Polaron Formation Energy Research Articles

Polarons: Energetics and their structural and electronic effects in ATiO3 perovskite systems

Understanding the formation of a polaron near vacancies in oxides is of vital importance for controlling defect properties and related functionalities. We examine the energetics and local structure of polarons in the vicinity of oxygen vacancies using density functional theory with the Hubbard on-site Coulombic correction. We systematically consider several $\mathrm{ATi}{\mathrm{O}}_{3}$ perovskite systems: cubic $\mathrm{SrTi}{\mathrm{O}}_{3}$ (c-STO), cubic $\mathrm{BaTi}{\mathrm{O}}_{3}$ (c-BTO), cubic $\mathrm{PbTi}{\mathrm{O}}_{3}$ (c-PTO), tetragonal $\mathrm{BaTi}{\mathrm{O}}_{3}$ (t-BTO), and tetragonal $\mathrm{PbTi}{\mathrm{O}}_{3}$ (t-PTO). The polaron formation energies vary by several orders of magnitude across the systems, where PTO systems have large polaron formation energies $(\ensuremath{\sim}\ensuremath{-}1.688\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$, c-BTO is intermediate (\ensuremath{-}0.234 eV), and c-STO and t-BTO have considerably smaller formation energies $(<\ensuremath{-}0.01\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$. The formation of a polaron is found to influence the charge density, atomic displacement, and electronic structure, with higher polaron energies corresponding to larger charge density changes and greater displacements of the ions surrounding the oxygen vacancy, especially the displacement of the first nearest neighbor A-site. Finally, a comparison of the projected band structures shows fictitious in-gap states present in the delocalized picture of the system moving to the conduction and valence bands in the polaron solution of the system, indicating an incompleteness of the description of a vacancy without considering charge localization as in the polaron picture. In this paper, we provide fundamental properties of polarons near vacancies, which can be used to control and tune defect, charge transport, magnetoelectric, and multiferroic properties of perovskite oxides.

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fr\"ohlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $\mathrm{\ensuremath{\Gamma}}$ point. We also incorporate SOC into a generalized Fr\"ohlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fr\"ohlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fr\"ohlich model, within the physically relevant energy range of the Fr\"ohlich interaction for materials with high phonon frequencies treated with SOC.

Polarons free from many-body self-interaction in density functional theory

Semilocal density functional theory generally fails in stabilizing polarons, because of its spurious inclusion of the electron self-interaction. This work addresses the concepts of many-body and one-body self-interaction, which are found to be connected through the dielectric constant within a unified theoretical formulation. The superiority of the many-body self-interaction is demonstrated, resulting in robust polaron formation energies. In this context, an efficient semilocal scheme for polaron localization is developed.

Variational polaron equations applied to the anisotropic Fröhlich model

Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as individual electron, phonon and electron-phonon contributions are obtained. We suggest an efficient gradient-based optimization algorithm and apply these equations to the generalized Fr\"ohlich model with anisotropic non-degenerate electronic bands, both in two- and three-dimensional cases. The effect of the divergence of Fr\"ohlich electron-phonon matrix elements at $\Gamma$-point is treated analytically, improving the convergence with respect to the sampling in reciprocal space. The whole methodology is validated by obtaining the known asymptotic solution of the standard Fr\"ohlich model in isotropic scenario and also by comparing our results with the Gaussian ansatz approach, showing the difference between the numerically exact and Gaussian trial wavefunctions. Additionally, decomposition of the energy into individual terms allows one to recover the Pekar's 1:2:3:4 theorem, which is shown to be valid even in the anisotropic case. We expect that the improvements in the formalism and numerical implementation will be applicable beyond the large polaron hypothesis inherent to Fr\"ohlich model.

Facile ab initio approach for self-localized polarons from canonical transformations

Electronic states in a crystal can localize due to strong electron-phonon (e-ph) interactions, forming so-called small polarons. Methods to predict the formation and energetics of small polarons are either computationally costly or not geared toward quantitative predictions. Here we show a formalism based on canonical transformations to compute the polaron formation energy and wavefunction using ab initio e-ph interactions. Comparison of the calculated polaron and band edge energies allows us to determine whether charge carriers in a material favor a localized small polaron over a delocalized Bloch state. Due to its low computational cost, our approach enables efficient studies of the formation and energetics of small polarons, as we demonstrate by investigating electron and hole polaron formation in alkali halides and metal oxides and peroxides. We outline refinements of our scheme and extensions to compute transport in the polaron hopping regime.

Role of the reorganization energy for charge transport in disordered organic semiconductors

While it is commonly accepted that the activation energy of the thermally activated polaron hopping transport in disordered organic semiconductors can be decoupled into a disorder and a polaron contribution, their relative weight is still controversial. This feature is quantified in terms of the so-called $C$ factor in the expression for the effective polaron mobility: ${\ensuremath{\mu}}_{e}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{E}_{a}/{k}_{B}T\ensuremath{-}C{(\ensuremath{\sigma}/{k}_{B}T)}^{2}]$, where ${E}_{a}$ and $\ensuremath{\sigma}$ are the polaron activation energy and the energy width of a Gaussian density of states (DOS), respectively. A key issue is whether the universal scaling relation (implying a constant $C$ factor) regarding the polaron formation energy is really obeyed, as recently claimed in the literature [Seki and Wojcik, J. Chem. Phys. 145, 034106 (2016)]. In the present work, we reinvestigate this issue on the basis of the Marcus transition rate model using extensive kinetic Monte Carlo simulations as a benchmark tool. We compare the polaron-transport simulation data with results of analytical calculations by the effective medium approximation and multiple trapping and release approaches. The key result of this study is that the $C$ factor for Marcus polaron hopping depends on first the degree of carrier localization, i.e., the coupling between the sites, further whether quasiequilibrium has indeed been reached, and finally the $\ensuremath{\sigma}/{E}_{a}$ ratio. This implies that there is no universal scaling with respect to the relative contribution of polaron and disorder effect. Finally, we demonstrate that virtually the same values of the disorder parameter $\ensuremath{\sigma}$ are determined from available experimental data using the $C$ factors obtained here irrespective of whether the data are interpreted in terms of Marcus or Miller-Abrahams rates. This implies that molecular reorganization contributes only weakly to charge transport, and it justifies the use of the zero-order Miller-Abrahams rate model for evaluating the DOS width from temperature-dependent charge transport measurements regardless of whether or not polaron effects are accounted for.

Towards a transferable design of solid-state embedding models on the example of a rutile TiO2 (110) surface.

In this work, we present general and robust transferable principles for the construction of quantum-mechanically treated clusters in a solid-state embedding (SSE) approach, beyond the still prevalent trial and error approach. Thereby, we probe the quality of different cluster shapes on the accuracy of chemisorption energies of small molecules and small polaron formation energies at the rutile TiO2 (110) surface as test cases. Our analyses show that at least the binding energies and electronic structures in the form of the density of states tend to be quite robust already for small, nonoptimal cluster shapes. In contrast to that, the description of polaron formation can be dramatically influenced by the employed cluster geometry possibly leading to an erroneous energetic ordering or even to a wrong prediction of the polaronic states themselves. Our findings show that this is mainly caused by an inaccurate description of the Hartree potential at boundary and surrounding atoms, which are insufficiently compensated by the embedding environment. This stresses the importance of the cluster size and shape for the accuracy of general-purpose SSE models that do not have to be refitted for each new chemical question. Based on these observations, we derive some general design criteria for solid state embedded clusters.

First-principles determination of electronic charge transport properties in polymer dielectrics using a crystalline-based model system

There are various models for describing the charge transport in polymers but it is unclear how to choose the appropriate one for a given system. In this study, we determine the relevant charge transfer model for several insulating polymers by evaluating the Marcus parameters for electron and hole transfer with the aid of first-principles calculations. As expected, except for electron transfer in polyethylene and isotactic polypropylene, non-adiabatic (polaron) hopping takes place in most polymers, owing to the small inter-chain electronic interactions (10–100 meV) and large polaron formation energy (100–1000 meV). Therefore, the first-principles based parameter-free, multi-scale modeling approach, which we developed for evaluating the hole transfer property in polyethylene, can be used to study the electronic carrier transport properties in wide variety of polymers. The computed Marcus parameters imply that the electron and hole mobilities in syndiotactic polystyrene and polytetrafluoroethylene are larger than the hole mobility in polyethylene and isotactic polypropylene, which agrees with experimental data. The strong chain-length dependence of the computed Marcus parameters indicates that slight change in the polymer structure can result in significant variations in the charge mobility.

Geometry Distortion and Small Polaron Binding Energy Changes with Ionic Substitution in Halide Perovskites.

Halide perovskites have demonstrated remarkable performance in optoelectronic applications. Despite extraordinary progress, questions remain about device stability. We report an in-depth computational study of small polaron formation, electronic structure, charge density, and reorganization energies of several experimentally relevant halide perovskites using isolated clusters. Local lattice symmetry, electronic structure, and electron-phonon coupling are interrelated in polaron formation in these materials. To illustrate this, first-principles calculations are performed on (MA/Cs/FA)Pb(I/Br)3 and MASnI3. Across the materials studied, electron small polaron formation is manifested by Jahn-Teller-like distortions in the central octahedron, with apical PbI bonds expanding significantly more than the equatorial bonds. In contrast, hole polarons cause the central octahedron to uniformly contract. This difference in manifestation of electron and hole polaron formation can be a tool to determine what is taking place in individual systems to systematically control performance. Other trends as the anion and cations are changed are established for optimization in specific optoelectronic applications.

Probing molecule-like isolated octahedra via phase stabilization of zero-dimensional cesium lead halide nanocrystals

Zero-dimensional (0D) inorganic perovskites have recently emerged as an interesting class of material owing to their intrinsic Pb2+ emission, polaron formation, and large exciton binding energy. They have a unique quantum-confined structure, originating from the complete isolation of octahedra exhibiting single-molecule behavior. Herein, we probe the optical behavior of single-molecule-like isolated octahedra in 0D Cesium lead halide (Cs4PbX6, X = Cl, Br/Cl, Br) nanocrystals through isovalent manganese doping at lead sites. The incorporation of manganese induced phase stabilization of 0D Cs4PbX6 over CsPbX3 by lowering the symmetry of PbX6 via enhanced octahedral distortion. This approach enables the synthesis of CsPbX3 free Cs4PbX6 nanocrystals. A high photoluminescence quantum yield for manganese emission was obtained in colloidal (29%) and solid (21%, powder) forms. These performances can be attributed to structure-induced confinement effects, which enhance the energy transfer from localized host exciton states to Mn2+ dopant within the isolated octahedra.

Predicting Oxygen Vacancy Polaron Size from D-Orbital Splitting in ABO3 (A=La, Sr; B=Mn, Fe, Co) Perovskites

Mixed Ionic Electronic Conducting (MIEC) transition metal oxide (ABO3) perovskites are utilized for catalytic,1 energy conversion,2,3 and other applications. The oxygen ionic conductivity of these MIECs depends on their oxygen vacancy concentration and ionic mobility. In turn, the oxygen ion concentration and mobility both depend on the charge of the B-site atom,4 which itself depends on factors such as the A site La/Sr ratio, the crystal structure, etc. Previous calculations demonstrated that the Fe atom charge state distribution observed in strontium ferrite (SrFeO3-δ) is caused by differences in the d-orbital splitting of octahedral (Oh) versus square pyramidal (SP) Fe-O coordination (Figure 1).5 This d-orbital splitting ensures that the two electrons left behind when a charge-neutral oxygen vacancy forms in cubic SrFeO3-δ are transferred to the second nearest Fe neighbors,5 resulting in a large oxygen vacancy polaron size that produces strong oxygen vacancy interactions at high oxygen nonstoichiometry. As a result, the oxygen vacancy formation energy increases with oxygen nonstoichiometry in cubic SrFeO3-δ.5 Previous calculations also demonstrated that in orthorhombic lanthanum ferrite (LaFeO3-δ) the formation of a neutral oxygen vacancy produces a polaron that is localized to the oxygen-vacancy-adjacent Fe atoms. Hence, in orthorhombic LaFeO3-δ the oxygen vacancies do not interact with increasing oxygen nonstoichiometry.6 The objective of the present work was to examine whether d-orbital splitting could also explain the oxygen vacancy behavior of other MIEC perovskites. Hence, the impact of d-orbital splitting on oxygen vacancy polaron size and formation energies in lanthanum strontium manganite and lanthanum strontium cobaltite were modeled for the first time. Here, the charge redistribution caused by oxygen vacancy formation was studied for six different compositions: LaFeO3-δ, SrFeO3-δ, LaMnO3-δ, SrMnO3-δ, LaCoO3-δ, and SrCoO3-δ. The GGA+U method with PAW potentials implemented in VASP was utilized for all the structural energy calculations. First, the Hubbard-U parameter was calibrated to describe the charge on the B-site atom (U = 3 was selected for Fe, as done previously).6 The oxygen vacancy formation energy as a function of oxygen non-stoichiometry (δ) was then calculated at 0 K in vacuum by varying the size of the supercell, with oxygen vacancy interactions being enabled by the periodic boundary conditions. The calculated polaron size for neutral-oxygen-vacancy–containing ABO3 structures are summarized in Table 1.In LaMnO3-δ, Mn3+ has an [Ar] 3d4 electronic configuration in Oh coordination. After the formation of a neutral oxygen vacancy, the two Mn atoms adjacent to the oxygen vacancy go from Oh to SP coordination and the excess electrons left behind by the removed oxygen are pushed to the a1g level of the second nearest neighboring Oh-Mn (instead of remaining localized to the b1g level of the SP-Fe). This long range charge transfer results in large polaron size. This behavior is in contrast with that of LaFeO3-δ. However, LaMnO3-δ and SrFeO3-δ exhibit comparable polaron sizes since Fe4+ has an [Ar] 3d4 electronic- configuration. In SrMnO3-δ, Mn4+ has a [Ar] 3d3 electronic configuration in Oh coordination. Therefore, the formation of a neutral oxygen vacancy localizes the electrons to the oxygen vacancy adjacent Mn atoms, producing a small polaron, as explained by the d-orgbial splitting in Figure 1. This d-orbital splitting analysis indicates that the polaron size in LSM > LSF > LSC. Additional work aimed at calculating the oxygen vacancy formation energies of other ABO3 compositions are in progress.

Effect of defects on the small polaron formation and transport properties of hematite from first-principles calculations

Hematite (α-Fe2O3) is a promising candidate as a photoanode material for solar-to-fuel conversion due to its favorable band gap for visible light absorption, its stability in an aqueous environment and its relatively low cost in comparison to other prospective materials. However, the small polaron transport nature in α-Fe2O3 results in low carrier mobility and conductivity, significantly lowering its efficiency from the theoretical limit. Experimentally, it has been found that the incorporation of oxygen vacancies and other dopants, such as Sn, into the material appreciably enhances its photo-to-current efficiency. Yet no quantitative explanation has been provided to understand the role of oxygen vacancy or Sn-doping in hematite. We employed density functional theory to probe the small polaron formation in oxygen deficient hematite, N-doped as well as Sn-doped hematite. We computed the charged defect formation energies, the small polaron formation energy and hopping activation energies to understand the effect of defects on carrier concentration and mobility. This work provides us with a fundamental understanding regarding the role of defects on small polaron formation and transport properties in hematite, offering key insights into the design of new dopants to further improve the efficiency of transition metal oxides for solar-to-fuel conversion.

Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials.

Solution-processed organometallic perovskites have rapidly developed into a top candidate for the active layer of photovoltaic devices. Despite the remarkable progress associated with perovskite materials, many questions about the fundamental photophysical processes taking place in these devices, remain open. High on the list of unexplained phenomena are very modest mobilities despite low charge carrier effective masses. Moreover, experiments elucidate unique degradation of photocurrent affecting stable operation of perovskite solar cells. These puzzles suggest that, while ionic hybrid perovskite devices may have efficiencies on par with conventional Si and GaAs devices, they exhibit more complicated charge transport phenomena. Here we report the results from an in-depth computational study of small polaron formation, electronic structure, charge density, and reorganization energies using both periodic boundary conditions and isolated structures. Using the hybrid density functional theory, we found that volumetric strain in a CsPbI3 cluster creates a polaron with binding energy of around 300 and 900 meV for holes and electrons, respectively. In the MAPbI3 (MA = CH3NH3) cluster, both volumetric strain and MA reorientation effects lead to larger binding energies at around 600 and 1300 meV for holes and electrons, respectively. Such large reorganization energies suggest appearance of small polarons in organometallic perovskite materials. The fact that both volumetric lattice strain and MA molecular rotational degrees of freedom can cooperate to create and stabilize polarons indicates that in order to mitigate this problem, formamidinium (FA = HC(NH2)2) and cesium (Cs) based crystals and alloys, are potentially better materials for solar cell and other optoelectronic applications.

Time-resolved magnetophotoluminescence studies of magnetic polaron dynamics in type-II quantum dots

We used continuous wave photoluminescence (cw-PL) and time resolved photoluminescence (TR-PL) spectroscopy to compare the properties of magnetic polarons (MP) in two related spatially indirect II-VI epitaxially grown quantum dot systems. In the ZnTe/(Zn,Mn)Se system the holes are confined in the non-magnetic ZnTe quantum dots (QDs), and the electrons reside in the magnetic (Zn,Mn)Se matrix. On the other hand, in the (Zn,Mn)Te/ZnSe system, the holes are confined in the magnetic (Zn,Mn)Te QDs, while the electrons remain in the surrounding non-magnetic ZnSe matrix. The magnetic polaron formation energies in both systems were measured from the temporal red-shift of the band-edge emission. The magnetic polaron exhibits distinct characteristics depending on the location of the Mn ions. In the ZnTe/(Zn,Mn)Se system the magnetic polaron shows conventional behavior with decreasing with increasing temperature T and increasing magnetic field B. In contrast, in the (Zn,Mn)Te/ZnSe system has unconventional dependence on temperature T and magnetic field B; is weakly dependent on T as well as on B. We discuss a possible origin for such a striking difference in the MP properties in two closely related QD systems.

Possible polaron formation of zigzag graphene nano-ribbon in the presence of Rashba spin–orbit coupling

In this article we study the role of Rashba spin–orbit coupling and electron–phonon interaction on the electronic structure of zigzag graphene nanoribbon with different width. The total Hamiltonian of nanoribbon is written in the tight binding form and the electron–electron interaction is modeled in the Hubbard term. We used a unitary transformation to reach an effective Hamiltonian for nano ribbon in the presence of electron–phonon interaction. Our results show that small Rashba spin orbit coupling annihilates the anti-ferromagnetic phase in the zigzag edges of ribbon and the electron–phonon interaction yields small polaron formation in graphene nano ribbon. Furthermore, Rashba type spin–orbit coupling increases (decreases) the polaron formation energy for up (down) spin state.

The nature of excess electrons in anatase and rutile from hybrid DFT and RPA.

The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid density functional theory (DFT) and the random phase approximation (RPA). Consistent with experiment, charge trapping and polaron formation is observed in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is observed also with standard hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amount of Hartree-Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with experimental data, is observed, and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calculations serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree-Fock exchange), as a suitable method to study the rich chemistry and physics of TiO2.

Thermopower and electrical resistivity of La1−xSrxMnO3 (x=0.2, 0.3): Effect of nanostructure on small polaron transport

Abstract In this work we report on thermopower S(T) and electrical resistivity ρ(T) measurements performed on La1−xSrxMnO3 (x = 0.2, 0.3) ceramic samples, obtained by cold compaction and sintering of mechanically alloyed nanocrystalline powders. The samples studied in this work display grain sizes between d ∼ 70 nm and O(2 μm). The effects induced by the nanostructure on the thermoelectric and electrical properties in the paramagnetic state have been studied and discussed in terms of current theories about small polaron electrical transport in manganites. The observed changes in the conductivity and thermopower activation energies can be interpreted as a consequence of enhanced carrier localization and higher polaron formation energy WH for nanocrystalline La1−xSrxMnO3.

Molecular Switch Controlled by Pulsed Bias Voltages

Recent experiments have shown that the current-voltage characteristics (I-V) of BPDN-DT (bipyridyl-dinitro oligophenylene-ethynylene dithiol) can be switched in a very controlled manner between "on" and "off" traces by applying a pulse in a bias voltage, V(bias). Here, the polaron formation energies are calculated to check a frequently held belief, namely, that the polaron formation can explain the observed bistability. These results are not consistent with such a mechanism. Instead, a conformational reorientation is proposed. The molecule carries an intrinsic dipole moment, which couples to V(bias). Ramping V(bias) exerts a force on the dipole that can reorient ("rotate") the molecule from the ground state ("off") into a metastable configuration ("on") and back. By elaborated electronic structure calculations, a specific path for this rotation is identified through the molecule's conformational phase space. It is shown that this path has sufficiently high barriers to inhibit thermal instability but that the molecule can still be switched in the voltage range of the junction stability. The theoretical I-Vs qualitatively reproduce the key experimental observations. A proposal for the experimental verification of the alternative mechanism of conductance switching is presented.

A Realistic Description of the Charge Carrier Wave Function in Microcrystalline Polymer Semiconductors

The electronic structure of the charge carrier in one of the most commonly used semiconducting polymers (poly(3-hexylthiophene (P3HT)) is described using a combination of classical and quantum chemical methods. It is shown that the carriers are localized in correspondence with long-lived traps which are present also in the crystalline phase of the polymer. The existence of activated transport for very ordered polymer phases (regardless of the strength of the polaron formation energy) is explained, and the trapped states, postulated by many phenomenological models, are described for the first time with chemical detail. It is shown that computational chemistry methods can be used to fill the gap between phenomenological descriptions of charge transport in polymers and microscopic descriptions of the individual quantum dynamic processes.

Dynamics in magneto-optical properties of digital magnetic Zn 1− xCd xSe quantum wells

We have studied dynamics in magneto-optical properties of digital magnetic Zn 1− x Cd x Se quantum wells (QWs). Various types of MnSe layers were digitally doped in the Zn 1− x Cd x Se QWs. The giant Zeeman shift energy and the field-induced enhancement of the photoluminescence (PL) intensity of excitons depend on the digital-doping profile. This can be attributed to the spatial overlap of the exciton wavefunction with the 0.5 monatomic-thick effective paramagnetic layers at the interfaces between the antiferromagnetic MnSe layers and non-magnetic Zn 1− x Cd x Se layers. The exciton magnetic polaron (MP) formation energy as large as 18.6 meV is observed in time-resolved PL spectra for the digital magnetic QWs. The MP formation energy and time are also affected by the digital-doping profile.