Electron-hole Interaction Research Articles

Spectral widths and Stokes shifts in InP-based quantum dots.

InP-based quantum dots (QDs) have Stokes shifts and photoluminescence (PL) line widths that are larger than in II-VI semiconductor QDs with comparable exciton energies. The mechanisms responsible for these spectral characteristics are investigated in this paper. Upon comparing different semiconductors, we find the Stokes shift decreases in the following order: InP > CdTe > CdSe. We also find that the Stokes shift decreases with core size and decreases upon deposition of a ZnSe shell. We suggest that the Stokes shift is largely due to different absorption and luminescent states in the angular momentum fine structure. The energy difference between the fine structure levels, and hence the Stokes shifts, are controlled by the electron-hole exchange interaction. Luminescence polarization results are reported and are consistent with this assignment. Spectral widths are controlled by the extent of homogeneous and inhomogeneous broadening. We report PL and PL excitation (PLE) spectra that facilitate assessing the roles of homogeneous and different inhomogeneous broadening mechanisms in the spectra of zinc-treated InP and InP/ZnSe/ZnS particles. There are two distinct types of inhomogeneous broadening: size inhomogeneity and core-shell interface inhomogeneity. The latter results in a distribution of core-shell band offsets and is caused by interfacial dipoles associated with In-Se or P-Zn bonding. Quantitative modeling of the spectra shows that the offset inhomogeneity is comparable to but somewhat smaller than the size inhomogeneity. The combination of these two types of inhomogeneity also explains several aspects of reversible hole trapping dynamics involving localized In3+/VZn2- impurity states in the ZnSe shells.

Electronic and optical properties of chemically modified 2D GaAs nanoribbons

We employed density functional theory calculations to investigate the electronic and optical characteristics of finite GaAs nanoribbons (NRs). Our study encompasses chemical alterations including doping, functionalization, and complete passivation, aimed at tailoring NR properties. The structural stability of these NRs was affirmed by detecting real vibrational frequencies in infrared spectra, indicating dynamical stability. Positive binding energies further corroborated the robust formation of NRs. Analysis of doped GaAs nanoribbons revealed a diverse range of energy gaps (approximately 2.672 to 5.132 eV). The introduction of F atoms through passivation extended the gap to 5.132 eV, while Cu atoms introduced via edge doping reduced it to 2.672 eV. A density of states analysis indicated that As atom orbitals primarily contributed to occupied molecular orbitals, while Ga atom orbitals significantly influenced unoccupied states. This suggested As atoms as electron donors and Ga atoms as electron acceptors in potential interactions. We investigated excited-state electron–hole interactions through various indices, including electron–hole overlap and charge-transfer length. These insights enriched our understanding of these interactions. Notably, UV–Vis absorption spectra exhibited intriguing phenomena. Doping with Te, Cu, W, and Mo induced redshifts, while functionalization induced red/blue shifts in GaAs-34NR spectra. Passivation, functionalization, and doping collectively enhanced electrical conductivity, highlighting the potential for improving material properties. Among the compounds studied, GaAs-34NR-edg-Cu demonstrated the highest electrical conductivity, while GaAs-34NR displayed the lowest. In summary, our comprehensive investigation offers valuable insights into customizing GaAs nanoribbon characteristics, with promising implications for nanoelectronics and optoelectronics applications.

Optical spectrum of ferrovalley materials: A case study of Janus H-VSSe

As opposed to the prototypical MoS2 with centroasymmetry, Janus ferrovalley materials such as H-VSSe are less symmetric with the mirror symmetry and time reversal symmetry broken, and hence possess spontaneous valley polarization and strong ferroelasticity. The optical transition is an important means to excite the valley carriers. We investigate the optical spectrum of H-VSSe by using the many-body perturbation-based GW approach and solving the Bethe–Salpeter equation (BSE) to include the electron–hole interactions. It is found that after the GW correction, the band gaps of the quasiparticle bands are much larger than those obtained by the normal density functional theory. The system is ferromagnetic and the valley gaps become non-degenerate due to spin–orbit coupling (SOC). The position of the lowest BSE peak is much lower than the quasiparticle band gap, indicating that the excitonic effect is large. The peak is split into two peaks by the SOC. The binding energy difference between these two BSE peaks is about the same as the difference between the inequivalent valley gaps. Our results show that in Janus H-VSSe the two lowest exciton peaks are from the two inequivalent valleys with different gaps, in contrast to the A and B exciton peaks of MoS2 which are from the same valley.

Circumventing the phonon bottleneck by multiphonon-mediated hot exciton cooling at the nanoscale

Nonradiative processes govern efficiencies of semiconductor nanocrystal (NC)-based devices. A central process is hot exciton cooling, or the nonradiative relaxation of a highly excited electron/hole pair to form a band-edge exciton. Due to quantum confinement effects, the timescale and mechanism of cooling are not well understood. A mismatch between electronic energy gaps and phonon frequencies has led to the hypothesis of a phonon bottleneck and extremely slow cooling, while enhanced electron-hole interactions have suggested ultrafast cooling. Experimental measurements of the cooling timescale range six orders of magnitude. Here, we develop an atomistic approach to describe phonon-mediated exciton dynamics and simulate cooling in NCs of experimentally relevant sizes. We find that cooling occurs on ~30 fs timescales in CdSe NCs, in agreement with the most recent measurements, and that the phonon bottleneck is circumvented through a cascade of multiphonon-mediated relaxation events. Furthermore, we identify NC handles for tuning the cooling timescale.

Electronic and Optical Properties of Finite Gallium Sulfide Nano Ribbons: A First-Principles Study

The electronic and optical properties of finite GaS nanoribbons are investigated using density functional theory calculations. The effect of size, edge termination, and chemical modification by doping and edge passivation are taken into account. The dynamical stability is confirmed by the positive vibration frequency from infrared spectra; further, the positive binding energies ensure the stable formation of the considered nanoribbons. Accurate control of the energy gap has been achieved. For instance, in armchair nanoribbons, energy gaps ranging from ~ 1 to 4 eV were obtained in varying sizes. Moreover, the energy gap can be increased by up to 5.98 eV through edge passivation with F-atoms or decreased to 0.98 eV through doping with Si-atoms. The density of states shows that the occupied molecular orbitals are dominated by S-atoms orbitals, while unoccupied ones are mostly contributed to by Ga orbitals. Thus, S-atoms will be the electron donor sites, and Ga-atoms will be the electron acceptors in the interactions that the nanoribbons might undergo. The nature of electron–hole interactions in the excited states was investigated using various indices, such as electron–hole overlapping, charge–transfer length, and hole–electron Coulomb attraction energy. The UV-Vis absorption spectra reveal a redshift by increasing the size in the armchair or the zigzag directions. Chemical functionalization shows a significant influence on the absorption spectra, where a redshift or blueshift can be achieved depending on the dopant or the attached element.

Impacts of dielectric screening on the luminescence of monolayer WSe2

Single layers of transition metal dichalcogenides (TMDCs), such as WSe2 have gathered increasing attention due to their intense electron–hole interactions, being considered promising candidates for developing novel optical applications. Within the few-layer regime, these systems become highly sensitive to the surrounding environment, enabling the possibility of using a proper substrate to tune desired aspects of these atomically-thin semiconductors. In this scenario, the dielectric environment provided by the substrates exerts significant influence on electronic and optical properties of these layered materials, affecting the electronic band-gap and the exciton binding energy. However, the corresponding effect on the luminescence of TMDCs is still under discussion. To elucidate these impacts, we used a broad set of materials as substrates for single-layers of WSe2, enabling the observation of these effects over a wide range of electrical permittivities. Our results demonstrate that an increasing permittivity induces a systematic red-shift of the optical band-gap of WSe2, intrinsically related to a considerable reduction of the luminescence intensity. Moreover, we annealed the samples to ensure a tight coupling between WSe2 and its substrates, reducing the effect of undesired adsorbates trapped in the interface. Ultimately, our findings reveal how critical the annealing temperature can be, indicating that above a certain threshold, the heating treatment can induce adverse impacts on the luminescence. Furthermore, our conclusions highlight the influence the dielectric properties of the substrate have on the luminescence of WSe2, showing that a low electrical permittivity favours preserving the native properties of the adjacent monolayer.

Structural, mechanical, dielectric and defect properties of Eu-doped BeO ceramics: A computational and experimental approach

BeO ceramics in the wurtzite (w-BeO) form either pure or doped with lanthanide ions present high Thermoluminescence (TL) and Optically Stimulated Luminescence (OSL) sensitivity. However, the mechanism of defect formation governing the charge carrier dynamics associated with the TL and OSL signals is not well understood yet. Thus, this work aims to develop a study on the structural, mechanical, dielectric, and defect properties of Europium ion–doped w-BeO ceramics. We develop a new set of potential parameters to describe the Be–O bond. By using these potential parameters, we describe the physical and chemical properties with good agreement. Defect calculations employing the Mott and Littleton two-region strategy show that the distorted structure of pure w-BeO ceramics favours the Frenkel–type defect formation in the basal plane of the crystal lattice. When doped with Eu3+, we observed a change in the defect arrangement. It replaces preferentially two Be sites, eliminating beryllium interstices and keeping the beryllium vacancy from the initial configuration. We also observed that it is unlikely the Eu3+/Eu2+ coexist due to the solution energy values. Lastly, we have observed a most significant electron–hole interaction which may be associated with the intrinsic luminescence band of the w-BeO ceramics. In addition, TL and OSL measurements are presented to corroborate the defect calculations. The results presented here bring new insight to elucidate the charge carrier dynamic associated with the luminescent properties.

First-principles study on the electronic and optical properties of AlSb monolayer

Using density functional theory and many-body perturbation theory, we systematically investigate the optoelectronic properties of AlSb monolayer, which has been recently synthesized by molecular beam epitaxy [ACS Nano 2021, 15, 5, 8184–8191]. After confirming the dynamical stability of the monolayer, we analyze its electronic properties at different levels of theory without (PBE, HSE03, HSE06) and with (G_0W_0, GW_0, and GW) electron-electron interaction. The results show that AlSb monolayer is a semiconductor with a direct quasiparticle band gap of 1.35 eV while its electronic structure is dominated by spin-orbit coupling. Also, we study the optical properties of the monolayer by solving the Bethe–Salpeter equation. In this regard, the effects of spin-orbit coupling, electron–electron correlation, and electron–hole interaction on the optical spectrum of the monolayer are evaluated. Based on the highest level of theory, the first bright exciton is found to be located at 0.97 eV, in excellent agreement with the experimental value (0.93 eV). Moreover, the exciton binding energy, effective mass, and Bohr radius are obtained 0.38 eV, 0.25 m_0, and 6.31 Å, respectively. This work provides a better understanding of the electronic, optical, and excitonic properties of AlSb monolayer and may shed light on its potential applications.

Nuclear Quantum Effects Prolong Charge Carrier Lifetimes in Hybrid Organic-Inorganic Perovskites.

Hybrid organic-inorganic perovskites (HOIPs) contain light hydrogen atoms that exhibit significant nuclear quantum effects (NQEs). We demonstrate that NQEs have a strong effect on HOIP geometry and electron-vibrational dynamics at both low and ambient temperatures, even though charges in HOIPs reside on heavy elements. By combining ring-polymer molecular dynamics (MD) and ab initio MD with nonadiabatic MD and time-dependent density functional theory and focusing on the most studied tetragonal CH3NH3PbI3, we show that NQEs increase the disorder and thermal fluctuations through coupling of the light inorganic cations to the heavy inorganic lattice. The additional disorder induces charge localization and decreases electron-hole interactions. As a result, the nonradiative carrier lifetimes are extended by a factor of 3 at 160 K and 1/3 at 330 K. The radiative lifetimes are increased by 40% at both temperatures. The fundamental band gap decreases by 0.10 and 0.03 eV at 160 and 330 K, respectively. By enhancing atomic motions and introducing new vibrational modes, NQEs strengthen electron-vibrational interactions. Decoherence, determined by elastic scattering, accelerates almost by a factor of 2 due to NQEs. However, the nonadiabatic coupling, driving nonradiative electron-hole recombination, decreases because it is more sensitive to structural distortions than atomic motions in HOIPs. This study demonstrates, for the first time, that NQEs should be considered to achieve an accurate understanding of geometry evolution and charge carrier dynamics in HOIPs and provides important fundamental insights for the design of HOIPs and related materials for optoelectronic applications.

Giant excitonic effects in vacancy-ordered double perovskites

Using first-principles GW plus Bethe-Salpeter equation calculations, we identify anomalously strong excitonic effects in several vacancy-ordered double perovskites Cs2MX6 (M = Ti, Zr; X = I, Br). Giant exciton binding energies about 1 eV are found in these moderate-gap, inorganic bulk semiconductors, pushing the limit of our understanding of electron-hole (e-h) interaction and exciton formation in solids. Not only are the exciton binding energies extremely large compared with any other moderate-gap bulk semiconductors, but they are also larger than typical 2D semiconductors with comparable quasiparticle gaps. Our calculated lowest bright exciton energy agrees well with the experimental optical band gap. The low-energy excitons closely resemble the Frenkel excitons in molecular crystals, as they are highly localized in a single [MX6]2- octahedron and extended in the reciprocal space. The weak dielectric screening effects and the nearly flat frontier electronic bands, which are derived from the weakly bonded [MX6]2- units, together explain the significant excitonic effects. Spin-orbit coupling effects play a crucial role in red-shifting the lowest bright exciton by mixing up spin-singlet and spin-triplet excitons, while exciton-phonon coupling effects have minor impacts on the strong exciton binding energies.

Photoexcitation of planar Wannier excitons by twisted photons

Photoexcitation of planar Wannier excitons by twisted photons in thin semiconductor films is investigated. The excitons are assumed to be already created. The explicit general formulas for transition probabilities between exciton states are derived. The selection rules for the projection of the total angular momentum are obtained. As examples, the Coulomb and Rytova–Keldysh electron–hole interaction potentials are considered. The use of planar excitons as a pure on-chip source of twisted photons is discussed. The formulas obtained also describe photoexcitation of states of electrons and holes bound to charged impurities in planar semiconductors.

Exchange-Driven Intermixing of Bulk and Topological Surface States by Chiral Excitons in Bi2Se3

Topological surface states (TSS) in the prototypical topological insulator (TI) Bi_{2}Se_{3} are frequently characterized using optical probes, but electron-hole interactions and their effect on surface localization and optical response of the TSS remain unexplored. Here, we use ab initio calculations to understand excitonic effects in the bulk and surface of Bi_{2}Se_{3}. We identify multiple series of chiral excitons that exhibit both bulk and TSS character, due to exchange-driven mixing. Our results address fundamental questions about the degree to which electron-hole interactions can relax the topological protection of surface states and dipole selection rules for circularly polarized light in TIs by elucidating the complex intermixture of bulk and surface states excited in optical measurements and their coupling to light.

Pseudopotential Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures: Excitonic effects in α−Al2O3

We present an ab initio description of optical and shallow-core x-ray absorption spectroscopies in a unified formalism based on the pseudopotential plane-wave method at the level of the Bethe-Salpeter equation (BSE) within Green's functions theory. We show that norm-conserving pseudopotentials are reliable and accurate not only for valence, but also for semicore electron excitations. In order to validate our approach, we compare BSE absorption spectra obtained with two different codes: the pseudopotential-based code EXC and the all-electron full-potential code Exciting. We take corundum $\alpha$-Al$_2$O$_3$ as an example, being a prototypical material that presents strong electron-hole interactions for both valence and core electron excitations. We analyze in detail the optical absorption spectrum as well as the Al L$_1$ and L$_{2,3}$ edges in terms of anisotropy, crystal local fields, interference and excitonic effects. We perform a thorough inspection of the origin and localization of the lowest-energy excitons, and conclude highlighting the purely electronic character off the pre-edge of L$_1$ and the dichroic nature of the optical and L$_{23}$ spectra.

Improved quasiparticle self-consistent electronic band structure and excitons in β−LiGaO2

The band structure of $\beta$-LiGaO$_2$ is calculated using the quasiparticle self-consistent QS$G\hat W$ method where the screened Coulomb interaction $\hat W$ is evaluated including electron-hole interaction ladder diagrams and $G$ is the one-electron Green's function. Improved convergence compared to previous calculations leads to a significantly larger band gap of about 7.0 eV. However, exciton binding energies are found to be large and lead to an exciton gap of about 6.0 eV if also a zero-point-motion correction of about $-0.4$ eV is included. These results are in excellent agreement with recent experimental results on the onset of absorption. Besides the excitons observed thus far, the calculations indicate the existence of a Rydberg-like series of exciton excited states, which is however modified from the classical Wannier exciton model by the anisotropies of the material and the more complex mixing of Bloch states in the excitons resulting from the Bethe-Salpeter equation. The exciton fine structure and the exciton wave functions are visualized and analyzed in various ways.

Linearly polarized emission from CdSe/CdS core-in-rod nanostructures: Effects of core position.

Semiconductor nanocrystals with an anisotropic morphology exhibit unique properties, most notably their linear polarization. The colloidal growth of semiconductor nanorods with core dots inside, also referred to as dot-in-rod (DIR) structure, has enabled the synthesis of anisotropic nanocrystals with better stability and controllable fluorescence polarization. In this study, we synthesize CdSe/CdS DIR nanocrystals, in which the position of the CdSe core particle can be controlled by using different ligand compositions during the CdS growth. Varying the core position within the DIR structure, e.g., from the center to the end of the DIR particles, results in a change in the degree of linear polarization. When the core is positioned at the center of the nanorod, the linear polarization turns out to be higher compared with tip-core DIRs. Time-resolved photoluminescence analysis reveals that the center-core DIRs have higher electron-hole interaction than tip-core DIRs because of weak uniaxial strain in center-core DIR that arises from lattice dislocations at the interface to relieve accumulated strain.

First-principles investigation on the structural, vibrational, mechanical, electronic, and optical properties of MSi2Z4 ( M : Pd and Pt, Z : N and P) monolayers

The recent synthesis of two-dimensional (2D) layered crystals of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ and ${\mathrm{WSi}}_{2}{\mathrm{N}}_{4}$ has received significant attention due to their novel properties and potential applications. The inclusion of silicon during chemical vapor deposition growth enhances the ambient stability of transition metal nitrides and enables large-scale growth in monolayer limit. The transition metal and nitrogen elements can potentially be replaced with other metal and pnictogen atoms, which can constitute a new and large 2D family. In this respect, based on first-principles calculations, we design $M{\mathrm{Si}}_{2}{Z}_{4}$ ($M$: Pd and Pt, $Z$: N and P) monolayers and investigate their structural, vibrational, mechanical, electronic, and optical properties. The dynamical, thermal, and mechanical stabilities of the proposed systems are confirmed through phonon band dispersion calculations, ab initio molecular dynamics simulations, and elastic tensor analyses, respectively. The computed Raman and infrared spectra of the nanosheets reveal that the frequency and the intensity of the most prominent peaks are specified by the type of pnictogen atom in the structures. The mechanical response of the considered systems in the elastic regime is investigated in terms of in-plane stiffness (${Y}_{\text{2D}}$) and the Poisson's ratio ($\ensuremath{\nu}$). The obtained values of ${Y}_{\text{2D}}$ indicate that $M{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayers are stiffer than $M{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$ nanosheets and the $\ensuremath{\nu}$ values are found to be within the same range and close to the ductile-brittle transition limit. The electronic structure investigation shows that while $M{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayers are quasidirect wide-band-gap semiconductors, the $M{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$ monolayers are semiconductors with an indirect narrow band gap. Additionally, these monolayers have isotropic optical spectra and, depending on the type of pnictogen atom, significant optical absorption peaks within the infrared, visible, and ultraviolet regions can be attained. Additionally, it is found that $M{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayers possess multiple bound excitons with strong exciton binding when electron-hole interactions are taken into account. Our results not only expand the class of 2D $M{\mathrm{Si}}_{2}{Z}_{4}$ crystals but also offer valuable insights on the physical properties of the designed systems and suggest them as promising materials in diverse optoelectronic applications.

Structural Reconstruction Modulated Physical Properties of Titanium Oxide at the Monolayer Limit

To suppress surface dangling bonds, monolayer oxides derived from non-layered bulks usually undergo a pronounced structural reconstruction. It remains challenging to resolve these structural reconstructions and the induced distinct modulation of intrinsic properties. In this study, the structural reconstruction-modulated electronic, polaronic, and exitonic properties of a non-layered oxide at the monolayer limit are unraveled. Based on first-principles calculations and tight-binding simulations for a stable titanium dioxide (TiO2) monolayer, we show that its distinct surface Kagome sublattices host a topologically nontrivial flat band at the valence band edge. The strong electron–hole interaction in this monolayer oxide gives rise to a large exciton binding energy of around 2.49 eV. Interestingly, the monolayer TiO2 also exhibits strong electron–lattice coupling, which favors the formation of small electron polarons and thus greatly reduces its band gap energy into the visible light range. This work could be useful to understand the structural reconstruction-induced modulation of exotic physical and chemical properties for a broad range of non-layered oxides at the monolayer limit.

Electron-phonon correlations inducing excitonic excitations in semimetal and semiconducting materials

The influence of phonons on the low-energy excitonic excitations at zero temperature in the extended Falicov-Kimball model has been investigated. In the framework of the unrestricted Hartree-Fock approximation, a set of self-consistent equations for the excitonic condensate order parameter and a lattice distortion is derived when both electron-phonon coupling and electron-hole Coulomb interaction are treated on an equal footing. The low-energy excitation properties of the excitonic condensate are addressed in signatures of the optical conductivity and the dynamical excitonic susceptibility function. The real part of the optical conductivity is evaluated by the Kubo linear response theory and the imaginary part of the dynamical excitonic susceptibility is found by adapting the random phase approximation. In the semimetal state, one always finds a sharp peak in the optical conductivity spectrum indicating the stability of the excitonic condensation in the BCS type if the correlation between electrons and phonons becomes significant. In contrast, the peak is smeared out on the semiconducting side indicating the stability of the BEC-type excitonic condensate. In this semiconducting side, the sharp peak signature appears and the system turns to the BCS-type excitonic condensation state by increasing the electron-phonon correlations. In either the semimetal or the semiconducting normal state, increasing the electron-phonon correlations always reinforces a low-energy sharp peak in the dynamical excitonic susceptibility spectrum, indicating the existence of the tightly bound excitonic excitations before the condensation state. Specifically, on the semiconducting side, the ``halo'' phase with the preformed excitons exiting outside of the BEC-excitonic condensation state has been specified. The halo phase becomes more recognizable by raising the electron-phonon correlations.

Analogy and dissimilarity of excitons in monolayer and bilayer of MoSe2

Excitons in thin layers of semiconducting transition metal dichalcogenides are highly subject to the strongly modified Coulomb electron–hole interaction in these materials. Therefore, they do not follow the model system of a two-dimensional hydrogen atom. We investigate experimentally and theoretically excitonic properties in both the monolayer (ML) and the bilayer (BL) of MoSe2 encapsulated in hexagonal BN. The measured magnetic field evolutions of the reflectance contrast spectra of the MoSe2 ML and BL allow us to determine g-factors of intralayer A and B excitons, as well as the g-factor of the interlayer exciton. We explain the dependence of g-factors on the number of layers and excitation state using first principles calculations. Furthermore, we demonstrate that the experimentally measured ladder of excitonic s states in the ML can be reproduced using the approach with the Rytova–Keldysh potential that describes the electron–hole interaction. In contrast, the analogous calculation for the BL case requires taking into account the out-of-plane dielectric response of the MoSe2 BL.

Signatures of the exciton gas phase and its condensation in monolayer 1T-ZrTe2

The excitonic insulator (EI) is a Bose-Einstein condensation (BEC) of excitons bound by electron-hole interaction in a solid, which could support high-temperature BEC transition. The material realization of EI has been challenged by the difficulty of distinguishing it from a conventional charge density wave (CDW) state. In the BEC limit, the preformed exciton gas phase is a hallmark to distinguish EI from conventional CDW, yet direct experimental evidence has been lacking. Here we report a distinct correlated phase beyond the 2×2 CDW ground state emerging in monolayer 1T-ZrTe2 and its investigation by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The results show novel band- and energy-dependent folding behavior in a two-step process, which is the signatures of an exciton gas phase prior to its condensation into the final CDW state. Our findings provide a versatile two-dimensional platform that allows tuning of the excitonic effect.