Distribution Of Intrinsic Point Defects Research Articles

Numerical investigation of impact of crystal diameter fluctuations on intrinsic point defects distribution in Si crystal grown by Czochralski method

Intrinsic point defects distribution is primarily controlled by the crystal pulling rate and temperature gradient directly at growth interface in silicon crystals grown using the Czochralski (Cz) method. The fluctuation in crystal diameter during the Cz process is one of the primary features associated with the temporal variation in growth process parameters, such as the pulling rate and heater power in the growth system, and which is expected to affect the thermal stress, defects, and dopant incorporation in a growing crystal. In this study, we numerically investigated the effect of temporal variation in crystal diameter on the intrinsic point defects distribution in a silicon crystal grown using the Cz method. The point defect dynamics in the crystal were numerically evaluated within a two-dimensional axisymmetric unsteady global heat and mass transport model for dynamically pulled silicon crystals, considering the shape of the crystal and diameter variation. Unsteady numerical simulations showed that the distribution of intrinsic point defects near crystal side surface in a growing silicon crystal significantly depends on the temporal variation in the crystal diameter.

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.

Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

During the growth of large diameter silicon single crystals with the industrial floating zone method, undesirable level of thermal stress in the crystal is easily reached due to the inhomogeneous expansion as the crystal cools down. Shapes of the phase boundaries, temperature field and elastic material properties determine the thermal stress distribution in the solid mono crystalline silicon during cylindrical growth. Excessive stress can lead to fracture, generation of dislocations and altered distribution of intrinsic point defects. Although appearance of ridges on the crystal surface is the decisive factor of a dislocation-free growth, the influence of these ridges on the stress field is not completely clear. Here we present the results of thermal stress analysis for 4” and 5” diameter crystals using a quasi-stationary three dimensional mathematical model including the material anisotropy and the presence of experimentally observed ridges which cannot be addressed with axis-symmetric models. The ridge has a local but relatively strong influence on thermal stress therefore its relation to the origin of fracture is hypothesized. In addition, thermal stresses at the crystal rim are found to increase for a particular position of the crystal radiation reflector.

Remote and Conjugated Modeling of Heat–Mass Transfer and Defect Formation in Technological Processes

The advanced development of computer technology and software makes possible remote simulation of physical processes in technological processes using complex software systems. Its advantage is that the users ( Clients ) carry out the main creative work (the preparation and treatment of the calculated data) on their own computers, but the long − time calculations are executed by means of Internet access on a remote supercomputer ( Server ) where the software package is installed. The presented examples illustrate an application of CrystmoNet code to a number of tasks related to the conjugated simulation of Czochralski silicon single crystal growth. They include results of conjugated calculations of the hydrodynamic processes occurring in the melt taking into account its crystallization and the radiation − conductive heat transfer in the entire volume of the crystal growth hot zone, as well as the thermal stresses and the distributions of intrinsic point defects in dislocation − free silicon single crystals.

Long range lateral migration of intrinsic point defects in n-type 4H-SiC

The lateral distributions of intrinsic point defects in n-type (0001) 4H-SiC have been investigated following room temperature irradiation with a focused beam of 10 keV protons. Laterally resolved deep level transient spectroscopy measurements reveal that the well-known and prominent Z1/2 and S1/2 centers display lateral diffusion lenghts on the order of 1 mm with negligible (if any) motion parallel to the direction of the c-axis. The migration occurs only in the presence of excess charge carriers generated during the proton irradiation, and no further motion takes place even under subsequent optical excitation of high intensity. Assuming one-dimensional geometry, an effective defect diffusivity in excess of 10−6 cm2/s is deduced by numerical modelling of the experimental data, corresponding to an energy barrier for migration of ∼0.2 eV. Possible mechanisms for the rapid migration, invoking charge carrier recombination as a necessary condition, are discussed, and especially, an association with the glide of partial dislocations along the (0001) basal plane is scrutinized in some detail.

Integrated modeling and verification of 2D grown‐in microdefect distributions in Cz dislocation‐free silicon single crystals

AbstractInfluence of the thermal shield on temperature zones, microdefect formation and occurrence of diameter distortion in Cz dislocation‐free silicon single crystal is analyzed. Results of integrated modeling of thermal field and distributions of intrinsic point defects (IPD) in the ingot shoulder and across the cylindrical body of grown silicon crystal are discussed. An application of the pre sent model of defect formation to rapid thermal annealing (RTA) of silicon wafers is shown. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of Czochralski silicon crystal growth on wafer quality: an extensive investigation using traditional and new characterization techniques

In this paper results on the relationship between Czochralski silicon crystal growth and wafer quality characteristics are presented. Several crystals grown with different oxygen content and growth parameters are examined. The growth parameters are varied in order to obtain different types and distributions of intrinsic point defects, namely vacancies and interstitials. Traditional and more recent characterization techniques are applied in this analysis, such as gate oxide integrity and light point defects evaluation, or high resolution lifetime mapping. In this way, a comprehensive picture is generated of the properties of a silicon wafer and how it is impacted by the crystal growth process.

Analytical Approximations for the Distributions of Intrinsic Point Defects in Grown Silicon Crystals

Analytical approximations for the distributions of vacancies and self-interstitials in Si crystals are derived in a one-dimensional point defect model. In the case of an unlimited high recombination rate all results depend only on the growth parameter P = V/G with V being the growth rate and G the temperature gradient at the melt/solid interface. For the critical growth parameter P crit , which separates the vacancy-dominated region from the interstitial-dominated region, the well-known relation of Voronkov is derived. This relation and also the first correction to P crit are in excellent agreement with recent experimental results published in literature. In the case of a limited recombination rate the transport equations were solved first of all by neglecting diffusion. This solution is completed by small correction terms using a special series expansion, which depend on the diffusivities. With this approximation important features such as the influence of the recombination and cooling rate on the distributions of intrinsic point defects can be analyzed.

Control of Defect Structures in CuGaSe2 Epitaxial Films

ABSTRACTAn in-situ annealing process, which is conducted in the growth chamber by exposing the film to a Se beam immediately after film deposition, is developed to control defect structures in CuGaSe2 epitaxial films. TEM observations showed that the films annealed at a temperature above 450°C could completely remove anti-phase domain boundaries and effectively annihilate threading dislocations. The annealing process also changes the distributions of intrinsic point defects in the film. Photoluminescence (PL) may reflect the microstructure improvement in the films. A suppress of the donor-to-acceptor transitions caused by antisite defects and an enhancement in the PL intensity were found in a annealed film.

Formation of the bands of anomalous oxygen precipitation in Czochralski-grown Si crystals

This paper reports some results on anomalous oxygen precipitation in CZ-grown Si crystals with uniform oxygen distribution and proposes a mechanism consistent with these observations. Experiments have been carried out on crystal growth with constant pulling rate, with a step change in pulling rate and temporary cessation of pulling. To modify thermal growth conditions, an additional heater has been used. The thermal history was specified following temperature measurements in the growing crystals. Distribution of microdefects has been investigated by etching and X-ray topography after 1000°C annealing for 24 h and Au diffusion at 1200°C. It was found that a band of anomalous oxygen precipitation emerged near sinks for vacancies and its shape was closely connected with that of the vacancy-depleted region. The band exhibits reduced or enhanced oxygen precipitation depending on thermal history during crystal growth in the ranges 1150–760°C and 760–610°C. After Au diffusion, a higher concentration of dislocation loops and stacking faults is revealed in the band. A mechanism is proposed to account for the results which also makes it possible to predict a configuration of the band and its behaviour upon heat treatments, starting from the thermal history and taking into account the distribution of intrinsic point defects in a growing crystal.