Current Projects

1. Detached Melt and Vapor Growth of InI in SUBSA Hardware

Supported by CASIS/NASA 3/1/2015 to 12/31/2017
Six single crystals of Indium Iodide (InI), will be grown at the International Space Station (ISS) using melt growth and vapor growth techniques. Both growth methods will utilize existing SUBSA hardware. Superior crystalline perfection and detector performance are expected, as a result of the absence of gravity-driven convection and stresses caused by the weight of the growing material. The SUBSA hardware will allow real-time visualization of both growth processes. InI has a low melting point of 365°C. Four samples will be processed by melt growth and four by vapor growth.
The SUBSA furnace was launched back to space in October of 2016.
Our samples (see Figure 1) were launched on April 18, 2017. Link to social media.
Figure 1. CASIS InI melt growth flight samples

2. Diffusion Coefficients of Dopants in Si and Ge Meltsß

To be supported by NASA 8/1/2017 to 12/31/2021

Diffusion coefficients in Si melts

a. Kodera (1963): CZ data and BPS theory

The key handbooks, “Technological Data of Silicon and Germanium” (Landolt-Bornstein, Vol. 17c [1]) and “Floating-Zone Silicon” [2], present the values of diffusion coefficients reported by H. Kodera (1963) [3]. Diffusion coefficient were calculated by applying the BPS model [4,5] to the segregation data obtained in Czochralski (CZ) crystal growth experiments. However, the following should be noted:
  • The CZ experiments were done at low RPM so that. Therefore, natural convection ‘boosted’ mass transfer, yielding inflated D-values.
  • In calculations, Kodera used for Si-melt “estimated” kinematic viscosity ν = 0.0106 cm/s2, while the acutal value is ν = 0.0035 cm/s2 (see Figure 2 from Glazov).
Figure 2. Diffusion coefficients of impurities in silicon melt plotted against tetrahedral covalent radii.
a) The diffusion coefficients in molten Si measured by Kodera [3] and b) reproduced by Keller and Mühlbauer “Floating-Zone Silicon” [2].

b. Turovskii (1962): CZ data and BPS theory

Turovskii [6] measured kinematic viscosity of Si, and obtained a solid value: ν=0.0028 cm/s2 (see Figure 2 ). Yet, the CZ experiments were conducted at low RPM, where Re2 ~ Grd. Note that Turovskii D-values depend on RPM (see Figure 3 below) which illustrates the fact that natural convection is not negligible. Therefore, the diffusion coefficients in [3] are inaccurate and ‘inflated’ by buoyancy driven flows.
Figure 3. D-values for Si-melts, reported by Turovskii (1962) [6].

c. Shashkov and Gurevich (1968): direct reservoir-capillary technique

Figure 4 shows the D-values measured by Shashkov and Gurevich (1968) [7] using the capillary-reservoir method. The data are plotted as a function of the tetrahedral covalent radius:
Figure 4. D-values of impurities in molten silicon reported by Shashkov and Gurevich [7].
a) Table of values. b) D-values as a function of the tetrahedral covalent radius, r0. Dashed lines are Kodera’s diffusion coefficients (1963) [3], calculated from CZ segregation data.

Discussion

The divergence between the capillary tube “direct” data (Shashkov and Gurevich [7]) and “indirect” CZ data (Kodera [3]) is significant. For the group III elements (B, Al, Ga, In, Tl), Kodera’s data have erroneous trend. Small atoms are expected to diffuse faster (see Stokes–Einstein eq. (1)). Yet, in Figure 3, thallium and indium diffuse faster than boron (DIn ~ 3 DB).

The key error made by Kodera was employing the BPS model at relatively low RPM. In BPS, natural convection is ignored [8,9]. Gravitational acceleration g does not appear in BPS model. The high D-values were reported at low RPM, where natural convection “enhanced” diffusion.

Unfortunately, Kodera did not report the crystal diameter, melt size, and the temperature difference ΔT in the melt, so that the level of natural convection can not be determined.


In summary:
The diffusion coefficients of impurities in molten Si, listed in the key handbooks, were obtained in indirect CZ experiments by Kodera [3] and are inaccurate because:

  • The diffusion coefficients have erroneous trend.
  • The “inflated” D-values were obtained at low rotation rates (5 and 10, 12 RPM) where natural convection dominates.
  • The BPS model is based on the forced laminar flow solution produced by an infinite rotating disc. Buoyancy driven flow (natural convection) is ignored, although it is dominant [8].
  • Schmidt number, Sc = ν/D is assumed to be infinite, although it is typically 10∠Sc∠30.
Furthermore:
  • Erroneous viscosity was assumed: for silicon νSi = 0.0106 [cm2/s]; for germanium,
    νGe = 0.0055 [cm2/s]. According to Glasov [10] and Kakimoto [2], νSi = 0.0035 [cm2/s] and νGe = 0.00135 [cm2/s]
For Ga-doped Ge, the range of D-values are from D=2.810-5 cm2/s (Garandet [11]) to D=2.110-4 cm2/s (Bourett [12]).

Key Hypothesis and Goals

Virtually all D-values reported in the literature, obtained by direct or indirect methods, have some degree of inaccuracy because of buoyancy driven natural convection. Better data can be generated by
a) using small diameter ampoules in Bridgman growth in microgravity, and by using
b) high rotation rates and precise modeling/calculations in CZ experiments.

Czochralski crystal growth at high rotation rate ω and small crystal

Growth experiments will be conducted using our ADL High Pressure Czochralski furnace (see Figure 5).

In the pioneering BPS paper [4,5], Burton et al. conducted Czochralski crystal growth experiments, growing d=2 cm crystals at high rotation rate ω (55 RPM to 1440 RPM). As noted earlier, they must have achieved steady symmetric laminar flow - unaffected by buoyancy forces. Remarkably, using their BPS equation, they reported the lowest values of the diffusion coefficients of Ga and Sb in Ge melts.

Considering our expertise in Czochralski growth and superb equipment available, we will grow doped crystals of Ge and Si, at 60 RPM, 120M RPM and 180 RPM. Then,
D-values will be calculated using the BPS, other models including our recent model presented in [8], and FE analysis. The goals of the CZ experiments are:

  • Measure indirectly the diffusion coefficients of B, Ga, and Si in Ge.
  • Measure indirectly the diffusion coefficients of B, P, Ga, Sb, In in Si.
  • To develop a ground facility at IIT for direct measurement of diffusion coefficients.
  • To use this facility determine the diffusion coefficients in molten Ge and Si. in the future.
Figure 5. Two high pressure ADL Czochralski pullers in Prof. Ostrogorsky’s laboratory at IIT.

References

  • [1] A. Muhlbauer, Technological Data of Silicon and Germanium, Landolt-Bornstein, Vol. 17c (Springer, Berlin, 1984).
  • [2] W. Keller and A. Mühlbauer, Preparation and Properties of Solid State Materials 5, Floating- Zone Silicon, Marcel Dekker, Inc. (1981).
  • [3] H. Kodera, Jpn. J. Appl. Phys. 2 (1963) 212.
  • [4] J.A. Burton, R.C. Prim, W.P. Slichter, Journal of Chemical Physics 21 (1953) 1987.
  • [5] J.A. Burton, R.C. Prim, W.P. Slichter, The Journal of Chemical Physics 21 (1953) 1987.
  • [6] B.M. Turovskii, Russian Journal of Physical Chem. 36, No.8 (1962) 983-985.
  • [7] Yu.M. Shaskov and V.M. Gurevich, Russian J. Physical Chemistry 24 (1968) 1082-1083.
  • [8] "Segregation and component distribution” A.G. Ostrogorsky and M.E. Glicksman, Handbook of Crystal Growth, Vol. II, Second Edition, P. Rudolph, Editor (2015) 995–1047.
  • [9] A.G. Ostrogorsky, “Effective convection coefficient for porous interface and solute segregation”, J. Crystal Growth 348 (2012) 97–105.
  • [10] Science Concept Review (SCR) Document for the SUBSA investigation (1998).
  • [11] J.P. Garandet, International Journal Of Thermophysics 28 (2007) 1285–1303.
  • [12] E. Bourret, J.J. Favier, O. Bourrel, Journal of the Electrochemical Society 128 (1981) 2438.





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