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The power needed to zone silicon crystals by radio frequency heating was analyzed. The heat loss mechanisms are examined. Curves are presented for power as a function of crystal diameter for commercial silicon zoning.
Floating-zone crystal growth under microgravity, though free from natural convection, can still be susceptible to Marangoni convection. The use of a ring heater in contact with most of the surface of the melt zone, has recently been considered as one way of reducing Marangoni convection in the melt zone. In order to study Marangoni convection in the melt zone in this modified floating-zone crystal growth process, a half-zone system was adopted. Computer simulation and direct observation of Marangoni convection in the half-zone system were carried out for two different cases. In the first case, the surface of the melt zone was completely free, while in the second it was mostly in contact with a quartz ring. The results of computer simulation and direct observation both indicated that in the second case Marangoni convection was significantly reduced near the melt/solid interface as well as in the bulk melt.
The float zone (FZ) growth method for silicon crystallization has advantages and disadvantages when compared to the other principal growth method, the Czochralski (CZ) technique. CZ growth is attractive for the following reasons: large diameters, high single crystal yields, low thermal gradients, low operator skill requirements, efficient power utilization, and low feed material costs. Some areas where FZ growth is advantageous include high purity, axial resistivity uniformity (on a macroscale), visibility of the growth region, low consumable material costs, and high growth rates.
This presentation will examine in detail the role of vibration-induced streaming flow in the context of float-zone crystal growth. It is very well known that during float-zone materials processing, the naturally occurring temperature gradients along the zone surface impose a thermocapillary flow in the zone. Under certain processing conditions, the thermocapillary flow can also become nonsteady (oscillatory). The presence of thermocapillary flow is detrimental to crystal quality, for it can promote non-uniform dopant distribution and crystal striations. To null this effect we have imposed a counter streaming flow in the zone, via end-wall vibration. This technique has been adapted to float-zone processing of Sodium Nitrate-Barium Nitrate eutectic alloys, under both steady and nonsteady thermocapillary flow conditions. The beneficial effects of counter streaming flow have been clearly brought out through the before and after comparisons of the crystal microstructure. In addition, we are also examining the theoretical underpinnings of the balancing of thermocapillary flows with vibration-driven counter flows in float-zones.
This presentation will examine in detail the role of vibration-induced streaming flow in the context of float-zone crystal growth. It is very well known that during float-zone materials processing, the naturally occurring temperature gradients along the zone surface impose a thermocapillary flow in the zone. Under certain processing conditions, the thermocapillary flow can also become nonsteady (oscillatory). The presence of thermocapillary flow is detrimental to crystal quality, for it can promote non-uniform dopant distribution and crystal striations. To null this effect we have imposed a counter streaming flow in the zone, via end-wall vibration. This technique has been adapted to float-zone processing of Sodium Nitrate-Barium Nitrate eutectic alloys, under both steady and nonsteady thermocapillary flow conditions. The beneficial effects of counter streaming flow have been clearly brought out through the before and after comparisons of the crystal microstructure. In addition, we are also examining the theoretical underpinnings of the balancing of thermocapillary flows with vibration-driven counter flows in float-zones.
Computer simulation was conducted to study a modified floating-zone crystal growth process, in which the melt surface is mostly covered with a heated ring. The growth of 6-mm diameter single crystals of NaNO3 was considered, and the effects of the following parameters were studied: (1) temperature of the ring, (2) growth rate, (3) surface tension-temperature coefficient of the melt, (4) thermal expansion coefficient of the melt, and (5) gravity. It was demonstrated that thermocapillary convection in the melt zone is reduced significantly in this modified process. The model was checked against the measured lengths of the meniscus near the growth front and axial temperature distribution in a growing crystal, and the agreement was good.
Computer simulation of steady-state axisymmetrical heat transfer and fluid flow was conducted to study thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity. The effects of key variables on the extent of thermocapillary flow in the melt zone, the shapes of melt/solid interfaces and the length of the melt zone were discussed. These variables are: (1) the temperature coefficient of surface tension (or the Marangoni number), (2) the pulling speed (or the Peclet number), (3) the feed rod radius, (4) the ambient temperature distribution, (5) the heat transfer coefficient (or the Biot number), and (6) the thermal diffusivity of the material (or the Prandtl number).
The energy-stability theory has been used to study the stability properties of thermocapillary convection in a half-zone model of the float-zone crystal-growth process. It is concluded that the energy theory provides a sufficient condition for stability to disturbances of arbitrary amplitude. Results of the computation of energy-stability limits are found to be in good agreement with experimentally measured bounds for oscillatory thermocapillary convection.
It has been demonstrated in floating-zone configurations utilizing silicone oil and nitrate salts that mechanically induced vibration effectively minimizes detrimental, gravity independent, thermocapillary flow. The processing parameters leading to crystal improvement and aspects of the on-going modeling effort are discussed. Plans for applying the crystal growth technique to commercially relevant materials, e.g., silicon, as well as the value of processing in a microgravity environment are presented.
Our previous experiments with NaNO3 float-zones revealed that steady thermocapillary flow can be balanced/offset by the controlled surface streaming flow induced by end-wall vibration. In the current experiments we are examining the effects of streaming flow on steadying/stabilizing nonsteady thermocapillary flow in such zones. To this effect we have set up a controlled NaNO3 half-zone experiment, where the processing parameters, like zone dimensions and temperature gradients, can be easily varied to generate nonsteady thermocapillary flows. In the present paper we present preliminary results of our investigations into stabilizing such flows by employing end-wall vibration.
Our previous experiments with NaNO3 float-zones revealed that steady thermocapillary flow can be balanced/offset by the controlled surface streaming flow induced by end-wall vibration. In the current experiments we are examining the effects of streaming flow on steadying/stabilizing nonsteady thermocapillary flow in such zones. To this effect we have set up a controlled NaNO3 half-zone experiment, where the processing parameters, like zone dimensions and temperature gradients, can be easily varied to generate nonsteady thermocapillary flows. In the present paper we present preliminary results of our investigations into stabilizing such flows by employing endwall vibration.
A crystal growth system, comprising: a furnace; a plurality of heating elements coupled to said furnace, each said plurality of heating elements defining a heat zone, each said heating element set to a desired temperature value; a plurality of thermocouples associated with respective heat zones to detect a temperature value; a translation system for passing an ampoule containing crystal growth material through said furnace into said heat zones and providing a positional location of said ampoule and; a multi-variable self-tuning temperature controller connected to said plurality of heating elements, said plurality of thermocouples and said translation system, said controller monitoring each said zone temperature value and upon considering the thermal interaction of heating zones and the moving thermal inertia of the ampoule, adjusting voltage input to said heat zones to obtain optimal crystal growth within said ampoule.
A crystal growth system, comprising: a furnace; a plurality of heating elements coupled to said furnace, each said plurality of heating elements defining a heat zone, each said heating element set to a desired temperature value; a plurality of thermocouples associated with respective heat zones to detect a temperature value; a translation system for passing an ampoule containing crystal growth material through said furnace into said heat zones and providing a positional location of said ampoule and; a multi-variable self-tuning temperature controller connected to said plurality of heating elements, said plurality of thermocouples and said translation system, said controller monitoring each said zone temperature value and upon considering the thermal interaction of heating zones and the moving thermal inertia of the ampoule, adjusting voltage input to said heat zones to obtain optimal crystal growth within said ampoule.
The objective of this research is to control the dynamics of multizone programmable crystal growth furnaces. Due to the inevitable heat exchange among different heating zones and the transient nature of the process, the dynamics of multizone furnaces is time varying, distributed, and therefore complex in nature. Electrical power to heating zones and the translational speed of the ampoule are employed as inputs to control the dynamics. Structural properties of the crystal is the ultimate aim of this adaptive control system. These properties can be monitored in different ways. Following an order of complexity, these may include: (1) on line measurement of the material optical properties such as the refractive index of crystal; (2) on line x-ray imaging of the interface topology; (3) on line optical quantification of the interface profile such as the determination of concavity or convexity of the interface shape; and (4) on line temperature measurement at points closest to the material such as measurements of the ampoule's outside and inside surface temperatures. The research performed makes use of the temperature and optical measurements, specified in (3) and (4) as the outputs of furnace dynamics. However, if the instrumentation is available, the proposed control methodology can be extended to the measurements listed in (1) and (2).
A PC-based computer control system to automate a high-temperature float zone growth of titanium carbide is reported. The control strategy of the computer control system relies on the relations derived from a combination of empirical relations and results from detailed mathematical analysis of the physical transports of the entire float zone assembly. A system control computer program was written to establish real-time determination of the size of the molten zone from a thermal image, control parameters from established relationships, and collected processed data to achieve control objectives. We found that the developed computer control allows the growth process to be operated nearer the stability limit. Any slight variations in growth conditions can be corrected in time to avoid any instability growth, which otherwise cannot be adjusted via manual control.
Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.
An apparatus for growing a monocrystalline body (30) from a polycrystalline feed rod (22) includes a heater (20) that is positioned to heat a short section of the polycrystalline rod (22) to create a molten zone (34). The heater (20) is formed to include a shaper (40) that contacts the polycrystalline rod (22) in the molten zone (34) and has a hole (46) to allow flow in the molten zone (34) between the polycrystalline rod (22) side and the monocrystalline body (30) side of the shaper. The shaper (40) has an edge (42) that defines the boundary of the cross-section of the monocrystalline body (30) that is formed as the molten material solidifies.
Marangoni flow was induced in a thin disk of molten tin with an atomically clean surface by heating it from below in an ultra high vacuum apparatus. The radial distribution of temperature was measured and no temperature oscillations were observed. Strong mechanical disturbances introduced at a Marangoni number of about 4300 died out quickly with time indicating that the system was stable. Mathematical models indicate that strong flows in a two cell structure exist under the conditions studied, and that the velocity profile in the cell near the surface is of the boundary layer type which varies rapidly with depth.