Intrinsic Point Defect Behavior Research Articles

Numerical simulations considering effects of thermal stress and impurities on the behavior of intrinsic point defects in Si crystal growing by Cz method

Numerical simulations considering effects of thermal stress and impurities on the behavior of intrinsic point defects in Si crystal growing by Cz method

Strain effects on the behavior of intrinsic point defects within the GaN/AlN interface

Defect behaviors in GaN-based compounds studied by using density functional theory have exhibited widely practical applications for optoelectronic devices. Ga is usually used to solubilize in AlN to release the lattice mismatch and the interface strain. In this study, we investigate the formation energies and diffusion barriers of intrinsic point defects within the GaN/AlN interface. The intrinsic defect with the lowest formation energy is positively charged N vacancy, and negatively charged Ga vacancy is the defect with second lower formation energy. Compared with the case in bulk GaN, the GaN/AlN interface promotes the generation of Ga vacancy and inhibits the generation of N vacancy. Meanwhile, the defect diffusion barrier of N vacancy within the GaN/AlN interface is higher than that in the bulk GaN. The hydrostatic compressive/ tensile strain significantly promotes the generation of these two vacancy defects, while biaxial tensile strain and the biaxial compressive strain slightly promote and inhibit the generation of these two vacancy defects, respectively. These interface and strain effects provide the significant information in understanding the electrical properties of GaN-based devices, especially under the extreme conditions. Our work therefore not only elucidates defect behaviors under different strains in GaN/AlN interface, but also paves the way for understanding and designing promising electronic devices with interface engineering.

First-principles investigations of intrinsic point defects and helium impurities in vanadium monocarbide

Helium (He) trapping at carbide precipitates is significant for understanding the macroscopic effects of He in the normal reduced activation ferritic/martensitic (RAFM) steels and castable nanostructured alloys (CNAs) under irradiation. In this study, the behavior of intrinsic point defects and He impurities in VC is investigated by first-principles calculations. The formation of carbon (C) vacancy is quite easy and vacancy makes covalent interaction of neighboring C and V atoms more obvious. Besides, the diffusion of vacancy in VC is significantly slower than that in Fe matrix. It's worth noting that the interaction between carbon vacancies is repulsive which means that the formation of large voids maybe difficult in VC. Apart from vacancy, He impurities are also investigated. Interstitial He is less stable and diffuses more easily inside VC precipitate than inside TaC and Fe matrix. Besides, vacancy can trap much more He in VC than in Fe matrix. The result means that vacancy-abundant VC particle may have stronger ability to trap He than Fe matrix. Due to the repulsion of vacancies, we suggest that the formation of large He bubbles in VC is difficult. That is to say, little He bubbles have a dispersive distribution in VC. These theoretical results can help to understand the behavior of vacancy and He impurities in VC precipitate and further the bubble formation at precipitate in normal RAFM steels and CNAs.

Unsteady numerical simulations considering effects of thermal stress and heavy doping on the behavior of intrinsic point defects in large-diameter Si crystal growing by Czochralski method

Abstract We conducted unsteady simulations of intrinsic point defect dynamics considering the effects of the thermal stress and dopant concentration in a large-diameter silicon crystal growing by the Czochralski (Cz) method. The thermal equilibrium concentration of the intrinsic point defects (vacancy, V, and self-interstitial Si atom, I) was simulated as a function of the thermal stress and the incorporated dopant concentration in a growing Si crystal, which was obtained through ab-initio calculations. Furthermore, point defect dynamics in the crystal were solved within a two-dimensional axisymmetric unsteady global heat and mass transport model by considering the thermal stress and the incorporation of a dopant using segregation for dynamically pulling Si crystal by the Cz method. The unsteady numerical simulations showed that the formation and the distribution of intrinsic point defects depend on the temporal variation of the thermal stress and the incorporated dopant concentration in a growing Si crystal.

Numerical analysis of effect of thermal stress depending on pulling rate on behavior of intrinsic point defects in large-diameter Si crystal grown by Czochralski method

We analyzed the effects of thermal stress and pulling rate on the behavior of intrinsic point defects in a silicon (Si) single crystal grown by the Czochralski (Cz) method using a numerical approach. The thermal equilibrium concentration of the intrinsic point defects (vacancy, V, and self-interstitial Si atom, I) was simulated as a function of thermal stress, which was obtained via ab -initio calculations. Furthermore, the point defect dynamics in the crystal were solved within a framework of a two-dimensional (2D) axisymmetric steady-state global heat and mass transport model of Si crystal growth by the Cz method. The numerical simulations revealed that both magnitude and distribution of the thermal stress depend on the pulling rate. Moreover, they impact the formation and distribution of intrinsic point defects in a growing Si single crystal.

Computer Simulation of Concentration Distribution of Intrinsic Point Defect Valid for All Pulling Conditions in Large-Diameter Czochralski Si Crystal Growth

To explain and engineer intrinsic point defect behavior in large-diameter single crystal Si grown using the Czochralski (CZ) method, a unified model valid for all pulling processes, crystal resistivities, and electrically inactive impurity concentrations that couples the effects of thermal stress, dopants, and interstitial oxygen (Oi) atoms is needed. We determined the thermal equilibrium concentration of intrinsic point defects (vacancy V and self-interstitial Si I) in CZ-Si crystal as functions of thermal stresses, type and concentration of dopant, and the concentration of Oi atoms. Global heat transfer during crystal growth in a puller was simulated using STR Group's CGSim software package. A visual distribution of V and I concentrations inside a growing doped and thermally stressed Si ingot is very useful for improving the quality of large-diameter CZ-Si crystals.

(Invited) Computer Simulation of Intrinsic Point Defect Distribution Valid for All Pulling Conditions in Large-Diameter Czochralski Si Crystal Growth

In order to explain and engineer the intrinsic point defect behavior in large-diameter single crystal Si growing by Czochralski (CZ) method, a unified model valid for all pulling processes, crystal resistivities and not electrically active impurity concentrations is needed by coupling the impacts of thermal stress and dopant atoms. This paper provides the thermal equilibrium concentration of intrinsic point defects (vacancy V and self-interstitial Si I) as functions of thermal stresses, type and concentration of dopant, and concentration of interstitial oxygen in CZ-Si crystal. Global heat transfer during crystal growth in a puller was simulated by CGSim package, software of STR Group, Inc. Visual distribution of V and I concentrations inside a growing Si ingot well explains the previous experimental results of impacts of thermal stress and heavy doping.

(Invited) Computer Simulation of Intrinsic Point Defect Distribution Valid for All Pulling Conditions in Large-Diameter Czochralski Si Crystal Growth

To explain and engineer intrinsic point defect behavior in large-diameter single crystal Si grown using the Czochralski (CZ) method, a unified model valid for all pulling processes, crystal resistivities, and electrically inactive impurity concentrations that couples the effects of thermal stress, dopants, and interstitial oxygen (Oi) atoms is needed. We determined the thermal equilibrium concentration of intrinsic point defects (vacancy V and self-interstitial Si I) in CZ-Si crystal as functions of thermal stresses, type and concentration of dopant, and the concentration of Oi atoms. Global heat transfer during crystal growth in a puller was simulated using STR Group’s CGSim software package. A visual distribution of V and I concentrations inside a growing doped and thermally stressed Si ingot is very useful for improving the quality of large-diameter CZ-Si crystals.

About the influence of deposited nitride layers on oxide precipitation after RTA pre‐treatment

In order to elucidate the influence of stress and in‐diffused nitrogen on oxide precipitation after rapid thermal annealing (RTA), we carried out experiments with one‐side and double‐sided nitride layers accompanied by simulation models which help to understand the behavior of intrinsic point defects, nitrogen, and strain. We found that the presence of a nitride layer of any thickness, within the rage which we investigated, in direct contact with the silicon surface is sufficient to markedly change the precipitation behavior of interstitial oxygen after RTA at 1175 and 1250 °C. The presence of the nitride layer during the stabilization and growth of the oxide precipitates is not of any influence on the precipitation behavior. Therefore, the RTA of wafers covered with silicon nitride is the crucial step controlling the bulk microdefect (BMD) depth profiles. A 10 nm oxide between silicon substrate and nitride layer prevents any change of the BMD depth profile. Only in a direct contact with the nitride layers the vacancy supersaturation, which enhanced the oxide precipitation compared to wafers without nitride layers, was generated. Nitrogen peaks below the silicon surface generated by in‐diffusion of nitrogen during RTA lead to an enhanced oxygen precipitation only for RTA at 1250 °C and not for RTA at 1175 °C. We propose a model based on very tiny coherent α‐Si3N4 precipitates generated at nitrogen‐vacancy (NV) complexes which can act as nucleation sites for oxygen precipitation. Because the stability of NV seems limited to temperatures above 1200 °C, it would not be effective for RTA at 1175 °C. RTA treatment of silicon wafers with one‐sided nitride layers at 1250 °C leads to very sharp and small defect denuded zones in subsequent annealing and would be suitable for proximity gettering. The depth of the denuded zone is nearly independent of the thickness of the nitride layer.

Theoretical Study of Impact of Internal and External Stresses on Thermal Equilibrium Concentrations of Intrinsic Point Defects in Doped Si Crystals

Intrinsic point defects (vacancy V and self-interstitial I) play an important role in a wide variety of processes in Si crystals. During large-diameter crystal growth, the thermal stress, which is the compressive internal stress, of around several tens of MPa is originated in Si crystals. In the LSI (Large Scale Integration) using Si substrate, external stress of around GPa order is applied to the channel region between source and drain in the MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) to enhance the carrier mobilities. These internal and external stresses affect V and I; thus, changing the thermal equilibrium concentrations (Ceq) of V and I in Si. To explain and engineer the intrinsic point defect behavior in Si crystals, such as in the growing Si crystals and in the channel region of Si wafers, the impact of internal or external stress on the Ceq of V (I) should be theoretically obtained in doped Si crystals. In this study, we calculated the formation energy (Ef) and relaxation volume (ΔVol) of V (I) from the 1st to 5th sites around dopant (B, C, Sn, P, and Sb) atoms in isotropically stressed Si by using density functional theory (DFT) to determine the formation enthalpy (Hf) of V and I. The impact of isotropic internal stress (σin) or isotropic external stress (σex) on the Ceq values of V (I) in doped Si was obtained using the Hf at each site around a dopant atom. The following important information was obtained from the Ceq of V (I) in doped Si crystals. (1) The Ef and ΔVol of V (I) around the dopant atoms change depending on the site position and dopant type, (2) Ef of V (I) and ΔVol of I around the dopant atoms are hardly affected by the stresses, while ΔVol of V around the dopant atoms changes due to the stresses, (3) B and C atoms make the Si crystal more I-rich, while Sn, P, and Sb atoms make the Si crystal more V-rich, and (4) the compressive σin makes the doped Si crystal more V-rich, and its impact depends on the type of dopant, while the σex has an opposite impact except for C. The data summarizing the impact of stress in doped Si are useful as the more precisely control of the point defect behavior is required in more advanced Si crystals.

Theoretical study of the impact of stress and interstitial oxygen on the behavior of intrinsic point defects in growing Czochralski Si crystals

For the development of crystal pulling processes for 450mm-diameter defect-free Si crystals, it is important to evaluate the impact of thermal stress on intrinsic point defect behavior during crystal growth. In a crystal growing from a melt, the melt/solid interface can be considered as being stress-free. Due to that the thermal stress in the growing substrate near the interface is internal plane stress. Previously, we evaluated the impact of (001) planar-isotropic stress on the formation enthalpy (Hf) of the vacancy (V) and the self-interstitial (I) using density functional theory (DFT) calculations, and explained quantitatively the published experimental values of the so-called “Voronkov criterion”. The thermal stress in a growing crystal is indeed planar but is not isotropic in the plane except for the central region of the crystal. The purpose of the present study is to estimate the impact of planar-anisotropic stress on the formation enthalpy Hf of V and I. It is found that the three stress dependencies of σx: σy=1: 1 (planar-isotropic), 2: 1, 5: 1 (planar-anisotropic) are close to each other, independent of the assumption of isotropic or anisotropic planar stress. This is the reason why the experimental results obtained over the whole radial direction of the crystal are well reproduced by the calculated results assuming planar-isotropic stress. A uniaxial stress dependence which is a good assumption for the crystal peripheral region, leads also to results that are close to those for the planar stress dependence. Also the mechanisms behind the experimentally observed impact of interstitial oxygen (Oi), introduced during Czochralski Si growth, on V and I concentrations are clarified. DFT calculations are performed to obtain the formation energies (Ef) of V and I at all sites within a sphere with 5Å radius around the Oi atom. Formation (vibration) entropy (Sf) calculations for V and I are also performed. It is found that both EfV and SfV of V in the zigzag-bond (1st, 2nd, 5th) including the Oi atom decrease while EfI of I is not affected by the Oi atom. “Total V” is defined as the sum of free V and V trapped by the Oi atoms. The total V concentration at the melting point is evaluated by considering the EfV and SfV at each site. The calculated V concentration increases by about 2.9% with 1×1018 Oicm−3 and agrees well with the experimentally estimated value of a few % increase with 1×1018 Oicm−3.

Thermal equilibrium concentration of intrinsic point defects in heavily doped silicon crystals - Theoretical study of formation energy and formation entropy in area of influence of dopant atoms-

It is well known that p-type, neutral and n-type dopants affect the intrinsic point defect (vacancy V and self-interstitial I) behavior in single crystal Si. By the interaction with V and/or I, (1) growing Si crystals become more V- or I-rich, (2) oxygen precipitation is enhanced or retarded, and (3) dopant diffusion is enhanced or retarded, depending on the type and concentration of dopant atoms. Since these interactions affect a wide range of Si properties ranging from as-grown crystal quality to LSI performance, numerical simulations are used to predict and to control the behavior of both dopant atoms and intrinsic point defects. In most cases, the thermal equilibrium concentrations of dopant-point defect pairs are evaluated using the mass action law by taking only the binding energy of closest pair to each other into account. The impacts of dopant atoms on the formation of V and I more distant than 1st neighbor and on the change of formation entropy are usually neglected. In this study, we have evaluated the thermal equilibrium concentrations of intrinsic point defects in heavily doped Si crystals. Density functional theory (DFT) calculations were performed to obtain the formation energy (Ef) of the uncharged V and I at all sites in a 64-atom supercell around a substitutional p-type (B, Ga, In, and Tl), neutral (C, Ge, and Sn) and n-type (P, As, and Sb) dopant atom. The formation (vibration) entropies (Sf) of free I, V and I, V at 1st neighboring site from B, C, Sn, P and As atoms were also calculated with the linear response method. The dependences of the thermal equilibrium concentrations of trapped and total intrinsic point defects (sum of free I or V and I or V trapped with dopant atoms) on the concentrations of B, C, Sn, P and As in Si were obtained. Furthermore, the present evaluations well explain the experimental results of the so-called “Voronkov criterion” in B and C doped Si, and also the observed dopant dependent void sizes in P and As doped Si crystals. The expressions obtained in the present work are very useful for the numerical simulation of grown-in defect behavior, oxygen precipitation and dopant diffusion in heavily doped Si. DFT calculations also showed that Coulomb interaction reaches approximately 30Å from p (n)-type dopant atoms to I (V) in Si.

シリコン単結晶育成中の点欠陥挙動に与える置換型ドーパントと熱応力の効果

The mechanisms behind the experimentally observed impact of the type and concentration of substitutional dopants on intrinsic point defect behavior in growing single crystal Si are clarified. On the basis of the density functional theory (DFT) calculated results, an appropriate model of intrinsic point defect behavior in heavily doped Si is proposed. Also one has to take into account the impact of thermal stress on intrinsic point defect behavior during single crystal Si growth. In order to explain the experimental results quantitatively, the dependence of the formation enthalpies of vacancy (V) and self-interstitial (I) on compressive plane stress was determined using DFT calculations. It is found that the compressive plane stress around 20 MPa shifts a growing Si crystal to more V-rich. 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.

Impact of Anisotropic Thermal Stress on Behavior of Grown-In Defects during Si Crystal Growth from a Melt

Anisotropic thermal stress near the melt/solid interface during growth of a Si crystal from a melt significantly affects control of grown-in defects when the diameter of the growing crystal is large. This effect on the behavior of intrinsic point defects in a growing Si crystal with 300-mm diameter was investigated by calculations and experiments. One has to take into account this effect in the development of a crystal-pulling process for 450-mm-diameter defect-free Si crystals.

In situ UHVEM irradiation study of intrinsic point defect behavior in Si nanowire structures

AbstractSi nanowire‐based Tunnel‐Field Effect Transistor (TFET) characteristics are intensively studied as function of nanowire diameter and doping. A significant reduction of B diffusion with decreasing nanowire diameter is e.g. observed and attributed to reduced transient enhanced diffusion close to the nanowire surface caused by the recombination and out‐diffusion of excess self‐interstitials. In an Ultra High Voltage Electron Microscope (UHVEM), the formation of self‐interstitial clusters can be studied in situ while varying e‐beam flux, irradiation temperature, impurity concentration and capping layers surrounding the nanowires.Results are presented on {113}‐defect formation in Si nanowires with diameters between 40 and 500 nm. The Si nanowires are embedded in SiO2 and are etched into an epitaxial Si stack on a heavily As doped Si substrate. The top layer of the epitaxial stack is in situ B doped or B implanted. In situ UHVEM studies are performed on focused ion beam prepared cross‐section samples, irradiating with different fluxes of 2 MeV electrons between room temperature and 375 °C. A strong dependence of {113}‐defect formation on nanowire radius and doping is observed. The observations are compared with simulations based on quasi‐chemical reaction rate theory. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Zinc vacancy related emission in homoepitaxial N-doped ZnO microrods

Vertically aligned N-doped ZnO microrods have been homoepitaxially grown on a high-quality ZnO template via chemical vapor transport method without employing any catalysts. In spite of the incorporation of nitrogen, the as-grown microrods exhibited excellent crystalline and optical quality, and the behavior of intrinsic point defects and impurity-related defects have been investigated in detail by the temperature-dependent photoluminescence spectra. The emissions at 3.377, 3.368, and 3.363eV are ascribed to free excitons, surface bound excitons and excitons bound to neutral shallow donors: zinc interstitials, respectively. The emissions at 3.359, 3.311, and 3.240eV correspond to the radiative recombination of excitons bound to neutral acceptors, free electrons to acceptors and donor acceptor pairs, all of which are originated from the same shallow acceptor of zinc vacancy clusters with its energy level of about 126meV above the valence band maximum. The isolated zinc vacancy is a deep acceptor, which results in the emission at 3.318eV and the green band emissions. This study suggests that the intrinsic point defects play an extremely important role in optical properties of ZnO besides the external dopants and the understanding of intrinsic defects is crucial to get stable p-type conductivity and finally realize a ZnO homojunction for optoelectronic applications.

Stress and doping impact on intrinsic point defect behavior in growing single crystal silicon (Phys. Status Solidi B 11/2014)

Stress and doping impact on intrinsic point defect behavior in growing single crystal silicon (Phys. Status Solidi B 11/2014)

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.

Density functional theory study on the impact of heavy doping on Si intrinsic point defect properties and implications for single crystal growth from a melt

Density functional theory (DFT) calculations are performed to obtain the formation energies of the vacancy V and the self-interstitial I at all sites within a sphere around the dopant atom with 6 Å radius for V and 5 Å radius for I in Si crystals. Substitutional p-type (B and Ga), neutral (C, Ge, and Sn), and n-type (P, As, Sb, and Bi) dopants were considered. The results show that the formation energies of V and I around dopant atoms change depending on the types and sizes of the dopants, i.e., depending on the electrical state and the local strain around the dopants. The dependence of the total thermal equilibrium concentrations of point defects (sum of free V or I and V or I around the dopants) at melting temperature on the type and concentration of each dopant is obtained. Further DFT calculations reveal that most of the total incorporated point defects from the melt contribute to pair recombination. An appropriate model of point defect behavior in heavily doped single crystal Si growing from a melt is proposed on the basis of DFT calculations. (1) The incorporated total V and I concentrations at melting point depend on the types and concentrations of dopants. (2) Most of the total V and I concentrations during Si crystal growth contribute to the pair recombination at temperatures much higher than those to form grown-in defects. The Voronkov model successfully explains all reported experimental results on intrinsic point defect behavior dependence on dopant type and concentration for heavily doped Si while taking the present model into consideration.