Properties Of Intrinsic Point Defects Research Articles

Cation-Disorder-Enhanced Unintentional Doping in MgSnN2

${\mathrm{Mg}\mathrm{Sn}\mathrm{N}}_{2}$ has recently attracted significant interest as a promising candidate for applications in green light-emitting diodes and photovoltaic absorbers. However, the experimentally synthesized ${\mathrm{Mg}\mathrm{Sn}\mathrm{N}}_{2}$ samples suffer from a high concentration of unintentionally doped electrons, and their origin is not fully understood yet. By performing first-principles calculations, we investigate the properties of intrinsic point defects and oxygen impurities in cation-ordered and -disordered wurtzite ${\mathrm{Mg}\mathrm{Sn}\mathrm{N}}_{2}$. It is found that the cation antisite defect ${\mathrm{Sn}}_{\mathrm{Mg}}$ is the predominant donor defect, contributing an electron concentration as high as ${10}^{17}\phantom{\rule{0.25em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ to cation-ordered ${\mathrm{Mg}\mathrm{Sn}\mathrm{N}}_{2}$. However, this value is 2--3 orders of magnitude lower than experimental observations (${10}^{19}\ensuremath{-}{10}^{20}\phantom{\rule{0.25em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). We further show that cation disorder significantly decreases the formation energies of defects, leading to a much higher electron concentration (${10}^{19}\phantom{\rule{0.25em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$) than in the case of the cation-ordered phase. The reduced formation energy can be understood by the energy gain due to the creation of energetically favorable local motif structures after the formation of defects. Hence, reducing the degree of cation disorder is beneficial for decreasing the densities of defects and self-doped carriers.

Heterogeneity of grain boundary properties in Cu2ZnSnS4: A first-principles study

Using first-principles density functional calculations, we investigate the structure and properties of previously unstudied grain boundaries (GBs) in the solar absorber material copper-zinc-tin-sulfide (CZTS). We identify four stable low-Σ value symmetric tilt GBs with low formation energies: Σ3 (111) and Σ5 (201), each with two different GB terminations. Compared to CdTe and CuInSe, GBs in the quaternary semiconductor CZTS exhibit a wider variety of electronic states due to the more complex chemical environment near the GB, including under-coordinated atoms and dangling bonds. Further analysis confirms that strong dangling bonds introduce deep gap states in all GBs studied. We also investigate segregation and electronic properties of intrinsic point defects to GBs and find that one of the Σ3 (111) GBs exhibits an abnormal defect segregation behavior that favors Cu-poor (Zn-rich) GB composition, which is beneficial for its overall performance.

Intrinsic defects at the interface of the FAPbI3/MAPbI3 superlattice: insight from first-principles calculations.

The use of a superlattice structure is an effective strategy to develop novel perovskites and obtain excellent light-absorbing materials. Based on first-principles calculations, we systematically studied the properties of intrinsic point defects at the interface of the FAPbI3/MAPbI3 superlattice. Our calculations show that charged defects are easier to form as compared to neutral ones at the superlattice interface due to low formation energies. Most defects with low formation energies have a shallow level in the band gap, and some deep level defects have high formation energies, so the superlattice perovskite exhibits high defect tolerance. PbI3+ is a dominant and detrimental defect, which acts as a non-radiative recombination center because it has low formation energy and a deep transition level. To avoid the generation of PbI3+ defects, it is suggested to synthesize FAPbI3/MAPbI3 superlattices under I-rich conditions. The calculated light absorption coefficients and photovoltaic performance parameters demonstrate that the presence of defects leads to a certain degree of reduction in light absorption and power conversion efficiency (PCE) of solar cells made of FAPbI3/MAPbI3 superlattices, but the excellent performance of the perovskite solar cell (PSC) is basically retained. The superlattice perovskites are still promising candidates for light-absorbing materials of PSCs. This study is expected to contribute to a better understanding of the properties of defects at the superlattice interface and provide theoretical support for the design of high performance PSCs.

Defect physics of intrinsic point defects in BiPO4 photocatalysts: a hybrid functional study.

In this work, the intrinsic point defect properties of bulk BiPO4 under different growth conditions are intensively investigated and explored using first-principles hybrid functional calculations. It is found that Bi vacancies and O vacancies are the primary native defects in BiPO4. Under O-poor conditions, BiPO4 acts as an intrinsic insulator because the O vacancy defects (donor) and the Bi vacancy defects (acceptor) compensate for each other. Under Bi-poor conditions, good p-type conductivity is observed in BiPO4, which affirms the observed p-type conductivity behavior in experiments. Bi vacancies in BiPO4 are very shallow, which make it an excellent acceptor and are mostly responsible for the p-type character. In addition, it is found that the primary Bi vacancy defects of BiPO4 hardly affect its electronic structure and optical absorption spectrum regardless of the charge states. In contrast, the neutral O vacancy defects in BiPO4 introduce an impurity energy level near the VBM and induce a new optical absorption peak at around 370 nm. Furthermore, the O vacancies should be favorable for enhancing the production and separation efficiencies of the photo-generated electrons and holes in BiPO4. While Bi vacancies easily provide p-type carriers, simultaneously, they could become the active sites for the photocatalytic reactions because of their dominant -3 charge state. Therefore, understanding the defect physics in BiPO4 photocatalysts is believed to be beneficial for more research in developing BiPO4 or BiPO4-based photocatalysts.

Ab initio study of intrinsic point defects in germanium sulfide

The energetic and electronic properties of intrinsic point defects in germanium sulfide (GeS) were studied using first-principles methods. Point defects including single-site (e.g., vacancies, interstitials, and anitisites) and double-site defects (e.g., Schottky defects, Frenkel pairs) were considered. It was found that the lowest formation energy for neutral defects is associated with the Schottky dimer (SD), independent of chemical potentials of the species, and not with vacancies, as previously reported for similar materials like GeSe, SnS and SnSe. Furthermore, SD were studied in these similar materials and found to be energetically more stable than neutral vacancies for GeSe and similarly stable to Sn vacancy defects in SnS and SnSe. Charged states of the defects were considered and found to be energetically preferred over neutral defects. On allowing the defects to charge, Ge2- vacancy (VGe−2) defects were found to be the most stable defects in both Ge-rich and Ge-poor environments; consistent with the experimentally reported nonstoichiometric nature of GeS. Negative formation energies were obtained for Ge vacancies, in both environmental conditions, and thus they are expected to form spontaneously. The electronic structure was affected by the incorporation of point defects. For Ge vacancies, the Fermi level shifted below the valence band maxima (VBM), indicating p-type conductivity in agreement with experimental observations. S vacancies introduced occupied defect states and hybridized with VBM, and the fundamental bandgap was retained, indicating no preferential conductivity. The possibility of doping GeS to obtain n-type conductivity was explored.

A First-Principles Study on Electronic and Magnetic Properties of Intrinsic Point Defects in SrO Crystals

A First-Principles Study on Electronic and Magnetic Properties of Intrinsic Point Defects in SrO Crystals

Atomic-scale understanding on the physics and control of intrinsic point defects in lead halide perovskites

Lead halide perovskites (LHPs) have attracted considerable attention as promising materials for photovoltaic and optoelectronic applications. Intrinsic point defects play an important role in determining the performance of semiconductor devices. LHPs exhibit strong ionic character and unique electronic structure; thus, their defect properties are quite different from conventional covalent bond semiconductors. Understanding the defect science is crucial to the performance optimization of LHP-based devices. State-of-the-art first-principles calculation methods enable one to explore atomistic mechanisms of various defect-related processes, and tremendous efforts from theoretical simulations have provided invaluable insights to the defect physics and defect control of LHPs. In this review, we summarize recent progress, made with the help of theoretical modeling, on atomic-scale understanding about intrinsic point defects and related processes in LHPs. The fundamental properties of intrinsic point defects in LHPs are first introduced, including defect formation energy, charge transition level, and defect tolerance and its origin. A particular emphasis is given to the effects of band edge position on calculated defect properties. The impact of these defects on structural properties, carrier dynamics, and photoluminescence of LHPs is then presented. Advanced strategies to engineer the defects in LHPs are also reviewed, such as growth condition, defect passivation, and doping. Finally, we discuss open issues and outline directions toward a better understanding of defects of LHPs from a theoretical perspective. The goal of the review is to provide a comprehensive summary of atomic-scale understanding of intrinsic point defects in LHPs and to help further related research in the perovskite community.

Native point defects in mono and bilayer phosphorene

We study the stability and electronic properties of intrinsic point defects, vacancy and self-interstitial, in mono- and bi-layer phosphorene. We calculate the formation energies, quasiparticle defect states and charge transition levels (CTLs) of these defects using \textit{ab initio} density functional theory (DFT) and GW approximation to the electron self-energy. Using the DFT + GW two paths formalism for studying interstitial in monolayer phosphorene, we show that with the inclusion of electrostatic corrections CTLs can be calculated reliably. Our calculations show that all the native point defects have low formation energies 0.9-1.6 eV in neutral state. Furthermore, we find that vacancy in phosphorene behaves as an acceptor-like defect which can explain the p-type conductivity in phosphorene. On the other hand, interstitial can show both acceptor- and donor-like behaviour.

The impact of point defects on the optical and electrical properties of cubic ZrO2

First-principles calculations based on the full-potential linear augmented plane wave approach are applied herein to investigate the electronic, optical, and electrical properties of intrinsic point defects in cubic ZrO2. The exchange–correlation potential is treated using the recent modified Becke–Johnson potential (TB-mBJ) proposed by Tran and Blaha in addition to the generalized gradient approximation (GGA), which successfully corrects the bandgap problem found in a wide range of materials when using the GGA alone. The energy of formation of the point defects is calculated after the optimization of atomic positions. The results indicate that the ZrO antisite has the lowest energy of formation and could be the acceptor defect responsible for the p-type conductivity of undoped cubic ZrO2. Besides, the TB-mBJ method is used to calculate various optical coefficients, including the complex refractive index and the absorption and transmittance coefficients. Furthermore, the electrical properties of each type of point defect are investigated by applying Boltzmann transport theory.

Intrinsic point defects in half-Heusler AuMnSn

Experimental evidences have revealed the existence of intrinsic defects in Half-Heusler AuMnSn (HH-AMS). In this work, using density-functional theory, we explore the energetics, electronic and magnetic properties of intrinsic point defects in HH-AMS crystal compound. The defects considered are antisite, interstice, vacancy and atom swap defects. We find relatively low negative formation energy for Au⇒Mn (Au atom in the Mn position) antisite, Sn⇒Mn antisite and Au interstitial defects, which suggests that they have high possibilities of being formed spontaneously during the crystal growth process. Other types of defects have positive formation energy which may be an indication of their existence in low concentration in the HH-AMS crystal. Furthermore, the Sn⇒Au antisite and Sn interstitial defects change ferromagnetic HH-AMS to a half-metallic ferromagnet which is an important material for spintronics applications.

Properties of intrinsic point defects and dimers in hexagonal boron nitride

Hexagonal boron nitride (hBN) is a wide gap 2D layered material with good insulating properties. Intrinsic point defects in hBN play an important role in its applications as a dielectric in 2D electronic devices. However, the electronic properties of these defects are still poorly understood. We have calculated the structure and properties of a wide range of intrinsic point defects in the bulk of hBN using hybrid density functional theory (DFT). These include vacancies and interstitial states of B and N as well as di- and tri-vacancies. For each isolated defect, multiple charge states are calculated, and for each charge state multiple spin states are investigated. Positions of defect charge transition levels in the band gap of hBN are calculated. In particular, we predict that B vacancies are likely to be negatively charged in contact with graphene and other metals. Calculations of the interaction between vacancies predict that divacancies in both B and N sublattices are strongly binding. Moreover, the interaction of single B and N vacancies in adjacent layers induces the creation of -N–N- and -B–B- molecular bridges, which greatly distort the local structure, leading to local bond weakening. These results provide further insight into the properties of defects which can be responsible for degradation of hBN based devices.

Thermodynamics and kinetics of intrinsic point defects in plutonium dioxides

Thermodynamic and kinetic properties of intrinsic point defects in plutonium dioxides (PuO2), including their formation, migration, and effects on oxygen (O) self-diffusion, are systematically studied using atomic simulations in this work. Coulomb interactions among charged defects and ions are found play a key factor in determining the energetics and structures of defects in PuO2, where point defects are energetically prefer to binding together forming defect pairs and less relaxation volumes are introduced by these bound point defects. Further calculations of defect migration properties reveal different migration mechanisms of O and Pu point defects, where O point defects prefer to migrate along [100] direction with an energy barrier of 0.31 eV by the vacancy mechanism, while Pu point defects prefer to migrate along [100] direction with an energy barrier of 2.57 eV by the interstitial mechanism. This confirms the cation sublattice is much more stable than the anion sublattice in the fluorite structure PuO2. Given the dominance of O defects in PuO2, their effects on O self-diffusion are investigated. Both vacancies and interstitials could significantly enhance O self-diffusivity. Under the Meyer-Neldel rule, activation energy and pre-exponential factors of O diffusion show a dependence of point defect concentrations. Specifically, internal stresses introduced by defects are found responsible for the different dependency of the activation energy on the vacancy and interstitial concentrations respectively. Finally, an empirical equation is derived to connect the point defect concentration, i.e. O/Pu ratio, and activation energy of O self-diffusion in PuO2.

Intrinsic point defects and the n - and p -type dopability of the narrow gap semiconductors GaSb and InSb

The presence of defects in the narrow-gap semiconductors GaSb and InSb affects their dopability and hence applicability for a range of optoelectronic applications. Here, we report hybrid density functional theory based calculations of the properties of intrinsic point defects in the two systems, including spin orbit coupling effects, which influence strongly their band structures. With the hybrid DFT approach we adopt, we obtain excellent agreement between our calculated band dispersions, structural, elastic and vibrational properties and available measurements. We compute point defect formation energies in both systems, finding that antisite disorder tends to dominate, apart from in GaSb under certain conditions, where cation vacancies can form in significant concentrations. Calculated self-consistent Fermi energies and equilibrium carrier and defect concentrations confirm the intrinsic $n$- and $p$-type behaviour of both materials under anion-rich and anion-poor conditions. Moreover, by computing the compensating defect concentrations due to the presence of ionised donors and acceptors, we explain the observed dopability of GaSb and InSb.

Complicated and Unconventional Defect Properties of the Quasi-One-Dimensional Photovoltaic Semiconductor Sb2Se3.

It was expected that the properties of intrinsic point defects would be simple in the binary semiconductor Sb2Se3. However, we show using first-principles calculations that the intrinsic defects in this quasi-one-dimensional (Q1D) semiconductor are unexpectedly complicated and different from those in conventional photovoltaic semiconductors such as CdTe or GaAs. First, the same type of defects located on non-equivalent atomic sites can have very different properties due to the low symmetry of the Q1D structure, which makes the properties of point defects complicated, even though there are only a few point defects. Second, uncommon defects such as the cation-replace-anion antisite SbSe, anion-replace-cation antisite SeSb, and even two-anion-replace-one-cation antisite 2SeSb, which are difficult to form in CdTe and GaAs, can have high concentrations and even be dominant in Sb2Se3 due to the weak van der Waals interactions and the large void space between different [Sb4Se6] n atomic chains of the Q1D structure. These defects produce a series of acceptor and donor levels in the band gap and make Sb2Se3 p-type under the Se-rich condition but n-type under the Se-poor condition. Five deep-level recombination-center defects are identified, and their formation is difficult to suppress, imposing a serious limit to the development of high-efficiency Sb2Se3 solar cells. Our study demonstrates that the defects can be complicated and unconventional in the binary compound semiconductors with low symmetry and Q1D structures, which can be classified as chemically binary while structurally multinary.

Impacts of thermal stress and doping on intrinsic point defect properties and clustering during single crystal silicon and germanium growth from a melt

This paper reviews recent considerable progress made in the last few years in understanding the behavior and properties of intrinsic point defects close to moving melt/solid Si interfaces during single crystal Si growth from a melt. The so called Voronkov criterion allows to determine whether the grown Si crystal is interstitial I- or vacancy V-rich. This criterion is written as the ratio Γ of the pulling rate v over the thermal gradient G at the interface. Crystals pulled with Γ above a critical value Γcrit are vacancy-rich while below Γcrit, they are interstitial-rich. Various expressions based on the intrinsic point defect thermal equilibrium concentration and diffusivity have been proposed to calculate Γcrit and are briefly discussed in this paper. Recently it was shown that the thermal stress at the interface and heavy doping with neutral and/or electrically active impurities, have a considerable impact on the intrinsic point defect balance and thus also on Γcrit. Furthermore, high energy barriers of formation energies of I and V around three or four atom layers from (001) free surface support a model in which the boundary conditions of the point defect concentrations at the surface in simulations can be set at fixed values. The situation is quite different for Ge single crystal pulling where the vacancy is always the dominant intrinsic point defect so that the Voronkov criterion cannot be applied. Prediction of vacancy cluster concentration/size distributions as a function of the pulling conditions is however still possible. The possibility of reaching Voronkov criterion conditions for Ge by doping with specific impurities is also discussed. Finally, impacts of stress and doping on self-diffusion in Si and Ge are evaluated with comparing the previous experimental results.

Review—Properties of Intrinsic Point Defects in Si and Ge Assessed by Density Functional Theory

During the last decade, considerable progress has been made in understanding the properties and behavior of the vacancy V and self-interstitial I in silicon (Si) and germanium (Ge) crystals. This is to a large extent due to the maturing of density functional theory (DFT) calculation techniques and the increase of computing power enabling to calculate not only the formation and migration energies of V and I, but also the interaction with impurities and with crystal surfaces. Furthermore, the impact of internal and external stress on formation and migration enthalpies of both intrinsic point defects has been clarified recently. In this paper an overview is given on recent assessments on the properties of intrinsic point defects in Si and Ge, and on the useful application of DFT calculations for the control and engineering of intrinsic point defects in Si and Ge single crystal growth from a melt.

In situ UHVEM study of {113}-defect formation in Si nanowires

Results are presented of a study of {113}-defect formation in vertical Si nanowire n-type tunnel field effect transistors with nanowire diameters ranging from 40 to 500 nm. The nanowires are etched into an epitaxial moderately As doped n-type layer grown on a heavily As doped Si substrate. p+ contacts on the nanowire are created by epitaxial growth of a heavily B doped layer. Using focused ion beam cutting, samples for irradiation are prepared with different thicknesses so that the nanowires are fully or partially embedded in the sample thickness. {113}-defects are created in situ by 2 MeV e-irradiation in an ultra-high voltage electron microscope between room temperature and 375 °C. The observations are discussed in the frame of intrinsic point defect properties, taking into account the role of dopants and capping layers. The important impact of the specimen thickness is elucidated.

PyDII: A python framework for computing equilibrium intrinsic point defect concentrations and extrinsic solute site preferences in intermetallic compounds

Point defects play an important role in determining the structural stability and mechanical behavior of intermetallic compounds. To help quantitatively understand the point defect properties in these compounds, we developed PyDII, a Python program that performs thermodynamic calculations of equilibrium intrinsic point defect concentrations and extrinsic solute site preferences in intermetallics. The algorithm implemented in PyDII is built upon a dilute-solution thermodynamic formalism with a set of defect excitation energies calculated from first-principles density-functional theory methods. The analysis module in PyDII enables automated calculations of equilibrium intrinsic antisite and vacancy concentrations as a function of composition and temperature (over ranges where the dilute solution formalism is accurate) and the point defect concentration changes arising from addition of an extrinsic substitutional solute species. To demonstrate the applications of PyDII, we provide examples for intrinsic point defect concentrations in NiAl and Al3 V and site preferences for Ti, Mo and Fe solutes in NiAl. Program summaryProgram title: PyDIICatalogue identifier: AEWI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: MIT LicenseNo. of lines in distributed program, including test data, etc.: 6123No. of bytes in distributed program, including test data, etc.: 40988Distribution format: tar.gzProgramming language: Python.Computer: Any computer with a Python interpreter.Operating system: Any which enable Python.RAM: Problem dependentClassification: 7.1.External routines: NumPy [1], Sympy [2], and Pymatgen [3].Nature of problem:Equilibrium intrinsic point defect concentrations and solute site preferences in intermetallic compounds.Solution method:Intrinsic point defect properties and solute site preference as a function of composition and temperature are computed within the grand-canonical, dilute-solution thermodynamic formalism developed by Woodward et al., Phys. Rev. B 63 (2001) 094103.Restrictions:The current version of PyDII supports generating inputs and parsing outputs for density functional calculations implemented in VASP. Defect energetics obtained from other computational methods or software can also be used to compute the defect properties by preparing the input in a format consistent with that of the JSON files provided in the example folder.Additional comments: This article describes version 1.0.0.Running time: Problem dependent

Stress and doping impact on intrinsic point defect behavior in growing single crystal silicon

For the mass‐production of 450 mm‐diameter defect‐free Si crystals, one has to take into account the impact of thermal stress on intrinsic point defect properties and behavior during single crystal growth from a melt. Very recently, first experimental evidence was published that the compressive thermal stress near the melt/solid interface makes a growing 300 mm diameter Czochralski Si crystal more vacancy‐rich. In order to explain these experimental results quantitatively, the dependence of the formation enthalpies of the vacancy (V) and the self‐interstitial (I) on compressive plane stress was determined using density functional theory (DFT) based calculations. It is found that compressive plane stress gives a higher stress dependence of the so‐called “Voronkov criterion” compared to isotropic stress. The calculated plane stress dependence is in excellent agreement with the published experimental values and should be taken into account in the development of pulling processes for 450 mm diameter defect‐free Si crystals. Also, the mechanisms behind the experimentally observed impact of the type and concentration of substitutional dopants on intrinsic point defect behavior and formation of grown‐in defects are clarified. On the basis of the DFT calculated results, an appropriate model of intrinsic point defect behavior in heavily doped Si is proposed. (i) The incorporated total V and I concentrations at the melting point depend on the types and concentrations of dopants. (ii) Most of the total V and I concentrations contribute to Frenkel pair recombination during Si crystal growth at temperatures much higher than those to form grown‐in intrinsic point defect clusters. The Voronkov model, while taking into account the present improvements, clearly explains all reported experimental results on grown‐in defects for heavily doped Si. The most important remaining problems with respect to intrinsic point defect behavior and properties during single crystal growth from a melt are also discussed.

Invited; Stress and Doping Impact on Intrinsic Point Defect Behavior in Growing Single Crystal Silicon

For the further development of 450 mm-diameter defect-free Si crystals, one has to take into account the impact of thermal stress on intrinsic point defect properties and behavior during single crystal growth from a melt. In this study, we evaluate the impact of thermal stress between -30 MPa (tensile) and 30 MPa (compressive), which probably covers the actual values in mass production for 450 mm-diameter crystals, on the so-called Voronkov criterion of dominant point defects.The dependence of the formation and migration enthalpies of vacancy V and self-interstitial I on the stress is evaluated by density functional theory (DFT). The obtained results are used to more accurately describe the impact of thermal stress on the critical (v/G)0. The impact of compressive thermal stress on (v/G)0 is predicted to shift the growing Si crystal more vacancy-rich, as recently confirmed experimentally by Nakamura et al (ECS Solid State Letters, 3 (2014) N5-N7). Furthermore, the dependence on the thermal stress of the process window for defect-free Si growth is clarified, which is important for the development of the pulling process of future large-diameter defect-free Si crystals.Also the mechanisms behind the experimentally observed impact of the type and concentration of substitutional dopants on intrinsic point defect behavior and formation of grown-in defects (voids and interstitial clusters) in a Si single crystal growing from a melt, are clarified. DFT calculations with 216-atom supercells are carried out to obtain the formation energies of V and I at all sites within a sphere around the dopant atom with 6 A radius for V and 5 A radius for I. P-type (B and Ga), neutral (C, Ge, and Sn) and n-type (P, As, Sb, and Bi) dopants are considered. The formation energies of V and I around dopant atoms change depending on the types and sizes of dopants. On the basis of the calculated results, an appropriate model of intrinsic point defect behavior in heavily doped Si is proposed. (1) The incorporated total V and I concentrations at the melting point depend on the types and concentrations of dopants. (2) Most of the total V and I concentrations contribute to Frenkel pair recombination during Si crystal growth at temperatures much higher than those to form grown-in intrinsic point defect clusters. The Voronkov model, while taking into account the present improvements, clearly explains all reported experimental results on grown-in defects for heavily doped Si.The proposed improved Voronkov model uniformly explains point defect behavior for all dopant types and concentrations, taking into account also thermal stress levels.