Silicon-on ceramic process. Silicon sheet growth and device development for the large-area silicon sheet and cell development tasks of the low-cost solar array project. Quarterly report No. 12, April 2, 1979-June 29, 1979 Page: 56 of 70
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(35)
= kA/j£ = pvL sin20
(36)
0 is approximately constant,
4
- T ). Equating this to the
A - ea(T 4 - T 4) • t/k
r o
and
kA/t = pvL sin 0 cos 0
4) The radiated flux density from the surface y =
provided that A is small, and equal to ea(Tp
vertical component in (3) gives
which establishes Equation (30) and confirms that A is small (A = 4. 9 deg
if t “ 0. 1 cm).
5) Combining Equations (30) and (36) also givt
sin0 cos0 a; 0«a ea (Tp4 - TQ4)/pvL
which establishes Equation (31). Finally, since 0 =* t/H, Equation (31)
may be rewritten
vt - ea(Tp4 - To4) • £/pL
or vt =- 0. 005 if £ =- 1 cm. (It has been already noted that l is somewhat
arbitrary. ) Since 0. 005 << 0. 97, the condition (24) for neglecting the
pcv term is satisfied.
Matching the Temperature Distribution to the Downstream Region
As observed previously, the component of latent heat carried downstream is much smaller
2 4
in asymmetric than in symmetric growth. In fact, since J = pvL sin 6 =- [caCIV, -
4 2 X p
Tq )] /pvLfrom Equations (35) and (31), the conservation principle for the wedge model
becomes
[eo(TF4 - To4)]2/pvLk = q^ ^ T (37)
F
For a cooling environment of 3 00°K along the whole silicon ribbon, q was found to be in the
102 to 104 deg/cm range (Figure 19), whereas the left-hand side of Equation (37) is much
smaller (e. g. , about 5 deg/cm for v = 0. 1 cm/sec). It is obvious that the cold downstream
environment is not compatible with the wedge model. We will see in more detail later
(Figure 26) what happens when we try to force the cold downstream environment on the
wedge model.
46
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Chapman, P.W.; Zook, J.D.; Heaps, J.D.; Grung, B.L.; Koepke, B. & Schuldt, S.B. Silicon-on ceramic process. Silicon sheet growth and device development for the large-area silicon sheet and cell development tasks of the low-cost solar array project. Quarterly report No. 12, April 2, 1979-June 29, 1979, report, July 31, 1979; United States. (https://digital.library.unt.edu/ark:/67531/metadc1065830/m1/56/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.