Theoretical prediction of intrinsic self-trapping of electrons and holes in monoclinic HfO2

s valence electrons in cations of metal oxides serving as descriptors for electron and hole polarons

In some metal oxides, an excess electron can give rise to the formation of a small polaron localized on a single site. However, there are still some metal oxides that exhibit the formation of a large polaron. The underlying mechanism behind this phenomenon remains unclear. In this study, we investigate polaron formation in metal oxides favorable for polaron formation using different functionals and through a review of the literature. Our findings indicate that the s valence electrons in cations could serve as a descriptor to classify the polarons in materials. In metal oxides with cations having ns (n ⩾ 5) valence electrons, excess charges trend to localize on several sites or form a two-dimensional shape, and even a large polaron, as these s electrons are delocalized in nature and have a large effect on p or d state polarons. The delocalized nature of ns (n ⩽ 4) valence electrons in cations is relatively small and does not affect the localization condition of p or d state polarons. Therefore, the excess charges in these metal oxides with ns (n ⩽ 4) valence electrons prefer to form a small polaron localizing on a single site. This work unveils the impact of the s valence in cations on polaron formation and provides a fundamental understanding of various types of polarons in metal oxides.

Role of oxygen vacancies in ferroelectric or resistive switching hafnium oxide

HfO2 shows promise for emerging ferroelectric and resistive switching (RS) memory devices owing to its excellent electrical properties and compatibility with complementary metal oxide semiconductor technology based on mature fabrication processes such as atomic layer deposition. Oxygen vacancy (Vo), which is the most frequently observed intrinsic defect in HfO2-based films, determines the physical/electrical properties and device performance. Vo influences the polymorphism and the resulting ferroelectric properties of HfO2. Moreover, the switching speed and endurance of ferroelectric memories are strongly correlated to the Vo concentration and redistribution. They also strongly influence the device-to-device and cycle-to-cycle variability of integrated circuits based on ferroelectric memories. The concentration, migration, and agglomeration of Vo form the main mechanism behind the RS behavior observed in HfO2, suggesting that the device performance and reliability in terms of the operating voltage, switching speed, on/off ratio, analog conductance modulation, endurance, and retention are sensitive to Vo. Therefore, the mechanism of Vo formation and its effects on the chemical, physical, and electrical properties in ferroelectric and RS HfO2 should be understood. This study comprehensively reviews the literature on Vo in HfO2 from the formation and influencing mechanism to material properties and device performance. This review contributes to the synergetic advances of current knowledge and technology in emerging HfO2-based semiconductor devices.

Band versus Polaron: Charge Transport in Antimony Chalcogenides

Antimony sulfide (Sb₂S₃) and selenide (Sb₂Se₃) are emerging earth-abundant absorbers for photovoltaic applications. Solar cell performance depends strongly on charge-carrier transport properties, but these remain poorly understood in Sb₂X₃ (X = S, Se). Here we report band-like transport in Sb₂X₃, determined by investigating the electron-lattice interaction and theoretical limits of carrier mobility using first-principles density functional theory and Boltzmann transport calculations. We demonstrate that transport in Sb₂X₃ is governed by large polarons with moderate Fröhlich coupling constants (α ≈ 2), large polaron radii (extending over several unit cells), and high carrier mobility (an isotropic average of >10 cm² V^-1 s^-1 for both electrons and holes). The room-temperature mobility is intrinsically limited by scattering from polar phonon modes and is further reduced in highly defective samples. Our study confirms that the performance of Sb₂X₃ solar cells is not limited by intrinsic self-trapping.

Assessment of the Morphological, Optical, and Photoluminescence Properties of HfO2 Nanoparticles Synthesized by a Sol-Gel Method Assisted by Microwave Irradiation

In this work, we optimized the synthesis of HfO₂ nanoparticles (NPs) with a nonaqueous sol-gel method assisted by microwave heating, with a direct surfactant-free extraction and stabilization in water. To tune the structural, morphological, and photophysical properties, we explored the influence of reaction time, heating temperature, and type and concentration of a salt precursor. The controlled size, shape, crystallinity associated with high stability, a good yield of production, and stabilization in water without any surfactant modification of these HfO₂ NPs open possibilities for future optoelectronic and biomedical applications. The investigation of their optical properties, revealed a high absorption in the UV range and the presence of a large band gap, originating in transparency at visible wavelengths. Under UV excitation, photoluminescence (PL) shows three emission bands centered at 305, 381, and 522 nm and are assigned to the vibronic transition of an excited OH^•* radical or to a self-trapped exciton, to threefold oxygen vacancies V_O3 with recombination to the valence band, and to defect level, respectively. The presence of oxygen vacancies associated with PL properties is particularly attractive for optoelectronic, photocatalysis, scintillator, and UV photosensor applications. Finally, by changing the nature of the hafnium precursor salt, using hafnium ethoxide or hafnium acetylacetonate, low-crystallized and aggregated NPs were obtained, which requires further investigation.

Optical properties of oxygen vacancies in HfO2 thin films studied by absorption and luminescence spectroscopy

Hafnium oxide thin films with varying oxygen content were investigated with the goal of finding the optical signature of oxygen vacancies in the film structure. It was found that a reduction of oxygen content in the film leads to changes in both, structural and optical characteristics. Optical absorption spectroscopy, using nanoKelvin calorimetry, revealed an enhanced absorption in the near-ultraviolet (near-UV) and visible wavelength ranges for films with reduced oxygen content, which was attributed to mid-gap electronic states of oxygen vacancies. Absorption in the near-infrared was found to originate from structural defects other than oxygen vacancy. Luminescence generated by continuous-wave 355-nm laser excitation in e-beam films showed significant changes in the spectral profile with oxygen reduction and new band formation linked to oxygen vacancies. The luminescence from oxygen-vacancy states was found to have microsecond-scale lifetimes when compared with nanosecond-scale lifetimes of luminescence attributed to other structural film defects. Laser-damage testing using ultraviolet nanosecond and infrared femtosecond pulses showed a reduction of the damage threshold with increasing number of oxygen vacancies in hafnium oxide films.

Intrinsic charge trapping in amorphous oxide films: status and challenges

We review the current understanding of intrinsic electron and hole trapping in insulating amorphous oxide films on semiconductor and metal substrates. The experimental and theoretical evidences are provided for the existence of intrinsic deep electron and hole trap states stemming from the disorder of amorphous metal oxide networks. We start from presenting the results for amorphous (a) HfO₂, chosen due to the availability of highest purity amorphous films, which is vital for studying their intrinsic electronic properties. Exhaustive photo-depopulation spectroscopy measurements and theoretical calculations using density functional theory shed light on the atomic nature of electronic gap states responsible for deep electron trapping observed in a-HfO₂. We review theoretical methods used for creating models of amorphous structures and electronic structure calculations of amorphous oxides and outline some of the challenges in modeling defects in amorphous materials. We then discuss theoretical models of electron polarons and bi-polarons in a-HfO₂ and demonstrate that these intrinsic states originate from low-coordinated ions and elongated metal-oxygen bonds in the amorphous oxide network. Similarly, holes can be captured at under-coordinated O sites. We then discuss electron and hole trapping in other amorphous oxides, such as a-SiO₂, a-Al₂O₃, a-TiO₂. We propose that the presence of low-coordinated ions in amorphous oxides with electron states of significant p and d character near the conduction band minimum can lead to electron trapping and that deep hole trapping should be common to all amorphous oxides. Finally, we demonstrate that bi-electron trapping in a-HfO₂ and a-SiO₂ weakens Hf(Si)-O bonds and significantly reduces barriers for forming Frenkel defects, neutral O vacancies and O^2- ions in these materials. These results should be useful for better understanding of electronic properties and structural evolution of thin amorphous films under carrier injection conditions.

Intrinsic electron trapping in amorphous oxide

We demonstrate that electron trapping at intrinsic precursor sites is endemic in non-glass-forming amorphous oxide films. The energy distributions of trapped electron states in ultra-pure prototype amorphous (a)-HfO₂ insulator obtained from exhaustive photo-depopulation experiments demonstrate electron states in the energy range of 2-3 eV below the oxide conduction band. These energy distributions are compared to the results of density functional calculations of a-HfO₂ models of realistic density. The experimental results can be explained by the presence of intrinsic charge trapping sites formed by under-coordinated Hf cations and elongated Hf-O bonds in a-HfO₂. These charge trapping states can capture up to two electrons, forming polarons and bi-polarons. The corresponding trapping sites are different from the dangling-bond type defects responsible for trapping in glass-forming oxides, such as SiO₂, in that the traps are formed without bonds being broken. Furthermore, introduction of hydrogen causes formation of somewhat energetically deeper electron traps when a proton is immobilized next to the trapped electron bi-polaron. The proposed novel mechanism of intrinsic charge trapping in a-HfO₂ represents a new paradigm for charge trapping in a broad class of non-glass-forming amorphous insulators.

In Situ Analysis of Oxygen Vacancies and Band Alignment in HfO2/TiN Structure for CMOS Applications

The density of oxygen vacancies characterization in high-k/metal gate is significant for semiconductor device fabrication. In this work, a new approach was demonstrated to detect the density of oxygen vacancies by in situ x-ray photoelectron spectroscopy (XPS) and ultraviolet photoelectron spectroscopy (UPS) measurement. Moreover, the band alignment of the structure with optical band gap measured by spectroscopic ellipsometry (SE) and valence band offset by UPS were reported. The specific areal density of oxygen vacancies in high-k dielectric of HfO₂/TiN was obtained by fitting the experiment data to be 8.202 × 10¹⁰cm^- 2. This study would provide an effective approach to characterize the oxygen vacancies based defects which cause threshold voltage shifts and enormous gate leakage in modern MOSFET devices.

Theoretical modeling of charge trapping in crystalline and amorphous Al2O3

The characteristics of intrinsic electron and hole trapping in crystalline and amorphous Al₂O₃ have been studied using density functional theory (DFT). Special attention was paid to enforcing the piece-wise linearity of the total energy with respect to electron number through the use of a range separated, hybrid functional PBE0-TC-LRC (Guidon et al 2009 J. Chem. Theory Comput. 5 3010) in order to accurately model the behaviour of localized states. The tuned functional is shown to reproduce the geometric and electronic structures of the perfect crystal as well as the spectroscopic characteristics of Mg_Al hole centre in corundum α-Al₂O₃. An ensemble of ten amorphous Al₂O₃ structures was generated using classical molecular dynamics and a melt and quench method and their structural characteristics compared with the experimental data. The electronic structure of amorphous systems was characterized using the inverse participation ratio method. Electrons and holes were then introduced into both crystalline and amorphous alumina structures and their properties calculated. Holes are shown to trap spontaneously in both crystalline and amorphous alumina. In the crystalline phase they localize on single O ion with the trapping energy of 0.38 eV. In amorphous phase, holes localize on two nearest neighbour oxygen sites with an average trapping energy of 1.26 eV, with hole trapping sites separated on average by about 8.0 Å. No electron trapping is observed in the material. Our results suggest that trapping of positive charge can be much more severe and stable in amorphous alumina rather than in crystalline samples.

Critical analysis of fragment-orbital DFT schemes for the calculation of electronic coupling values

We present a critical analysis of the popular fragment-orbital density-functional theory (FO-DFT) scheme for the calculation of electronic coupling values. We discuss the characteristics of different possible formulations or "flavors" of the scheme which differ by the number of electrons in the calculation of the fragments and the construction of the Hamiltonian. In addition to two previously described variants based on neutral fragments, we present a third version taking a different route to the approximate diabatic state by explicitly considering charged fragments. In applying these FO-DFT flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole transfer), we find that our new scheme gives improved electronic couplings for HAB7 (-6.2% decrease in mean relative signed error) and greatly improved electronic couplings for HAB11 (-15.3% decrease in mean relative signed error). A systematic investigation of the influence of exact exchange on the electronic coupling values shows that the use of hybrid functionals in FO-DFT calculations improves the electronic couplings, giving values close to or even better than more sophisticated constrained DFT calculations. Comparing the accuracy and computational cost of each variant, we devise simple rules to choose the best possible flavor depending on the task. For accuracy, our new scheme with charged-fragment calculations performs best, while numerically more efficient at reasonable accuracy is the variant with neutral fragments.

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.

On the thermoluminescence properties and mechanism of LuPO4:Eu sintered materials

Thermoluminescence (TL) of X-rayed LuPO₄:Eu sintered materials was investigated as a function of the processing parameters and Eu concentration.

Modelling of oxygen vacancy aggregates in monoclinic HfO2: can they contribute to conductive filament formation?

Formation of metal rich conductive filaments and their rearrangements determine the switching characteristics in HfO2 based resistive random access memory (RRAM) devices. The initiation of a filament formation process may occur either via aggregation of pre-existing vacancies randomly distributed in the oxide or via generation of new oxygen vacancies close to the pre-existing ones. We evaluate the feasibility of vacancy aggregation processes by calculating the structures and binding energies of oxygen vacancy aggregates consisting of 2, 3 and 4 vacancies in bulk monoclinic (m)-HfO2 using density functional theory (DFT). We demonstrate that formation of neutral oxygen vacancy aggregates is accompanied by small energy gain, which depends on the size and shape of the aggregate. In the most strongly bound configurations, vacancies are unscreened by Hf cations and form voids within the crystal, with the larger aggregates having larger binding energy per vacancy (-0.11 to  -0.18 eV). The negatively charged di-vacancy was found to have similar binding energies to the neutral one, while the positively charged di-vacancy was found to be unstable. Thus aggregation process of either neutral or negatively charged oxygen vacancies is energetically feasible.

Density Functional Calculations of Native Defects in CH3NH3PbI3: Effects of Spin-Orbit Coupling and Self-Interaction Error

Native point defects play an important role in carrier transport properties of CH3NH3PbI3. However, the nature of many important defects remains controversial due partly to the conflicting results reported by recent density functional theory (DFT) calculations. In this Letter, we show that self-interaction error and the neglect of spin-orbit coupling (SOC) in many previous DFT calculations resulted in incorrect positions of valence and conduction band edges, although their difference, which is the band gap, is in good agreement with the experimental value. This problem has led to incorrect predictions of defect-level positions. Hybrid density functional calculations, which partially correct the self-interaction error and include the SOC, show that, among native point defects (including vacancies, interstitials, and antisites), only the iodine vacancy and its complexes induce deep electron and hole trapping levels inside of the band gap, acting as nonradiative recombination centers.

Electron small polarons and their transport in bismuth vanadate: a first principles study

Hybrid density functional calculations demonstrate small polaron formation in electron-doped BiVO₄, and predict the polaron hopping barrier to increase with lattice constant and also the possible concentration-dependence of electron mobility.

The transport properties of oxygen vacancy-related polaron-like bound state in HfOx

The oxygen vacancy-related polaron-like bound state migration in HfOx accounting for the observed transport properties in the high resistance state of resistive switching is investigated by the density functional theory with hybrid functional. The barrier of hopping among the threefold oxygen vacancies is strongly dependent on the direction of motion. Especially, the lowest barrier along the <001> direction is 90 meV, in agreement with the experimental value measured from 135 K to room temperature. This hopping mainly invokes the z-directional motion of hafnium and threefold oxygen atoms in the vicinity of the oxygen vacancy resulted from the synergized combination of coupled phonon modes. In the presence of surface, the lowest barrier of hopping between the surface oxygen vacancies is 360 meV along the <101> direction, where the significant surface perpendicular motion of hafnium and twofold oxygen atoms surrounding the oxygen vacancy is identified to facilitate this type of polaron-like bound state migration. Thus, the migration on the surfaces could be more important at the high temperature.

Self-trapping of single and paired electrons in Ge2Se3

We report the theoretical prediction of single and paired electron self-trapping in Ge(2)Se(3). In finite atomic cluster, density functional calculations, we show that excess single electrons in Ge(2)Se(3) are strongly localized around single germanium dimers. We also find that two electrons prefer to trap around the same germanium dimer, rupturing a neighboring Ge-Se bond. Localization is less robust in periodic, density functional calculations. While paired electron self-trapping is present, as shown by wavefunction localization around a distorted Ge-Ge dimer, single-electron trapping is not. This discrepancy appears to depend only on the boundary conditions and not on the exchange-correlation potential or basis set. For single- and paired-electron trapping, we report the adiabatic barriers to motion and we estimate hopping rates and freeze-in temperatures. For the single trapped electron, we also predict the (73)Ge and (77)Se hyperfine coupling constants.

Two-dimensional polaronic behavior in the binary oxides m-HfO2 and m-ZrO2

We demonstrate that the three-dimensional (3D) binary monoclinic oxides HfO2 and ZrO2 exhibit quasi-2D polaron localization and conductivity, which results from a small difference in the coordination of two oxygen sublattices in these materials. The transition between a 2D large polaron into a zero-dimensional small polaron state requires overcoming a small energetic barrier. These results demonstrate how a small asymmetry in the lattice structure can determine the qualitative character of polaron localization and significantly broaden the realm of quasi-2D polaron systems.

Growth, structure, and thermal conductivity of yttria-stabilized hafnia thin films

Yttria-stabilized hafnia (YSH) films of 90 nm thickness have been produced using sputter-deposition by varying the growth temperature (T(s)) from room-temperature (RT) to 400 °C. The effect of T(s) on the structure, morphology, and thermal conductivity of YSH films has been investigated. Structural studies indicate that YSH films crystallize in the cubic phase. The lattice constant decreases from 5.15 to 5.10 Å with increasing T(s). The average grain size (L) increases with increasing T(s); L-T(s) relationship indicates the thermally activated process of the crystallization of YSH films. The analyses indicate a critical temperature to promote nanocrystalline, cubic YSH films is 300 °C, which is higher compare to that of pure monoclinic HfO(2) films. Compared to pure nanocrystalline hafnia, the addition of yttria lowers the effective thermal conductivity. The effect of grain size on thermal conductivity is also explored.

Hole localization in molecular crystals from hybrid density functional theory

We use first-principles computational methods to examine hole trapping in organic molecular crystals. We present a computational scheme based on the tuning of the fraction of exact exchange in hybrid density functional theory to eliminate the many-electron self-interaction error. With small organic molecules, we show that this scheme gives accurate descriptions of ionization and dimer dissociation. We demonstrate that the excess hole in perfect molecular crystals forms self-trapped molecular polarons. The predicted absolute ionization potentials of both localized and delocalized holes are consistent with experimental values.

Electron and hole trapping in polycrystalline metal oxide materials

Electron and hole trapping by grain boundaries and dislocations in polycrystalline materials is important for wide ranging technological applications such as solar cells, microelectronics, photo-catalysts and rechargeable batteries. In this article, we first give an overview of the computational and methodological challenges involved in modelling such effects. This is followed by a discussion of two recent studies we have made on electron/hole trapping in wide gap insulators. The results suggest that such effects can be important for many applications which we discuss. These computationally demanding calculations have made extensive use of both the HPCx and HECToR services.