Amphoteric Defect Research Articles

Can a bistable amphoteric native defect model explain the photo-induced transformation of MAPbI3 thin films?

Hybrid organic-inorganic perovskites such as MAPbI3 hold great promise for photovoltaic applications with power conversion efficiencies already exceeding 26 %. Despite the unprecedented advantages of these materials in photovoltaics and optoelectronics they exhibit a range of complex phenomena under light illumination that remain poorly understood. Here we use a combination of photoluminescence (PL) spectroscopy, cathodoluminescence imaging and theoretical calculations to correlate PL fluctuations in MAPbI3 thin films with changes in the spatial distribution and concentration of native defects. We demonstrate that short-term illumination results in a more homogeneous distribution of emitting and quenching sites, whereas prolonged illumination causes PL quenching. Our findings support the conclusion that the photo-induced transformation of MAPbI3 can be explained within a bistable amphoteric native defect model, wherein a neutral native defect can undergo a transition between a donor-like and acceptor-like configuration.

WITHDRAWN: Vacancies and antisites investigation at InAlAs/InGaAs hetero-interface: A first-principles study

The vacancies and antisites at InAlAs/InGaAs hetero-interface have been investigated by first-principles calculation based on hybrid density functional (HSE06). We propose an approach to obtain the chemical potentials based on the growth process of hetero-junction. The valence-band maximum of hetero-interface supercell is aligned with the reference of the average electrostatic potential of bulk material. The VIn, VGa, and VAl defects are deep acceptors, while VAs-1, VAs-2, and VAs-3 defects would behave as donor defects. The antisites are amphoteric defects, whereas they will only behave as donor defects due to the Fermi-level should be below the conduction-band minimum of InGaAs side. For InAlAs/InGaAs devices, the impact of the cation vacancies (acceptors) and antisites (donors) is associated to the bias conditions, while it is bias-independent for As vacancies (donors).

Intrinsic point defects investigation in InAlAs with extrapolated defect transition level

The intrinsic point defects in InAlAs have been studied by first-principles calculations, with a simplified approach to rescale the charge transition levels from the semilocal to the hybrid functional level. Both antisite defects and vacancy defects exhibit a high sensitivity to growth conditions. For Al-poor, In-poor and As-poor growth conditions, AsAl, AsIn and VAs demonstrate the lowest defect formation energy, respectively. All antisite defects including AsIn, AsAl, InAs and AlAs, exhibit donor-like behavior in the band gap as well as VAs. Both VIn and VAl are amphoteric defects, which can behave as donor defects or acceptor defects.

(Invited) Universal Alignment of Surface and Bulk Oxygen Levels in Semiconductors

Lattices of most semiconductors have a large density of intrinsic and extrinsic defects which gives rise to effects such as surface Fermi level (EF) pinning, dopant compensation, asymmetrical p versus n-doping, and device degradation. Oxygen and hydrogen are the two most important impurities in semiconductors because of their ubiquitous presence in growth and device processing environments and consequently their incorporation strongly influences electronic and electrical properties. Therefore, a deeper understanding of the interaction of these species with the semiconductor surface and bulk defects is necessary for enabling the development of devices based on them such as photovoltaic and photocatalytic systems, fuel cells, and many others. Analysis of the reported surface work function values and the substitutional bulk O-defect energies show that the surface Fermi level of position in a broad range of group IV, III-V, II-VI, and I-III-VI2 semiconductors with physisorbed O2 lies universally at approximately -5.1 eV below the vacuum level. Similarly, results show that the energy of the bulk substitutional O-related amphoteric defects incorporated during crystal growth also has a universal energy of ~ -5.0 eV with respect to the vacuum level for most of the investigated semiconductors. It is shown that the process of ‘surface transfer doping’ that involves an adsorbed nanoscale water film on the semiconductor surface is likely responsible for the universal alignment of oxygen levels. Figure 1

Optimization and detail analysis of novel structure Pb-free CsGeI3-based all-inorganic perovskite solar cells by SCAPS-1D

In this work, a novel structure of all inorganic PSC (TCO/TiO2/CsGeI3/MoO3/Back Metal contact) has been numerically investigated and optimized. Initially, we simulated the structure by using different optoelectronic parameters found in literature that are substantiated theoretically and experimentally and obtained a PCE of 19.81%. After that, we have turned up a detailed analysis by varying the parameters including the thickness of the light-harvesting layer, ETL, and HTL, bulk defects and amphoteric defect of the light-harvesting layer, interfacial defects, operating temperature, series resistance, and work function to obtain optimum values. The efficiency as high as 22.85% has been achieved along with Voc = 1.16 Volt, Jsc = 23.97 mA/cm2, and FF = 82.25%, respectively for the optimized structure of PSC. We also investigated the capacitance-voltage (C-V) and Mott-Schottky (MS) plots for in depth understanding of the performance variation. The detailed analysis and optimized parameters of this study, we believe, will be useful in synthesising toxic element-free CsGeI3-based all-inorganic PSCs with higher efficiency and stability, paving the way for PSC commercialization.

Magnetic Order, Electrical Doping, and Charge-State Coupling at Amphoteric Defect Sites in Mn-Doped 2D Semiconductors.

Two-dimensional (2D) dilute magnetic semiconductors (DMSs) are attractive material platforms for applications in multifunctional nanospintronics due to the prospect of embedding controllable magnetic order within nanoscale semiconductors. Identifying candidate host material and dopant systems requires consideration of doping formation energies, magnetic ordering, and the tendency for dopants to form clustered domains. In this work, we consider the defect thermodynamics and the dilute magnetic properties across charge states of 2D-MoS2 and 2D-WS2 with Mn magnetic dopants as candidate systems for 2D-DMSs. Using hybrid density functional calculations, we study the magnetic and electronic properties of these systems across configurations with thermodynamically favorable defects: 2D-MoS2 doped with Mn atoms at sulfur site (MnS), at two Mo sites (2MnMo), on top of a Mo atom (Mn-top), and at a Mo site (MnMo). While the majority of the Mn-defect complexes provide trap states, MnMo and MnW are amphoteric, although previously predicted to be donor defects. The impact of cluster formation of these amphoteric defects on magnetic ordering is also considered; both MnMo-MnMo (2Mn2Mo) and MnW-MnW (2Mn2W) clusters are found to be stable in ferromagnetic (FM) ordering. Interestingly, we observed the defect charge state dependent magnetic behavior of 2Mn2Mo and 2Mn2W clusters in 2D-TMDs. We investigate that the FM coupling of 2Mn2Mo and 2Mn2W clusters is stable in only a neutral charge state; however, the antiferromagnetic (AFM) coupling is stable in the +1 charge state. 2Mn2Mo clusters provide shallow donor levels in AFM coupling and deep donor levels in FM coupling. 2Mn2W clusters lead to trap states in the FM and AFM coupling. We demonstrate the AFM to FM phase transition at a critical electron density nce = 3.5 × 1013 cm-2 in 2D-MoS2 and 2D-WS2. At a 1.85% concentration of Mn, we calculate the Curie temperature of 580 K in the mean-field approximation.

Distinctive Deep-Level Defects in Non-Stoichiometric Sb2 Se3 Photovoltaic Materials.

Characterizing defect levels and identifying the compositional elements in semiconducting materials are important research subject for understanding the mechanism of photogenerated carrier recombination and reducing energy loss during solar energy conversion. Here it shows that deep‐level defect in antimony triselenide (Sb2Se3) is sensitively dependent on the stoichiometry. For the first time it experimentally observes the formation of amphoteric SbSe defect in Sb‐rich Sb2Se3. This amphoteric defect possesses equivalent capability of trapping electron and hole, which plays critical role in charge recombination and device performance. In comparative investigation, it also uncovers the reason why Se‐rich Sb2Se3 is able to deliver high device performance from the defect formation perspective. This study demonstrates the crucial defect types in Sb2Se3 and provides a guidance toward the fabrication of efficient Sb2Se3 photovoltaic device and relevant optoelectronic devices.

Doping limitation due to self-compensation by native defects in In-doped rocksalt Cd x Zn1−x O

Cadmium oxide (CdO)–ZnO alloys (Cd x Zn1−x O) exhibit a transformation from the wurtzite to the rocksalt (RS) phase at a CdO composition of ∼70% with a drastic change in the band gap and electrical properties. RS–Cd x Zn1−x O alloys (x > 0.7) are particularly interesting for transparent conductor applications due to their wide band gap and high electron mobility. In this work, we synthesized RS–Cd x Zn1−x O alloys doped with different concentrations of In dopants and evaluated their electrical and optical properties. Experimental results are analyzed in terms of the amphoteric native defect model and compared directly to defect formation energies obtained by hybrid density functional theory (DFT) calculations. A saturation in electron concentration of ∼7 × 1020 cm−3 accompanied by a rapid drop in electron mobility is observed for the RS–Cd x Zn1−x O films with 0.7 ⩽ x < 1 when the In dopant concentration [In] is larger than 3%. Hybrid DFT calculations confirm that the formation energy of metal vacancy acceptor defects is significantly lower in RS–Cd x Zn1−x O than in CdO, and hence limits the free carrier concentration. Mobility calculations reveal that due to the strong compensation by native defects, RS–Cd x Zn1−x O alloys exhibit a compensation ratio of >0.7 for films with x < 0.8. As a consequence of the compensation by native defects, in heavily doped RS–Cd x Zn1−x O carrier-induced band filling effect is limited. Furthermore, the much lower mobility of the RS–Cd x Zn1−x O alloys also results in a higher resistivity and reduced transmittance in the near infra-red region (λ > 1100 nm), making the material not suitable as transparent conductors for full spectrum photovoltaics.

Design and Modelling of Eco-Friendly CH3NH3SnI3-Based Perovskite Solar Cells with Suitable Transport Layers

An ideal n-i-p perovskite solar cell employing a Pb free CH3NH3SnI3 absorber layer was suggested and modelled. A comparative study for different electron transport materials has been performed for three devices keeping CuO hole transport material (HTL) constant. SCAPS-1D numerical simulator is used to quantify the effects of amphoteric defect based on CH3NH3SnI3 absorber layer and the interface characteristics of both the electron transport layer (ETL) and hole transport layer (HTL). The study demonstrates that amphoteric defects in the absorber layer impact device performance significantly more than interface defects (IDL). The cell performed best at room temperature. Due to a reduction in Voc, PCE decreases with temperature. Defect tolerance limit for IL1 is 1013 cm−3, 1016 cm−3 and 1012 cm−3 for structures 1, 2 and 3 respectively. The defect tolerance limit for IL2 is 1014 cm−3. With the proposed device structure FTO/PCBM/CH3NH3SnI3/CuO shows the maximum efficiency of 25.45% (Voc = 0.97 V, Jsc = 35.19 mA/cm2, FF = 74.38%), for the structure FTO/TiO2/CH3NH3SnI3/CuO the best PCE is obtained 26.92% (Voc = 0.99 V, Jsc = 36.81 mA/cm2, FF = 73.80%) and device structure of FTO/WO3/CH3NH3SnI3/CuO gives the maximum efficiency 24.57% (Voc = 0.90 V, Jsc = 36.73 mA/cm2, FF = 74.93%) under optimum conditions. Compared to others, the FTO/TiO2/CH3NH3SnI3/CuO system provides better performance and better defect tolerance capacity.

Annealing Induced Saturation in Electron Concentration for V-Doped CdO

As-grown Ar-deposited Cd1−xVxO and Ar/O2-deposited Cd1−yVyO feature lower and higher electron concentrations than 4 × 1020 cm−3, respectively. After isothermal and isochronal annealing under N2 ambient, we find that the two series exhibit a decrease or increase in electron concentrations until ~4 × 1020 cm−3 which is close to Fermi stabilization energy (EFS) level of CdO, with the assistance of native defects. An amphoteric defects model is used to explain the changing trends in electron concentrations. The tendencies in mobility further confirm our results. This work may provide some strategies to predict the electrical properties in CdO.

Universal alignment of surface and bulk oxygen levels in semiconductors

Oxygen and hydrogen are the two most important impurities in semiconductors because of their ubiquitous presence in growth and device processing environments, and consequently, their incorporation strongly influences electronic and electrical properties. Therefore, a deeper understanding of the interaction of these species with the semiconductor surface and bulk defects is necessary for enabling the development of devices based on them, such as photovoltaic and photocatalytic systems and fuel cells. It is shown here, through the analysis of the reported surface work function values and substitutional bulk O-defect energies, that the surface Fermi level of semiconductors with physisorbed O2 lies universally at approximately −5.1 eV below the vacuum level. Similarly, the results show that the energy of substitutional bulk O-related amphoteric defects incorporated during the crystal growth also has a universal energy of ∼−5.0 eV with respect to the vacuum level for most semiconductors investigated. It is shown that the process of “surface transfer doping” involving an adsorbed water film on the semiconductor surface is likely responsible for the universal alignment of oxygen levels.

Defect Study and Modelling of SnX3-Based Perovskite Solar Cells with SCAPS-1D.

Recent achievements, based on lead (Pb) halide perovskites, have prompted comprehensive research on low-cost photovoltaics, in order to avoid the major challenges that arise in this respect: Stability and toxicity. In this study, device modelling of lead (Pb)-free perovskite solar cells has been carried out considering methyl ammonium tin bromide (CH3NH3SnBr3) as perovskite absorber layer. The perovskite structure has been justified theoretically by Goldschmidt tolerance factor and the octahedral factor. Numerical modelling tools were used to investigate the effects of amphoteric defect and interface defect states on the photovoltaic parameters of CH3NH3SnBr3-based perovskite solar cell. The study identifies the density of defect tolerance in the absorber layer, and that both the interfaces are 1015 cm−3, and 1014 cm−3, respectively. Furthermore, the simulation evaluates the influences of metal work function, uniform donor density in the electron transport layer and the impact of series resistance on the photovoltaic parameters of proposed n-TiO2/i-CH3NH3SnBr3/p-NiO solar cell. Considering all the optimization parameters, CH3NH3SnBr3-based perovskite solar cell exhibits the highest efficiency of 21.66% with the Voc of 0.80 V, Jsc of 31.88 mA/cm2 and Fill Factor of 84.89%. These results divulge the development of environmentally friendly methyl ammonium tin bromide perovskite solar cell.

The Bright Side and Dark Side of Hybrid Organic–Inorganic Perovskites

The previously developed bistable amphoteric native defect (BAND) model is used for a comprehensive explanation of the unique photophysical properties and for understanding the remarkable performance of perovskites as photovoltaic materials. It is shown that the amphoteric defects in donor (acceptor) configuration capture a fraction of photoexcited electrons (holes) dividing them into two groups: higher energy bright and lower energy dark electrons (holes). The spatial separation of the dark electrons and the dark holes and the k-space separation of the bright and the dark charge carriers reduce electron hole recombination rates, emulating the properties of an ideal photovoltaic material with a balanced, spatially separated transport of electrons and holes. The BAND model also offers a straightforward explanation for the exceptional insensitivity of the photovoltaic performance of polycrystalline perovskite films to structural and optical inhomogeneities. The blue-shifted radiative recombination of bright electrons and holes results in a large anti-Stokes effect that provides a quantitative explanation for the spectral dependence of the laser cooling effect measured in perovskite platelets.

Experimental exploration of the amphoteric defect model by cryogenic ion irradiation of a range of wide band gap oxide materials

The evolution of electrical resistance as function of defect concentration is examined for the unipolar n-conducting oxides CdO, β-Ga2O3, In2O3, SnO2 and ZnO in order to explore the predictions of the amphoteric defect model. Intrinsic defects are introduced by ion irradiation at cryogenic temperatures, and the resistance is measured in-situ by current–voltage sweeps as a function of irradiation dose. Temperature dependent Hall effect measurements are performed to determine the carrier concentration and mobility of the samples before and after irradiation. After the ultimate irradiation step, the Ga2O3 and SnO2 samples have both turned highly resistive. In contrast, the In2O3 and ZnO samples are ultimately found to be less resistive than prior to irradiation, however, they both show an increased resistance at intermediate doses. Based on thermodynamic defect charge state transitions computed by hybrid density functional theory, a model expanding on the current amphoteric defect model is proposed.

Role of polarity in SiN on Al/GaN and the pathway to stable contacts

Despite being the most widely used dielectric for passivation of GaN-based lateral devices, amorphous silicon-nitride still faces many stability challenges, which arise from its complex bulk electronic and interface properties on the polar (Al)GaN surfaces. In this investigation, SiN has been applied as an ultra-thin interlayer (∼3–5 nm) in vertical contact structures on Ga-polar and N-polar GaN templates to study the metal–insulator–semiconductor- (MIS-) like system and better understand the interaction between the polar surface and its dielectric overlayer. We describe the role of amphoteric ≡Si centers in SiN in passivating and providing the polarization countercharge to Al/GaN of different polarities. The consequent requirements of the concentration profile of the amphoteric defects and the corresponding chemical profile of SiN is discussed. The importance of SiN surface termination and their influence on the interface potential on Al/GaN that determines device performance and reliability is also shown. Finally, a pathway to highly stable and reliable ohmic contacts to n-type Ga-polar GaN without instabilities associated with metal directly alloying with GaN as in the case of traditional contacts is proposed.

On the predictive, quantitative properties of the amphoteric native defect model

The amphoteric native defect model phenomenologically explains and categorizes observed background doping concentrations and accounts for the doping limitations in compound semiconductors. Here, we test and verify the model’s capabilities as a quantitative, predictive tool. We demonstrate that the nature, (donor or acceptor), of non-stoichiometry related vacancy-like defects in the (Al,Ga,In)(As,Sb) system is determined by the position of the intrinsic Fermi energy, EFi at the growth temperature relative to the Fermi level stabilization energy, EFS, a universal energy reference located at 4.9 eV below the vacuum level. We show that a dramatic and predictable conduction type-flip from n- to p-type occurs when EFi is deliberately shifted from below to above EFS.

A comprehensive defect study of tungsten disulfide (WS2) as electron transport layer in perovskite solar cells by numerical simulation

Abstract In this study, an ideal planar perovskite solar cell (PSC) has been proposed and simulated by using Tungsten Disulfide (WS2) as an electron transport layer (ETL). Effects of various amphoteric defect states of PSC based on CH3NH3PbI3−xXx absorber layer and the interface properties of both ETL and hole transport layer (HTL) are quantitatively analysed by SCAPS-1D numerical simulator. Results show that the device performance is highly influenced by amphoteric defects in the absorber layer rather than the interface defects layer (IDL). It is also revealed that the quantitative tolerable range in CH3NH3PbI3−xXx and IDLs are less than 1015 cm−3 and 1016 cm−3, respectively. The PSC exhibits better performance in the range of 10 °C–40 °C and degrades gradually at higher temperature. With the proposed structure, the simulation finds the highest power conversion efficiency (PCE) of PSC to be 25.70% (Voc = 1.056 V, Jsc = 25.483 mA/cm2, and FF = 88.54%).

Bistable Amphoteric Native Defect Model of Perovskite Photovoltaics.

The past few years have witnessed unprecedented rapid improvement of the performance of a new class of photovoltaics based on halide perovskites. This progress has been achieved even though there is no generally accepted mechanism of the operation of these solar cells. Here we present a model based on bistable amphoteric native defects that accounts for all key characteristics of these photovoltaics and explains many idiosyncratic properties of halide perovskites. We show that a transformation between donor-like and acceptor-like configurations leads to a resonant interaction between amphoteric defects and free charge carriers. This interaction, combined with the charge transfer from the perovskite to the electron and hole transporting layers results in the formation of a dynamic n-i-p junction whose photovoltaic parameters are determined by the perovskite absorber. The model provides a unified explanation for the outstanding properties of the perovskite photovoltaics, including hysteresis of J-V characteristics and ultraviolet light-induced degradation.

Free Carrier Absorption Assisted Photoelectrochemistry of Silicon

Free-carrier absorption (FCA) in semiconductor is a process which carriers within conduction or valence band absorbs near-bandgap photon energies to transfer themselves into a higher energy state without generating electron-hole pairs. The energy absorption activates phonon scattering and is generally considered to have undesirable impact on the performance of electronic or optical devices. Here we find, in an electrochemical processing of silicon, the FCA not only has a significate impact on chemical reaction but also contributed to the formation of nanocrystals. By the effect of FCA, nanocrystals form directly on the bulk surface via a rate-limited photo-electrochemistry processing. The formation mechanism of silicon quantum dots as follows: phonon scattering is generated at the photo-absorption site with its nearby atoms from absorbing laser as an hole-countercurrent to reduce redox reaction for dissolving silicon and caused amphoteric defects around the point. To proving the concept, we employed a 0.9 W/cm2, 1310 nm laser that can penetrate through silicon but be absorbed by free-carriers. After anodizing, a brilliant non-etching spot irradiated by the laser appeared on the black surface of P++ silicon substrate. Under He-Cd laser photoexcitation, we found the photoluminescence in the spot was enhanced to 450% than the around porous silicon forming in dark in the vicinity of the spot.

Oxygen Polyvacancies as Conductive Filament in Zirconia: First Principle Simulation

ZrO2 is the high-κ dielectric perspective for nonvolatile memory applications [1]. Currently ZrO2 is investigated as potential active medium for the Resistive Random Access Memory [2]. One of the wide spread model of resistive effect based on the filament formation/dissociation. The simplest filament model is a chain of oxygen vacancies, i.e. oxygen polyvacancy. The study of oxygen vacancies chain formation possibility (energy benefit) in ZrO2and their ability to participate in conduction is of great theoretical and practical interest. The modeling was carried out in the ZrO2 cubic (c-), tetragonal (t-) and monoclinic (m-) phase. Simulations were performed in terms of the hybrid DFT using a B3LYP functional in the Quantum-ESPRESSO code. The 192-atom c-, t-ZrO2, and 96-atom m-ZrO2 supercells were used to simulate the oxygen polyvacancy. Each subsequent atom removal from the supercell is determined from the point of view of the minimum formation energy. This model reflects a gradual increase in the polyvacancy size. The trap thermal E th and optical E optionization energies are estimated by the formulas offered in [3]. The calculated band gap values of 5.7, 6.1 and 5.6 eV for c-, t- and m-ZrO2are consistent with the corresponding experimental values 5.1, 5.78, and 5.83 eV [4]. The 4- and 3-fold coordinated (4f and 3f) O vacancy formation energies, 6.11 and 6.17 eV, predict the 4f vacancies prevalence in the real structure. The Kohn–Sham levels of five VO charged states (q = -2, -1, 0, 1, 2) localized in the band gap indicate that any type of oxygen vacancies can capture both electrons and holes. The second added electron leads either to the singlet (V-2(s)) or a triplet (V-2(t)) defect state, and the latter is 0.06 eV lower in energy. The significant depth of negatively charged defect levels indicates a polaronic effect. The defect peaks width lower than 0.1 eV in TDOS spectra indicate the charge localization in space. The charge density spatial distribution of the excess charge also confirms the charge localization. The positive charge is distributed evenly between the nearest Zr atoms. An additional electron leads to a charge density distribution among two closest to each other Zr atoms, and one can say that there is a kind of Zr-Zr bond. The calculated values of E th can be interpreted as the energy gain when the conduction band bottom electron capture onto the defect. The positive E th values indicate that the charge capture to the O vacancy in m-ZrO2 is energetically favorable. Thus, an oxygen vacancy in the ZrO2 is the amphoteric defect, it can act as the electron and hole trap, and participate in charge transport. The calculated values are consisted with E th = 1.15 [5] for ZrO2, and E th = 1.25 eV, E opt=2.5 eV for the HfO2 [6]. For V0 and V+, a good agreement of the calculation and experiment is observed. The O polyvacancy atomic structure in c-, t - and m-ZrO2 (Fig. 1) shows that each subsequent vacancy forms near the already existing one, and no more than the 2 removed O atoms relate to any Zr atom. One can assume that this result is valid for amorphous ZrO2, and the external electric field determines the preferred direction of the vacancies chains growth. This is consistent with the filament model of resistive switching. For t-ZrO2, the energetically favorable O polyvacancy atomic structure is a chain along the [100] direction. Each subsequent removal of oxygen atom adds one filled level to the band gap. These levels are distributed on the band gap preferentially localized close to the monovacancy level. The oxygen polyvacancy growth in size yields a broad defective band in the energy spectrum of ZrO2 filled with electrons. Since, for the single oxygen vacancy, the extra electron forms something like a Zr-Zr bond, one can assume that ZrO2 can acquire conductivity, which is carried out through the channel of the Zr ions separating the vacancies in this polyvacancy chain. The work was supported by the Russian Science Foundation, grant #16-19-00002. The modeling was performed on a cluster of the Institute of Semiconductor Physics SB RAS. [1] X.D.Huang, R.P.Shi, P.T.Lai, Appl. Phys. Lett. 104, 162905 (2014). [2] C.-H.Lai, H.-W. Chen, C.-Y.Liu, Materials 9, 551 (2016). [3] D.Muñoz Ramo, J.L.Gavartin, A.L.Shluger, et al.Phys. Rev. B 75, 205336 (2007). [4] R.H.French, S.J.Glass, F.S.Ohuchi, et al.Phys. Rev. B 49, 5133 (1994). [5] G.Jegert, A.Kersch, W.Weinreich, et al.Appl. Phys. Lett. 96, 062113 (2010). [6] V.A.Gritsenko, T.V.Perevalov, D.R.Islamov, Physics Reports 613, 1 (2016). Figure 1