The Experts below are selected from a list of 174 Experts worldwide ranked by ideXlab platform
Jan Vanhellemont - One of the best experts on this subject based on the ideXlab platform.
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Control of Intrinsic Point Defects in Single-Crystal Si and Ge Growth from a Melt
Defects and Impurities in Silicon Materials, 2020Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The so called Voronkov criterion defines a critical value Γ crit of the ratio \(\varGamma = v/G\) of the pulling rate v over the thermal gradient G at the crystal-melt/interface of a growing crystal. For Γ > Γ crit , the crystal is vacancy-rich and can contain large vacancy clusters that are detrimental for gate oxide performance and for thin film epitaxial growth. For Γ < Γ crit , the crystal is self-interstitial-rich and in the worst case will contain dislocation clusters. For Γ ≈ Γ crit , the crystal is free of grown-in Intrinsic Point Defect clusters and optimal for device processing. Analytical expressions have been derived describing Γ crit as function of Intrinsic Point Defect parameters. The impact of thermal stress \(\sigma _{th}\) at the crystal-melt interface and of crystal doping on Γ crit will be clarified. As \(\sigma _{th}\) increases with increasing crystal diameter, controlling G and v will become a real challenge for the development of future 450 mm diameter, Defect free Si crystals. The possible application of the Voronkov criterion for Ge single-crystal growth from a melt will also briefly be discussed. Besides the impact of stress on Intrinsic Point Defect formation energies and diffusivities, DFT calculations also suggest that near the crystal-melt interface, assumed to be stress free, the formation energy of the Intrinsic Point Defects is lower than in the bulk of the crystal. This leads to thermal equilibrium concentrations of Intrinsic Point Defects at the crystal-melt interface that are considerably different from those in the bulk which should be taken into account when applying the Voronkov criterion and also for Intrinsic Defect engineering in general. The Voronkov criterion was established for a flat interface. During crystal growth the crystal-melt interface is however curved which will have a significant impact on the diffusion of the Intrinsic Point Defects. The impact of this curvature is discussed in detail both theoretically and experimentally.
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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-
Journal of Crystal Growth, 2017Co-Authors: Koji Kobayashi, Shunta Yamaoka, Kouji Sueoka, Jan VanhellemontAbstract:Abstract 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 ( E f ) 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 ( S f ) 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 30 A from p (n)-type dopant atoms to I ( V ) in Si.
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Density functional theory study of dopant effect on formation energy of Intrinsic Point Defects in germanium crystals
Journal of Crystal Growth, 2017Co-Authors: Shunta Yamaoka, Koji Sueoka, Koji Kobayashi, Jan VanhellemontAbstract:During the last decade the use of single crystal germanium (Ge) layers and structures in combination with silicon (Si) substrates has led to a revival of Defect research on Ge. Ge is used because of the much higher carrier mobility compared to Si, allowing to design devices operating at much higher frequencies. A major issue for the use of Ge single crystal wafers is the fact that all Czochralski-grown Ge (CZ-Ge) crystals are vacancy-rich and contain vacancy clusters that are much larger than the ones in Si. In contrast to Si, control of Intrinsic Point Defect concentrations has not yet been realized at the same level in Ge crystals due to the lack of experimental data especially on dopant effects. In this study, we have evaluated with density functional theory (DFT) calculations the dopant effect on the formation energy (Ef) of the uncharged vacancy (V) and self-interstitial (I) in Ge and compared the results with those for Si. The dependence of the total thermal equilibrium concentrations of Point Defects (sum of free V or I and V or I paired with dopant atoms) at melting temperature on the type and concentration of various dopants is obtained. It was found that (1) Ge crystals will be more V-rich by Tl, In, Sb, Sn, As and P doping, (2) Ge crystals will be more I-rich by Ga, C and B doping, (3) Si doping has negligible impact. The dopant impact on Ef of V and I in Ge has a narrower range and is smaller than that in Si. The obtained results are useful to control grown-in V and I concentrations, and will perhaps also allow to develop Defect-free “perfect” Ge crystals.
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impacts of thermal stress and doping on Intrinsic Point Defect properties and clustering during single crystal silicon and germanium growth from a melt
Journal of Crystal Growth, 2017Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Piotr śpiewak, Koji SueokaAbstract:Abstract 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 Γ crit are vacancy-rich while below Γ crit , they are interstitial-rich. Various expressions based on the Intrinsic Point Defect thermal equilibrium concentration and diffusivity have been proposed to calculate Γ crit 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 Γ crit . 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.
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Intrinsic Point Defect behavior close to silicon melt/solid interface
2015 China Semiconductor Technology International Conference, 2015Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The impact of various crystal pulling process and silicon material parameters on the so called Voronkov criterion for “perfect” crystal pulling is revised. It is shown that thermal stress effects should be taken into account in particular for the development of the 450 mm diameter single crystal silicon pulling technology. An improved Voronkov criterion is proposed and its application illustrated showing that all published experimental results on grown-in Defects dependence on doping and crystal pulling conditions can be explained at least semi-quantitatively.
Koji Sueoka - One of the best experts on this subject based on the ideXlab platform.
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Control of Intrinsic Point Defects in Single-Crystal Si and Ge Growth from a Melt
Defects and Impurities in Silicon Materials, 2020Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The so called Voronkov criterion defines a critical value Γ crit of the ratio \(\varGamma = v/G\) of the pulling rate v over the thermal gradient G at the crystal-melt/interface of a growing crystal. For Γ > Γ crit , the crystal is vacancy-rich and can contain large vacancy clusters that are detrimental for gate oxide performance and for thin film epitaxial growth. For Γ < Γ crit , the crystal is self-interstitial-rich and in the worst case will contain dislocation clusters. For Γ ≈ Γ crit , the crystal is free of grown-in Intrinsic Point Defect clusters and optimal for device processing. Analytical expressions have been derived describing Γ crit as function of Intrinsic Point Defect parameters. The impact of thermal stress \(\sigma _{th}\) at the crystal-melt interface and of crystal doping on Γ crit will be clarified. As \(\sigma _{th}\) increases with increasing crystal diameter, controlling G and v will become a real challenge for the development of future 450 mm diameter, Defect free Si crystals. The possible application of the Voronkov criterion for Ge single-crystal growth from a melt will also briefly be discussed. Besides the impact of stress on Intrinsic Point Defect formation energies and diffusivities, DFT calculations also suggest that near the crystal-melt interface, assumed to be stress free, the formation energy of the Intrinsic Point Defects is lower than in the bulk of the crystal. This leads to thermal equilibrium concentrations of Intrinsic Point Defects at the crystal-melt interface that are considerably different from those in the bulk which should be taken into account when applying the Voronkov criterion and also for Intrinsic Defect engineering in general. The Voronkov criterion was established for a flat interface. During crystal growth the crystal-melt interface is however curved which will have a significant impact on the diffusion of the Intrinsic Point Defects. The impact of this curvature is discussed in detail both theoretically and experimentally.
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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
Journal of Crystal Growth, 2020Co-Authors: Yuji Mukaiyama, Koji Sueoka, Susumu Maeda, Masaya Iizuka, Vasif M MamedovAbstract: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.
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invited computer simulation of Intrinsic Point Defect distribution valid for all pulling conditions in large diameter czochralski si crystal growth
AiMES 2018 Meeting (September 30 - October 4 2018), 2018Co-Authors: Koji Sueoka, Yuji Mukaiyama, Koji Kobayashi, Hiroaki Fukuda, Shunta Yamaoka, Susumu Maeda, Masaya Iizuka, Vasif M MamedovAbstract: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.
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impacts of thermal stress and doping on Intrinsic Point Defect properties and clustering during single crystal silicon and germanium growth from a melt
Journal of Crystal Growth, 2017Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Piotr śpiewak, Koji SueokaAbstract:Abstract 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 Γ crit are vacancy-rich while below Γ crit , they are interstitial-rich. Various expressions based on the Intrinsic Point Defect thermal equilibrium concentration and diffusivity have been proposed to calculate Γ crit 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 Γ crit . 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.
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Density functional theory study of dopant effect on formation energy of Intrinsic Point Defects in germanium crystals
Journal of Crystal Growth, 2017Co-Authors: Shunta Yamaoka, Koji Sueoka, Koji Kobayashi, Jan VanhellemontAbstract:During the last decade the use of single crystal germanium (Ge) layers and structures in combination with silicon (Si) substrates has led to a revival of Defect research on Ge. Ge is used because of the much higher carrier mobility compared to Si, allowing to design devices operating at much higher frequencies. A major issue for the use of Ge single crystal wafers is the fact that all Czochralski-grown Ge (CZ-Ge) crystals are vacancy-rich and contain vacancy clusters that are much larger than the ones in Si. In contrast to Si, control of Intrinsic Point Defect concentrations has not yet been realized at the same level in Ge crystals due to the lack of experimental data especially on dopant effects. In this study, we have evaluated with density functional theory (DFT) calculations the dopant effect on the formation energy (Ef) of the uncharged vacancy (V) and self-interstitial (I) in Ge and compared the results with those for Si. The dependence of the total thermal equilibrium concentrations of Point Defects (sum of free V or I and V or I paired with dopant atoms) at melting temperature on the type and concentration of various dopants is obtained. It was found that (1) Ge crystals will be more V-rich by Tl, In, Sb, Sn, As and P doping, (2) Ge crystals will be more I-rich by Ga, C and B doping, (3) Si doping has negligible impact. The dopant impact on Ef of V and I in Ge has a narrower range and is smaller than that in Si. The obtained results are useful to control grown-in V and I concentrations, and will perhaps also allow to develop Defect-free “perfect” Ge crystals.
Eiji Kamiyama - One of the best experts on this subject based on the ideXlab platform.
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Control of Intrinsic Point Defects in Single-Crystal Si and Ge Growth from a Melt
Defects and Impurities in Silicon Materials, 2020Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The so called Voronkov criterion defines a critical value Γ crit of the ratio \(\varGamma = v/G\) of the pulling rate v over the thermal gradient G at the crystal-melt/interface of a growing crystal. For Γ > Γ crit , the crystal is vacancy-rich and can contain large vacancy clusters that are detrimental for gate oxide performance and for thin film epitaxial growth. For Γ < Γ crit , the crystal is self-interstitial-rich and in the worst case will contain dislocation clusters. For Γ ≈ Γ crit , the crystal is free of grown-in Intrinsic Point Defect clusters and optimal for device processing. Analytical expressions have been derived describing Γ crit as function of Intrinsic Point Defect parameters. The impact of thermal stress \(\sigma _{th}\) at the crystal-melt interface and of crystal doping on Γ crit will be clarified. As \(\sigma _{th}\) increases with increasing crystal diameter, controlling G and v will become a real challenge for the development of future 450 mm diameter, Defect free Si crystals. The possible application of the Voronkov criterion for Ge single-crystal growth from a melt will also briefly be discussed. Besides the impact of stress on Intrinsic Point Defect formation energies and diffusivities, DFT calculations also suggest that near the crystal-melt interface, assumed to be stress free, the formation energy of the Intrinsic Point Defects is lower than in the bulk of the crystal. This leads to thermal equilibrium concentrations of Intrinsic Point Defects at the crystal-melt interface that are considerably different from those in the bulk which should be taken into account when applying the Voronkov criterion and also for Intrinsic Defect engineering in general. The Voronkov criterion was established for a flat interface. During crystal growth the crystal-melt interface is however curved which will have a significant impact on the diffusion of the Intrinsic Point Defects. The impact of this curvature is discussed in detail both theoretically and experimentally.
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impacts of thermal stress and doping on Intrinsic Point Defect properties and clustering during single crystal silicon and germanium growth from a melt
Journal of Crystal Growth, 2017Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Piotr śpiewak, Koji SueokaAbstract:Abstract 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 Γ crit are vacancy-rich while below Γ crit , they are interstitial-rich. Various expressions based on the Intrinsic Point Defect thermal equilibrium concentration and diffusivity have been proposed to calculate Γ crit 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 Γ crit . 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.
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Intrinsic Point Defect behavior close to silicon melt/solid interface
2015 China Semiconductor Technology International Conference, 2015Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The impact of various crystal pulling process and silicon material parameters on the so called Voronkov criterion for “perfect” crystal pulling is revised. It is shown that thermal stress effects should be taken into account in particular for the development of the 450 mm diameter single crystal silicon pulling technology. An improved Voronkov criterion is proposed and its application illustrated showing that all published experimental results on grown-in Defects dependence on doping and crystal pulling conditions can be explained at least semi-quantitatively.
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Intrinsic Point Defect behavior close to silicon melt solid interface
China Semiconductor Technology International Conference, 2015Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The impact of various crystal pulling process and silicon material parameters on the so called Voronkov criterion for “perfect” crystal pulling is revised. It is shown that thermal stress effects should be taken into account in particular for the development of the 450 mm diameter single crystal silicon pulling technology. An improved Voronkov criterion is proposed and its application illustrated showing that all published experimental results on grown-in Defects dependence on doping and crystal pulling conditions can be explained at least semi-quantitatively.
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stress and doping impact on Intrinsic Point Defect behavior in growing single crystal silicon
Physica Status Solidi B-basic Solid State Physics, 2014Co-Authors: Koji Sueoka, Eiji Kamiyama, Jan Vanhellemont, Kozo NakamuraAbstract: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.
Brian F Donovan - One of the best experts on this subject based on the ideXlab platform.
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impact of Intrinsic Point Defect concentration on thermal transport in titanium dioxide
Acta Materialia, 2017Co-Authors: Brian F Donovan, Daniel M Long, Ali Moballegh, Nicole Creange, Elizabeth C Dickey, Patrick E HopkinsAbstract:Abstract The thermal conductivity of functional oxide materials can be significantly impacted by variations in Point Defect concentration, especially at high concentrations where Defect interactions can result in extended Defects and secondary phase formation. In this work, we systematically study the impact of high Point Defect concentrations on thermal transport in rutile TiO 2 . Using atmospherically controlled annealing, we vary equilibrium Point Defect concentrations and measure the resulting thermal conductivity using time domain thermoreflectance. We verify our results with analytical modeling and find that it is not until very high Defect concentrations ( > 0.5 mol.%) that the phonon thermal conductivity is impacted. We vary the partial pressure of oxygen to low enough levels that sub-stoichiometric Magneli phases form and find that these highly Defective phases severely reduce the thermal conductivity and anisotropy from Intrinsic levels.
Kozo Nakamura - One of the best experts on this subject based on the ideXlab platform.
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Control of Intrinsic Point Defects in Single-Crystal Si and Ge Growth from a Melt
Defects and Impurities in Silicon Materials, 2020Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The so called Voronkov criterion defines a critical value Γ crit of the ratio \(\varGamma = v/G\) of the pulling rate v over the thermal gradient G at the crystal-melt/interface of a growing crystal. For Γ > Γ crit , the crystal is vacancy-rich and can contain large vacancy clusters that are detrimental for gate oxide performance and for thin film epitaxial growth. For Γ < Γ crit , the crystal is self-interstitial-rich and in the worst case will contain dislocation clusters. For Γ ≈ Γ crit , the crystal is free of grown-in Intrinsic Point Defect clusters and optimal for device processing. Analytical expressions have been derived describing Γ crit as function of Intrinsic Point Defect parameters. The impact of thermal stress \(\sigma _{th}\) at the crystal-melt interface and of crystal doping on Γ crit will be clarified. As \(\sigma _{th}\) increases with increasing crystal diameter, controlling G and v will become a real challenge for the development of future 450 mm diameter, Defect free Si crystals. The possible application of the Voronkov criterion for Ge single-crystal growth from a melt will also briefly be discussed. Besides the impact of stress on Intrinsic Point Defect formation energies and diffusivities, DFT calculations also suggest that near the crystal-melt interface, assumed to be stress free, the formation energy of the Intrinsic Point Defects is lower than in the bulk of the crystal. This leads to thermal equilibrium concentrations of Intrinsic Point Defects at the crystal-melt interface that are considerably different from those in the bulk which should be taken into account when applying the Voronkov criterion and also for Intrinsic Defect engineering in general. The Voronkov criterion was established for a flat interface. During crystal growth the crystal-melt interface is however curved which will have a significant impact on the diffusion of the Intrinsic Point Defects. The impact of this curvature is discussed in detail both theoretically and experimentally.
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impacts of thermal stress and doping on Intrinsic Point Defect properties and clustering during single crystal silicon and germanium growth from a melt
Journal of Crystal Growth, 2017Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Piotr śpiewak, Koji SueokaAbstract:Abstract 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 Γ crit are vacancy-rich while below Γ crit , they are interstitial-rich. Various expressions based on the Intrinsic Point Defect thermal equilibrium concentration and diffusivity have been proposed to calculate Γ crit 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 Γ crit . 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.
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Intrinsic Point Defect behavior close to silicon melt/solid interface
2015 China Semiconductor Technology International Conference, 2015Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The impact of various crystal pulling process and silicon material parameters on the so called Voronkov criterion for “perfect” crystal pulling is revised. It is shown that thermal stress effects should be taken into account in particular for the development of the 450 mm diameter single crystal silicon pulling technology. An improved Voronkov criterion is proposed and its application illustrated showing that all published experimental results on grown-in Defects dependence on doping and crystal pulling conditions can be explained at least semi-quantitatively.
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Intrinsic Point Defect behavior close to silicon melt solid interface
China Semiconductor Technology International Conference, 2015Co-Authors: Jan Vanhellemont, Eiji Kamiyama, Kozo Nakamura, Koji SueokaAbstract:The impact of various crystal pulling process and silicon material parameters on the so called Voronkov criterion for “perfect” crystal pulling is revised. It is shown that thermal stress effects should be taken into account in particular for the development of the 450 mm diameter single crystal silicon pulling technology. An improved Voronkov criterion is proposed and its application illustrated showing that all published experimental results on grown-in Defects dependence on doping and crystal pulling conditions can be explained at least semi-quantitatively.
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stress and doping impact on Intrinsic Point Defect behavior in growing single crystal silicon
Physica Status Solidi B-basic Solid State Physics, 2014Co-Authors: Koji Sueoka, Eiji Kamiyama, Jan Vanhellemont, Kozo NakamuraAbstract: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.
