CAPILLARY  THEORY  AND  CRYSTALLIZATION  MODELING  FOR  SOLAR  CELLS  

   

GERMAN  OLIVEROS  

 ADVISORS:  ERIK  YDSTIE  (CHEME)  AND  SRIDHAR  SEETHARAMAN  (MSE)  

 ESI  MEETING  2013  

MOTIVATION  

Czochralski  Process  

Sawing   accounts   for   30%   of  wafer   fabrica4on   costs   and  generates   up   to   50%   of  material  losses  

Diamond  Wire  CuMng  

The  missing  link:  growing  crystals  directly  from  the  melt  

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HORIZONTAL  RIBBON  GROWTH  

Picture  taken  from:  P.  Daggolu.,  A.  Yeckel,  C.E.  Bleil,  and  J.J.  Derby.  “Thermal-­‐capillary  analysis  of  the  horizontal  ribbon  growth  of  silicon  crystals”.  Journal  of  Crystal  Growth,  355:129-­‐139,2012.  

Advantages  

1.  High  growth  rates  

2.  Produc^on  of  ribbons  with  

poten^ally  large  surface  areas  

3.  Shaping  of  the  wafer  does  not  

require  a  die  

 

Opera4onal  Difficul4es  

1.  Dendri^c  and  uneven  growth  

2.  Down-­‐growth  

3.  Material  supply  

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HORIZONTAL  RIBBON  GROWTH:  THE  MISSING  LINK?  

•  First  con^nuous  design  patented  

by  William  Shockley  in  1959:  

 

 

Germanium  ribbons   Ice  ribbons  

•  First  experimental  

work  published  by  

Carl  Bleil  in  1968:  

•  Improvements  to  the  process  and  

produc^on  of  a  silicon  ribbon  

reported  by  Bossi  Kudo  in  1979:  

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HORIZONTAL  RIBBON  GROWTH:  THE  MISSING  LINK?  

Ice  ribbons  at  CMU   Bleil’s  Ice  ribbons  

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HORIZONTAL  RIBBON  GROWTH  

Despite  more  than  50  years  of  efforts,  many  technical  problems  need  to  be  solved  in  order  to  

guarantee   a   con^nuous   and   stable   ribbon   produc^on.   In   his   seminal   inves4ga4on,   Kudo  

reported  the  following  issues:  

Melt  spill-­‐over   Freezing  of  the  ribbon  to  the  crucible  

Dendri4c  growth  

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AVOIDING  MELT-­‐SPILL  OVER  

y

x h2

h1 β

θ

σ

Melt

l t

Crucible

Ribbon Theory  of  capillarity  (Young-­‐Laplace)  

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AVOIDING  MELT-­‐SPILL  OVER  

0 3 6 9 12 150

20

40

60

80

100

120

140

160

180

β [Degrees]

θ [D

egre

es]

l = 30 cm

0 3 6 9 12 150

20

40

60

80

100

120

140

160

180

β [Degrees]

θ [D

egre

es]

l = 5 cm

Sta4cally  Stable  

Meniscus   Sta4cally  Stable  Meniscus  

Meniscus  does  not  exist  

Meniscus  freezes  to  crucible  

Meniscus  does  not  exist  

Meniscus  freezes  to  crucible  

Molten  silicon  si9ng  on  a  graphite  crucible  (300  microns  wafer)  

Meniscus  recedes  from  corner  

Melt  spills  over   Melt  spills  over  

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AVOIDING  DENDRITIC  GROWTH  

Apply  Perturba^on  Crystal  

Melt   I(y,t)  =  I(y,t)  +  δ(t)  sin  (ωx)    

Crystal  

Melt  

Grows?  

Decays?  

Crystal  

Melt  

Crystal  

Melt  

Mullins-­‐Sekerka  Stability  Theory:  

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AVOIDING  DENDRITIC  GROWTH  

"↓$ &↓'$ ()↓$   /(, = -↓$ (↓↑2 )↓$ /(/↑2  

"↓0 &↓'0 ()↓0   /(, = -↓0 (↓↑2 )↓0 /(/↑2   (&↓0   /(, =1(↓↑2 &↓0 /(/↑2  

&↓$ =2&↓0 

-↓$ ()↓$ /(/ − -↓0 ()↓0 /(/ =ρ∆345/4,  −1(&↓0 /(/ = 45/4, (&↓0∗ − &↓$∗ ) )↓0 = )↓8 + 4)↓9 /4& &↓0 

Solid  

Interface  Condi^ons  

-()↓$   /(, =σε()↑4 − )↓↑4 ↓∞ )

(&↓$   /(: =0

Top  

Vy(y,t)  

Qs(y,t)  

Ql(y,t)  

ΔH  

Ny(y,t)

Liquid  

Qrad

“Hot”  (or  Insulated)  

(&↓$   /(: =0

)= )↓$  Bokom  

ASSUMPTIONS  

a)  Unidirec^onal  solidifica^on  b)  Neglect  convec^on  in  the  melt  

“Cold”  

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AVOIDING  DENDRITIC  GROWTH  

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AVOIDING  DENDRITIC  GROWTH  

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AVOIDING  DENDRITIC  GROWTH  

Apply  Perturba^on  Crystal  

Melt   I(y,t)  =  I(y,t)  +  δ(t)  sin  (ωx)    

Crystal  

Melt  

Grows?  

Decays?  

Crystal  

Melt  

Crystal  

Melt  

0 5 10 15 20 25 30

-0.5

-0.4

-0.3

-0.2

-0.1

0

Fδ

Position of the interface [mm] 13

THANKS  

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