Wilfried von Ammon

The dependence of bulk defects on the axial temperature gradient of silicon crystals during Czochralski growth

Abstract 4″, 6″ and 8″ Cz crystals were grown with different heat shields which protect the growing crystals against radiation emitted from the melt surface and hot graphite parts, thereby determining their thermal environment. It was found that the critical pull rate, at which the oxidation induced stacking fault (OSF) ring vanishes in the wafer centre, varies with the crystal diameter and the type of heat shield. A calculation of the axial temperature gradient at the solid/liquid interface for each crystal diameter/heat shield combination revealed that the critical pull rate is proportional to this axial temperature gradient G, which, in turn, is a function of the crystal diameter and heat shield. Thus, the critical pull rate is entirely determined by the axial gradient G. The OSF ring appears in the wafer centre when the equation V G = C crit = 1.3 × 10 7t-3 cm 2 min −1 K −1 holds (V is the pull rate). For V G > C crit flow pattern/D-defects are observed, whereas V G crit describes the condition for the growth of large pit defects.

Point Defect Dynamics and the Oxidation‐Induced Stacking‐Fault Ring in Czochralski‐Grown Silicon Crystals

A model is presented and analyzed for the dynamics of intrinsic point defects, vacancies, and self-interstitials, in single-crystal silicon. Computations and asymptotic analysis are used to describe the appearance of the oxidation-induced stacking-fault ring (OSF ring) created during the cooling of silicon crystals in the Czochralski growth process. The model predicts that the OSF ring separates an inner region supersaturated with vacancies from a self-interstitial rich outer region. The OSF ring corresponds to a region of no net excess of either point defect. Simulations of the dynamics of the OSF ring with changes in the crystal growth rate (V) and the axial temperature gradient at the melt/crystal interface (G) accurately predict experimental data for a wide range of growth conditions when point defect thermophysical properties (equilibrium concentrations and diffusivities) are fit to a single set of experimental data. The point defect properties determined this way are within the range of values reported in the literature. Asymptotic analysis of the point defect dynamics model gives a simple mechanistic picture for the development of the point defect supersaturations and yields a closed-form expression for the critical value of (V/G) for the location of the OSF ring. This expression is in excellent agreement with the predictions of simulation and with the empirical correlation determined from experiments.

The Dependence of Ring‐Like Distributed Stacking Faults on the Axial Temperature Gradient of Growing Czochralski Silicon Crystals

The ring diameter of ring-like distributed oxidation induced stacking faults (OSF) in Czochralski grown silicon crystals has been investigated as a function of pull rate and the calculated axial temperature gradient G at the solid/liquid interface of the growing crystals. It is shown that the radial position of the OSF ring can be predicted from the empirically found equation V/G(r) = 1.3 x 10 -3 cm 2 min -1 K -1 , where r is the radial distance from the center of the crystal. This equation is only in accordance with experimental results, if G(r) is calculated directly at the growth interface. As G(r) is strongly dependent on the axial distance from the growth interface, it is concluded that the radial location of the OSF ring is predominantly determined by point-defect processes in the close vicinity of the growth interface of the growing crystal. It is shown that the presently known theoretical approaches to explain the radial OSF ring variation are probably not consistent with the above results.

On the dynamics of the oxidation-induced stacking-fault ring in as-grown Czochralski silicon crystals

The behavior of the oxidation-induced stacking-fault ring (OSF ring) in Czochralski (CZ)-grown silicon crystals is predicted based on the dynamics of point defects during growth. Preexponential constants for the equilibrium point defect concentrations and diffusivities are determined by fitting the predictions of the model to a single set of experimental data for OSF-ring dynamics. Other experimental data is well fit by this model. Moreover, point defect properties used are consistent with other estimates. Asymptotic analysis of the point defect model leads to a closed-form expression for the dependence of the OSF-ring location on processing conditions and thermophysical properties of point defects at the melting temperature. These results indicate that differentiation between defect types in CZ-grown material can be done entirely on the basis of point defect dynamics.

Effects of various magnetic field configurations on temperature distributions in Czochralski silicon melts

Magnetic fields are of growing interest for improvement of the silicon Czochralski crystal growth process. The use of steady magnetic fields provides suppression of turbulent fluctuations due to their damping action on the melt flow. Recent literature data on magnetic fields show that a relatively low field strength allows to control heat and mass transfer in laboratory scale melts. This contribution presents experimental results of temperature measurements in industrial scale silicon Czochralski melts under different magnetic field conditions. Temperature distributions are obtained by using thermocouples to detect temperatures in the melt and at the crucible wall during a crystal growth process. In addition we report on results of numerical simulations carried out for growth parameters and magnetic fields as used in the experiments. All experimental data are compared with the results from numerical simulation and discussed with respect to their implication on improving the quality of the grown crystals.

Physical modelling of the melt flow during large-diameter silicon single crystal growth

Abstract The reported investigations concern physical modelling of Czochralski growth of silicon large-diameter single crystals. InGaSn eutectic was used as a modelling liquid, employing actual criteria of the real process (Prandtl, Reynolds, Grashof numbers, etc.) and geometric similarity. A multi-channel measuring system was used to collect and process the temperature and flow velocity data. The investigations were focused on the study of heat transfer, in particular, the instability of the “cold zone” of the melt at the crystallization front.

Challenges for economical growth of high quality 300 mm CZ Si crystals

The changeover from 200 mm to 300 mm is required by the semiconductor industry due to the necessity for larger chip sizes and demand for decreasing cost. However, the cost for 300 mm crystal growth is likely to rise owing to larger puller, enlargement of hot zone, expensive silica crucibles and longer growth process times caused by lower growth rates and longer cooling rates. Simultaneously, the conditions are more complex and disadvantageous to the required higher qualities in comparison to smaller wafer diameters (e. g. position of OSF ring). This paper gives an overview about the challenges for 300 mm growth and approaches to provide appropriate solutions (e.g. application of magnetic systems, optimization of growth parameters by integration of numerical simulation).

Analysis of the Nucleation Kinetics of Oxide Precipitates in Czochralski Silicon

Although oxide precipitation in Czochralski (CZ) silicon is investigated since decades, it is still not fully understood. This however is prerequisite for accurate modeling of precipitate generation during thermal processes of device fabrication and the creation of getting sites for metal impurities. A few years ago, the so-called magic denuded zone process was discovered which offers the possibility to establish well defined vacancy concentrations in silicon wafers by RTA treatments. This is of great advantage for the investigation of the influence of vacancies on oxide precipitation more into detail. The aim of this work is to study the impact of vacancies on the nucleation of oxide precipitates in order to obtain deeper understanding of the type of nuclei and nucleation sites with their impact on the nucleation kinetics.

Modelling of Morphological Changes by Surface Diffusion in Silicon Trenches

We present a three - Dimensional model of surface diffusion which describes the time evolution and topography changes of deep trenches under low pressure hydrogen anneal and compare the results with experimental observations. A phase diagram for regular arranged cylindrical trenches was derived by using a genetic optimization algorithm. Seven different structural phases of the final bubble / layer arrangement out of the trench array anneal could be predicted. The impact of perturbations in the regular . trench array is discussed too and the change in the phase diagram - shrinkage of the stable region for single top layer formation - is calculated .

Formation of stacking faults in nitrogen-doped silicon single crystals

The behavior of the ring-like distribution of oxidation-induced stacking faults (OSFs) in nitrogen-doped Czochralski grown single silicon crystals was investigated as a function of the nitrogen and oxygen content. It was found that the inner and outer boundary of the OSF ring is shifted towards the crystal center with higher nitrogen concentration, while, at the same time, the width of the OSF ring increases. This result can be explained by a qualitative model which takes into account the nitrogen-induced change in the temperature-dependent variation of the vacancy concentration. Without nitrogen doping the OSF ring disappears if the oxygen content drops below a critical value. However, the OSF ring reappears at a sufficient nitrogen doping level. The lower the oxygen content, the higher the nitrogen concentration must be to observe an OSF ring. It is shown that this can be understood using the same qualitative model if a critical width of the OSF ring is introduced below which the OSF ring is no longer detectable.