Effects of Hartree, exchange, and correlation energy on intersubband transitions

Bloss, Walter L.

doi:10.1063/1.344073

Cited by 75 publications

(42 citation statements)

References 15 publications

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“…[5,12,13] For the intersubband absorption energies, we include depolarization shift and excitonic effects. [5,11] For physical parameters of the nitrides, we use those recently recommended by Vurgaftman et al [14] Temperature effects enter the calculations through their influence on AlN and GaN band gaps, the thermal expansion influencing the piezoelectric fields, and the two-dimensional Fermi distribution of the electrons.…”

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confidence: 99%

Temperature stability of intersubband transitions in AlN/GaN quantum wells

Berland

Stattin

Farivar

et al. 2010

Applied Physics Letters

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Temperature dependence of intersubband transitions in AlN/GaN multiple quantum wells grown with molecular beam epitaxy is investigated both by absorption studies at different temperatures and modeling of conduction-band electrons. For the absorption study, the sample is heated in increments up to 400 • C. The self-consistent Schrödinger-Poisson modeling includes temperature effects of the band-gap and the influence of thermal expansion on the piezoelectric field. We find that the intersubband absorption energy decreases only by ∼ 6 meV at 400 • C relative to its room temperature value.Intersubband transitions in nitride-based semiconductor heterostructures hold great promise for optoelectronic devices. The high band-offset between gallium nitride (GaN) and aluminum nitride (AlN) enables intersubband transitions in the near-infrared regime (λ = 1-4 µm). Thus, intersubband devices such as modulators, detectors, and quantum cascade lasers (QCLs) have the potential to operate at wavelengths useful for fiberoptic communication. QCLs also have the potential to be used when measuring characteristic absorption of small molecules. There are several studies of intersubband absorption in AlN/GaN heterostructures.[1-6] These typically show a peak at 500 to 900 meV with full width half maximum (FWHM) in the range of 60 to 200 meV. An intersubband device should operate at and above 300 K, often with the condition of a negligible change in transition energy. Temperature dependence of the transition energy, up to room temperature, has been reported for intersubband absorption in InAs/AlSb multiple quantum well (MQW) structures [7] and for interband photoluminescence in nitride-based AlN/GaN MQW structures.[8] The huge piezoelectric fields introduce an additional temperature-dependent effect in the nitride MQW structures, because the different thermal expansions of AlN and GaN induce a temperature dependent strain in the structures.In this letter, we demonstrate that the peak position of intersubband transitions red shifts only ∼ 6 meV as the temperature of the sample is increased from 25 • to 400 • C. This aspect of thermal robustness could be vital for the operation of nitride-based QCLs since their ultrafast LO-scattering rates and high intersubband energy would cause them to heat significantly. The temperature effects are studied for MQW structures both experimentally by measuring the absorption at different temperatures, and theoretically by a self-consistent solution to the Schrödinger-Poisson equations for the conductionband electrons. The nitride-semiconductor heterostructures are characterized by huge internal electric fields, which arise from the exceptionally large spontaneous and piezoelectric fields. A proper account of these fields are crucial for an accurate description and characterization of the quantum well states, and they require that the complete structure is considered in the design of heterostructures.The set of MQW structures (A -C) are grown in a Varian Gen II modular molecular beam epitaxy (MBE) system....

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confidence: 99%

Temperature stability of intersubband transitions in AlN/GaN quantum wells

Berland

Stattin

Farivar

et al. 2010

Applied Physics Letters

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“…In the electrostatic limit (c → ∞) we can drop the transverse electric field contribution in equation (25) and find the following dispersion equation:…”

Section: Dispersion Dependence For Two-fluid Model Of Electronsmentioning

confidence: 99%

“…Large contribution of the exchange interaction in the two-dimensional electron gas of GaAs microstructures is demonstrated experimentally [24] and theoretically within the local density approximation [25]. Hence, we consider the Coulomb exchange interaction contribution in spectrum of the Langmuir waves (plasmons) and the SEAWs (spin plasmons) in terms of the SSE-QHD.…”

Section: Introductionmentioning

confidence: 99%

Extraordinary waves in two dimensional electron gas with separate spin evolution and Coulomb exchange interaction

Andreev

2017

Physics of Plasmas

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Hydrodynamics analysis of waves in two-dimensional degenerate electron gas with the account of separate spin evolution is presented. The transverse electric field is included along with the longitudinal electric field. The Coulomb exchange interaction is included in the analysis. In contrast with the three-dimensional plasma-like mediums the contribution of the transverse electric field is small. We show the decrease of frequency of both the extraordinary (Langmuir) wave and the spinelectron acoustic wave due to the exchange interaction. Moreover, spin-electron acoustic wave has negative dispersion at the relatively large spin-polarization. Corresponding dispersion dependencies are presented and analyzed.

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“…In the crudest approximation 8,9 , the depolarization shift αN S is proportional to N S d eff and the excitonic shift βN S is proportional to (N S /d eff ) 1/3 , where d eff is the effective well width 1 . Experimentally, αN S can be determined from the measured value of E CD − E SD ; βN S can be estimated only when there is information about E 10 .…”

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confidence: 99%

“…based on the local-density functional theory 6,7,8 , where N S is the sheet electron concentration in a QW, E 10 is the intersubband energy separation that includes static many-body corrections, and αN S and βN S are dynamical many-body corrections (called the depolarization shift and excitonic shift) due to the direct and exchangecorrelation intersubband Coulomb interactions, respectively. In the crudest approximation 8,9 , the depolarization shift αN S is proportional to N S d eff and the excitonic shift βN S is proportional to (N S /d eff ) 1/3 , where d eff is the effective well width 1 .…”

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Intersubband electronic Raman scattering in narrow GaAs single quantum wells dominated by single-particle excitations

et al. 2004

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We measured resonant Raman scattering by intersubband electronic excitations in GaAs/AlAs single quantum wells (QWs) with well widths ranging from 8.5 to 18 nm. In narrow (less than ∼ 10 nm) QWs with sufficiently high electron concentrations, only single-particle excitations (SPEs) were observed in intersubband Raman scattering, which was confirmed by the well-width dependence of Raman spectra. We found characteristic variations in Raman shift and line shape for SPEs with incident photon energy in the narrow QWs.Intersubband electronic excitations in quantum wells (QWs) are strongly affected by many-body Coulomb interactions 1 . In electronic Raman scattering in doped QWs, two types of intersubband collective excitations have been confirmed by many researchers 2 since the first reports by Abstreiter and Ploog 3 and by Pinczuk et al. 4 in 1979: a collective charge-density wave (CDW) appears if the polarizations of incident and scattered lights are parallel ( ), whereas a collective spin-density wave (SDW) appears if they are crossed (⊥).The CDW and SDW excitation energies are given by 1,5based on the local-density functional theory 6,7,8 , where N S is the sheet electron concentration in a QW, E 10 is the intersubband energy separation that includes static many-body corrections, and αN S and βN S are dynamical many-body corrections (called the depolarization shift and excitonic shift) due to the direct and exchangecorrelation intersubband Coulomb interactions, respectively. In the crudest approximation 8,9 , the depolarization shift αN S is proportional to N S d eff and the excitonic shift βN S is proportional to (N S /d eff ) 1/3 , where d eff is the effective well width 1 . Experimentally, αN S can be determined from the measured value of E CD − E SD ; βN S can be estimated only when there is information about E 10 . Later, in 1989, Pinczuk et al. reported 10 that not only CDW and SDW but also single-particle excitations (SPEs) are observed in intersubband electronic Raman scattering and their transition energy is E 10 for modulation-doped 25-nm GaAs/Al 0.3 Ga 0.7 As single QWs with N S = (1.5−3)×10 11 cm −2 . SPEs are observed for both the parallel and crossed polarizations and seem to become stronger 10,11 at higher values of N S . * submitted to Phys. Rev. B.There are many other reports on intersubband electronic Raman scattering for wide (more than ∼ 20 nm) GaAs QWs. It will be interesting to measure Raman scattering also in narrower QWs, considering β/α ∼ (N S d eff 2 ) −2/3 . However, there are only a few reports for narrower GaAs QWs 12,13 because interface roughness makes Raman peaks broader and more difficult to observe. To our knowledge, such an experiment has never been reported for a single QW.In this paper, we report resonant Raman scattering by the lowest (0 → 1) intersubband electronic excitations in a set of modulation-doped GaAs/AlAs single QWs with well widths ranging from 8.5 to 18 nm. We found unexpected results that parallel-and crossed-polarization Raman spectra of narrow QWs had only a si...

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Effects of Hartree, exchange, and correlation energy on intersubband transitions

Cited by 75 publications

References 15 publications

Temperature stability of intersubband transitions in AlN/GaN quantum wells

Temperature stability of intersubband transitions in AlN/GaN quantum wells

Extraordinary waves in two dimensional electron gas with separate spin evolution and Coulomb exchange interaction

Intersubband electronic Raman scattering in narrow GaAs single quantum wells dominated by single-particle excitations

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