Solid State Chemistry of Energy Conversion and Storage

7 Recrystallization of Semiconducting Polycrystalline Ribbons Using the

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Peltier Effect

S. VOJDANI and R. HASHEMIAN Materials and Energy Research Center, Arya Mehr University of Technology, P.O. Box 41-2927, Tehran, Iran

A new approach to zone refining thin semiconductor ribbons or films necessary for the production of low-cost solar cells is investigated using the Peltier effect. The results indicate that under certain conditions the Peltier current tends to stabilize the freezing interface allowing an increase in the grain size of a thin film.

/ C o m m e r c i a l p r o d u c t i o n of s i l i c o n solar cells r o u t i n e l y y i e l d s h i g h l y ^

r e l i a b l e devices h a v i n g a d e q u a t e

(~12%)

efficiencies.

These de

v i c e s h a v e b e e n d e s i g n e d t o operate i n t h e s p a c e e n v i r o n m e n t a n d h a v e p r o v e d v e r y s u i t a b l e f o r this a p p l i c a t i o n . H o w e v e r , f o r t e r r e s t r i a l a p p l i cations t h e y h a v e a serious d e f e c t — t h e i r cost is too h i g h b y a t least o n e o r d e r of m a g n i t u d e . T h e most i m p o r t a n t factors i n t h e d e v i c e cost a r e t h e expensive p r o d u c t i o n of l a r g e s i n g l e - c r y s t a l boules a n d t h e w a f e r i n g o f these crystals t o g i v e t h i n slices s u i t a b l e f o r use i n devices. T w o processes have been considered for producing cheap wafers: s i n g l e crystals i n t h e f o r m o f t h i n

ribbons

( a ) the growth of

so that e x p e n s i v e w a f e r i n g is

a v o i d e d ( J ) , a n d ( b ) t h e d e p o s i t i o n o f films o n s u i t a b l e substrates b y heteroepitaxial t e c h n i q u e s — C V D , sputtering, evaporation ( 2 ) , a n d more recently L P E ( 3 ) .

H e t e r o e p i t a x i a l films g e n e r a l l y give l o w efficiency

w h e n u s e d i n solar cells b e c a u s e of a r e d u c t i o n i n o p e n - c i r c u i t v o l t a g e a n d m i n o r i t y c a r r i e r l i f e t i m e associated

with

t h e presence

of

grain

boundaries. H o w e v e r , i f t h e g r a i n size is sufficiently l a r g e ( 4 , 5 ) (e.g., f o r S i , 1 0 0 - 1 0 0 0 ^ m ) , a d e q u a t e efficiency is o b t a i n e d . T h e p r o d u c t i o n of s i l i c o n solar cells b y t h i n o r t h i c k film t e c h n i q u e s w i l l p r o b a b l y r e q u i r e a p r o c 134

Goodenough and Whittingham; Solid State Chemistry of Energy Conversion and Storage Advances in Chemistry; American Chemical Society: Washington, DC, 1977.

7.

vojDANi

Semiconducting

AND HASHEMiAN

Polycrystalline

essing step that enlarges the c r y s t a l l i t e size i n the

film.

135

Ribbons

Two

techniques

h a v e a l r e a d y b e e n suggested for this p r u p o s e : c r y s t a l l i z a t i o n of S i films b y means of a s c a n n i n g e l e c t r o n or laser b e a m ( 6 ) a n d heat t r e a t m e n t of C V D - g r o w n S i films i n a n i n e r t a t m o s p h e r e ( 7 ) .

Another alternative w i l l

b e passage of m o l t e n z o n e ( z o n e r e f i n i n g ) across t h e film u n d e r

con

t r o l l e d c o n d i t i o n s to increase the g r a i n size. F o r t h e p u r p o s e of z o n e r e f i n i n g a t h i n p o l y c r y s t a l l i n e

film,

four


problems must be considered: (a)

the m o l t e n z o n e m u s t b e v e r y n a r r o w to p r e v e n t t h e b r e a k - u p

of t h e l i q u i d i n t o globules b e c a u s e of surface t e n s i o n , unless t h e l i q u i d w e t s the substrate (e.g., S i wets c a r b o n ) ; (b)

the molten semiconductor

must not be contaminated b y

the

substrate; (c)

the m o l t e n z o n e m u s t m o v e across the film w i t h u n i f o r m v e l o c i t y

so t h a t s o l i d i f i c a t i o n c a n p r o c e e d , i n a c o n t r o l l e d m a n n e r ; a n d (d)

the i n t e r f a c e b e t w e e n s o l i d a n d l i q u i d m u s t b e p l a n a r so t h a t ,

u p o n s o l i d i f i c a t i o n of t h e m o l t e n zone, a n i m p r o v e m e n t i n c r y s t a l l i t e size is a t t a i n e d . A c h i e v i n g a c c e p t a b l e results w i t h t h i n films d e m a n d s c o n t r o l of t h e z o n i n g process,

a n d this is difficult to a t t a i n i n a n i n h e r e n t l y s m a l l -

v o l u m e c r y s t a l l i z a t i o n process.

H e n c e i t is i n t e r e s t i n g to e x a m i n e the

p o s s i b i l i t y of u s i n g t h e P e l t i e r effect. S i n c e the t w o s o l i d - m e l t interfaces also constitute b o u n d a r i e s

between

phases

h a v i n g different e l e c t r i c a l

resistivities, the passage of a d i r e c t c u r r e n t t h r o u g h t h e s a m p l e

causes

P e l t i e r h e a t i n g at one interface a n d c o o l i n g at the other. T h i s c o u l d cause t h e z o n e to m o v e a n d has t h e a d v a n t a g e of l o c a l i z e d heat s u p p l y a n d e x t r a c t i o n p r e c i s e l y at the interfaces, f a c i l i t a t i n g c o n t r o l .

T h e process

w a s t r i e d m a n y years ago f o r b u l k crystals ( 8 ) b u t w a s d i s c a r d e d b e c a u s e a l a r g e c u r r e n t w a s n e e d e d f o r l a r g e - a r e a samples t o p r o v i d e

adequate

i n t e r f a c e h e a t i n g a n d c o o l i n g . T h i s l i m i t a t i o n is not i m p o r t a n t f o r z o n i n g t h i n films, a n d , a d d i t i o n a l l y , there is n o n e e d to p r o v i d e a l l t h e h e a t f o r z o n e m e l t i n g f r o m the d i r e c t c u r r e n t ; the s a m p l e c a n b e p l a c e d i n a f u r n a c e to p r o v i d e a u x i l i a r y h e a t i n g . T h e p u r p o s e o f u s i n g P e l t i e r c u r r e n t is t o a l l o w the z o n e w i d t h a n d p o s s i b l y t h e i n t e r f a c e t o p o l o g y to be stabilized. T h e r e m a i n d e r of this c h a p t e r presents a t h e o r e t i c a l a n d e x p e r i m e n t a l i n v e s t i g a t i o n of t h e s o l i d i f i c a t i o n process i n t h e presence

of a

direct

c u r r e n t as a first step t o w a r d s P e l t i e r z o n i n g . Theory A l l s y m b o l s u s e d i n this analysis are d e f i n e d i n t h e " N o m e n c l a t u r e " section.

T h e rate p e r u n i t a r e a at w h i c h P e l t i e r heat is d e l i v e r e d


136

SOLID S T A T E

CHEMISTRY

to ( o r e x t r a c t e d f r o m ) a s o l i d - l i q u i d i n t e r f a c e t h r o u g h w h i c h a d i r e c t c u r r e n t of d e n s i t y J is p a s s i n g is ( 9 ) p

Q

P

=

(1)

aT J» m

F o r t h e t h e o r e t i c a l analysis, a t h i n r i b b o n of s e m i c o n d u c t o r is c o n s i d e r e d as s h o w n i n F i g u r e 1. T h e s a m p l e is p l a c e d i n a c y l i n d r i c a l f u r n a c e a t


ζ

τ,

τ

2

Figure 1. A thin ribbon of semiconductor with the reference axes used for the theo retical modeling a m b i e n t t e m p e r a t u r e T . A d i r e c t c u r r e n t 7 is p a s s e d t h r o u g h i t , w h i l e A

t h e ends of t h e s a m p l e are k e p t a t t e m p e r a t u r e s T i a n d T

2

T h e r e l e v a n t heat b a l a n c e e q u a t i o n s a r e as f o l l o w s .

respectively.

I n the solid region

for u n i t v o l u m e :

Ks

U+

J.'p. -

j

w(T*

-

TV) =

c^ p8

(2)

I n the l i q u i d region for unit volume: +

(3)

A t the interface between solid a n d l i q u i d :

I n t h e f o r m u l a t i o n of E q u a t i o n s 2, 3, a n d 4 t h e f o l l o w i n g assumptions have been made: ( a ) T h e s a m p l e consists of s o l i d a n d l i q u i d regions. ( b ) H e a t loss f r o m t h e s a m p l e results f r o m r a d i a t i o n f r o m t h e s u r faces a n d c o n d u c t i o n t h r o u g h t h e ends o n l y .


7.

v o p A N i AND HASHEMiAN

Semiconducting

Polycrystalline

Ribbons

137

(c)

p a n d pi are c o n s i d e r e d constants.

(d)

T h e s a m p l e is s y m m e t r i c a l l y l o c a t e d i n t h e f u r n a c e w i t h r a d i a l

B

symmetry, a n d the ambient temperature T (e)

A

is constant.

T h e a m b i e n t t e m p e r a t u r e is close to t h e m e l t i n g p o i n t .

( f ) T h e t e m p e r a t u r e is constant a l o n g the y a n d ζ axes; o n l y v a r i a t i o n a l o n g the χ axis is c o n s i d e r e d . I n the r e g i o n of t h e m o l t e n z o n e t h e r e c a n b e n o v a r i a t i o n i n Τ a l o n g the χ axis b e c a u s e

of t h e

two-phase


condition. (g)

At χ =

0, Τ =

Tu at χ — α, Τ =

(h)

S t e a d y state c o n d i t i o n s exist.

T . 2

τ "κ

1200 1 0

4

1

1

8

12

1

1

.

16

20

24

1 —

28

χ (m)

Figure 2. Temperature profile across the sample as a function current. Peltier heating and cooling are neglected.

of


138

SOLID STATE

CHEMISTRY

U s i n g the a b o v e a s s u m p t i o n s , E q u a t i o n s 2, 3, a n d 4 w e r e

solved

c o m p u t a t i o n a l l y f o r g e r m a n i u m , since this m a t e r i a l w a s to b e u s e d , for convenience, i n initial experiments.

R e p r e s e n t a t i v e values u s e d f o r the

p a r a m e t e r s i n t h e equations are s h o w n i n t h e N o m e n c l a t u r e section.

The

solutions a l l o w e d the z o n e w i d t h a n d t h e completeness of one m e l t i n g to b e r e l a t e d to t h e e x p e r i m e n t a l c o n d i t i o n s u s e d a n d p a r t i c u l a r l y to t h e direct current

flowing.

Theoretical Modeling. Downloaded by UNIV OF SOUTHERN CALIFORNIA on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch007

semiconductor

ribbon

Passage of a c u r r e n t t h r o u g h a s a m p l e

of

c o n t a i n i n g a m o l t e n zone has t w o effects: i t w i l l

c h a n g e the z o n e w i d t h W

a n d t h e d e g r e e of m e l t i n g w i t h i n the zone.

T h i s l a t t e r is d e s c r i b e d i n terms of a p a r a m e t e r γ w h i c h w i l l b e a f u n c t i o n of d i s t a n c e a l o n g the χ axis; γ = 0 defines a s o l i d r e g i o n , γ =

1 a liquid

r e g i o n , a n d 0 < γ < 1 a r e g i o n of p a r t i a l m e l t , so t h a t , across the a r e a of t h e z o n e at a p o i n t x, t h e f r a c t i o n y(x)

of the area w i l l b e m o l t e n .

F i g u r e 2 shows the c a l c u l a t e d t e m p e r a t u r e profile a l o n g the s a m p l e f o r v a r i o u s currents w h e n P e l t i e r h e a t i n g a n d c o o l i n g are n e g e l e c t e d i n t h e c a l c u l a t i o n s . T h e changes are c a u s e d s i m p l y b y different levels of J o u l e h e a t i n g . T h e z o n e w i d t h d e p e n d s o n the t e m p e r a t u r e s Γι a n d a n d also, as s h o w n i n the figure, o n the c u r r e n t F i g u r e 3 shows the d e p e n d e n c e t e m p e r a t u r e s Γι a n d T

2

of zone w i d t h ( W )

(assumed equal)

T

2

flowing. a n d γ o n the

for three different c u r r e n t s .

A t the m e l t i n g p o i n t W is a b o u t 3 c m , b u t r e d u c i n g T

x

and T

2

to a b o u t

2 3 ° Κ b e l o w this v a l u e r e d u c e s W to less t h a n 1 m m . T h e w i d t h is a g a i n s h o w n to d e p e n d o n t h e c u r r e n t . T h e d e g r e e of m e l t i n g of t h e z o n e is d e t e r m i n e d b y the c u r r e n t o n l y ( f o r g i v e n a m b i e n t t e m p e r a t u r e )

and

n o t b y the t e m p e r a t u r e at t h e ends of the s a m p l e . T h e d e p e n d e n c e W

of

a n d γ o n a m b i e n t t e m p e r a t u r e is s h o w n i n F i g u r e 4, w h e r e b o t h are

seen to decrease as T

A

decreases.

T h u s i n c o m p l e t e m e l t i n g of t h e z o n e w i t h t h e passage of c u r r e n t has b e e n o b s e r v e d a n d p r e d i c t e d f r o m the m a t h e m a t i c a l m o d e l . T h e reason f o r this p h e n o m e n o n is associated w i t h the different resistivities of t h e m e l t a n d the s o l i d (pi'.p = B

1:8 f o r G e ) , w h i c h , i n t h e event of i n c o m p l e t e

z o n e m e l t i n g , causes t h e c u r r e n t to c h a n n e l t h r o u g h t h e m e l t r e g i o n . T h i s w i l l increase the J o u l e h e a t i n g i n this r e g i o n , thus c a u s i n g the m o l t e n r e g i o n to g r o w .

A steady state w i l l b e r e a c h e d w h e n J o u l e h e a t i n g i n

the m e l t is b a l a n c e d b y h e a t loss f r o m the m e l t to the s o l i d a n d also b y t h e u s u a l h e a t losses b y c o n d u c t i o n a l o n g the χ axis a n d b y r a d i a t i o n . W e c a n n o w p r o c e e d to i n c o r p o r a t e the effect of P e l t i e r h e a t i n g a n d c o o l i n g at t h e t w o interfaces. L e t us assume t h a t a m o l t e n z o n e is f o r m e d , p e n e t r a t i n g the s p e c i m e n u n i f o r m l y to a d e p t h y

0

as s h o w n i n F i g u r e 5a.

T h e m o l t e n z o n e is c o n f i n e d b y t h e d o t t e d l i n e A B C D .

Peltier cooling

w i l l o c c u r at the i n t e r f a c e A B ( c u r r e n t g o i n g f r o m s o l i d to l i q u i d ) , a n d P e l t i e r h e a t i n g w i l l o c c u r at t h e i n t e r f a c e D C ( c u r r e n t g o i n g f r o m l i q u i d


7.

v o p A N i AND HASHEMiAN

Semiconducting

Polycrystalline

Ribbons


I

1 V

1200

1202

1204

1206

1208

Τ (°K)

Figure 3.

Dependence of W and γ on the ambient T for different currents

temperature

A

W

32

I

1195

,

1200

1

'

]20B

1210

Τ

°K

Figure 4. Dependence of W and γ on the end temperatures as a function of different currents: T , = 1200°K, T = 1205°K f


139


140

SOLID STATE

ι.

's

Figure

to s o l i d ) .

5.

Δ

CHEMISTRY

.1

χ

-

Schematic illustrating the effect of l zone solidification

p

on

A s the m o l t e n r e g i o n is at the m e l t i n g p o i n t , P e l t i e r h e a t

a b s o r b e d f r o m the i n t e r f a c e A B a n d e v o l v e d at the i n t e r f a c e D C is e x p e c t e d to c h a n g e the s h a p e a n d p o s i t i o n of these interfaces.

L e t us

n o w t a k e a segment of w i d t h Δχ i n t h e m o l t e n z o n e as s h o w n i n F i g u r e 5 b . S i n c e t h e b o t t o m s o l i d - l i q u i d b o u n d a r y is n o t p a r a l l e l to the c u r r e n t flow ( t h e slope dj/dx = 0 ) , a n d since the t w o phases h a v e different r e s i s t i v i ties, there is a net c u r r e n t 7 across the i n t e r f a c e , w h i c h causes the P e l t i e r P

effect. T h e i n t e r f a c e b e t w e e n s o l i d a n d l i q u i d is t a k e n as a l i n e segment of g r a d i e n t dj/dx f o u n d c o m p u t a t i o n a l l y . T h e f o r m u l a t i o n t o find dj/dx, a n d c o n s e q u e n t l y t h e final shapes a n d positions of interfaces A B a n d D C u p o n the passage of c u r r e n t 7, are g i v e n as f o l l o w s . T h e equations f o r t h e currents p a s s i n g t h r o u g h the segment a r e : 7 + 7 = 7' + V = 1

S

1

J i + I

7

(5)

- J i '

(6)

Ji =

δΛ

(7)

Ji' -

δΛ'

(8)

p

W h e r e δ is the r a t i o of the s o l i d to the l i q u i d r e s i s t i v i t y . R e a r r a n g i n g Γ

E q u a t i o n s 5, 6, 7, a n d 8 g i v e s :


7.

vojDANi A N D

Semiconducting

HASHEMiAN

Polycrystalline

141

Ribbons

w h e r e δ = δ — 1. F r o m E q u a t i o n 9 t h e P e l t i e r c o o l i n g at the i n t e r f a c e Γ

kkf is g i v e n as:

H o w e v e r , the h e a t g e n e r a t e d i n the slice c a u s e d b y t h e J o u l e h e a t i n g is


given by:

w h i l e o r i g i n a l l y , w h e n no z o n e s h a p i n g c a u s e d b y t h e P e l t i e r effect is c o n s i d e r e d , w e w o u l d get

^=(^Τ^

Δ Χ

( 1 2 )

as the a m o u n t of J o u l e h e a t i n g i n t h e segment. F o r the e q u i h b r i u m s i t u a t i o n the excess J o u l e h e a t i n g c a u s e d b y s u c h z o n e s h a p i n g m u s t b e e q u a l to the loss of e n e r g y c a u s e d b y the P e l t i e r effect, t h a t i s , Q

p

=

_

Q i

Q

a n d after s u b s t i t u t i n g f o r Ç

K

ψ

=

J 0

p

[ _ J _

_

_ J ^ ]

Λ*

(13)

f r o m E q u a t i o n 10 w e o b t a i n

%= ~

Sy2

+

° ~

{8y

b

)

+

°

(14)

by

w h e r e Κ is a constant a n d _aT A{Sy

K

m

+

0

b)

^

Spil

S o l u t i o n of the d i f f e r e n t i a l e q u a t i o n , 14, w i t h the b o u n d a r y

conditions

gives the shape of the s o l i d - l i q u i d i n t e r f a c e ( Α Β ' i n F i g u r e 5 a ) . i n t e r f a c e shape for t w o different currents I =

2 A and I =

This

2.3 A has b e e n

c o m p u t a t i o n a l l y e v a l u a t e d ; the results are g i v e n i n F i g u r e s 6 a a n d 6 b . N o t e t h a t t h e interface c u r v e a l w a y s starts f r o m p o i n t A (see 5a).

Figure

T o d e t e r m i n e the p o s i t i o n of the l i q u i d - s o l i d b o u n d a r y , i.e., the

segment B ' D ' , w e c o n s i d e r the cross s e c t i o n s h o w n i n F i g u r e 7 a at the b o u n d a r y B D ' . T h e equations for e q u i h b r i u m h e a t flow a n d t h e c u r r e n t r

c o n d i t i o n at s u c h a n i n t e r f a c e is g i v e n as:


SOLID STATE

1=2

CHEMISTRY

A

T = J207 K e

A


T , " 1200 " K

0

2

H

6

8

10

12

M

Xm

Figure 6a. Molten zone movement: (1) without Peltier current, (2) with Peltier current. l = 2.0 A. p

1=2.3

A

T = 1207 Κ e

A

\ = 1200° Κ

Figure 6b. Molten zone movement: (1) without Peltier current, (2) with Peltier current. l = 2.3 A. p


7.

vojDANi

Semiconducting

AND HASHEMiAN

Polycrystalline

Ribbons

143

(16) where

c(Sy +


and T

L

and T

R

(17)

b)'

s t a n d f o r t h e t e m p e r a t u r e of the s a m p l e at the l e f t s i d e

a n d t h e right side of B ' D ' , r e s p e c t i v e l y . H o w e v e r , t h e t e m p e r a t u r e at the left side of B ' D ' is constant ( T

m

), b e c a u s e b o t h m e l t a n d s o l i d are present

( a s s u m p t i o n v i ) , a n d therefore, w e get dT^/dx

0. T h u s E q u a t i o n 16 is

r e d u c e d to

(18) or after s u b s t i t u t i n g f o r h f r o m E q u a t i o n 17 w e o b t a i n dT

R

dx

S T / y KA Sy + b r

m

(19)

S

O n the other h a n d , h a v i n g t h e b o u n d a r y t e m p e r a t u r e s T a n d T i n t h e s o l i d r e g i o n at the right side of Β Ό ' ( F i g u r e 7 ) w e c a n c o m p u t e t h e D' m

2

Figure 7. Schematic for de termining the shape and posi tion of the interface t e m p e r a t u r e profile i n this r e g i o n . M o r e s p e c i f i c a l l y , s i n c e the l e n g t h of this s o l i d r e g i o n L is a f u n c t i o n of x, t h e t e m p e r a t u r e g r a d i e n t dT^/dx is s

o b t a i n e d as a f u n c t i o n of x, i.e.,

(20)


144

SOLID STATE

o r after s u b s t i t u t i n g f o r dT /dx R

CHEMISTRY

i n E q u a t i o n 19 w e o b t a i n aKTJ KA

y hy + b

B

(21)

o r after the a p p r o p r i a t e m a n i p u l a t i o n y is f o u n d as a f u n c t i o n of χ


y =

(22)

î(x)

A s a r e s u l t , s o l u t i o n of E q u a t i o n 14 w i t h b o u n d a r y c o n d i t i o n g i v e n i n E q u a t i o n 22 w i l l p r o v i d e e n o u g h i n f o r m a t i o n f o r c o m p u t i n g t h e s h a p e a n d t h e size of the m o l t e n z o n e w h e n b o t h J o u l e h e a t i n g a n d t h e P e l t i e r p h e n o m e n o n are effective. Experimental F o r t h e present experiments G e a n d I n S b r i b b o n s w e r e p r e p a r e d f r o m p o l y c r y s t a l l i n e ingots. T h e d i m e n s i o n s of t h e r i b b o n w e r e v a r i e d , a l w a y s k e e p i n g the r i b b o n thickness b e l o w one m m . T h e s p e c i m e n w a s h e l d b e t w e e n t w o c a r b o n b l o c k s a t t a c h e d to a c e r a m i c substrate. N i c k e l c h r o m i u m w i r e s w e r e c o n n e c t e d to the c a r b o n b l o c k s t o pass t h e d i r e c t c u r r e n t . T h e a s s e m b l y w a s t h e n l o c a t e d i n a v a c u u m c h a m b e r , a n d the sample was heated b y a tungsten element w o u n d around a silica tube. F i g u r e 8 shows a t y p i c a l s a m p l e a n d the s c h e m a t i c e x p e r i m e n t a l a r r a n g e ment. Thermocouples T T , T , a n d T continuously monitored the end t e m p e r a t u r e s , a m b i e n t t e m p e r a t u r e , a n d the s p e c i m e n s t e m p e r a t u r e i n t h e m i d d l e . T h e e x p e r i m e n t a l p r o c e d u r e w a s to raise t h e t e m p e r a t u r e u

2

A

8

Figure 8a. Schematic showing the sample setup: (1) holding clamp, (2) silica tube, (3) sample, (4) heating coil, and (5) supporting base.

Figure

8b.

Actual Ge ribbon sample holder.

in a


7.

vojDANi

AND HASHEMiAN

Semiconducting

Polycrystalline

145

Ribbons

of t h e f u r n a c e s l o w l y u n t i l t h e s p e c i m e n w a s close t o T , so t h a t the f o r m a t i o n of the z o n e c o u l d b e o b s e r v e d u n d e r v a r i o u s e x p e r i m e n t a l c o n d i t i o n s . W h e n t h e z o n e w a s e s t a b l i s h e d i n t h e absence of a n y d i r e c t c u r r e n t , i t w a s p o s s i b l e to observe t h e effect of a p p l y i n g s u c h a c u r r e n t b y o b s e r v i n g the associated z o n e m o v e m e n t . m

Results and

Discussion

Solidification of the Molten Zone in the Presence of Peltier Current. Downloaded by UNIV OF SOUTHERN CALIFORNIA on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch007

W h e n t h e t e m p e r a t u r e of a r i b b o n w a s s l o w l y r a i s e d to n e a r t h e m e l t i n g p o i n t w i t h n o c u r r e n t p a s s i n g t h r o u g h , u s u a l l y the s p e c i m e n b e g a n

to

m e l t n e a r the m i d d l e , the m o l t e n z o n e e x t e n d i n g o u t w a r d s i n a s y m m e t r i c a l m a n n e r u n t i l t h e steady state w a s r e a c h e d .

T o assist t h e f o r m a t i o n

of the m o l t e n zone, w e often m a d e a transverse c u t of 0.3 m m d e e p across the m i d d l e of the r i b b o n to p r o v i d e a r e g i o n of h i g h resistance. I n m a n y cases t h e t e m p e r a t u r e of the s a m p l e w a s r a i s e d to just b e l o w t h e m e l t i n g p o i n t w h i l e a d i r e c t c u r r e n t w a s p a s s e d t h r o u g h t h e s a m p l e , so t h a t the m o l t e n z o n e w a s c r e a t e d p a r t l y b y J o u l e h e a t i n g . U n d e r these c o n d i t i o n s t h e z o n e b e c a m e e x t e n d e d m o r e t o one side t h a n the other ( r e l a t i v e to t h e p o i n t of i n i t i a t i o n ) d u r i n g t h e n o n - s t e a d y state p e r i o d , the d i r e c t i o n a l i t y of the effect d e p e n d i n g o n the d i r e c t i o n of t h e c u r r e n t ( F i g u r e 9).

T h e m o l t e n z o n e has m o v e d t o the left side of the transverse cut,

w i t h n o m e l t i n g o n the right side as is e v i d e n t f r o m t h e s a w m a r k s . W h e n the c u r r e n t w a s

reversed, the molten zone reversed

its d i r e c t i o n

of

movement.

Figure 9. InSb sample with a transverse cut in the middle showing surface movement of the molten zone to the left. Ip = 1.95 A , T , = T = 361°C. 2

T h e r e w e r e t w o i m p o r t a n t features o b s e r v e d

d u r i n g most of

the

experiments. F i r s t , the m o l t e n z o n e d i d not e x t e n d c o m p l e t e l y across the section of the s p e c i m e n . E x a m p l e s of these samples a r e s h o w n i n F i g u r e s 4 a n d 5. I n F i g u r e 10 the m o l t e n z o n e has m o v e d to the right a n d has n o t c o m p l e t e l y p e n e t r a t e d t h e d e p t h of t h e

ribbon.

I n F i g u r e 11, w h e n

the c u r r e n t is r e d u c e d , the m e l t o n l y p a r t i a l l y covers the surface of the ribbon. T h e second feature concerns the c h a n g e i n the z o n e shape w i t h a n d without the direct current.

It h a d been

a s s u m e d o r i g i n a l l y t h a t the

a p p l i e d c u r r e n t w o u l d c o o l one i n t e r f a c e a n d heat the other, c a u s i n g


146

SOLID STATE

CHEMISTRY

Figure 10. InSb sample showing par tial melting across the sample thick ness. Ip = 1.5 A, T , = Ί = 398°C. Downloaded by UNIV OF SOUTHERN CALIFORNIA on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch007

$

Figure 11. InSb sample showing par tial melting on the surface, A current of 1 A was first passed from right to left; the current was then reversed thus reversing the zone movement. The current was then reduced to half, causing the melt to decrease in width. t h e z o n e to m o v e . T h i s w a s n o t observed.

I n s t e a d , o n l y the l e a d i n g e d g e

m o v e d , e x t e n d i n g the w i d t h of the z o n e . T h e o r e t i c a l m o d e l l i n g of the s y s t e m p r e d i c t s this b e h a v i o r b e c a u s e the c u r r e n t causes J o u l e h e a t i n g as w e l l as P e l t i e r h e a t i n g a n d c o o l i n g . globules f o r m e d o n the surface.

W h e n the s p e c i m e n w a s c o o l e d ,

T h i s w a s c a u s e d b y t h e f r e e z i n g of the

surface of t h e s a m p l e w h i l e m o l t e n m a t e r i a l s t i l l existed b e l o w .

This

m e l t w a s s u b j e c t e d to pressure d u r i n g the c o o l i n g process a n d f o r c e d its w a y u p t h r o u g h w e a k spots i n t h e f r o z e n surface.

S i m i l a r b e h a v i o r is

o b s e r v e d w h e n m o l t e n g e r m a n i u m is s o l i d i f i e d i n a c r u c i b l e . Conclusion T h e results p r e s e n t e d i n this p a p e r i n d i c a t e t h a t t h e P e l t i e r effect itself is n o t a d e q u a t e f o r t h e process of z o n i n g t h i n films. T h e r e are t w o reasons for t h i s : ( a ) i t is difficult to o b t a i n a f u l l y m e l t e d n a r r o w z o n e across a ribbon o r t h i n film, m a i n l y b e c a u s e of t h e effect of J o u l e h e a t i n g ; (b)

the r e s i s t i v i t y of

geneous.

the p o l y c r y s t a l l i n e

film

is i n e v i t a b l y

inhomo-

W h e n m o l t e n z o n e is m o v e d b y the a p p l i c a t i o n of a P e l t i e r

current, the m e l t i n g interface

does n o t r e m a i n stable since

"current

c h a n n e l i n g " w i l l t e n d to b r e a k u p the interface. T h i s c u r r e n t c h a n n e l i n g effect o n the other h a n d has a s t a b i l i z i n g effect o n the f r e e z i n g i n t e r f a c e as i l l u s t r a t e d o n a n e x p a n d e d

scale i n F i g u r e 12.

I n this

figure,

for

s i m p l i c i t y , the m e l t i n g i n t e r f a c e is a s s u m e d to b e flat, a n d the s o l i d i f y i n g i n t e r f a c e is a s s u m e d t o b e i r r e g u l a r , c a u s i n g l o w a n d h i g h r e s i s t i v i t y p a t h s w i t h i n t h e i n t e r f a c e r e g i o n . T h u s t h e r a t e of f r e e z i n g at t h e i n t e r f a c e varies across i t , a l w a y s t e n d i n g to m a k e t h e i n t e r f a c e p l a n a r . T h i s



7.

vopANi

AND HASHEMiAN

Semiconducting

Polycrystalline

147

Ribbons

Figure 12. Schematic illustrating the current chan nelling effect tending to stabilize the interface: (1) liquid, (2) solid effect is p r e s e n t l y b e i n g i n v e s t i g a t e d . T o c o n c l u d e , i t c a n b e

suggested

t h a t f o r t h e p u r p o s e of z o n i n g a t h i n s e m i c o n d u c t i n g film, t h e c o m b i n a t i o n of a n e x t e r n a l source to create a m o l t e n z o n e a n d P e l t i e r c u r r e n t t o stabilize the freezing interface should result i n more control over

the

s o l i d i f i c a t i o n process, p r o v i d e d t h a t the v e l o c i t y of z o n i n g is n o t h i g h e n o u g h t o a l l o w r e n u c l e a t i o n b e f o r e t h e f r e e z i n g interface. Nomenclature R e p r e s e n t a t i v e v a l u e s of the v a r i o u s p a r a m e t e r s o r G e are g i v e n i n parentheses. L e n g t h of s a m p l e ( c m )

a A

Amps

A

C r o s s s e c t i o n a l area of s a m p l e ( c m ) 2

b

S a m p l e thickness ( c m )

c

Sample w i d t h ( c m )

C

P 8

(C ) p l

d (d ) %

l

J ( 11 ) s

Specific heat of s o l i d ( l i q u i d ) [ ( 2 . 1 2 ) , ( 2 . 3 ) J / d e g / c m ] 3

D e n s i t y of s o l i d ( l i q u i d ) [ ( 5 . 3 ) g / c m ] 3

Current through solid ( l i q u i d ) ( A )

J ( Ji )

C u r r e n t density through solid ( l i q u i d ) ( A )

/

Peltier current ( density ) ( A )

B

K , (Ki)

T h e r m a l c o n d u c t i v i t y of s o l i d ( l i q u i d )

1 (subscript)

Liquid

L

L a t e n t heat of s o l i d i f i c a t i o n [ ( 2 . 1 6 X

Ρ

C r o s s s e c t i o n a l p e r i m e t e r ( 2c + 2b ) ( c m )

B

[(0.24),(0.24)W/cm]

s (subscript)

Solid

t

Time

Τ

Absolute temperature ( ° K )

T

A

l(fi)(]/cm )] 3

(sec)

A m b i e n t temperature ( ° K ) M

*

J

1 i S

Chemical

Society Library 1155 16th St. N. W. Goodenough and Whittingham; Solid State Chemistry of Energy Conversion and Storage Washington, D. Society: C. 20036 Advances in Chemistry; American Chemical Washington, DC, 1977.

148

SOLID STATE

CHEMISTRY

τ., ( τ ο

w χ

a

F r a c t i o n of t h e area m e l t e d R a t i o of t h e s o l i d - t o - l i q u i d r e s i s t i v i t y (δ — δ — 1 ) Γ

R e s i s t i v i t y of s o l i d ( l i q u i d ) [ ( 8 Χ 1 0 " ) , ( H ) " ) ( Ω - c m ) ] Downloaded by UNIV OF SOUTHERN CALIFORNIA on June 18, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch007

4

4

E m i s s i v i t y of s o l i d ( l i q u i d ) [ ( 0.2 ) , ( 0.2 ) ] σ

S t e f a n - B o l t z m a n n constant [5.68 Χ 10" ] 12

Acknowledgment W e w o u l d l i k e t o a c k n o w l e d g e m a n y h e l p f u l discussions w i t h E . A . D . W h i t e d u r i n g t h e p r e p a r a t i o n of this p a p e r . T h a n k s a r e also d u e to E . A f s h a r i f o r c o m p u t e r p r o g r a m m i n g , a n d t o S. A l s a e e f o r carrying out the experiments.

Literature Cited 1. Cizek, T. F., Schwuttke, G. H., "Proceedings of the Photovoltaic Power Gen eration Conference," Hamburg, Deutsche Gesellschaft für Luft-und Raum fahrt e.V., Köhn, Germany, 1974, p. 159. 2. Fang, P. H., "International Congress le Soleil au Service de l'Homme," p. 111, UNESCO House, Paris, 1973. 3. Brissot, J. J., Belouet, C., "Comples International Meeting," Dhahran, Saudi Arabia, 1975. See also Brissot, J. J., French Patent PV. 912.050 nr. 1.343.740 (1972). 4. Hammond, A. L., Science (1974) 184, 1359. 5. Wolf, M., "Proceedings of the Photovoltaic Power Generation Conference," Hamburg, 1974, p. 699. 6. Fan, John C. C., Zeiger, H. J., Appl. Phys. Lett. (1975) 27 (4), 224. 7. Ocwens, C. Daey, Heigligers, H., Appl. Phys. Lett. (1957) 26, 269. 8. Pfann, W. G., Benon, Κ. E., Wermich, J. H., J. Electron. (1957) 2, 597. 9. Vojdani, S., Dabiri, A. E., Tavakoli, M., J. Electrochem. Soc. (1975) 122, 1400. RECEIVED July 27, 1976.


Solid State Chemistry of Energy Conversion and Storage

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