Ground-state Excitonic Transition Research Articles

Quantum interference between the optical Stark effect and resonant harmonic generation in WS2

An applied field can modulate optical signals by resonance shifting via the Stark effect. The optical Stark effect (OSE) uses ultrafast light in the transparency region of a material to shift resonances with speeds limited by the pulse duration or system coherence. In this Letter we investigate the OSE in resonant optical harmonic generation (OHG) using the ground state exciton transition of WS2 with a variety of morphologies. Multidimensional pump-harmonic-probe measurements, in which the probe is second- or third-harmonic emission, reveal not only large Stark shifts that are commensurate with the large optical susceptibilities common to WS2 excitons, but also behaviors more complex than simple OSE treatments predict. We show how a new manifestation of the Stark Effect, brought forth by coherent photon exchange between the pump and OHG fundamental fields, can strongly enhance or suppress OHG.

Time-Resolved Stark Spectroscopy in CdSe Nanoplatelets: Exciton Binding Energy, Polarizability, and Field-Dependent Radiative Rates.

We present a study of the application potential of CdSe nanoplatelets (NPLs), a model system for colloidal 2D materials, as field-controlled emitters. We demonstrate that their emission can be changed by 28% upon application of electrical fields up to 175 kV/cm, a very high modulation depth for field-controlled nanoemitters. From our experimental results we estimate the exciton binding energy in 5.5 monolayer CdSe nanoplatelets to be EB = 170 meV; hence CdSe NPLs exhibit highly robust excitons which are stable even at room temperature. This opens up the possibility to tune the emission and recombination dynamics efficiently by external fields. Our analysis further allows a quantitative discrimination of spectral changes of the emission energy and changes in PL intensity related to broadening of the emission line width as well as changes in the intrinsic radiative rates which are directly connected to the measured changes in the PL decay dynamics. With the developed field-dependent population model treating all occurring field-dependent effects in a global analysis, we are able to quantify, e.g., the ground state exciton transition dipole moment (3.0 × 10-29 Cm) and its polarizability, which determine the radiative rate, as well as the (static) exciton polarizability (8.6 × 10-8 eV cm2/kV2), all in good agreement with theory. Our results show that an efficient field control over the exciton recombination dynamics, emission line width, and emission energy in these nanoparticles is feasible and opens up application potential as field-controlled emitters.

Investigation of PbS nanocrystals sensitized extremely thin absorber (ETA) solar cell

Colloidal PbS nanocrystals (NCs) were prepared by an environmental friendly route. The as-prepared colloidal PbS nanocrystals were characterized by powdered X-ray diffraction and high-resolution transmission electron microscopy (HR-TEM). The ground state excitonic transition energies determined from the position of the first excitonic absorption peaks (2.5nm±0.2 (J1), 2.8nm±0.15 (J2) and 3.1nm±0.3 (J3) were 1.71, 1.35 and 1.15eV respectively). These PbS nanocrystals were then used to sensitize a nanostructured ZnO–SnO2 electrode by using In2S3 as a buffer layer. The results showed that sensitization procedure of PbS NCs with electrode played a significant role in the charge separation and transport. The cell fabricated by PbS NCs in which linker molecules were exchanged on the surface of electrode showed considerably higher incident to photon conversion efficiency (IPCE) compared to pre-ligand modified PbS NCs. The findings presented here can potentially be applied for the design of low-cost ETA devices for commercial applications.

Quantitative interpretation of the excitonic splittings in aluminum nitride

We address the interpretation of the splitting between the ground state excitonic transition which indicates the energy of the lowest direct band gap in AlN bulk films and epilayers, and a 36–38 meV higher energy companion. We demonstrate that this splitting is consistent with the initial interpretation in terms of 1 s –2 s excitonic splitting by using a calculation of the exciton binding energy which includes mass anisotropy and anisotropy of the dielectric constant. Analytical expressions are proposed to compute the evolution of 1 s and 2 s excitonic energies using an anisotropy parameter. We show that the values of the dielectric constant that are required to fit the data are ≈ 8.7 and ≈ 10, values different from the couple of values ≈ 7.33 and ≈ 8.45 erroneously obtained after a fitting procedure using a spherical description of the long range Coulomb interaction and the classical textbook n -2 spectrum of the excitonic eigenstates. Starting from now, our values are the recommended ones.

Damping of Exciton Rabi Rotations by Acoustic Phonons in Optically ExcitedInGaAs/GaAsQuantum Dots

We report experimental evidence identifying acoustic phonons as the principal source of the excitation-induced-dephasing (EID) responsible for the intensity damping of quantum dot excitonic Rabi rotations. The rate of EID is extracted from temperature dependent Rabi rotation measurements of the ground-state excitonic transition, and is found to be in close quantitative agreement with an acoustic-phonon model.

Refractive Index Dynamics and Linewidth Enhancement Factor in $p$-Doped InAs–GaAs Quantum-Dot Amplifiers

Using a pump-probe differential transmission experiment in heterodyne detection, we measured the refractive index dynamics at the ground-state excitonic transition in electrically pumped InAs/GaAs quantum-dot amplifiers emitting near 1.3 mum at room temperature. We compare three samples differing only in the level of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -doping, and interpret the measured index changes taking into account the gain dynamics in these devices. We find that in absorption, the excess hole density due to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -doping accelerates the recovery and reduces the refractive index change, since filling of the hole states by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -doping shifts the induced changes in the hole population toward high energy states. Conversely, in gain, the reduced electron reservoir in the excited states in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -doped devices results in slower gain recovery dynamics and in larger refractive index changes compared to undoped devices operating at the same modal gain. The linewidth enhancement factor inferred from these measurements shows that <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -doping is effective in reducing this parameter mainly due to the larger differential gain in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -doped devices in the gain regime.

Multiphoton microscopy based on four-wave mixing of colloidal quantum dots

We demonstrate a novel multiphoton imaging modality based on the detection of four-wave mixing (FWM) from colloidal nanoparticles. This third-order signal is excited and detected in resonance with the ground-state excitonic transition of CdSe∕ZnS quantum dots. We measure transversal and axial resolutions of 140 and 590nm, respectively, significantly improved compared to the one-photon diffraction limit. The coherent FWM signal is detected using a heterodyne technique which rejects incoherent background for improved image contrast compared to fluorescence methods. As sensitivity limit, we estimate a minimum number of 10dots∕Hz detectable in the focal volume.

Effect of uniaxial stress on the polarization of light emitted fromGaN∕AlNquantum dots grown on Si(111)

Cathodoluminescence (CL) measurements of the ground-state excitonic transition of vertically stacked $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ quantum dots (QDs) exhibited an in-plane linear polarization anisotropy in close proximity to microcracks. Microcracks form as a result of a mismatch of the thermal expansion coefficient between the $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ layers and the Si(111) substrate. In close proximity to the cracks, the layers are found to be under uniaxial tensile stress, whereas the film is under biaxial tensile stress for distances greater than $\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the cracks. The microcracks serve as an excellent stressor through which the strain tensor of the $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ QDs can be reproducibly modified for studies of strain-induced changes in the optical and electronic properties by using a spatially resolved probe, such as with CL. Changes in the optical properties of the QDs are attributed to stress-dependent variations of the band edges and the electric field along [0001], which is caused by charge polarization. Such changes in the field will subsequently affect the oscillator strength between electrons and holes. Three-dimensional $6\ifmmode\times\else\texttimes\fi{}6$ $\mathbit{k}\ensuremath{\cdot}\mathbit{p}$ calculations of the QD electron and hole wave functions and eigenstates were performed to examine the influence of biaxial and uniaxial tensile stresses on the polarization-dependent momentum matrix element in varying proximity to the microcracks. The model reveals that a change from biaxial to uniaxial stress alters the admixture of ${p}_{x}$ and ${p}_{y}$ characters of the band edges and the ground-state hole wave function, changes the shape and direction of elongation of the hole isosurfaces, and accounts well for the subsequent anisotropy in the polarization dependent optical transitions.

Accurate methods for study of light emission from quantum wells confined in a microcavity

Photomodulated reflectance (PR) and conventional reflectance studies have been performed on an InGaP/AlGaInP/Al/sub x1/Ga/sub y1/As/Al/sub x2/Ga/sub y2/As resonant-cavity light emitting diode structure in the red spectral region. The PR spectra show prominent signals from the Fabry-Perot cavity mode and the quantum-well (QW) ground state excitonic transition. This high-precision technique, and its variations as functions of incidence angle and temperature, as reported in this article, allow one to investigate light emission from the QW confined in a microcavity with relation to the Fabry-Perot mode, and is the only known nonconductive, nondestructive method of doing so.

Theory of Ultrafast Rayleigh Scattering in Semiconductor Quantum Wells

The Rayleigh scattering of light at resonance with the ground state exciton transition in quantum wells is studied by means of a microscopic model. The disorder-induced localization of the exciton center-of-mass leads to characteristic features of the scattered intensity which can help understanding the outcome of secondary emission experiments. In particular, the connection between time-resolved scattering and energy-level statistics, and the enhancement of the backscattered intensity in angle-resolved measurements are discussed.

Reflectance and Photomodulated Reflectance Studies of Cavity Mode and Excitonic Transitions in an InGaAs/GaAs/AlAs/AlGaAs VCSEL Structure

Angle dependent photomodulated reflectance (PR) and conventional reflectance (R) studies have been performed on an InGaAs/GaAs/AlAs/AlGaAs vertical-cavity surface-emitting laser (VCSEL) structure at room temperature. The PR spectra show three prominent signals: one from the ground-state excitonic transition in the InGaAs quantum well (QW) embedded deep in the structure; Franz-Keldysh oscillations (FKO) from the GaAs layers; and a PR signal attributed to the cavity mode, whereas in the R spectra only the cavity mode is clearly visible. It is found that the ground-state QW transition is not in resonance with the cavity mode. The period of the FKOs shows that the built-in electric field is about 18 kV/cm. The energy positions of the excitonic features are not dependent on the angle of incidence, in contrast to that of the cavity mode, whose angular dependence can be fitted with a very simple model. The full R spectrum of the VCSEL structure has also been calculated using a Jones matrix formalism which not only predicts the actual angular dependence of the cavity mode, but also permits a determination of the layer thicknesses in the VCSEL structure by fitting to the experimental R spectrum. Excellent fits are achieved using only two adjustable parameters; the Ga and Al growth rates, which are found to be 5.3% less, and 2.9% greater, than nominal, respectively. Modelling of the measured PR spectrum of an etched sample shows that the In composition of the QW is 5% higher than the nominal value.

Origin of the Blue Shift Observed in Highly Strained (Ga, In)As Quantum Wells Grown on GaAs(001) Vicinal Surfaces

The photoluminescence energy of strained (Ga, In)As quantum wells grown on (001) GaAs slightly misoriented (2°-6°) towards (111)A exhibits a blue shift when compared to quantum wells grown on perfectly oriented substrates. It is shown that this observation is linked to a blue shift of intrinsic ground state excitonic transition energies. This effect is studied as a function of substrate misorientation angle, well width and indium surface segregation level. In order to understand its origin, various hypotheses were examined: regular shrinkage of well width due to terrace edges, additionnal stress of the well material at the step edges, and orientation dependent In segregation. It appears that the first two combined effects provide the best description of the experimental tendency.

Electroreflectance studies of InGaAs/GaAs asymmetric step quantum wells

Electroreflectance (ER) spectra of InGaAs/GaAs asymmetric step quantum wells (ASQWS) have been investigated under an applied electric field up to 130 kV cm-1 at 120 and 300 K. From the ER lineshape analysis the field dependences of the electron and heavy-hole ground-state excitonic transition energies, their intensities and the linewidth broadening have been determined. Some weak features due to the transitions involving excited quantum states have also been observed. The spectroscopic data have been compared with calculations performed by the transfer matrix method. The Stark shift of approximately 40 meV at a field of 100 kV cm-1 for the ground-state exciton transition is found to exceed significantly that in the square quantum well. The considerable change in ER lineshape and the rapid rise in linewidth broadening with increasing electric field are shown to be mainly caused by the effects of exciton quenching and tunnelling of carriers out of the well, which occur in the ASQWS studied here in high electric fields.

Large Stark shift of the interband transition in two-step quantum wells

Large and near-linear Stark shifts of the electron-heavy-hole ground state excitonic transition were observed in photoluminescence (PL) measurements for a two-step quantum-well (TSQW) structure. The Stark shift was 40 meV while a corresponding square well shifted only 20 meV at a field of 70 kV/cm. The observed Stark shifts agreed well with calculations. The large Stark shift of the TSQW was achieved on a global-to-local state transition realized via tailor-made quantum well (QW) parameters. This structure is an ideal candidate for optoelectronic devices based on the quantum confined Stark effect (QCSE). >

A quantum statistical theory of linewidths of radiative transitions due to compositional disordering in semiconductor alloys

A quantum statistical formalism has been developed for the excitonic luminescence linewidths and line shapes in semiconductor binary alloys due to band-gap fluctuations caused by the random distributions of the alloy components in an applied magnetic field. The virtual crystal approximation is used to estimate the local band-gap variations. The shifts of the excitonic transition energy due to the band-gap fluctuations are obtained using the first-order perturbation theory. A Gaussian line shape is obtained for the excitonic transition using standard statistical techniques. This formalism is applied to calculate the linewidths and line shapes associated with the ground-state excitonic transition as a function of alloy composition and magnetic-field strength in AlxGa1−xAs and InxGa1−xP alloys. The resulting linewidths and line shapes are in good agreement with the available low-temperature photoluminescence data; however, the calculated linewidths are consistently smaller than the measured values. The possible mechanisms responsible for this discrepancy are discussed. A comparison of excitonic linewidths obtained from the present theory with those calculated earlier is also presented.

New theory of linewidths of radiative transitions due to disordering in semiconductor alloys

A quantum mechanical formalism for the excitonic photoluminescence linewidth in semiconductor alloys due to band gap fluctuations caused by the random distributions of alloy components is presented. Using a quantum mechanical description for the excitonic system, the mean deviation of its transition energy due to the statistical potential fluctuations is calculated using a first-order perturbation theory. We then apply this formalism to calculate the linewidth of the ground state excitonic transition as a function of composition. Specifically, the excitonic linewidth in AlxGa1−xAs alloy as a function of Al concentration is calculated and compared with earlier models and available low-temperature photoluminescence data.

Quaternary quantum wells for electro-optic intensity and phase modulation at 1.3 and 1.55 μm

We demonstrate for the first time that large quantum-confined Stark effect can be obtained in high quality InGaAsP/InP quantum well p-i-n heterostructures. The compositional flexibility of this material system is particularly suited for quantum well device applications in optical communications systems operating between 1.55 and 1.3 μm. We measure the magnitude of the shift of the ground-state exciton transition with applied electric field and find that it is significantly enhanced over ternary wells. We have also determined the electro-optic intensity and phase modulation response in these structures.