Dislocation-free Silicon Single Crystals Research Articles

Mechanics of Defects in Dislocation-Free Silicon Single Crystals

The problems of defect mechanics in dislocation-free silicon single crystals are relevant and technically significant due to the intensive development of microelectronics, which imposes increasingly high demands on minimizing the level of micro- and nanodefects in silicon wafers used to manufacture microelectronic chips. The solution of these problems is associated with the study of the regularities of thermomechanical processes both at the stage of growing silicon single crystals and at subsequent thermal annealing of wafers cut from them. The article provides an overview of theoretical and experimental work aimed at developing ways to control these processes. This includes the development of physical concepts of defect formation in dislocation-free single-crystal silicon and the development of mathematical models corresponding to different temperature ranges, implemented both during the growth of a single crystal and during thermal annealing of wafers cut from it. Thus, near the crystallization temperature, the processes of fast recombination and diffusion transfer of intrinsic point defects (vacancies and interstitial silicon atoms) are simulated, while at lower temperatures, the processes of their agglomeration into microdefects (pores and clusters of interstitial silicon atoms) are simulated. The verification of such models is illustrated for two experimental processes of growing silicon single crystals with a diameter of 150 mm by the Czochralski method, as well as for the process of rapid high-temperature thermal annealing of silicon wafers cut on their basis.

Mechanics of Growing and Heat Treatment Processes of Monocrystalline Silicon

One of the urgent problems of mechanics is the study of the regularities of thermomechanical processes that affect the formation of microdefects in dislocation-free silicon single crystals both at the stage of their growth from the melt by the main industrial technology called the Czochralski method, and in subsequent heat treatment technologies of the wafers cut from them. This requires the development of coupled thermomechanical models both for the melt-crystal system, taking into account the crystallization process, and for the entire volume of the thermal unit of industrial growth plants, so that, taking into account the calculated “thermal history” of growing a particular silicon single crystal using modern models of defect formation, determine the regularities of the recombination and transfer processes. intrinsic point defects with their agglomeration into microdefects in monocrystalline silicon. This article provides a brief overview of the work carried out at IPMech RAS in this direction.

The New Software for Research and the Modelling of Grown-in Microdefects in Dislocation-Free Silicon Single Crystals

As a virtual experimental device for research and the modelling of grown-in microdefects formation in dislocation-free silicon single crystals the software is proposed. The software is built on the basis on diffusion model of grown-in microdefects formation and allows the use of computer to investigate the defect structure of silicon monocrystals with a diameter up to 400 mm.

100 Jahre Einkristallzucht aus der Schmelze

AbstractIm August 1916 reichte der Deutsch‐Pole Jan Czochralski eine Publikation über die Wachstumsgeschwindigkeit von Metallkristallen bei der Zeitschrift für physikalische Chemie ein. Daher wird 1916 als das Jahr der Entdeckung des Czochralski‐Kristallzuchtverfahrens angesehen. Im Metall‐Laboratorium der AEG, wo Czochralski zunächst arbeitete, wurden seine Forschungsarbeiten nicht gebührend anerkannt, sodass er zur Metallbank und Metallurgischen Gesellschaft (später: Metallgesellschaft) nach Frankfurt wechselte, wo er bald zum Laborleiter und Oberingenieur aufstieg. In Frankfurt machte er sich mit Forschungen zu Metallen und technischen Legierungen rasch einen Namen. Die Entdeckung des Czochralski‐Kristallzuchtverfahrens gehört zu den wichtigsten technologischen Erfindungen des 20. Jahrhunderts, die aber erst in dessen zweiten Hälfte mit dem Aufstieg der Halbleiterindustrie ökonomische Bedeutung erlangte. Heute werden 95 % der Weltproduktion an Siliciumeinkristallen nach dem Czochralski‐Verfahren hergestellt. Der Umsatz der Halbleiter‐Industrie betrug 2015 etwa 335 Milliarden US‐Dollar, wobei die Kristallzucht nach dem Czochralski‐Verfahren jeweils der erste Schritt bei der Herstellung ist. Der größte Teil der heute gefertigten Siliciumeinkristalle hat einen Durchmesser von 300 mm. Die industrielle Produktion von Einkristallen mit 450 mm Durchmesser scheitert bisher nicht an technologischen, sondern an ökonomischen Problemen.

Complex formation in semiconductor silicon within the framework of the Vlasov model of a solid state

The formation of silicon–carbon and silicon–oxygen complexes during cooling after the growth of dislocation-free silicon single crystals has been calculated using the Vlasov model of crystal formation. It has been confirmed that the complex formation begins in the vicinity of the crystallization front. It has been shown that the Vlasov model of a solid state can be used not only for the investigation of hypothetical ideal crystals, but also for the description of the formation of a defect structure of real crystals.

Diffusion model of the formation of growth microdefects: A new approach to defect formation in crystals (Review)

Theoretical studies of defect formation in semiconductor silicon play an important role in the creation of breakthrough ideas for next-generation technologies. A brief comparative analysis of modern theoretical approaches to the description of interaction of point defects and formation of the initial defect structure of dislocation-free silicon single crystals has been carried out. Foundations of the diffusion model of the formation of structural imperfections during the silicon growth have been presented. It has been shown that the diffusion model is based on high-temperature precipitation of impurities. The model of high-temperature precipitation of impurities describes processes of nucleation, growth, and coalescence of impurities during cooling of a crystal from 1683 to 300 K. It has been demonstrated that the diffusion model of defect formation provides a unified approach to the formation of a defect structure beginning with the crystal growth to the production of devices. The possibilities of using the diffusion model of defect formation for other semiconductor crystals and metals have been discussed. It has been shown that the diffusion model of defect formation is a platform for multifunctional solution of many key problems in modern solid state physics. Fundamentals of practical application of the diffusion model for engineering of defects in crystals with modern information technologies have been considered. An algorithm has been proposed for the calculation and analysis of a defect structure of crystals.

On the problem of the consistency of the high-temperature precipitation model with the classical nucleation theory

The adequacy of the model of high-temperature precipitation in dislocation-free silicon single crystals to the classical theory of nucleation and growth of second-phase particles in solids has been considered. It has been shown that the introduction and consideration of thermal conditions of crystal growth in the initial equations of the classical nucleation theory make it possible to explain the precipitation processes occurring in the high-temperature range and thus extend the theoretical basis of the application of the classical nucleation theory. According to the model of high-temperature precipitation, the smallest critical radius of oxygen and carbon precipitates is observed in the vicinity of the crystallization front. Cooling of the crystal is accompanied by the growth and coalescence of precipitates. During heat treatments, the nucleation of precipitates starts at low temperatures, whereas the growth and coalescence of precipitates occur with an increase in the temperature. It has been assumed that the high-temperature precipitation of impurities can determine the overall kinetics of defect formation in other dislocation-free single crystals of semiconductors and metals.

Diffusion model of the formation of growth microdefects as applied to the description of defect formation in heat-treated silicon single crystals

The diffusion model of the formation of growth microdefects has been considered as applied to the description of defect formation in heat-treated silicon single crystals. It has been shown that, in the framework of the proposed kinetic model of defect formation, the formation and development of the defect structure during the growth of a crystal and its heat treatment can be considered within a unified context. The mathematical apparatus of the diffusion model can provide a basis for the development of a program package for the analysis and calculation of the formation of growth and postgrowth microdefects in dislocation-free silicon single crystals. It has been demonstrated that the diffusion model of the formation of growth and post-growth microdefects allows one to determine necessary conditions for the growth of a crystal and the regimes of its heat treatment for the preparation of a precisely defined defect structure.

Structural Scheme of Information System for Defect Engineering of Dislocation-free Silicon Single Crystals

The article is devoted to solving the problem of automation of the calculations and analysis of the defect structure of dislocation-free silicon single crystals. As a result, of development of information system kinetics of interaction of point defects at any time of crystal growth or heat treatments can be investigated. The solution to this problem will allow to simulate and to grow crystals with a predetermined defect structure, as well as manage it in the processes in subsequent technological treatments. The article presents the main aspects of information system for defect engineering of the dislocation-free silicon single crystals. The software structure and technology implementation has been considered. Structural scheme<b> </b>of information system was presented. It is assumed that with the help of this information system will be possible to control the defect structure at various stages of manufacture of devices based on silicon.

Analysis and calculation of the formation of grown-in microdefects in dislocation-free silicon single crystals

The physical model of the formation of grown-in microdefects in dislocation-free Si single crystals has been analyzed. The mathematical models used to describe the processes of defect formation in crystals during their growth are proven to be adequate to the physical model. A technique is proposed to determine and calculate the defect structure in dependence of the crystal growth conditions (growth technique, growth rate, temperature gradients, cooling rate). It is shown that the theoretical study of the real crystal structure in the dependence of the thermal growth conditions using an original virtual technique for analyzing and calculating the formation of grown-in microdefects is a new experimental technique.

A kinetic model of the formation and growth of interstitial dislocation loops in dislocation free silicon single crystals

A kinetic model of the formation and growth of dislocation loops in course of consequent as-grown crystal's cooling has been proposed It demonstrates that dislocation loops are formed following the processes of high-temperature precipitation of background oxygen and carbon impurities during crystal growth. Elastic deformation caused by growing precipitate is released due to the formation and growth of dislocation loops. Interstitial dislocation loops are formed, when the crystal growth ratio is Vg/G<ξcrit. We have compared the kinetic model calculation data with the experimental research findings related to the formation of dislocation loops.

A New Method for Research of Grown-In Microdefects in Dislocation-Free Silicon Single Crystals

As a virtual experimental device for analysis and calculation of grown-in microdefects formation in undoped silicon dislocation-free single crystals the software is proposed. The software is built on the basis on diffusion model of formation, growth and coalescence of grown-in microdefects. Diffusion model describes kinetics of defect structure changes during cooling after growth on crystallization temperature to room temperature. The software allows the use of personal computer to investigate the defect structure of dislocation-free silicon single crystals with a diameter on 30 mm to 400 mm grown by floating-zone and Czochralski methods.

Kinetic model of growth and coalescence of oxygen and carbon precipitates during cooling of As-grown silicon crystals

A kinetic model of growth and coalescence of oxygen and carbon precipitates has been proposed. This model in combination with the kinetic model of the formation of oxygen and carbon precipitates represents a unified model of precipitation in as-grown dislocation-free silicon single crystals during their cooling in the temperature range from 1683 to 300 K. It has been demonstrated that the results of the calculations are in good agreement with the experimental data obtained from investigations of grown-in microdefects.

Kinetics of high-temperature precipitation in dislocation-free silicon single crystals

The defect structure of dislocation-free silicon single crystals has been calculated using the approximate solution of the Fokker-Planck partial differential equations. It has been demonstrated that the precipitation starts to occur near the crystallization front due to the disappearance of excess intrinsic point defects on sinks whose role is played by oxygen and carbon impurities.

Kinetics of formation of vacancy microvoids and interstitial dislocation loops in dislocation-free silicon single crystals

The formation of vacancy microvoids and A-microdefects has been calculated according to the model of point defect dynamics in the absence of recombination of intrinsic point defects at high temperatures. It has been assumed that this solution is possible in the case where the precipitation of impurities begins in the vicinity of the crystallization front. It has been demonstrated that the formation of vacancy microvoids has a homogeneous nature and that the interstitial dislocation loops are predominantly formed through the deformation mechanism.

Modeling of defect formation processes in dislocation-free silicon single crystals

A new alternative model of the formation and transformation of grown-in microdefects in dislocation-free silicon single crystals is proposed. The basic concepts of the alternative mathematical model of the formation of secondary grown-in microdefects are considered. It is shown that vacancy micropores are formed in a narrow temperature range of 1130–1070°C. This is caused by a sharp decrease in the concentration of background impurity which does not form agglomerates (they arise in the temperature range of 1420–1150°C upon crystal cooling).

A Selective Review of the Simulation of the Defect Structure of Dislocation-Free Silicon Single Crystals

A brief review of the current state of theoretical description of the formation of the defect structure of dislocation-free silicon single crystals was carried out. Emphasis was placed on a new diffusion model of formation grown-in microdefects. It is shown that the diffusion model can describe the high-temperature precipitation of impurities during the cooling of the crystal after growth. Shown that the model of the dynamics of point defects can be considered as component part of the diffusion model for formation grown-in microdefects.

Modeling of the defect structure in dislocation-free silicon single crystals

A mathematical model of the formation of primary grown-in microdefects on the basis of dissociation diffusion is presented. Cases of “vacancy-oxygen” (V + O) and “carbon-interstitial” (C + I) interaction near the crystallization front are considered for dislocation-free Si single crystals grown by the floating-zone and Czochralski methods. The approximate analytical expressions obtained by setting 1D and 2D temperature fields in a crystal are in good agreement with the heterogeneous mechanism of formation of grown-in microdefects.

On the recombination of intrinsic point defects in dislocation-free silicon single crystals

The recombination of intrinsic point defects in dislocation-free silicon single crystals is investigated. It is established experimentally and confirmed by thermodynamic calculations that this process in the vicinity of the crystallization front is hindered by the recombination barrier. The recombination parameters (such as the recombination barrier height, the recombination time, and the recombination factor) for the model describing the dynamics of point defects at low and high temperatures are evaluated in terms of the heterogeneous mechanism of nucleation and transformation of grown-in microdefects. It is confirmed that the decomposition of a supersaturated solid solution of point defects can occur according to two mechanisms, namely, the vacancy and interstitial mechanisms. Vacancies and intrinsic interstitial silicon atoms find sinks in the form of oxygen and carbon background impurities. It is demonstrated that the formation of “intrinsic-point-defect-impurity” pairs is a dominant process in the vicinity of the melting temperature.

Theoretical and experimental study of the formation of grown-in and as-grown microdefects in dislocation-free silicon single crystals grown by the Czochralski method

A complex theoretical and experimental investigation is performed, including the following stages. (i) Simulation of the processes of the recombination of intrinsic point defects and the formation of grown-in microdefects in dislocation-free Si single crystals 200 mm in diameter grown in modern commercial heating units. The simulation takes into account the thermal history of the defect growth. Modified designs of heating units are analyzed to compare the results of the simulation of thermal processes during the growth of Si single crystals 200 mm in diameter with a shield in the crucible region. The thermal history of the crystal is simulated, the recombination of intrinsic point defects near the crystallization front is analyzed, and the formation of vacancy microdefects in the temperature range t = 1200–900°C is modeled. This simulation made it possible to determine the effect of a heat shield on the processes of v-i recombination and microdefect formation. (ii) Microdefects in s-grown crystals and in crystals subjected to thermal treatments are investigated by optical and electron microscopy; specific features of the generation and motion of dislocations are analyzed for Si wafers containing microdefects of different types, formed as a result of the decomposition of the supersaturated solid solution of oxygen during multistep heat treatments of Si wafers. (iii) The three-dimensional problem of determining the field of elastic stresses caused by the wafer weight is solved in the isotropic approximation for 200-and 300-mm Si wafers placed on three or symmetrically arranged point supports of different areas.