Floating Zone Growth of Silicon

Muižnieks, A.; Virbulis, J.; Lüdge, Anke; Riemann, H.; Werner, Nico

doi:10.1016/b978-0-444-63303-3.00007-9

Cited by 16 publications

(8 citation statements)

References 42 publications

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“…With larger depth of the crystallization interface and therefore smaller interface angle, in general an increase of thermal stress is expected. Von Mises stress invariant is commonly used as a universal measure for the stress impact on dislocation generation and fracture [3]. Influence of the ridge and process parameters on von Mises stress on the crystal surface is shown in Fig.…”

Section: Calculation Resultsmentioning

confidence: 99%

“…However, currently the ingot diameter is limited to 200 mm with the two main impediments being the crystal fracture due to thermal stress with related dislocation generation and electrical breakdown at the inductor main slit [3]. One of the first reported calculations of thermal stress in the silicon crystal during FZ growth was part of a global axis-symmetric quasi-steady model including electromagnetic field and heat transfer for a 4" crystal diameter [4].…”

Section: Introductionmentioning

confidence: 99%

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

Plāte¹,

Krauze

Virbulis

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract.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.

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Section: Calculation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Plāte¹,

Krauze

Virbulis

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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“…In addition, the operator must form a certain shape in which the crystal diameter is first reduced (called "necking") and then increase the diameter of the crystal to obtain a single crystal. Since the dynamics of the melt state depending on the input parameters are non-linear and complicated, it is difficult to simulate the FZ crystal growth process, as has been achieved for other crystal growth methods [29][30][31][32][33] . Thus, it is necessary to predict the dynamics of FZ crystal growth from the operation trajectories.…”

Section: Introductionmentioning

confidence: 99%

Data-driven automated control algorithm for floating-zone crystal growth derived by reinforcement learning

Harada

Tosa

Omae

et al. 2023

Preprint

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The complete automation of materials manufacturing with high productivity is a key problem in some materials processing. In floating zone (FZ) crystal growth, which is a manufacturing process for semiconductor wafers such as silicon, an operator adaptively controls the input parameters in accordance with the state of the crystal growth process. Since the operation dynamics of FZ crystal growth are complicated, automation is often difficult, and usually the process is manually controlled. Here we demonstrate automated control of FZ crystal growth by reinforcement learning using the dynamics predicted by Gaussian mixture modeling (GMM) from small numbers of trajectories. Our proposed method of constructing the control model is completely data-driven. Using an emulator program for FZ crystal growth, we show that the control model constructed by our proposed model can more accurately follow the ideal growth trajectory than demonstration trajectories created by human operation. Furthermore, we reveal that policy optimization near the demonstration trajectories realizes accurate control following the ideal trajectory.

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“…Floating zone method is a promising technique to growth single crystals with the advantage of containerless environment, which is widely used for the growth of high-precision silicon, super alloys and other semiconductor material [1][2][3]. Marangoni convection driven by surface tension gradient has a dramatic effect on distribution of impurity concentration in melt, due to existence of free surface in floating zone growth system [4,5].…”

Section: Introductionmentioning

confidence: 99%

Effect of aspect ratio on coupled solute-thermocapillary convection instability in half-zone liquid bridge

et al. 2022

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Floating zone method is an important technology for growth of high-integrity and high-uniformity single crystal materials due to its free of crucible contamination. However, capillary convection in the melt is a great challenge to floating zone crystal growth. In this paper, numerical simulations are performed to investigate the coupled solute-thermocapillary convection in SixGe1-x system of the half-zone liquid bridge. And the impact of aspect ratio (As) is also investigated on stability of capillary convection. For As=0.5, the results show that pure solute capillary convection is very weak, which presents 2-D axisymmetric structure. The temperature field is mainly determined by thermal diffusion, while the concentration field is dominated by convection and solute diffusion together. Coupled solute-thermocapillary convection exhibits 3-D periodic and rotating oscillatory flow with the azimuthal wavenumber m=4, while the pure thermocapillary convection presents a 3-D steady non-axisymmetric flow while solute capillary convection is absent. This means that instability of convection will increase when two kinds of capillary convection are coupled. When the height of the liquid bridge is changed from 5 mm to 10 mm with a constant radius of 10 mm, azimuthal wave number (m) of coupled capillary convection shows a strong dependence on aspect ratio. The relationship between the azimuthal wave number and aspect ratio can be written as m?As= 2 or m?As=2.2. Further results indicated that when velocity of the monitoring point is large, corresponding concentration is also high at that moment, but the phases of concentration and velocity are not completely synchronized.

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Floating Zone Growth of Silicon

Cited by 16 publications

References 42 publications

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

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

Data-driven automated control algorithm for floating-zone crystal growth derived by reinforcement learning

Effect of aspect ratio on coupled solute-thermocapillary convection instability in half-zone liquid bridge

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