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NASA NTRS1982

Capillary forces exerted by liquid drops caught between crossed cylinders. A 3-D meniscus problem with free contact line

The Young-Laplace equation is solved for three-dimensional menisci between crossed cylinders, with either the contact line fixed or the contact angle prescribed, by means of the Galerkin/finite element method. Shapes are computed, and with them the practically important quantities: drop volume, wetted area, capillary pressure force, surface tension force, and the total force exerted by the drop on each cylinder. The results show that total capillary force between cylinders increases with decreasing contact angle, i.e. with better wetting. Capillary force is also increases with decreasing drop volume, approaching an asymptotic limit. However, the wetted area on each cylinder decreases with decreasing drop volume, which raises the question of the optimum drop volume to strive for, when permanent bonding is sought from solidified liquid. For then the strength of the bond is likely to depend upon the area of contact, which is the wetted area when the bonding agent was introduced in liquid form.

Patzek, T. W.↗

NASA NTRS1980

Continuous coating of silicon-on-ceramic

Growth of sheet silicon on low-cost substrates has been demonstrated by the silicon coating with inverted meniscus (SCIM) technique. A mullite-based ceramic substrate is coated with carbon and then passed over a trough of molten silicon with a raised meniscus. Solidification occurs at the trailing edge of the downstream meniscus, producing a silicon-on-ceramic (SOC) layer. Meniscus shape and stability are controlled by varying the level of molten silicon in a reservoir connected to the trough. The thermal conditions for growth and the crystallographic texture of the SOC layers are similar to those produced by dip-coating, the original technique of meniscus-controlled growth. The thermal conditions for growth have been analyzed in some detail. The analysis correctly predicts the velocity-thickness relationship and the liquid-solid interface shape for dip-coating, and appears to be equally applicable to SCIM-coating. Solar cells made from dip-coated SOC material have demonstrated efficiencies of 10% on 4-sq cm cells and 9.9% on 10-sq cm cells.

Heaps, J. D.↗

NASA NTRS2013

Stability of Menisci in Detached Bridgman Growth

Detached growth, also referred to as dewetted growth, is a Bridgman crystal growth process in which the melt is in contact with the crucible wall but the crystal is not. A meniscus bridges the gap between the top of the crystal and the crucible wall. The meniscus shape depends on the contact angle of the melt with the crucible wall, the growth angle of the melt with respect to the solidifying crystal, the gas pressure differential, the Weber number describing the rotation rate of the crucible, and the Bond number. Only some of the meniscus shapes are stable and the stability criterion is the sign of the second variation of the potential energy upon admissible meniscus shape perturbations. The effects of confined gas volumes above and below the melt and crucible rotation are evaluated. The analysis is applicable to the non-stationary case where the crystal radius changes during growth. Static stability maps (crystal radius versus pressure differential) are obtained for a series of Bond numbers, growth angles and Weber numbers. Also, the specific cases of Ge and InSb, in both terrestrial and microgravity conditions, are analyzed. Stability was found to depend significantly on whether the interior surface was considered to be microscopically rough or smooth, corresponding to pinned or unpinned states. It was also found that all meniscus shapes are statically stable in a microgravity environment.

Mazuruk, K.↗

NASA NTRS2013

Stability of Menisci in Detached Bridgman Growth

Mazuruk, Konstantin↗

NASA NTRS2009

Influence of Containment on Defects in GeSi Crystals

Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10(exp -5) m. A small meniscus bridges the gap between the top of the crystal and the wall. Key parameters involved in achieving detached growth are the contact angle between the melt and crucible and the pressure differential across the meniscus. Sessile drop measurements were used to determine the wetting angles of Ge(sub 1-x)Si(sub x) melts on a variety of substrates and found that the highest wetting angles were achieved with pyrolitic boron nitride (pBN). GeSi crystals have been repeatedly grown detached in pBN crucibles but only occasionally in crucibles with lower wetting angles. Experiments have been conducted to assess the effect of pressure differential across the meniscus in sealed crucibles. This was done by adjusting the temperature profile after partial melting of the starting material. In a separate set of experiments, the pressure was controlled by connecting the volume below the meniscus to a regulated gas supply. The experiments were in agreement with calculations which predicted that stable detachment will only occur in crucibles with a low wetting angle over a relatively narrow range of pressure differential. Detached-grown crystals exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction.

Volz, M. P.↗

NASA NTRS2011

Existence and Stability of Menisci in Detached Bridgman Growth

Detached growth, also referred to as dewetted growth, is a Bridgman crystal growth process in which the melt is in contact with the crucible wall but the crystal is not. A meniscus bridges the gap between the top of the crystal and the crucible wall. The Young-Laplace capillary equation was used to calculate the crystal radii of detached states as a function of the pressure differential across the meniscus. The detached states depend on the contact angle of the melt with the crucible wall, the growth angle of the melt with respect to the solidifying crystal, and the Bond number. A static stability analysis was performed on the calculated detached states. The stability criterion was the sign of the second variation of the potential energy upon admissible meniscus shape perturbations. The conditions considered corresponded to the growth of Ge and InSb, in both terrestrial and microgravity conditions. Stability was found to depend significantly on whether the interior surface was considered to be microscopically rough or smooth, corresponding to pinned or unpinned states. It was also found that all meniscus shapes which are single-valued functions of the radius are statically stable in a microgravity environment.

Volz, M. P.↗

NASA NTRS1976

Silicon ribbon growth by a capillary action shaping technique

The crystal growth method described is a capillary action shaping technique. Meniscus shaping for the desired ribbon geometry occurs at the vertex of a wettable die. As ribbon growth depletes the melt meniscus, capillary action supplies replacement material. A capillary die is so designed that the bounding edges of the die top are not parallel or concentric with the growing ribbon. The new dies allow a higher melt meniscus with concomitant improvements in surface smoothness and freedom from SiC surface particles, which can degrade perfection.

Schwuttke, G. H.↗

NASA NTRS1977

Silicon ribbon growth by a capillary action shaping technique

The crystal-growth method under investigation is a capillary action shaping technique. Meniscus shaping for the desired ribbon geometry occurs at the vertex of a wettable dye. As ribbon growth depletes the melt meniscus, capillary action supplies replacement material. The configuration of the technique used in our initial studies is shown. The crystal-growth method has been applied to silicon ribbons it was found that substantial improvements in ribbon surface quality could be achieved with a higher melt meniscus than that attainable with the EFG technique.

Schwuttke, G. H.↗

NASA NTRS1977

Silicon ribbon growth by a capillary action shaping technique

Substantial improvements in ribbon surface quality are achieved with a higher melt meniscus than that attainable with the film-fed (EFG) growth technique. A capillary action shaping method is described in which meniscus shaping for the desired ribbon geometry occurs at the vertex of a wettable die. As ribbon growth depletes the melt meniscus, capillary action supplies replacement material. Topics discussed cover experimental apparatus and growth procedures; die materials investigations, fabrication and evaluation; process development for 25 mm, 38 mm, 50 mm and 100 mm silicon ribbons; and long grain direct solidification of silicon. Methods for the structural and electrical characterization of cast silicon ribbons are assessed as well as silicon ribbon technology for the 1978 to 1986 period.

Schwuttke, G. H.↗

NASA NTRS1980

Method of growing a ribbon crystal particularly suited for facilitating automated control of ribbon width

A method of growing a ribbon crystal is described wherein a meniscus of molten semiconductor material attached to vertical movable seed is lifted at a rate substantially equal to the rate at which the meniscus freezes. The method is characterized by the steps of continuously sensing the brightness of the growth region of the ribbon in selected areas across the ribbon width for detecting changes in the intensity of the brightness of the selected areas, and modifying the temperature of the meniscus and pulling speed in response to changes detected in the intensity for controlling the geometry of the ribbon.

Ciszek, T. F.↗

NASA NTRS1984

Process and apparatus for growing a crystal ribbon

A process and apparatus is disclosed for growing a crystal ribbon of a substance of theoretically infinite length from a melt of the substance. A pair of fixedly positioned edge defining members are partially submerged into the melt so as to break the surface of the melt at a predetermined distance from one another. The edge defining members are wettable by the melt and the predetermined distance substantially corresponds to the width of the crystal ribbon to be grown. The crystal ribbon is grown by contacting the surface of the melt with a seed ribbon between the edge defining members whereby a meniscus of the melt is established on the seed ribbon. The meniscus is stabilized by the meniscus of the melt on the edge defining members. Pulling the seed crystal ribbon away from the melt results in continuous growth of the crystal ribbon.

Thornhill, J. W.↗

NASA NTRS2001

Stability of Detached Grown Germanium Single Crystals

Detachment of the melt meniscus from the crucible during semiconductor Bridgman growth experiments has been observed in recent years, especially under microgravity experiments. Under earth conditions, the hydrostatic pressure counteracts the mechanism, whereby it is more difficult to achieve detached Bridgman growth. Attempts to get stable detached growth under terrestrial conditions have been discussed in the literature and have been the subject of recent experiments in our own group. The advantage of crystals grown without wall contact is obvious: In general, they possess a higher crystal quality than conventional Bridgman grown crystals with wall contact. However, due to the interaction of different parameters such as the wetting behavior of the melt with the crucible, and the dependence of the growth angle with the shape of the melt meniscus, the mechanism leading to detachment is very complicated and not completely understood. We have grown several doped and undoped Germanium crystals with the detached Bridgman and the normal Bridgman growth technique. Pyrolytic boron nitride containers were used for all growth experiments. In the detached grown crystals the typical gap thickness between the pBN crucible and the crystal is in the range of 10 to 100 micrometers, which was determined by performing profilometer measurements. Etch pit density measurements were also performed and a comparison between detached and attached grown crystals will be given. An interesting feature was detected on the surface of a detached grown crystal. Strong surface striations with an average axial distance of 0.5 mm were observed around the whole circumference. The maximum fluctuation of the gap thickness is in the range of 5-10 micrometers. These variations of the detached gap along the crystal axis can be explained by a kind of stiction of the melt/crucible interface and thus by a variation of the meniscus shape. This phenomenon leading to the fluctuation of the gap thickness will be discussed in detail.

Schweizer, M.↗

NASA NTRS2002

Stability of Detached Grown Germanium Single Crystals

Detachment of the melt meniscus from the crucible during semiconductor Bridgman growth experiments has been observed in recent years especially, under microgravity experiments. Under earth conditions, the hydrostatic pressure counteracts the mechanism, whereby it is more difficult to achieve detached Bridgman growth. Attempts to get stable detached growth under terrestrial conditions have been discussed in the literature and have been the subject of recent experiments in our own group. The advantage of crystals grown without wall contact is obvious: In general, they possess a higher crystal quality than conventional Bridgman grown crystals with wall contact. However, due to the interaction of different parameters such as the wetting behavior of the melt with the crucible, and the dependence of the growth angle with the shape of the melt meniscus, the mechanism leading to detachment is very complicated and not completely understood. We have grown several doped and undoped Germanium crystals with the detached Bridgman and the normal Bridgman growth technique. Pyrolytic boron nitride containers were used for all growth experiments. In the detached grown crystals the typical gap thickness between the pBN crucible and the crystal is in the range of 10 to 100 microns, which was determined by performing profilometer measurements. Etch pit density measurements were also performed and a comparison between detached and attached grown crystals will be given. An interesting feature was detected on the surface of a detached grown crystal. Strong surface striations with an average axial distance of 0.5mm were observed around the whole circumference. The maximum fluctuation of the gap thickness is in the range of 5-10 microns. These variations of the detached gap along the crystal axis can be explained by a kind of stiction of the melt/crucible interface and thus by a variation of the meniscus shape. This phenomenon leading to the fluctuation of the gap thickness will be discussed in detail.

Schweizer, M.↗

NASA NTRS2009

On Favorable Thermal Fields for Detached Bridgman Growth

The thermal fields of two Bridgman-like configurations, representative of real systems used in prior experiments for the detached growth of CdTe and Ge crystals, are studied. These detailed heat transfer computations are performed using the CrysMAS code and expand upon our previous analyses [14] that posited a new mechanism involving the thermal field and meniscus position to explain stable conditions for dewetted Bridgman growth. Computational results indicate that heat transfer conditions that led to successful detached growth in both of these systems are in accordance with our prior assertion, namely that the prevention of crystal reattachment to the crucible wall requires the avoidance of any undercooling of the melt meniscus during the growth run. Significantly, relatively simple process modifications that promote favorable thermal conditions for detached growth may overcome detrimental factors associated with meniscus shape and crucible wetting. Thus, these ideas may be important to advance the practice of detached growth for many materials.

Stelian, Carmen↗

NASA NTRS2009

Stability of Detached Solidification

Bridgman crystal growth can be conducted in the so-called "detached" solidification regime, where the growing crystal is detached from the crucible wall. A small gap between the growing crystal and the crucible wall, of the order of 100 micrometers or less, can be maintained during the process. A meniscus is formed at the bottom of the melt between the crystal and crucible wall. Under proper conditions, growth can proceed without collapsing the meniscus. The meniscus shape plays a key role in stabilizing the process. Thermal and other process parameters can also affect the geometrical steady-state stability conditions of solidification. The dynamic stability theory of the shaped crystal growth process has been developed by Tatarchenko. It consists of finding a simplified autonomous set of differential equations for the radius, height, and possibly other process parameters. The problem then reduces to analyzing a system of first order linear differential equations for stability. Here we apply a modified version of this theory for a particular case of detached solidification. Approximate analytical formulas as well as accurate numerical values for the capillary stability coefficients are presented. They display an unexpected singularity as a function of pressure differential. A novel approach to study the thermal field effects on the crystal shape stability has been proposed. In essence, it rectifies the unphysical assumption of the model that utilizes a perturbation of the crystal radius along the axis as being instantaneous. It consists of introducing time delay effects into the mathematical description and leads, in general, to stability over a broader parameter range. We believe that this novel treatment can be advantageously implemented in stability analyses of other crystal growth techniques such as Czochralski and float zone methods.

Mazuruk, K.↗

NASA NTRS2002

Fluid Interfaces of Triangular Containers in Reduced Gravity Environments

Capillary dominated fluid dynamics will be examined in a reduced-gravity environment onboard the KC-135; in particular, the behavior of the lower portion of the meniscus in triangular tank geometries. Seven clear acrylic tanks were constructed to view seven angles of the four geometries. Silicon oil with two different viscosities, 2cs and 5cs silicon oil, were used on different days of the flight. Six tanks and one control tank are filled with a certain viscosity fluid for each flight day. During each parabola, three tanks are tested at time. The experimental tanks are exchanged between parabola sets on the KC-135. The 60deg -60deg -60deg control tank is viewed throughout the flight. To gather data, two digital video cameras and one digital still camera are placed perpendicular the viewing surface. To provide a greater contrast in the meniscus, an EL backlighting sheet was used to backlight the tanks. These images and video are then digitized, passed through NASA's mini-tracker software, and compared to a theory published my M. M. Weislogel, "Fluid Interface Phenomena in a Low-Gravity Environment: Recent Results from Drop Tower Experimentation." By focusing on a lower portion of the meniscus and using longer periods of reduced gravity, this experiment may confirm that a stationary point exists on the fluid surface. This information will enable better designing of propellant management devices, especially satellite propellant refilling and gas venting. Also, biological and material processing systems in reduced gravity environments will benefit from this data.

Guttromson, Jayleen↗

NASA NTRS2015

Crystal Growth of Germanium-Silicon Alloys on the ISS

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The experiments are part of the investigation "Influence of Containment on the Growth of Silicon-Germanium" (ICESAGE). The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. This meniscus can exist over a much larger range of processing parameters in microgravity and the meniscus is more stable under microgravity conditions. The plans for the flight experiments will be described.

Volz, M. P.↗

NASA NTRS2017

Growth Angle: A Microscopic View

A microscopic continuum mechanical model of the growth angle is proposed. It is based on the van der Waals type framework that is used for surface force phenomena. The obtained augmented Laplace type integro-differential equations are, in general, difficult to analyze. Here we focused primarily on the particular case of equal melt and crystal surface energies. We derived an approximate equation for the meniscus shape, and obtained an analytical relationship between the contact and the growth angle. Interestingly, the same result can be obtained using the macroscopic model of Herring. The case of a macroscopically sharp corner is also considered. For this case, the macroscopic angle is not defined and it can be any angle between the contact angles of both flat surfaces. The microscopic model yields the smooth shape for the meniscus that also is not unique, but depends on the initial position of the meniscus.

Mazuruk, Konstantin↗