Influence of nonparabolicity on boundary conditions in semiconductor quantum wells

Milanović, V.; Radovanović, J.; Ramović, S.

doi:10.1016/j.physleta.2009.06.038

Cited by 12 publications

(10 citation statements)

References 6 publications

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“…If the concentration of ionized impurities is not extensive, we may adopt that the potential energy U(z) originates from the conduction-band discontinuity only. The two boundary conditions at the interface of two semiconductors are described in detail in [20]. The second boundary condition is derived by double integration of the Schršdinger equation and imposes the conservation of probability current.…”

Section: Theoretical Considerationmentioning

confidence: 99%

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Possibilities of achieving negative refraction in QCL-based semiconductor metamaterials in the THz spectral range

et al. 2014

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This is a repository copy of Possibilities of achieving negative refraction in QCL- ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.-1- Possibilities of achieving negative refraction in QCL- Abstract:One of the challenges in the design of metamaterialsÕ unit cells is the reduction of losses caused by the metallic inclusions. In order to overcome this obstacle, it has been proposed to use the active medium as the unit cell. Quantum cascade lasers are great candidates for the active medium materials since they are able to provide high values of optical gain. In this paper we investigate and compare two quantum cascade structures optimized for emission frequencies lower than 2 THz and simulate the effect of a strong magnetic field applied perpendicularly to the layers.Comprehensive description of conduction-band nonparabolicity is used to calculate the electronic structure, and subsequently evaluate the longitudinal optical phonon and interface roughness scattering rates and solve the system of rate equations which govern the distribution of carriers among the Landau levels. Once we assess the degree of population inversion, we have all the necessary information about the permittivity component along the growth direction of the structure and may determine the conditions under which the structure displays negative refraction.

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Section: Theoretical Considerationmentioning

confidence: 99%

“…As pointed out above, it is very important to compensate the losses by using active metamaterials with high values of optical gain. Therefore, a QCL-like structure may be a good solution since it offers the possibility to generate substantial optical gain via carrier injection at specific frequencies [20].…”

Section: T B =mentioning

confidence: 99%

Possibilities of achieving negative refraction in QCL-based semiconductor metamaterials in the THz spectral range

et al. 2014

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“…Ekenberg in [2] determined the coefficients in the expansion of the dispersion relation up to the fourth order in wavevector, by using 14-band k•p calculation presented in [1]. This results in a fourth-order differential equation with boundary conditions obtained by double integration, which fulfill the requirement for probability current conservation [3]. In [4] the authors presented the model from [2,3] and its application to QCL structures by using the transfer matrix method (TMM).…”

Section: Introductionmentioning

confidence: 99%

“…This results in a fourth-order differential equation with boundary conditions obtained by double integration, which fulfill the requirement for probability current conservation [3]. In [4] the authors presented the model from [2,3] and its application to QCL structures by using the transfer matrix method (TMM). Modeling of NPE represents a nonlinear eigenvalue problem, thus it is preferable to develop an approximate solution.…”

Section: Introductionmentioning

confidence: 99%

Analysis of dipole matrix element in quantum well and quantum cascade laser under the influence of external magnetic field

Demić¹,

Radovanović²,

Milanović³

2016

Serb J Electr Eng

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We present a method for modeling nonparabolicity effects (NPE) in quantum nanostructures by using second order perturbation theory. We will analyze application of this model on a quantum well without external electric field and a quantum cascade laser (QCL). This model will allow us to examine the influence of magnetic field on dipole matrix element in QCL structures which will give better insight how NPE can disrupt gain of QCL structures.

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“…In addition, the material parameters relevant for the effects considered in this work (especially the band nonparabolicity coefficients) are known more accurately, however, the presented numerical procedure is practically independent of the material system. Strong effects of band nonparabolicity [10] result in subtle changes of the lasing wavelength at magnetic fields which maximize the gain, thus providing a path for fine--tuning of the wavelength of output radiation. Another prospective application of QCL immersed in intense magnetic field is for the design of novel (active) metamaterials where optical losses can be compensated by adding sufficient gain [11,12].…”

Section: Introductionmentioning

confidence: 99%

Charge Carrier Transport in Quantum Cascade Lasers in Strong Magnetic Field

et al. 2011

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We have developed a comprehensive rate equations based model for calculating the optical gain in the active region of a quantum cascade laser in magnetic field perpendicular to the structure layers, which takes into account all the relevant scattering channels. The model is applied to gain-optimized quantum cascade laser active region, obtained by a systematic optimization procedure based on the use of genetic algorithm, which we have previously set up for designing novel structures and improving performance of existing ones. It has proven to be very efficient in generating optimal structures which emit radiation at specified wavelengths corresponding to absorption fingerprints of particular harmful pollutants found in the atmosphere. We also illustrate another interesting prospective application of quantum cascade laser-type structures: the design of metamaterials with tunable complex permittivity, based on amplification via intersubband transitions. In this case, the role of the magnetic field is to assist the attainment of sufficient optical gain (population inversion), necessary to effectively manipulate the permittivity and fulfill the conditions for negative refraction (left-handedness).PACS: 72.10.−d, 73.21.Fg IntroductionThe mechanism of photon generation in quantum cascade laser (QCL) is based on transitions between the quasi-bound states which are associated with an ultrashort excited state lifetime corresponding to electronlongitudinal optical (LO) phonon scattering [1]. Application of a strong magnetic field has proven to be a sensitive instrument for studying and controlling these intersubband processes as it provides a path for modulating the laser output properties [2-6]. In effect, the field introduces additional quantization of the in-plane electron motion and creates a series of the Landau levels (LLs) instead of two-dimensional subbands, which resembles a quantum box structure. LLs are magnetically tunable and, depending on their configuration, phonon emission is either inhibited or resonantly enhanced. This leads to a strong modulation of the population inversion and consequently the optical gain, as a function of magnetic field.We have previously developed an automated design procedure for structural parameters optimization of the active region of mid-infrared quantum cascade laser, with the goal of maximizing the output properties, in particular the optical gain, at predefined wavelengths compliant with selected application [4][5][6][7][8]. In mid-infrared devices, the desired emission wavelength imposes the required separations between the active laser energy states, while the spacing between the lower laser level and the ground state is set by the LO phonon energy (which facilitates the population inversion by allowing the fast emptying of the lower laser state by means of nonradiative transitions). The relationships between parameters of interest are very complex, making the optimization process

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Influence of nonparabolicity on boundary conditions in semiconductor quantum wells

Cited by 12 publications

References 6 publications

Possibilities of achieving negative refraction in QCL-based semiconductor metamaterials in the THz spectral range

Possibilities of achieving negative refraction in QCL-based semiconductor metamaterials in the THz spectral range

Analysis of dipole matrix element in quantum well and quantum cascade laser under the influence of external magnetic field

Charge Carrier Transport in Quantum Cascade Lasers in Strong Magnetic Field

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