The results are found to be new and interesting, especially when a DC electric field is included in the calculations.