Effects of an intense, high-frequency laser field on bound states in Ga1 − xIn x N y As1 − y/GaAs double quantum well
© Ungan et al.; licensee Springer. 2012
Received: 16 July 2012
Accepted: 4 October 2012
Published: 31 October 2012
Within the envelope function approach and the effective-mass approximation, we have investigated theoretically the effect of an intense, high-frequency laser field on the bound states in a Ga x In1 − xN y As1 − y/GaAs double quantum well for different nitrogen and indium mole concentrations. The laser-dressed potential, bound states, and squared wave functions related to these bound states in Ga1 − xIn x N y As1 − y/GaAs double quantum well are investigated as a function of the position and laser-dressing parameter. Our numerical results show that both intense laser field and nitrogen (indium) incorporation into the GaInNAs have strong influences on carrier localization.
Recently, the evolution of the growth techniques such as molecular beam epitaxy and metal-organic chemical vapor deposition combined with the use of the modulation-doped technique made it possible the fabrication of low-dimensional heterostructures such as single and multiple quantum wells, quantum wires, and quantum dots. In these systems, the restriction on the motion of the charge carriers allows us to control the physical properties of the structures. The studies on these systems offer a wide range of potential applications in the development of semiconductor optoelectronic devices[1–5].
GaInNAs/GaAs quantum well (QW) lasers have been attracting significant scientific interest mainly due to their applications in 1.3- or 1.55-μm optical fiber communication[6–12]. These lasers are predominantly based on GaInAsP alloys on the InP substrates, which have a higher temperature sensitivity compared to shorter wavelength lasers that are grown on GaAs substrates. The high-temperature sensitivity is primarily due to Auger recombination and the weak electron confinement resulting from the small conduction band offset in the GaInAsP/InP material system. GaInNAs alloys grown on GaAs substrates have been proposed as a possible alternative to the GaInAsP/InP system for achieving lasers with high-temperature performance. The deeper conduction band well and the larger electron effective mass will provide better confinement for electrons and better match of the valence and conduction band densities of state, which leads to a higher characteristic temperature and higher operating temperature, higher efficiency, and higher output power[6–13].
As known, high-frequency intense laser field (ILF) considerably affects the optical and electronic properties of semiconductors[14–20]. Because when an electronic system is irradiated by ILF, the potential of the system is modified which affects significantly the bound state energy levels, a feature that has been observed in transition energy experiments. The design of new efficient optoelectronic devices depends on the understanding on the basic physics involved in this interaction process. Thus, the effects of a high-frequency ILF on the confining potential and the corresponding bound state energy levels are a very important problem. This problem has been a subject of great interest, and an enormous amount of literature has been devoted to this field[21–27]. However, up to now, to the best of our knowledge, no theoretical studies have been focused on the bound states in Ga1 − xIn x N y As1 − y/GaAs double quantum well (DQW) under the ILF.
The purpose of this work is to investigate the effect of ILF, nitrogen (N), and indium (In) mole fractions on the bound states in Ga1 − xIn x N y As1 − y/GaAsDQW. The paper is organized as follows: in the ‘Theoretical overview’ section, the essential theoretical background is described. The next section is the ‘Results and discussion’ section, and finally, our calculations are given in the ‘Conclusions’ section.
where e and m* are absolute value of the electric charge and effective mass of an electron; c, the velocity of the light; A0, the amplitude of the vector potential; and I, the intensity of ILF.
where V(r, α0) is the dressed confinement potential which depends on ω and I only through α0.
where V0 is the conduction band offset at the interface; L = Lw1 + Lw2 + L b , Lw1 = Lw2, the well width; L b , the barrier width; Θ, the Heaviside unit step function which satisfies Θ(z) = 1 − θ(−z); and θ, the unit step function.
In calculating the wave function ψ(z), we ensured that the eigenvalues are independent of the chosen infinite potential well width L s and that the wave functions are localized in the well region of interest. This method, which gives accuracies greater than 0.001 meV, is well controlled, gives the DQW eigenfunctions, and is easily applied to situations of varying potential and effective mass.
Results and discussion
where x and y are the In and N compositions in Ga1 − xIn x N y As1 − y, respectively; EC 0, the energy in the absence of N; and E C , E N , and V NC , the bandgap energies of InGaAs at Γ point, the energy of the isolated N level in the InGaAs host material, and the coefficient describing the coupling strength between E N and the InGaAs conduction band, respectively.
In this work, we have investigated mainly the effects of the ILF, N, and In concentrations on the bound states in Ga1 − xIn x N y As1 − y/GaAs DQW. The calculations were performed within the effective-mass and envelope-wave function approximations. The frequency and corresponding laser intensity for α0 = 150 Å are 30 THz and 1.8 × 1010 W/cm2, respectively. The corresponding applied field intensity is the order of the crystal damage threshold intensity that can be avoided by using high-power pulsed CO2 lasers, etc. Fortunately, the current generation of free electron lasers can provide intense laser fields in the frequency range of 0.2 to 3,226 THz, with field strengths up to approximately 100 kV/cm. Therefore, our results can be tested by using the applied field intensity lower than the breakdown limit of the corresponding semiconductors.
Our numerical results reveal that ILF creates an additional geometric confinement on the electronic states in the DQW; the effect of the N (In) concentration on the electronic states increases with the effect of ILF. We can tune the electronic structure and main optical properties of the system which depend on intersub-band transitions by changing the N (In) concentration together with the laser field. We hope that our calculation results can stimulate further investigations of the related physics as well as device applications of dilute nitrides.
This work was supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) for a research grant COST 109 T650 and was partially supported by the Scientific Research Project Fund of Cumhuriyet University under the project number F-360.
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