Volz, M. P. — Page 2

NASA NTRS2014

Behavior of Particle Depots in Molten Silicon During Float-Zone Growth in Strong Magnetic Fields

Solar cells made from directionally solidified silicon cover 57% of the photovoltaic industry's market [1]. One major issue during directional solidification of silicon is the precipitation of foreign phase particles. These particles, mainly SiC and Si3N4, are precipitated from the dissolved crucible coating, which is made of silicon nitride, and the dissolution of carbon monoxide from the furnace atmosphere. Due to their hardness and size of several hundred micrometers, those particles can lead to severe problems during the wire sawing process for wafering the ingots. Additionally, SiC particles can act as a shunt, short circuiting the solar cell. Even if the particles are too small to disturb the wafering process, they can lead to a grit structure of silicon micro grains and serve as sources for dislocations. All of this lowers the yield of solar cells and reduces the performance of cells and modules. We studied the behaviour of SiC particle depots during float-zone growth under an oxide skin, and strong static magnetic fields. For high field strengths of 3T and above and an oxide layer on the sample surface, convection is sufficiently suppressed to create a diffusive like regime, with strongly dampened convection [2, 3]. To investigate the difference between atomically rough phase boundaries and facetted growth, samples with [100] and [111] orientation were processed.

Jauss, T.↗

NASA NTRS2013

Evolution of the Shape of Detached GeSi Crystals in Microgravity

A series of GeSi crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. An objective of these experiments is to understand the mechanisms of detached Bridgman growth, a process in which a gap exists between the growing semiconductor crystal and the crucible wall. Crystals grown without wall contact 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. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus.

Volz, M. P.↗

NASA NTRS2013

Evolution of the Shape of Detached GeSi Crystals in Microgravity

A series of GeSi crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. An objective of these experiments is to understand the mechanisms of detached Bridgman growth, a process in which a gap exists between the growing semiconductor crystal and the crucible wall. Crystals grown without wall contact 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. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus.

Volz, M. P.↗

NASA NTRS2013

Crystal Shape Evolution in Detached Bridgman Growth

Detached (or dewetted) Bridgman crystal growth defines that process in which a gap exists between a growing crystal and the crucible wall. Existence of the gap provides several advantages, including no sticking of the crystal to the crucible wall, reduced thermal and mechanical stresses, reduced dislocations, and no heterogeneous nucleation by the crucible. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus. The effect of a tapered crucible on dynamic stability is also described

Volz, M. P.↗

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

Crystal Shape Evolution in Detached Bridgman Growth

Detached (or dewetted) Bridgman crystal growth defines that process in which a gap exists between a growing crystal and the crucible wall. Existence of the gap provides several advantages, including no sticking of the crystal to the crucible wall, reduced thermal and mechanical stresses, reduced dislocations, and no heterogeneous nucleation by the crucible. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus. The effect of a tapered crucible on dynamic stability is also described.

Volz, M. P.↗

NASA NTRS2012

Influence of Containment on the Growth of Silicon-Germanium: A Materials Science Flight Project

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 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. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction. The plans for the flight experiments will be described.

Volz, M. P.↗

NASA NTRS2012

Influence of Containment on the Growth of Silicon-Germanium: A Materials Science Flight Project

This investigation involves the comparison of results achieved from three types of crystal growth of germanium and germanium-silicon alloys: (1) Float zone growth (2) Bridgman growth (3) Detached Bridgman growth crystal The fundamental goal of the proposed research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon (GeSi) crystals (silicon concentration in the solid up to 5 at%) for three different growth configurations in order to quantitatively assess the improvements of crystal quality possible by detached growth.

Volz, M. P.↗

NASA NTRS2012

Reduction of Defects in Germanium-Silicon

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. Ge1-xSix crystals have been repeatedly grown detached in pBN crucibles. 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. Experiments have also been conducted to assess the effect of pressure differential across the meniscus in sealed crucibles. The experiments were in agreement with calculations which predicted that stable detachment will only occur in crucibles with a high wetting angle and over a relatively narrow range of pressure differential. Calculations also indicate that the conditions for stable detached growth are greatly expanded in a microgravity environment.

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 NTRS2011

On Transients in Detached Bridgman Growth

In detached Bridgman growth, a gap exists between the growing crystal and the crucible wall. According to crystal shape stability theory, only specific gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. The transient shapes are calculated assuming that the growth angle is constant. Anisotropy and dynamic contact angle effects are considered. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. However, heat transfer will influence the crystal-melt interface shape. The local angles and the crystal-melt-vapor triple junction are analyzed and the applicability of the Herring formula is discussed. A potential microgravity experiment is proposed which would enhance our understanding of the detached growth dynamic stability problem.

Mazuruk, K.↗

NASA NTRS2011

Material Development of Faraday Cup Grids for the Solar Probe Plus Mission

The Solar Probe Plus mission will launch a spacecraft to the Sun to study it's outer atmosphere. One of the instruments on board will be a Faraday Cup (FC) sensor. The FC will determine solar wind properties by measuring the current produced by ions striking a metal collector plate. It will be directly exposed to the Sun and will be subject to the temperature and radiation environment that exist within 10 solar radii. Conducting grids within the FC are biased up to 10 kV and are used to selectively transmit particles based on their energy to charge ratio. We report on the development of SiC grids. Tests were done on nitrogen-doped SiC starting disks obtained from several vendors, including annealing under vacuum at 1400 C and measurement of their electrical properties. SiC grids were manufactured using a photolithographic and plasma-etching process. The grids were incorporated into a prototype FC and tested in a simulated solar wind chamber. The energy cutoffs were measured for both proton and electron fluxes and met the anticipated sensor requirements.

Volz, M. P.↗

NASA NTRS2010

Meniscus Shapes in Detached Bridgman Growth

In detached Bridgman crystal growth, most of the melt is in contact with the ampoule wall, but the crystal is separated from the wall by a small gap, typically 1-100 micrometers. A liquid free surface, or meniscus, bridges across this gap at the position of the melt-crystal interface. Meniscus shapes have been calculated for the case of detached Bridgman growth in cylindrical ampoules by solving the Young-Laplace equation. Key parameters affecting meniscus shapes are the growth angle, contact angle of the meniscus to the ampoule wall, the pressure differential across the meniscus, and the Bond number, a measure of the ratio of gravitational to capillary forces. In general, for specified values of growth and contact angles, solutions exist only over a finite range of pressure differentials. For intermediate values of the Bond number, there are multiple solutions to the Young-Laplace equations. There are also cases where, as a function of pressure differential, existence intervals alternate with intervals where no solutions exist. The implications of the meniscus shape calculations on meniscus stability are discussed.

Volz, M. P.↗

NASA NTRS2010

Linear Stability of Binary Alloy Solidification for Unsteady Growth Rates

An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.

Mazuruk, K.↗

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 NTRS2009

Numerical Optimization of the Thermal Field in Bridgman Detached Growth

The global modeling of the thermal field in two vertical Bridgman-like crystal growth configurations, has been performed to get optimal thermal conditions for a successful detached growth of Ge and CdTe crystals. These computations are performed using the CrysMAS code and expand upon our previous analysis [1] that propose a new mechanism involving the thermal field and meniscus position to explain stable conditions for dewetted Bridgman growth. The analysis of the vertical Bridgman configuration with two heaters, used by Palosz et al. for the detached growth of Ge, shows, consistent with their results, that the large wetting angle of germanium on boron nitride surfaces was an important factor to promote a successful detached growth. Our computations predict that by initiating growth much higher into the hot zone of the furnace, the thermal conditions will be favorable for continued detachment even for systems that did not exhibit high contact angles. The computations performed for a vertical gradient freeze configuration with three heaters representative of that used for the detached growth of CdTe, show favorable thermal conditions for dewetting during the entirely growth run described. Improved thermal conditions are also predicted for coated silica crucibles when the solid-liquid interface advances higher into the hot zone during the solidification process. The second set of experiments on CdTe growth described elsewhere has shown the reattachment of the crystal to the crucible after few centimeters of dewetted growth. The thermal modeling of this configuration shows a second solidification front appearing at the top of the sample and approaching the middle line across the third heater. In these conditions, the crystal grows detached from the bottom, but will be attached to the crucible in the upper part because of the solidification without gap in this region. The solidification with two interfaces can be avoided when the top of the sample is positioned below the middle position of the third furnace.

Stelian, C.↗

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 NTRS2008

Interface Shape Control using Localized Heating during Bridgman Growth

Numerical calculations were performed to assess the effect of localized radial heating on the melt-crystal interface shape during vertical Bridgman growth. System parameters examined include the ampoule, melt and crystal thermal conductivities, the magnitude and width of localized heating, and the latent heat of crystallization. Concave interface shapes, typical of semiconductor systems, could be flattened or made convex with localized heating. Although localized heating caused shallower thermal gradients ahead of the interface, the magnitude of the localized heating required for convexity was less than that which resulted in a thermal inversion ahead ofthe interface. A convex interface shape was most readily achieved with ampoules of lower thermal conductivity. The conditions under which convection in the melt must be considered were determined.

Volz, M. P.↗