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Positively and Negatively Charged Trions in ZnSe-Based Quantum Wells
Abstract
Excitons and charged excitons (trions) are investigated in ZnSe-based quantum well structures with (Zn,Be,Mg)Se and (Zn,Mg)(S,Se)
barriers by means of magneto-optical spectroscopy. Binding energies of negatively (X−) and positively (X+) charged excitons are measured as functions of quantum well width, free carrier density and in external magnetic fields up
to 47 T. The binding energy of X− shows a strong increase from 1.4 to 8.9 meV with decreasing quantum well width from 19.0 to 2.9 nm. The binding energies
of X+ are about 25% smaller than the X− binding energies in the same structures. The magnetic field behavior of X− and X+ binding energies differ qualitatively. With growing magnetic field strength, X− increases its binding energy by 35–150%, while for X+ the binding energy decreases by 25%.
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Optical spectra associated with transitions that create or annihilate charged excitons X- or X+ can be observed in quantum well heterostructures containing an electron gas or a hole gas, respectively. A review is given of properties of trion states in CdTe quantum wells in zero field and of the magnetic field-dependence of the circular polarization and oscillator strength of the trion optical resonance. The possibility that disorder is needed to stabilise trion states in concentrated 2D electron or hole systems is discussed.
We report on magneto-optical studies of ZnSe/(Zn,Mg)(S,Se) quantum wells with n-type and p-type modulation doping. Negatively and positively charged excitons related to the heavy-hole exciton states are found and identified by their polarization properties. Negatively charged excitons formed with light-hole exciton states are observed. Their binding energy is about 20% less than that related to the heavy-hole exciton. The exciton and trion parameters (radiative and nonradiative dampings) are determined.
A variational calculation of the ground-state energy of neutral excitons and of positively and negatively charged excitons (trions) confined in a single-quantum well is presented. We study the dependence of the correlation energy and of the binding energy on the well width and on the hole mass. The conditional probability distribution for positively and negatively charged excitons is obtained, providing information on the correlation and the charge distribution in the system. A comparison is made with available experimental data on trion binding energies in GaAs-, ZnSe-, and CdTe-based quantum well structures, which indicates that trions become localized with decreasing quantum well width.
Optical spectroscopy at T=2K reveals systematically a low-energy companion to the features of heavy- and light-hole excitons localized on CdTe 1-ML-high islands, buried in wide ZnTe/(Zn,Mg) Te quantum wells. These transitions are assigned to a negatively charged excitonic complex (trion) from magnetoreflectance and photoluminescence results. A mechanism of formation of the trion is proposed. A clear correlation is found between the exciton energies, which depend on the size and strain of the islands, and the trion binding energy, which varies between 1 and 3 meV.
A concept of mixed exciton-trion states is formulated theoretically and proved experimentally for II–VI semiconductor quantum wells with a two-dimensional electron gas. The concept considers the resonances of neutral excitons and charged excitons (trions) as mixed (with each other) via their interaction with free electrons. Reflectivity spectra of modulation-doped ZnSe/(Zn,Mg)(S,Se) and CdTe/(Cd,Mg)Te quantum wells are analyzed. A good qualitative agreement of the experimental results with model calculations is achieved.
A simple model variational function is proposed for an adequate unified description of X+ and X− two-dimensional trions over the entire range of electron-to-hole mass ratios with the use of a minimum number of variable
parameters.
Excitons and charged excitons (trions) are investigated in ZnSe-based quantum well structures with (Zn,Be,Mg)Se and (Zn,Mg)(S,Se) barriers by means of magneto-optical spectroscopy. Binding energies of negatively () and positively (X+) charged excitons are measured as functions of quantum well width, free carrier density and in external magnetic fields up to 47 T. The binding energy of shows a strong increase from 1.4 to 8.9 meV with decreasing quantum well width from 190 to 29 A. The binding energies of X+ are about 25% smaller than the binding energy in the same structures. The magnetic field behavior of and X+ binding energies differ qualitatively. With growing magnetic field strength, increases its binding energy by 35-150%, while for X+ it decreases by 25%. Zeeman spin splittings and oscillator strengths of excitons and trions are measured and discussed.
An optical method is suggested to determine the concentration of two-dimensional electrons in modulation-doped quantum wells at low and moderate electron densities between 10^{9} and 2x10^{11} cm^{-2}. The method is based on an analysis of magneto-reflectivity spectra of charged excitons (trions). The circular polarization degree and the oscillator strength of the charged excitons contain information about the density and spin polarization of two-dimensional electron gas. The method is applied to CdTe/(Cd,Mg)Te and ZnSe/Zn,Mg)(S,Se) heterostructures.
Low-temperature magneto-photoluminescence studies of negatively charged excitons (X- trions) are reported for n-type modulation-doped ZnSe/Zn(Cd,Mn)Se quantum wells over a wide range of Fermi energy and spin-splitting. The magnetic composition is chosen such that these magnetic two-dimensional electron gases (2DEGs) are highly spin-polarized even at low magnetic fields, throughout the entire range of electron densities studied (5e10 to 6.5e11 cm^-2). This spin polarization has a pronounced effect on the formation and energy of X-, with the striking result that the trion ionization energy (the energy separating X- from the neutral exciton) follows the temperature- and magnetic field-tunable Fermi energy. The large Zeeman energy destabilizes X- at the nu=1 quantum limit, beyond which a new PL peak appears and persists to 60 Tesla, suggesting the formation of spin-triplet charged excitons. Comment: 5 pages (RevTex), 4 embedded EPS figs. Submitted to PRB-RC
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We present the results of photoluminescence experiments on the negatively charged exciton X- in GaAs/AlxGa1-xAs quantum wells (QW) in high magnetic fields (<~50T). Three different QW widths are used here: 100, 120, and 150Å. All optically allowed transitions of X- are observed, enabling us to experimentally verify its energy-level diagram. All samples behave consistently with this diagram. We have determined the binding energy Eb of the singlet and triplet state of X- between 23 and 50 T for the 120 and 150ÅQW, while only the triplet Eb is observed for the 100ÅQW. A detailed comparison with recent theoretical calculations shows an agreement for all samples across this entire field range.
We investigate the formation, interaction, and dephasing of negatively charged excitons (trions) in ZnSe/Zn0.9Mg0.1Se single quantum wells by polarization, intensity, and temperature dependent spectrally resolved transient four-wave mixing. The trion transition shows a binding energy of 2.8 meV and is discriminated from the biexciton by its polarization dependence. The coherent dynamics of the four-wave mixing response is in fair agreement with calculations based on extended optical Bloch equations. Temperature dependent measurements exhibit a significant enhancement of the exciton dephasing below 40 K due to the presence of trions and incoherent electrons which are optically excited from the GaAs substrate and captured by the quantum well.
We report magneto-optical studies of ZnSe/(Zn,Mg)(S,Se) quantum wells with n-type modulation doping. Polarized photoluminescence and spin-flip Raman scattering spectroscopy is used to investigate the energy and spin structure of neutral and negatively charged excitons. The binding energy of charged excitons changes very little in magnetic fields up to 15 T. An inverted population of neutral exciton spin sublevels is found in magnetic fields; it is associated with the spin-dependent formation of charged excitons.
Optical and magneto-optical properties are studied for II-VI semiconductor multiple quantum wells (MQWs) doped with donors in the barriers to give electron concentrations of 2 1010 to 6 1011 cm-2 in the well layers. Following on from the recent identification of negatively charged excitons X- (two electrons bound to one hole) in CdTe/Cd1-xZnxTe MQWs, this paper presents more specifically the circular polarisation of the luminescence associated with X- and with the normal exciton X (one electron and one hole) in this type of structure. Very similar magneto-optical properties are observed for modulation doped Zn0.9Cd0.1Se/ZnSe MQWs, and X- is identified in these wells with a binding energy as large as 7 meV for the second electron at 50Å, well-width.
We compare the photoluminescence spectra of the negatively and positively charged excitons in GaAs quantum wells. We use a structure which enables us to observe both complexes within the same sample. We find that their binding energy and Zeeman splitting are very similar at zero magnetic field, but evolve very differently at high fields. We discuss the implications of these observations on our understanding of the charge excitons structure in high magnetic fields.
Magnetic semiconductors offer a unique possibility for strongly tuning the intrinsic alloy disorder potential with applied magnetic field. We report the direct observation of a series of steplike reductions in the magnetic alloy disorder potential in single ZnSe/Zn(Cd, Mn)Se quantum wells between 0 and 60 T. This disorder, measured through the linewidth of low-temperature photoluminescence spectra, drops abruptly at ~19, 36, and 53 T, in concert with observed magnetization steps. Conventional models of alloy disorder (developed for nonmagnetic semiconductors) reproduce the general shape of the data, but markedly underestimate the size of the linewidth reduction.
DOI:https://doi.org/10.1103/PhysRevLett.1.450
The oscillator strength of negatively charged excitons (trions) in ZnSe/(Zn,Mg)(S,Se) quantum-well structures with n-type modulation doping is studied by means of reflectivity as a function of electron concentration, temperature, and external magnetic fields. The trion oscillator strength is found to increase linearly with increasing electron concentration up to 6×1010cm-2. The trion nonradiative damping shows no dependence on the electron concentration or external magnetic field. An optical method, based on the analysis of the polarization of the trion line, is proposed to investigate two-dimensional electron gases of low density from 109 up to 1011cm-2.
We present a systematic study of optical transitions in a modulation doped Cd1-xMnxTe quantum well with variable concentration of the hole gas. Using a semimagnetic semiconductor as the quantum well material allowed us to control independently the total hole concentration and its distribution between the two spin subbands (by a small magnetic field). Therefore, in transmission experiment we analyze population effects and distinguish the influence of spin-independent effects (screening) from spin-dependent ones (phase-space filling and intensity stealing). The observed variation of the exciton (X) and charged exciton (X+) oscillator strengths can be accounted for assuming that the influence of phase-space filling is negligible and the variation of oscillator strength due to screening is found to be similar for both exciton species. We also show that the X+ dissociation energy significantly increases with the population of preexisting carriers with the appropriate spin.
The ground-state energy of the negatively charged exciton in a semiconductor quantum well is calculated assuming finite band offsets in a two-band model within the envelope-function approximation with isotropic electron and hole masses. A variational 66-term Hylleraas-type wave function has been used. The stability against dissociation into an exciton and a free electron is investigated in the cases of GaAs/Ga1-xAlxAs and CdTe/Cd1-xZnxTe quantum wells with several compositions and different values of the well width. A stable binding is obtained in all cases. The calculated transition energies are in reasonable agreement with the available experimental values. A particular experiment is proposed in order to identify charged excitons and to distinguish them from neutral donor bound excitons.
We calculate, to high accuracy, the states of the quantum-well negatively charged exciton X- in a perpendicular magnetic field. Two GaAs structures are considered: a 100-Å “narrow” well and a 300-Å “wide” well. The calculations cover a magnetic field range from 5 T to 50 T. In the narrow well, the ground state is shown to switch from singlet to triplet, at about 30 T, in agreement with the prediction of a triplet ground state obtained using the lowest-Landau-level approximation. In the wide well, the singlet is still the ground state at 50 T because electron-hole correlations perpendicular to the well plane enhance its binding energy more than that of the triplet. We also calculate electron-electron correlation functions for the X- states and demonstrate that in the singlet the motions of the two electrons are correlated, while in the triplet they are anticorrelated. We show that the triplet binding energies in the wide well are in good agreement with experimental data; the singlet values, however, turn out to be considerably smaller than those measured.
A microstructure has been designed in which an electron gas is created optically with variable density. ZnSe and BeTe quantum wells are separated by a BeZnMgSe alloy with band gap 3 eV. When electron-hole pairs are created by ultraviolet light in the barriers, electrons accumulate in the ZnSe quantum well, and holes in the BeTe quantum well. This is because the BeTe valence band lies 900 meV higher than that of ZnSe. Reflectivity and luminescence spectra of the ZnSe well show the destabilization of excitons by an electron gas and formation of trions. The metastable charge-separated state has a very long lifetime (2 s at 2 K). © 1998 American Institute of Physics.
We report observation of positively charged excitons (${\mathit{X}}^{+}$) in GaAs quantum wells remotely doped with acceptors. Upon reducing the excess hole density, by photoexciting carriers in the doped barrier layer, we observe the neutral excitonic transition strengthen relative to ${\mathit{X}}^{+}$. Further confirmation of the ${\mathit{X}}^{+}$ assignment is provided by its temperature and magnetic-field dependence. We observe both the antisymmetric (singlet) and symmetric (triplet) ${\mathit{X}}^{+}$ spin states.
Singlet and triplet states of negatively charged excitons (trions) in ZnSe/(Zn,Be,Mg)Se quantum wells have been studied by means of photoluminescence in pulsed magnetic fields up to 50 T. Singlet state binding energies, measured for different well widths ranging from 48 to 190 Å, show a monotonic increase with growing magnetic fields with a tendency to saturation. This behavior is in qualitative agreement with results of model calculations. Quantitatively, the binding energy of singlet states is underestimated by about 50%. The triplet state assigned to the “dark” triplet becomes detectable in magnetic fields above 15 T. A crossover of the triplet and singlet states is expected in magnetic fields of about 50 T.
We implement optical spectroscopy to study charged excitons (trions) in modulation-doped GaAs/AlGaAs quantum wells. We observe
for the first time several new trions: the positively charged exciton, the light-hole negatively charged exciton and the triplet
state of the negatively charged exciton.
An optical nonlinearity at very low light levels in a CdTe/CdZnTe single quantum well at 4 K is reported. Excitation above the band gap produces a significant decrease in the heavy‐hole exciton absorption at intensities down to μW/cm<sup>2</sup>. The dependence of the change in absorption on the pump intensity is sample dependent and is strongly sublinear. At low pump intensity the recovery of the absorption after switching off the pump is exponential with a time constant of about 150 ms, which is nearly independent of pump intensity up to ∼3 mW/cm<sup>2</sup>. Above 30 μW/cm<sup>2</sup> an additional process on a time scale ∼100 μs is observed. The rise time after turning on the pump varies inversely as pump intensity. It is shown that the nonlinearity arises from the presence of excess electrons in the CdTe quantum well, which reduce the excitonic absorption by phase‐space filling. These electrons are charge compensated by holes trapped in the barrier. The time and intensity dependence of the optical nonlinearity can be fitted by a kinetic model of the trapping, in which a range of traps with different recovery times participates. © 1995 American Institute of Physics.
The electronic and optical properties of the ground state of the excitonic trions corresponding to an exciton bound to an electron or a hole are studied theoretically for 2D semiconductors in the whole range of the electron-to-hole effective mass ratio. The energies are calculated variationally using a 22-terms Hylleraas-type trial wave function. It is confirmed that, as in the 3D case, the 2D trions are stable for any value of the effective mass ratio. The binding energies amount to about ten times those we obtain in the 3D case using the same wave function. Therefore, the experimental observation of the trions should be very more easy in 2D than in 3D semiconductors. We deduce the shape of the lines arising from transitions between free electrons or holes and 2D excitonic trions states and compare it to the 3D results.
The polarization- and excitation-intensity-dependent photoluminescence of the negatively charged trion is investigated for ZnSe single quantum wells embedded in ternary and quaternary barriers. The measurements were performed in magnetic fields up to 11.8 T perpendicular to the quantum well. The spin-singlet state of the trion is clearly identified. In contrast to GaAs quantum wells, the increase of the trion binding energy through the magnetic field is found to be negligible, which is explained by the relatively small spatial extent of the trionic wave function in wide-band-gap materials. For magnetic fields beyond 7 T a resonance becomes stabilized that is identified as excited trion spin-triplet state because of its anticorrelation with the trion spin-singlet state behavior for increasing excitation energy.
The negatively charged exciton X- is identified by its circular polarization properties in 1.7 K magentoabsorption spectra of CdTe/Cd1-xZnxTe multiple quantum wells modulation doped with electron concentrations Ns~=2×1010 to 1.5×1011 cm-2. The binding energy of the second electron of X- is 0.20 3D Rydbergs at 100 Å well width. The species X- and the neutral exciton X exist in zero field for low Ns. At Ns=1.45×1011 cm-2 a Fermi edge singularity is seen at B=0 but X- appears with field, at filling factor nu=2, while X appears at nu=1.
The dependence of the optical absorption spectrum of a semiconductor quantum well on two-dimensional electron concentration n(e) is studied using CdTe samples. The trion peak (X-) seen at low n(e) evolves smoothly into the Fermi edge singularity at high n(e). The exciton peak (X) moves off to high energy, weakens, and disappears. The X,X- splitting is linear in n(e) and closely equal to the Fermi energy plus the trion binding energy. For Cd0.998Mn0.002Te quantum wells in a magnetic field, the X,X- splitting reflects unequal Fermi energies for M = +/-1/2 electrons. The data are explained by Hawrylak's theory of the many-body optical response including spin effects.
- D R Yakovlev
- J Puls
- G V Mikhailov
- G V Astakhov
- V P Kochereshko
- W Ossau
- J Nürnberger
- W Faschinger
- F Henneberger
- G Landwehr
- DR Yakovlev