Photovoltaic Solar Cells

6 Photovoltaic Solar Cells SIGURD WAGNER

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Bell Laboratories, Holmdel, N. J. 07733 Solar cells convert incident light to electrical power. They are semiconductor diodes with two key functions: separa tion of electrical charge in energy, and in space. Absorption of light quanta by the semiconductor separates electron -hole pairs by the band gap energy; the output voltage is proportional to this energy. The electric field associated with the semiconductor junction separates electrons and holes in space, leading to an external current. The voltage -current product, or output power, thus depends on light absorption, charge transport, and type of junction. In this paper we consider cell characteristics, power conversion efficiencies, alternative cell structures, and approaches to the development of inexpensive cells.

T j h o t o v o l t a i c solar cells c o n v e r t i n c i d e n t l i g h t t o e l e c t r i c i t y . S o l a r p o w e r , the p r o d u c t of p h o t o n flux a n d p h o t o n energy, is t u r n e d i n t o e l e c t r i c a l p o w e r , t h e p r o d u c t of e l e c t r i c a l c u r r e n t a n d o u t p u t voltage. cells a r e c o n c e p t u a l l y s i m p l e a n d r u g g e d devices.

Solar

Therefore, widespread

use of p h o t o v o l t a i c converters is v e r y a t t r a c t i v e . H o w e v e r , solar elec t r i c i t y is a b o u t o n e h u n d r e d times m o r e power.

expensive t h a n c o n v e n t i o n a l

T o a l a r g e extent, i t w i l l b e t h e task o f chemists t o find i m p r o v e d

m a t e r i a l s a n d processes t o m a k e p h o t o v o l t a i c p o w e r cost c o m p e t i t i v e . Semiconductor

Diodes

S e m i c o n d u c t o r s c o m b i n e t w o c h a r a c t e r i s t i c properties w h i c h m a k e t h e m s u i t a b l e f o r p h o t o v o l t a i c cells (1, 2, 3).

First, numerous

semicon

ductors e x h i b i t t h e p r o p e r a b s o r p t i o n characteristics f o r solar r a d i a t i o n . S e c o n d , a space c h a r g e c a n b e i n t r o d u c e d i n a s m a l l r e g i o n of a s e m i c o n d u c t o r , w h i l e most of i t r e m a i n s n e u t r a l a n d c o n d u c t i n g .

T h i s is t h e

space charge of a j u n c t i o n . A s i m p l e w a y to p i c t u r e t h e c o n s t r u c t i o n o f a pn j u n c t i o n is s h o w n i n F i g u r e l a . W e start w i t h t w o pieces of t h e 109

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

110

SOLID S T A T E

CHEMISTRY

s e m i c o n d u c t o r (e.g., s i l i c o n ) , one of w h i c h is η-type, t h e other, p - t y p e . I n η-Si, t y p i c a l l y 1 0

17

cm"

3

( 2 p p m a ) , d o n o r i m p u r i t i e s w i t h five v a l e n c e

electrons (e.g., p h o s p h o r u s ) h a v e b e e n i n t r o d u c e d to m a k e t h e h i g h l y resistive p u r e S i a n e l e c t r i c c o n d u c t o r w i t h t h e c u r r e n t b e i n g c a r r i e d b y free electrons. T h e p i e c e of η-Si is n e u t r a l , h o w e v e r , b e c a u s e t h e free electrons are e x a c t l y c o m p e n s a t e d b y t h e donor impurities.

fixed

(nonmobile)

ionized

I n p - S i , d o p e d w i t h acceptor impurities like boron,

c u r r e n t is c a r r i e d b y free holes. H o w e v e r , there is s t i l l a finite d e n s i t y of Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch006

electrons i n p - S i , a n d of holes i n η-Si. T h i s d e n s i t y is d e t e r m i n e d b y t h e c o n c e n t r a t i o n of t h e r e s p e c t i v e m a j o r i t y carrier, η o r p , t h r o u g h t h e e q u i l i b r i u m constant exp (-E /kT)

jm — N N C

where N and N c

V

—

g

n?

are t h e effective densities of states i n the c o n d u c t i o n a n d

y

valence bands, E

is t h e b a n d g a p , a n d k is B o l t z m a n n s constant. I n S i ,

g

pn at 3 0 0 ° K is 2.1 Χ 1 0

2 0

c m " . H e r e rti is t h e c a r r i e r c o n c e n t r a t i o n f o r 6

u n d o p e d (intrinsic) S i . Imagine j o i n i n g the η a n d the ρ halves. W h e n t h e y m a k e contact, electrons diffuse f r o m η i n t o ρ a n d holes f r o m ρ i n t o η because of t h e i r r e s p e c t i v e c o n c e n t r a t i o n d r o p across t h e i n t e r f a c e . O n c e m a j o r i t y carriers h a v e d i f f u s e d i n t o t h e o t h e r s i d e a n d thus h a v e b e c o m e m i n o r i t y carriers, t h e y r e c o m b i n e w i t h t h e l o c a l m a j o r i t y c a r r i e r

(a) η

e

+

"» ©

Ρ

h* Θ

"

n

If !& 3©i

SPACE CHARGE

DISTANCE Figure 1.

Schematic construction

of a p n homodiode


6.

WAGNER

Photovoltaic

Solar

111

Cells

to p r e v e n t t h e p r o d u c t p n f r o m e x c e e d i n g t h e e q u i l i b r i u m v a l u e .

The

excess c h a r g e is t a k e n u p b y the fixed i o n i z e d i m p u r i t i e s w h i c h

now

become uncompensated.

N e t c h a r g e is t h e r e b y i n t r o d u c e d to the o r i g i

n a l l y n e u t r a l ρ a n d η h a l v e s . T h i s charge, t h e space c h a r g e d e n o t e d i n


F i g u r e l a , i n t r o d u c e s a field a c c o r d i n g to dE

p_

dx

€e 0

w h e r e χ is the o n e - d i m e n s i o n a l c o o r d i n a t e for distance, Ε the e l e c t r i c field,

ρ the c h a r g e d e n s i t y , c t h e r e l a t i v e d i e l e c t r i c constant, a n d c

0

the

p e r m i t t i v i t y of free space. T h e field increases u n t i l i t prevents net d i f f u s i o n r e s u l t i n g f r o m t h e difference i n c a r r i e r c o n c e n t r a t i o n .

I n other words, the electrochemical

p o t e n t i a l of a g i v e n c a r r i e r , e l e c t r o n o r h o l e , is n o w u n i f o r m t h r o u g h o u t the p-n

diode.

T h i s e l e c t r o c h e m i c a l e q u i l i b r i u m c o n d i t i o n is u s u a l l y

expressed w i t h t h e F e r m i l e v e l , F i n F i g u r e l b . T h e F e r m i l e v e l denotes the e l e c t r o c h e m i c a l p o t e n t i a l of electrons.

I t is h i g h ( c l o s e t o t h e c o n

d u c t i o n b a n d C ) i n η-Si a n d l o w (close to v a l e n c e b a n d V ) i n p - S i . T h e reference l e v e l is u s u a l l y the center of t h e b a n d g a p E

u

w i t h t h e v a l u e of

the F e r m i l e v e l g i v e n b y

E

n

= E +kT\n

—

{

E q u a l i z a t i o n of the F e r m i l e v e l i n t h e t w o h a l v e s of a d i o d e r e q u i r e s t h e i n t r o d u c t i o n o f a n e l e c t r i c a l p o t e n t i a l difference as s h o w n o n the

right

i n F i g u r e l b . T h i s p o t e n t i a l difference, t h e d i f f u s i o n v o l t a g e V , is g i v e n D

b y the i n i t i a l difference b e t w e e n the F e r m i levels i n t h e η a n d ρ regions, E

n

—

E: p

q

7Lp

( n „ a n d rip d e n o t e e l e c t r o n c o n c e n t r a t i o n o n the η-side a n d o n the p - s i d e , r e s p e c t i v e l y , a n d q is the m a g n i t u d e of the e l e c t r o n i c charge. ) T h e m o s t o u t s t a n d i n g c h a r a c t e r i s t i c of a d i o d e is t h a t i t passes c u r r e n t easily i n o n e d i r e c t i o n b u t n o t i n t h e other w h e n a n e x t e r n a l v o l t a g e is a p p l i e d . I n the f o r w a r d , or "easy" d i r e c t i o n , electrons flow f r o m η to p , a n d holes f r o m ρ to n . I n t h e reverse, or " d i f f i c u l t " d i r e c t i o n , electrons

flow

from

ρ to n , a n d holes f r o m η t o p. T h i s effect results f r o m the a v a i l a b i l i t y of a l a r g e d e n s i t y of electrons f o r t r a n s p o r t i n t o p - S i , a n d of holes i n t o n - S i ( f o r w a r d ) , a n d of the n o n a v a i l a b i l i t y of electrons f o r c u r r e n t t r a n s p o r t f r o m ρ i n t o n , a n d of holes f r o m η i n t o ρ ( r e v e r s e ) .

T h e o r e t i c a l treat-


112

SOLID S T A T E

CHEMISTRY

m e n t of the m o s t s i m p l e case shows t h a t the reverse c u r r e n t is a constant 7

0

i n d e p e n d e n t of a p p l i e d v o l t a g e a n d t h a t t h e f o r w a r d c u r r e n t I i n

creases a p p r o x i m a t e l y e x p o n e n t i a l l y w i t h a p p l i e d v o l t a g e V ,

w h e r e A is a p a r a m e t e r w h i c h d e p e n d s o n the d e t a i l e d m e c h a n i s m of Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch006

current

flow.

W h e n j u n c t i o n s are m a d e b e t w e e n n - a n d p - t y p e regions of s e m i c o n d u c t o r as i n the p r e c e d i n g e x a m p l e o f n S i / p S i , p n

one

homodiodes

are f o r m e d ( F i g u r e 2 ) . T h e s e m i c o n d u c t o r space c h a r g e associated w i t h d i o d e s c a n b e i n t r o d u c e d i n t w o o t h e r w a y s w h i c h p r o v e of i n c r e a s i n g importance

in

solar

cell

research

[pGaAs/nAJAs (4), p l n P / n C d S

and

development.

(5), p C u S / n C d S (6), 2

Heterodiodes etc.]

are p r e

p a r e d f r o m t w o different s e m i c o n d u c t o r s of o p p o s i t e c o n d u c t i v i t y t y p e . I n Schottky barrier diodes, w h i c h are p r o d u c e d b y depositing a m e t a l film o n a s e m i c o n d u c t o r [ p S i / C r ( 7 ) , n G a A s / P t ( 8 ) ] , t h e space c h a r g e is b u i l t u p o n l y i n the s e m i c o n d u c t o r .

Heterodiodes w i t h one h i g h l y

HOMODIODE

HETERODIODE

SCHOTTKY

DIODE

BARRIER

Cr

Journal of Crystal Growth

Figure

2. Band diagrams of a homodiode, a heterodiode, and a Schottky barrier diode (63)


6.

WAGNER

Photovoltaic

Solar

113

Cells

c o n d u c t i n g ( " d e g e n e r a t e " ) p a r t n e r c a n also b e v i e w e d as S c h o t t k y b a r r i e r diodes. T h i s s u b g r o u p i n c l u d e s diodes m a d e of a s e m i c o n d u c t o r a n d a c o n d u c t i n g t r a n s p a r e n t glass ( p S i / n I n 0 ) 2

3

( 9 , J O ) . P r o m i s i n g results

h a v e b e e n o b t a i n e d r e c e n t l y w i t h m e t a l o x i d e - s e m i c o n 3 u c t o r cells.

These

are m o d i f i e d S c h o t t k y c a r r i e r diodes w h i c h c o n t a i n a v e r y t h i n ( 1 0 - 3 0 Â ) oxide layer between (Au)

the s e m i c o n d u c t o r

(nGaAs)

a n d the m e t a l

film

( J J ) . T h i n o x i d e layers h a v e also b e e n d e t e c t e d i n specimens

of

s i l i c o n - b a s e d cells that h a d o r i g i n a l l y b e e n c o n c e i v e d as S c h o t t k y b a r r i e r Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch006

diodes

(7).

Diodes Operating

as Solar Cells

W h e n a solar c e l l is i l l u m i n a t e d , a reverse c u r r e n t J , w h i c h is l a r g e L

c o m p a r e d w i t h J , is generated. 0

F i g u r e 3 a shows h o w l i g h t q u a n t a a r r i v

i n g at the cell's surface p e n e t r a t e the d i o d e , are a b s o r b e d , a n d generate e l e c t r o n hole p a i r i n either the η or the ρ r e g i o n . T h e s e a d d i t i o n a l charge carriers increase t h e pn p r o d u c t a b o v e t h e e q u i l i b r i u m v a l u e of n ^ . T h e c a r r i e r p o p u l a t i o n tends t o r e t u r n to e q u i l i b r i u m , a n d c a n d o this i n t w o w a y s . T h e m i n o r i t y c a r r i e r c a n lose its energy a n d disappear by immediately recombining w i t h a majority car rier,

i.e., b y r e v e r s i n g the process of its g e n e r a t i o n , or the m i n o r i t y

c a r r i e r c a n diffuse to the j u n c t i o n a n d d r i f t i n the field of t h e p-n

junction

to the side w h e r e i t is the m a j o r i t y c a r r i e r . T h i s is d e s i r a b l e for a solar c e l l b e c a u s e excess negative a n d p o s i t i v e c h a r g e is not a n n i h i l a t e d b y r e c o m b i n a t i o n w i t h i n the d i o d e b u t o n l y after flowing t h r o u g h a n exter n a l c i r c u i t w h e r e i t c a n d o w o r k . T h e t w o extreme m o d e s of o p e r a t i n g a c e l l are s h o w n i n F i g u r e s 3 b a n d 3c.

U n d e r short-circuit conditions

( F i g u r e 3 b ) the e x t e r n a l c i r c u i t does not offer a n y resistance to c u r r e n t flow.

A l l the p h o t o c u r r e n t t h e n flows t h r o u g h the e x t e r n a l c i r c u i t . TTiis

short-circuit current J

s c

is t h e m a x i m u m c u r r e n t one c a n o b t a i n f r o m a

solar c e l l . U n d e r o p e n - c i r c u i t c o n d i t i o n s w i t h infinite e x t e r n a l resistance ( F i g u r e 3c)

the reverse p h o t o c u r r e n t

flows

i n i t i a l l y , b u t the carriers

c a n n o t r e c o m b i n e t h r o u g h the e x t e r n a l c i r c u i t . T h e y a c c u m u l a t e i n t h e i r respective halves of the d i o d e , electrons i n t h e η p o r t i o n a n d holes i n the ρ p o r t i o n , a n d p a r t i a l l y compensate its space charge.

T h i s effect is

i d e n t i c a l to t h a t of t h e e x t e r n a l a p p l i c a t i o n of a f o r w a r d b i a s , i.e., a f o r w a r d c u r r e n t begins to flow. S t e a d y state is r e a c h e d w h e n the reverse p h o t o c u r r e n t is c o m p e n s a t e d b y t h a t f o r w a r d c u r r e n t . T h e c o r r e s p o n d i n g steady-state f o r w a r d v o l t a g e is c a l l e d t h e o p e n - c i r c u i t v o l t a g e , VOc, a n d is t h e m a x i m u m v o l t a g e a t t a i n a b l e . N o t e that no p o w e r short-circuit ( J , V = 8 C

(J χ V ) 0)

is d r a w n f r o m the c e l l i n either t h e

or t h e o p e n - c i r c u i t

(V^, 1 =

0)

condition.

P o w e r is d e l i v e r e d o n l y w h e n t h e e x t e r n a l l o a d resistor Rex is (Figure 3d).

T h e voltage V

o p

finite

is s m a l l e r t h a n V * . b e c a u s e most of t h e



114

SOLID STATE

CHEMISTRY

Journal of Crystal Growth

Figure 3. Band diagram of a homodiode solar cell: (a) showing creation f electron-hole pairs by absorption of light quanta; (b) short circuit conition; (c) open circuit condition; ana (a) under finite external load (63)

3

I

_

1

I CuInSe /CdS

40

ci" ι

ι 2

I$c

Ε ο

E) g

i n F i g u r e 6a. O b v i o u s l y , f o r m a x i m u m o u t p u t c u r r e n t

one w i l l use s e m i c o n d u c t o r s w i t h s m a l l b a n d gaps. H o w e v e r , the o u t p u t p o w e r depends o n t h e p r o d u c t of c u r r e n t 7 turn V

0 P

op

a n d voltage V

is p r o p o r t i o n a l to the b a n d gap energy.

o p

.

and in

B e c a u s e of t h e e n s u i n g

trade-off b e t w e e n c u r r e n t a n d v o l t a g e , the o u t p u t p o w e r has a m a x i m u m v a l u e w h i c h lies b e t w e e n 1.0 a n d 1.5 e V , as i n d i c a t e d b y the F X E

g

curve

i n F i g u r e 6b. I n a m o r e d e t a i l e d c o n s i d e r a t i o n w h i c h i n c l u d e s the m e c h a n i s m of c u r r e n t flow i n the d i o d e , the t y p i c a l m a x i m u m efficiency curves m a r k e d η are o b t a i n e d . T h e p o w e r efficiency η is d e f i n e d as t h e r a t i o of e x t r a c t e d e l e c t r i c a l p o w e r to i n c i d e n t solar p o w e r F . i n

N o t e t h a t the

efficiency drops w i t h i n c r e a s i n g t e m p e r a t u r e , a n d d r a s t i c a l l y so f o r s e m i c o n d u c t o r s w i t h l o w b a n d gaps (18).

Applications i n v o l v i n g h i g h oper

a t i n g t e m p e r a t u r e s , e.g., w i t h solar concentrators, w i l l f a v o r r e l a t i v e l y l a r g e b a n d - g a p m a t e r i a l s . A n a l t e r n a t i v e a p p r o a c h t o w a r d e s t i m a t i n g the


6.

WAGNER

Photovoltaic

Solar

119

Cells


WAVELENGTH

1

(^m)

2

3 ENERGY

4

(eV)

Figure 6. (a) Fraction of solar photons (AM2) with energy higher than the band gap E , F(hv > E ), as a function of energy. The band gap (dashed line) illustrates the contribution of output voltage to the current-voltage product, (b) The product F Χ Ε showing a maximum between 1.0 and 1.5 eV. Typical theoretical solar efficiencies η at 25° and 100 C from a detailed calculation. g

g

σ

e

o p t i m u m b a n d g a p considers t h e t h e r m o d y n a m i c e q u i l i b r i u m b e t w e e n t h e s u n a n d t h e solar c e l l ; the r e s u l t is a n u l t i m a t e ( i d e a l ) η

=

E

g

χ

F(hv

> E J / P i n , of 4 4 % at E

g

=

1.1 e V ( 1 9 ) .

efficiency,

A n u m b e r of

r e p o r t e d s e m i c o n d u c t o r s w i t h b a n d gaps i n t h e v i c i n i t y o f t h e o p t i m u m r a n g e are l i s t e d i n T a b l e I I .


120

SOLID STATE

Table II.


Si AlAs GaP GaAs InP CdS CdSe CdTe CuInSe

Properties of Semiconductors Used in Solar Cells

Band Gap at S00K (eV) Direct or Indirect

Material

Cu S

1.2, i

Cu Se Cu Te ln 0

1.2, d ( ? ) U,d(?) 2.62, i

2

2

2

2

3

Direct

Structure and Parameters

1.11,i 2.16, i 2.25, i 1.43, d 1.34, d 2.42, d 1.7, d 1.44, d 1.01, d

2

CHEMISTRY

Use (Absorber/ Window)

Lattice (Ά)

A W W A A W A A A

d i a m o n d , a = 5.431 z i n c blende, ο = 5.661 z i n c blende, a = 5.451 z i n c blende, α = 5.654 z i n c blende, a = 5.869 w u r t z i t e , ο = 4.137, c = 6.716 w u r t z i t e , α = 4.29, c = 7.03 z i n c blende, a= 6.488 c h a l c o p y r i t e , a = 5.78, c = 11.60 orthorhombic (chalcocite),a = 11.86, b = 27.32, c = 13.49 fee ( f l u o r i t e ) , a = 5.75 h e x a g o n a l , a = 12.5, b = 21.7 b . c . c , a = 10.11

and Indirect Band

A A A W

Gap

A p a r t f r o m t h e e n e r g y of the f o r b i d d e n gap, the n a t u r e of t h e a b s o r p t i o n process, d i r e c t o r i n d i r e c t , is a n i m p o r t a n t c o n s i d e r a t i o n i n the s e l e c t i o n of a s e m i c o n d u c t o r

(Figure 7).

I n indirect gap materials the

l o w e s t c o n d u c t i o n b a n d m i n i m u m lies at a m o m e n t u m different f r o m t h e v a l e n c e b a n d m a x i m u m . O n l y a p h o t o n hv is r e q u i r e d f o r e x c i t a t i o n of a n e l e c t r o n f r o m the v a l e n c e to the c o n d u c t i o n b a n d i n the d i r e c t - g a p case. W i t h a n i n d i r e c t g a p t h e t r a n s i t i o n takes p l a c e o n l y w h e n assisted b y a p h o n o n hp, the q u a n t u m of l a t t i c e v i b r a t i o n . A l t h o u g h the t y p i c a l e n e r g y of a p h o n o n is s m a l l ( ~ 0 . 0 5 m e V ) ,

its m o m e n t u m ,

l a r g e i n c o m p a r i s o n w i t h that of a p h o t o n , ~

is

~h/a,

h/λ ( w h e r e a is the c r y s t a l

l a t t i c e p a r a m e t e r , λ the w a v e l e n g t h of t h e a b s o r b e d l i g h t ) . T h e a b s o r p t i o n of the p h o t o n c a n b e a c c o m p a n i e d b y e i t h e r a b s o r p t i o n (as d e p i c t e d i n F i g u r e 7 ) o r e m i s s i o n of p h o n o n s .

I n e i t h e r case, t h e n e e d f o r p h o n o n

assistance g r e a t l y reduces the t r a n s i t i o n p r o b a b i l i t y a n d therefore

the

a b s o r p t i o n coefficient a f o r the i n c i d e n t l i g h t . A t t e n u a t i n g t h e l i g h t to 1/e of its i n i t i a l i n t e n s i t y r e q u i r e s a p a t h l e n g t h ( t h e a b s o r p t i o n l e n g t h 1/a)

w h i c h is greater f o r i n d i r e c t g a p t h a n f o r d i r e c t g a p m a t e r i a l s .

T h i s difference is i l l u s t r a t e d i n F i g u r e 8 w i t h t h e a b s o r p t i o n curves f o r a t y p i c a l d i r e c t ( I n P ) (20, 21) a n d a t y p i c a l i n d i r e c t ( S i ) (22,23) conductor.

In InP ( E

g

=

1.34 e V , A = g

hc/E

g

t h a n 1 μπι f o r a n y p h o t o n e n e r g y a b o v e E . g

1.12 μπι)

1/a is 1 0 0 μ α ι at λ =

=

semi

0.93 /xm) 1/a is s m a l l e r

I n S i (E = g

1.11 e V , k

g

=

1 /xm w h i l e i t approaches 1 /xm, t h e v a l u e

t y p i c a l f o r d i r e c t gaps, o n l y at a w a v e l e n g t h of 0.5 /xm.


WAGNER

Photovoltaic

Sofor Cells CB


DIRECT GAP

INDIRECT GAP

Figure 7. Absorption of a photon in (a) a direct gap semiconductor and (b) an indirect gap semiconductor with phonon assistance PHOTON ENERGY (eV)

0.5

1.0 WAVELENGTH (μπι)

Figure 8. Absorption coefficient (a) and absorption length (1/a) for a typical direct-gap semiconductor, InP, and a typical indirect gap semiconductor, Si (63)


122

SOLID STATE

CHEMISTRY

Photocurrent I n solar cells m a d e of d i r e c t - g a p s e m i c o n d u c t o r s

the p-n

junction

c a n b e p o s i t i o n e d s u c h t h a t a l l t h e i n c i d e n t l i g h t is a b s o r b e d vicinity.

A s a result, photogenerated

i n its

m i n o r i t y carriers n e e d n o t t r a v e l

f a r t h e r t h a n a f e w m i c r o m e t e r s to cross the j u n c t i o n space charge. I n a n i n d i r e c t - g a p m a t e r i a l l i k e S i the a b s o r p t i o n takes p l a c e w i t h i n a s l a b ~ 100 i o n t h i c k .

M i n o r i t y carriers m u s t t r a v e l o v e r lengths of u p

to


100 /xm t o r e a c h t h e j u n c t i o n . I t is v e r y expensive t o p r o d u c e s i l i c o n of a q u a l i t y p e r m i t t i n g m i n o r i t y carriers t o diffuse o v e r this distance i n s t e a d of r e c o m b i n i n g w i t h a m a j o r i t y c a r r i e r . S o l a r g r a d e s i l i c o n m u s t b e

of

h i g h p u r i t y a n d c r y s t a l l i n e p e r f e c t i o n . M a n y i m p u r i t i e s , other t h a n those i n t e n d e d as d o p a n t s , a n d i m p e r f e c t i o n s r e d u c e t h e m i n o r i t y c a r r i e r l i f e time τ , the t i m e the d e n s i t y of p h o t o e x c i t e d c a r r i e r d e c a y s to 1/e of its i n i t i a l v a l u e . D u r i n g its l i f e the m i n o r i t y c a r r i e r diffuses, u n d e r its o w n c o n c e n t r a t i o n g r a d i e n t , t o w a r d t h e j u n c t i o n . I f its l i f e t i m e is t o o short, its d i f f u s i o n l e n g t h w i l l b e too short. I t w i l l not r e a c h the j u n c t i o n a n d w i l l therefore n o t flow t h r o u g h the e x t e r n a l c i r c u i t . S e v e r a l r e c o m b i n a t i o n processes p a r t i c i p a t e i n l i m i t i n g the l i f e t i m e of a c a r r i e r :

P r e s e n t l y i t suffices t o c o n s i d e r o n l y t w o of these. b i n a t i o n is t h e reverse of the e x c i t a t i o n process.

Band-to-band recom

I f i t is t h e o n l y r e c o m

bination m e c h a n i s m operating, the highest lifetime achievable for a g i v e n m a t e r i a l is o b t a i n e d .

I n direct materials band-to-band

recombination

a n d also r e c o m b i n a t i o n t h r o u g h e l e c t r o n i c levels associated w i t h c r y s t a l line imperfections

or i m p u r i t i e s h a v e h i g h p r o b a b i l i t y a n d l e a d to

r e l a t i v e l y short l i f e t i m e of

~ 10 ns.

a

I n indirect materials i t requires

assistance b y p h o n o n s a n d thus p e r m i t s l o n g c a r r i e r l i f e , ~ 10 /xs.

These

t y p i c a l l i f e t i m e s are o r d e r - o f - m a g n i t u d e v a l u e s b e c a u s e t h e y d e p e n d

on

t h e d e n s i t y of m a j o r i t y carriers ( w i t h o n e of w h o m t h e m i n o r i t y c a r r i e r is to r e c o m b i n e ) .

T h e carrier diffusion length

is p r o p o r t i o n a l t o t h e s q u a r e r o o t of the c a r r i e r l i f e t i m e a n d is therefore t y p i c a l l y one t o t w o orders of m a g n i t u d e s l a r g e r f o r i n d i r e c t t h a n f o r d i r e c t m a t e r i a l . ( L is also l a r g e r f o r electrons t h a n f o r holes since i n m o s t s e m i c o n d u c t o r s t h e e l e c t r o n m o b i l i t y is 1 0 - 1 0 0 times greater t h a n t h a t of h o l e s . ) O n one h a n d , t h e l o n g e r i n d i r e c t d i f f u s i o n l e n g t h appears to


6.

WAGNER

compensate

Photovoltaic

Sohr

123

Cells

for the equally longer indirect absorption length.

O n the

o t h e r h a n d , t h e d i f f u s i o n l e n g t h i n i n d i r e c t g a p m a t e r i a l s is m o r e suscep t i b l e to i m p u r i t i e s a n d defects w h i c h i n t r o d u c e e l e c t r o n i c levels n e a r the center of the b a n d g a p a n d p r o m o t e r e c o m b i n a t i o n b y alternate e m i s s i o n of holes a n d electrons.

T h e a p p r o p r i a t e l i f e t i m e T is i n v e r s e l y p r o p o r t

t i o n a l to t h e c o n c e n t r a t i o n of these defects i V . t


T t

~"

1_ N Va t

t

( H e r e ν is the t h e r m a l v e l o c i t y of c h a r g e c a r r i e r s , a n d σ t h e r e c o m b i n a 4

t i o n cross s e c t i o n of t h e p a r t i c i p a t i n g defect. )

H i g h defect density a n d

associated e l e c t r i c fields m a k e g r a i n b o u n d a r i e s effective sinks f o r m i n o r i t y carriers. F o r efficient c u r r e n t c o l l e c t i o n i n d i r e c t g a p m a t e r i a l s m u s t c o n t a i n s i n g l e crystals l a r g e r t h a n ~ 100 t o n . G r a i n s i n d i r e c t g a p m a t e r i a l s need not be larger than a f e w micrometers.

F o r this r e a s o n p o l y c r y s t a l -

l i n e cells i n t h i n film f o r m are a n a t t r a c t i v e a l t e r n a t i v e w h e n p r e p a r e d f r o m direct gap materials. F r e e surfaces are t o a n e v e n greater extent t h a n g r a i n b o u n d a r i e s sites of h i g h d e f e c t d e n s i t y i V . B e c a u s e of the l a r g e v a l u e s of iV t e n c o u n Bt

8

t e r e d , the l i f e t i m e f o r a m i n o r i t y c a r r i e r r e a c h i n g t h e surface, τ

β ί

=

l / i V u a , is so short that t h e surface c a n b e a s i n k f o r m i n o r i t y c a r r i e r s e t

e t

a l m o s t as effective as a p - n j u n c t i o n . T h e effect of free surfaces c a n b e r e d u c e d i n several ways.

T h e surface c a n b e p a s s i v a t e d , i.e., p r o v i d e d

w i t h a c o a t i n g w h i c h reduces N t h i n film of S i 0

2

8 t

. S i l i c o n cells c a n b e c o v e r e d w i t h a

g r o w n b y t h e r m a l o x i d a t i o n . T h e p-n

junction can be

m o v e d close to t h e surface so t h a t f e w photons are a b s o r b e d b e t w e e n the s u r f a c e a n d t h e j u n c t i o n , a n d o n l y a s m a l l f r a c t i o n of carriers is susceptible to surface r e c o m b i n a t i o n .

photogenerated

I n c r e a s i n g resistance of

t h e t h i n l a y e r b e t w e e n the p - n j u n c t i o n a n d t h e s u r f a c e imposes a p r a c t i c a l l i m i t to this m e t h o d of r e d u c i n g the f r a c t i o n of p h o t o c u r r e n t lost b y surface r e c o m b i n a t i o n .

M e t a l contacts to t h e f r o n t of the solar c e l l are

s p a c e d to a l l o w i l l u m i n a t i o n of t h e s e m i c o n d u c t o r .

T o r e a c h these c o n

tacts c u r r e n t i n t h e t o p l a y e r flows p a r a l l e l to t h e p-n p-n

junction.

When

junctions are s h a l l o w e r t h a n ~ 1 t o n , resistance loss i n the t o p l a y e r

leads to a r e d u c e d fill factor a n d m a y o u t w e i g h the g a i n i n p h o t o c u r r e n t . A n a d d i t i o n a l d r a w b a c k of this a p p r o a c h lies i n the difficult t e c h n o l o g y of p r e p a r i n g v e r y s h a l l o w junctions w i t h r e p r o d u c i b l y h i g h solar effi ciency.

I r r e p r o d u c i b i l i t y has p l a g u e d h o m o d i o d e cells m a d e of i n d i r e c t

g a p ( S i ) a n d d i r e c t g a p [ G a A s (24),

InP (25)]

m a t e r i a l s . I n S i this

p r o b l e m has b e e n l a r g e l y o v e r c o m e b y efficient use of t h e l a r g e f r a c t i o n of t h e p h o t o c u r r e n t g e n e r a t e d b e l o w the p-n

j u n c t i o n of this i n d i r e c t g a p

m a t e r i a l , a n d b y i n t r o d u c t i o n of e l e c t r i c a l fields i n the b u l k regions


(26).

124

SOLID S T A T E

Heterodiodes

and Schottky

Barrier

I n direct-gap semiconductors w i t h heterodiodes

Diodes

h i g h efficiencies

a n d S c h o t t k y b a r r i e r diodes.

gap semiconductor

CHEMISTRY

i n a heterodiode

have been

reached

Ideally the large-band-

s h o u l d n o t a b s o r b solar l i g h t .

s h o u l d act solely as a w i n d o w t h r o u g h w h i c h l i g h t penetrates to a b s o r b e d b y the s m a l l - g a p s e m i c o n d u c t o r .

I n t r u e heterodiodes t h e space

c h a r g e lies at the i n t e r f a c e b e t w e e n t h e t w o s e m i c o n d u c t o r s of Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch006

conductivity type. nCdS

(27),

It be

opposite

E x a m p l e s are p G a A s / n A l A s , p l n P / n C d S , p C d T e /

p C u S / n C d S , p C u I n S e / n C d S (28), 2

2

a b s o r b i n g s m a l l - g a p s e m i c o n d u c t o r is w r i t t e n

(by

first).

convention,

the

A heteroface

cell

contains a h o m o d i o d e w i t h a s h a l l o w j u n c t i o n that is p a s s i v a t e d w i t h a large-gap semiconductor.

T h e p r o m i n e n t e x a m p l e f o r this t y p e is t h e

n G a A s / p G a A s / p A U G a i - û A s (13, 29, 30)

c e l l w h i c h has r e a c h e d efficien

cies as h i g h as 2 1 % . M a n y combinations between able for heterodiode

semiconductors

are p o t e n t i a l l y a v a i l

cells. H i g h solar efficiency c a n b e e x p e c t e d f o r a

s m a l l e r n u m b e r of t r u e heterodiodes ments t h e i r c o m p o n e n t s

b e c a u s e of t h e n u m e r o u s r e q u i r e

h a v e to m e e t (31, 32).

T h e small-gap material

m u s t b e i n the o p t i m u m r a n g e f o r h i g h efficiency, 1.0-1.5 e V . It m u s t b e c o m b i n e d w i t h a l a r g e - g a p m a t e r i a l of o p p o s i t e c o n d u c t i v i t y t y p e . (E

g

= 2.42 e V ) is u s e d as a " w i n d o w " i n several heterodiodes.

CdS

Because

of s e l f - c o m p e n s a t i o n of a c c e p t o r i m p u r i t i e s , i t c a n b e m a d e o n l y n - t y p e a n d thus u s u a l l y r e q u i r e s p - t y p e partners. A n o t h e r i m p o r t a n t c o n d i t i o n is t h a t of m a t c h i n g l a t t i c e structures a n d i n t e r a t o m i c distances.

For

instance, G a A s a n d A l A s b o t h h a v e z i n c b l e n d e structures w i t h a differ ence i n l a t t i c e parameters of o n l y 0 . 1 2 %

at r o o m t e m p e r a t u r e .

(Ill)

p l a n e s of z i n c b l e n d e t y p e I n P a n d ( 0 0 0 1 ) of w u r t z i t e C d S m a t c h t o within 0.32%.

Unsaturated ("dangling")

bonds resulting from lattice

m i s m a t c h l e a d to a h i g h d e n s i t y of e l e c t r o n i c states of energies t h e b a n d gap.

within

T h e s e states, w h e n l o c a t e d i n the j u n c t i o n space c h a r g e ,

c a n act as r e c o m b i n a t i o n centers r a i s i n g I

0

and reducing V

o c

. T h e y can

also t r a p c h a r g e p e r m a n e n t l y , i n t r o d u c e a sheet of charge i n t h e i n t e r f a c e a n d t h e r e b y f o r m electrostatic barriers to t h e passage of

photocurrent.

A r e q u i r e m e n t m o r e precise t h a n t h a t f o r different c o n d u c t i v i t y t y p e is that the partners e x h i b i t a l a r g e difference

i n w o r k f u n c t i o n φι,

the

e n e r g y r e q u i r e d to m o v e a n e l e c t r o n f r o m t h e F e r m i t o t h e v a c u u m l e v e l . T h e d i f f u s i o n voltage V

D

of a h e t e r o d i o d e c o n s i s t i n g of materials A a n d Β

is =

I ΦΑ — ΦΒ|

a n d determines t h e m a x i m u m a t t a i n a b l e V lates to the e l e c t r o n affinity χ

ΐ9

o c

. Another requirement re

i.e., the p o t e n t i a l difference b e t w e e n the


6.

WAGNER

Photovoltaic

Solar

Cells

125

c o n d u c t i o n b a n d a n d the v a c u u m l e v e l , χ! of t h e partners has t o b e s u c h t h a t n o " s p i k e " o r " w e l l " is p r o d u c e d , at the interface, i n t h a t b a n d edge w h e r e t h e p h o t o - g e n e r a t e d m i n o r i t y carriers flow. I t m a y a p p e a r t h a t these c o n d i t i o n s , s o m e of w h i c h c a n b e r e l a x e d i n specific devices, are so n u m e r o u s a n d s t r i n g e n t as to b e p r o h i b i t i v e . H o w e v e r , heterodiodes h a v e b e e n t h e m a i n v e h i c l e s f o r the i n c o r p o r a t i o n of d i r e c t g a p s e m i c o n d u c t o r s i n solar cells, b o t h for h i g h efficiency ( e.g., G a A s / A U G a x . ^ A s ) a n d f o r t h i n - f i l m cells (e.g., C u S / C d S ) . T h e r e f o r e , Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch006

2

r e s e a r c h i n this field is i n t e n s i v e . I n a b r o a d sense, S c h o t t k y b a r r i e r s are also heterodiodes

since

a

space charge is e s t a b l i s h e d at the i n t e r f a c e b e t w e e n t w o m a t e r i a l s . T h e space c h a r g e resides e x c l u s i v e l y i n t h e s e m i c o n d u c t o r since t h e m e t a l w i t h its h i g h c o n c e n t r a t i o n of free electrons c a n n o t s u p p o r t a n e l e c t r i c field.

I n i d e a l S c h o t t k y b a r r i e r diodes t h e b a n d b e n d i n g is e q u a l to the

difference b e t w e e n the w o r k f u n c t i o n s φ of the s e m i c o n d u c t o r a n d t h e Ι

m e t a l . T y p i c a l m e t a l / s e m i c o n d u c t o r c o m b i n a t i o n s are A u (11) ( h i g h φ ) o n n - G a A s ( l o w φ) a n d A l (33) φ).

or C r (7)

or P t

(8)

( l o w φ) o n p - S i ( h i g h

B e c a u s e of e l e c t r o n i c states i n the b a n d g a p at the m e t a l / s e m i c o n -

d u c t o r i n t e r f a c e , the b u i l t - i n v o l t a g e is n e a r l y i n d e p e n d e n t of φπιβίβΐ f o r b a r r i e r s or s e m i c o n d u c t o r s w i t h E £ 2 e V . T h e s e e l e c t r o n i c states " p i n " g

the b a n d edges at the interface b y r e l e a s i n g or p i c k i n g u p charge. p i n n i n g reduces V

D

The

f r o m the i d e a l v a l u e w h i c h i n t u r n results i n l o w V

o c

.

N e v e r t h e l e s s , h i g h efficiencies h a v e b e e n o b t a i n e d w i t h v e r y t h i n

(50-

100 A ) m e t a l layers w h i c h a r e v i r t u a l l y t r a n s p a r e n t to solar l i g h t .

Such

S c h o t t k y b a r r i e r cells generate h i g h p h o t o c u r r e n t s because of efficient use o f the short w a v e l e n g t h p o r t i o n to w h i c h h o m o d i o d e s are c o m p a r a t i v e l y i n s e n s i t i v e b e c a u s e of surface r e c o m b i n a t i o n losses

(heterodiodes

are

i n s e n s i t i v e to short w a v e l e n g t h l i g h t because of a b s o r p t i o n i n the w i n d o w material). M e t a l - i n s u l a t o r - s e m i c o n d u c t o r ( M I S ) diodes represent a n a p p r o a c h t o w a r d i m p r o v e m e n t of V

o c

o v e r S c h o t t k y b a r r i e r cells (11,

The

34).

i n s u l a t o r f r e q u e n t l y is a n a t i v e o x i d e f o r m e d o n the s u r f a c e of s e m i c o n d u c t o r wafers ( S i , G a A s ) d u r i n g storage.

W h e n true Schottky barriers

are f o r m e d , this o x i d e l a y e r is c l e a n e d off b e f o r e the m e t a l film is d e p o s i t e d . F o r the f a b r i c a t i o n of M I S d i o d e s , i t is left o n t h e s e m i - c o n d u c tor. M I S cells e x h i b i t l a r g e r V increased V

o c

o c

t h a n s i m p l e S c h o t t k y b a r r i e r cells.

is t e n t a t i v e l y a s c r i b e d to e i t h e r a r e d u c t i o n i n I

Q

The

b y the

i n s u l a t o r or to a n a d d i t i o n a l voltage d r o p across the i n s u l a t o r o r i g i n a t i n g at c h a r g e t r a p p e d i n e l e c t r o n i c states t h a t reside at the i n s u l a t o r - s e m i c o n d u c t o r interface. T h e i n s u l a t o r c a n also r e d u c e t h e p h o t o c u r r e n t J . L

T h i c k n e s s a n d e l e c t r o n i c p r o p e r t i e s of the t h i n i n s u l a t o r films are c r i t i c a l f o r o p t i m u m tradeoff b e t w e e n i n c r e a s e d

and reduced Z . L


126

SOLID S T A T E C H E M I S T R Y

Table III.

Solar Cells* m ciency (%)

Single/ Polycryst.

Cell

Air Mass

Refer ence

0 0

85 S7 38 39


Silicon: pSi/nSi nSi/pSi nSi/pSi nSi/pSi nSi/pSi pSi/nSi pSi/nCdS pSi/nIn 0 pSi/Cr pSi/Al 2

Gallium

S S ribbon Ρ Ρ amorphous S S S s

3

6 15 10 1 6 2 5 6 8 8

40 ω 41 9,10 7 S3

arsenide:

s

pGaAs/nGaAs pGaAs/iiAlAs p n G a A s / p A l j j G a i . »As nGaAs/pGaP pGaAs/nGaP nGaAs/Au(MIS) nGaAs/Pt Indium

s s s s s Ρ

11 19 21 8 7 15 5

s s Ρ

7 15 5

s Ρ

12 6

61 27

4 ~2 7 5 1 4 8 6 2 12 4

46 36 47 8 48 49 50 50 62 51 52

Π

4

13 42 43 11 8

phosphide:

plnP/nlnP plnP/nCdS plnP/nCdS Cadmium

2 2

25 U 45

telluride:

pCdTe/wCdS pCdTe/nCdS Semiconductors

containing

pCu S/nSi pCu S/nCdS pCu S/nCdS pCui.gSe/nGaAs pCui Se/nInP pCu Se/nCdSe pCu Te/nCdTe pCu Te/nCdTe pCuInSu/nCdS pCuInSe /nCdS pCuInSe /nCdS 2

2

2

8

2

2 2

2 2

transition

metals: S S Ρ Ρ Ρ Ρ s Ρ Ρ s Ρ

0 — — — — — —

1 —

"The layer on top of the cell is listed first for homodiodes; in heterodiodes the principal absorbing semiconductor is written first. Published efficiencies are rounded off to integers.


6.

WAGNER

Photovoltaic

Solar

127

Cells

T a b l e I I I presents a list of p u b l i s h e d p h o t o v o l t a i c solar cells w i t h d a t a a b o u t c r y s t a l l i n i t y , efficiency, a n d t e s t i n g c o n d i t i o n s .

Cells w i t h

m a x i m u m r e p o r t e d efficiencies are s h o w n i n a d d i t i o n t o the first r e p o r t e d silicon (35) and C u S / C d S (36)

cells.

2

Reduction

of Cost of Solar Cells

T h e o n l y solar cells t h a t are c o m m e r c i a l l y a v a i l a b l e are s i l i c o n h o m o -


diodes. T h e i r c a p i t a l cost p e r u n i t p o w e r d e l i v e r e d is a p p r o x i m a t e l y 100 t i m e s t h a t of c o n v e n t i o n a l p o w e r sources.

O n e reason f o r its h i g h cost

is the s m a l l v o l u m e of p r o d u c t i o n w h i c h does n o t p e r m i t e c o n o m y of scale. T h e p r i n c i p a l f a c t o r i n the h i g h p r i c e , h o w e v e r , is the n e e d f o r w a f e r s of h i g h l y p u r e a n d h i g h l y perfect m a t e r i a l . M e t a l l u r g i c a l - g r a d e S i is p r e p a r e d b y r e d u c t i o n of S i 0 t i o n i t is c o n v e r t e d t o S i H C l

3

2

w i t h C i n a r c furnaces. F o r p u r i f i c a

w h i c h is d i s t i l l e d .

Pure polycrystalline

s i l i c o n is t h e n o b t a i n e d b y p y r o l y s i s . S i n g l e crystals are p u l l e d b y the C z o c h r a l s k i m e t h o d f r o m t h e m e l t . T h e s i n g l e - c r y s t a l b o u l e s are c u t i n t o slices w h i c h are p o l i s h e d to r e m o v e m e c h a n i c a l d a m a g e .

T h e actual cell

f a b r i c a t i o n i n v o l v e s c o n t r o l l e d i n - d i f f u s i o n of a d o p a n t to f o r m a p - n j u n c t i o n , a p p l i c a t i o n of b a c k contact a n d f r o n t contact g r i d , a n d e v a p o r a t i o n of a n antireflection c o a t i n g . It is o b v i o u s t h a t t h e p r e s e n t - d a y m a n u f a c t u r e of S i c e l l p r o d u c e s s m a l l a c t i v e areas w h i l e b e i n g l a b o r - i n t e n s i v e . S e v e r a l strategies are b e i n g p u r s u e d t o r e d u c e c e l l costs.

T h e most

o b v i o u s is to raise t h e o u t p u t p e r c e l l a r e a b y i n c r e a s i n g c e l l efficiency, a n d b y u s i n g i n e x p e n s i v e collectors, o r concentrators, t o a c h i e v e h i g h e r p o w e r d e n s i t y . F i g u r e 9 presents a s c h e m a t i c of p o w e r c o n v e r s i o n losses occurring i n a typical Si cell (53). b y raising V

o c

T h e efficiency c a n s t i l l b e i m p r o v e d

( r e d u c i n g the v o l t a g e l o s s ) , b y m o r e efficient c o l l e c t i o n of

p h o t o - g e n e r a t e d carriers ( r e d u c i n g r e c o m b i n a t i o n l o s s ) , b y u s i n g b e t t e r m a t c h e d antireflection coatings, a n d b y r e d u c i n g series resistance.

At

best, one m i g h t d o u b l e t h e efficiency p e r u n i t a r e a , p r o b a b l y w i t h a s i m u l t a n e o u s increase i n m a n u f a c t u r i n g cost. I n e x p e n s i v e

concentrators

c o m b i n e d w i t h s m a l l a c t i v e c e l l area, i.e., large c o n c e n t r a t i o n ratios, are p r e s e n t l y u n d e r c o n s i d e r a t i o n for S i ( 5 4 )

and G a A s (55)

cells. S i n g l e -

c r y s t a l G a A s cells w h e n p r o d u c e d i n d i v i d u a l l y are e x p e c t e d to b e

con

s i d e r a b l y m o r e expensive t h a n S i cells b e c a u s e of t h e h i g h cost of G a A s w a f e r s ( a b o u t 10 times that of S i w a f e r s ) , a n d p a r t i c u l a r l y b e c a u s e m o s t G a A s - b a s e d cells are p r o d u c e d b y the v e r y expensive l i q u i d - p h a s e - e p i taxy method.

H o w e v e r , G a A s heterodiodes

have reached the highest

efficiency yet o b t a i n e d , a n d , c o m p a r e d w i t h S i , the efficiency of G a A s b a s e d c e l l is less affected

b y o p e r a t i o n at e l e v a t e d t e m p e r a t u r e , a n

i m p o r t a n t a d v a n t a g e for c o n c e n t r a t o r a p p l i c a t i o n s . T h e other a p p r o a c h t o w a r d less expensive solar energy is to r e d u c e t h e cost p e r c e l l area w h i l e r e t a i n i n g u s e f u l efficiency.

The two main


128

SOLID STATE

CHEMISTRY

IUU NOT ABSORBED (hv « Eg)

g 76 ABSORBED, BUT EXCESS ENERGY (hv -Eg) CONVERTED TO HEAT


ë £

44 38

BASIC FILL FACTOR (DIODE EQUATION]

LU Ο OC LU

°-

VOLTAGE LOSS (V /E ) oc

19 13 11 0 >

g

RECOMBINATION LOSS REFLECTION, SERIES RESISTANCE, FILL FACTOR OUTPUT POWER

Figure 9. Illustration of the principal contributions to power loss during photovoltaic conversion in a typical silicon cell ( 53 ) avenues are t h e d e v e l o p m e n t o f m e t h o d s f o r i n e x p e n s i v e g r o w t h o f s i n g l e crystals a n d t h e f a b r i c a t i o n o f p o l y c r y s t a l l i n e t h i n - f i l m cells. Silicon

ribbons

the edge-defined

2.5 c m w i d e a n d ~ 0.02 c m t h i c k c a n b e g r o w n b y

film-fed

t e c h n i q u e at rates o f ~ 2 c m / m i n ( 3 8 ) .

These

r i b b o n s e x h i b i t v e r y h i g h c r y s t a l l i n i t y ; solar cells u p t o 1 0 % efficient have been produced.

T h e t e c h n i q u e is b a s e d o n t h e c o n t r o l l e d s o l i d i f i c a

t i o n o f a r i b b o n o f m o l t e n s i l i c o n p u l l e d , w i t h a seed c r y s t a l , f r o m a slot l i k e c a p i l l a r y w h i c h is i m m e r s e d i n a s i l i c o n m e l t . T h i s process, w h i c h is a m e n a b l e t o a u t o m a t i o n , avoids t h e u s u a l s l i c i n g a n d p o l i s h i n g step. A s i m i l a r b u t less d e v e l o p e d t e c h n o l o g y is t h e d e n d r i t i c w e b g r o w t h f r o m s i l i c o n melts ( 5 6 ) . H e r e a ribbon is p u l l e d , w i t h o u t a d i e , b y t w o b o u n d i n g d e n d r i t e s w h o s e g r o w t h is started w i t h a seed. T h i n - f i l m p o l y c r y s t a l l i n e cells represent another a p p r o a c h t o cost r e d u c t i o n . P r o d u c t i o n o f t h e C u S / C d S cells, t h e best k n o w n

example

2

f o r s u c h cells ( 6 ) , t y p i c a l l y i n v o l v e s p r e p a r a t i o n o f a c o n d u c t i n g s u b strate, e.g., Z n - p l a t e d C u sheet, e v a p o r a t i o n o f a 2 0 - 4 0 / x m t h i c k C d S film,

a b r i e f e t c h o f t h e C d S f o l l o w e d b y a 10-sec d i p i n C u C l

2

solution

w h i c h forms a C u S l a y e r w i t h a f e w t h o u s a n d A thickness, a 2 - m i n a c t i v a 2

tion anneal i n a i r at 250°C;

finally,

c o n t a c t g r i d a n d a n t i - r e f l e c t i o n coat

i n g are p r o d u c e d , a n d a t r a n s p a r e n t c o v e r is a p p l i e d w i t h e p o x y r e s i n . This thin-film cell should b e amenable to highly automated production. A n o t h e r a d v a n t a g e is t h e e c o n o m i c a l u s e o f s e m i c o n d u c t o r s w h i c h m a y c o n t a i n c o m p a r a t i v e l y r a r e elements ( C d , G a , I n ) a n d w h i c h e v e n w h e n a b u n d a n t ( S i ) are expensive w h e n p u r i f i e d f o r solar use. H i g h e s t r e p o r t e d efficiencies f o r the C u S / C d S c e l l a r e ~ 7 % . 2

H i g h e r values a r e


6.

WAGNER

Photovoltaic

Solar

129

Cells

p r e d i c t e d f o r m o d i f i e d cells w h i c h c o n f o r m better to c e r t a i n r e q u i r e ments f o r i d e a l heterodiodes,

viz., lattice m a t c h a n d proper

electron

affinities; the a l l o y i n g of C d S w i t h Z n S has b e e n a step i n this d i r e c t i o n T h e C u S / C d S c e l l has b e e n p l a g u e d b y r a p i d d e g r a d a t i o n w h i l e

(47).

2

i n o p e r a t i o n . I t has b e e n p r o p o s e d to r e d u c e f a i l u r e c a u s e d b y r e a c t i o n of C u S w i t h a m b i e n t 0 2

a n d H 0 b y c a r e f u l e n c a p s u l a t i o n , a n d to a v o i d

2

2

e l e c t r o c h e m i c a l d e c o m p o s i t i o n of C u S u n d e r the cell's o w n

photovoltage

2

b y m a k i n g this s e m i c o n d u c t o r s t r i c t l y s t o i c h i o m e t r i c .

(57) Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/ba-1977-0163.ch006

It is nevertheless d e s i r a b l e to d e v e l o p alternatives. I n t e r e s t i n g results have been

obtained w i t h polycrystalline Si homodiodes prepared

c h e m i c a l v a p o r d e p o s i t i o n (40).

by

T h e s m a l l c r y s t a l l i t e size, a n d to some

extent the c o m p a r a t i v e l y h i g h i m p u r i t y content, conflict w i t h t h e neces sity f o r l a r g e m i n o r i t y c a r r i e r d i f f u s i o n l e n g t h a n d h a v e l i m i t e d the effi c i e n c y to date to a b o u t

6%.

T h e C u I n S e / C d S (51) 2

a n d I n P / C d S (44)

heterodiodes

prepared

i n s i n g l e c r y s t a l f o r m i n or l a b o r a t o r y are a t t r a c t i v e c a n d i d a t e s f o r t h i n film

cells. A l t h o u g h the first t h i n - f i l m C u I n S e / C d S cells w i t h η — 2

4%

h a v e a l r e a d y b e e n p r o d u c e d ( 5 2 ) , w e h a v e f o c u s e d o u r a t t e n t i o n o n the I n P / C d S c e l l because of the greater e x p e r i e n c e a c c u m u l a t e d w i t h I n P . S i n g l e - c r y s t a l I n P / C d S cells are v e r y stable to d e g r a d a t i o n i n the atmos p h e r e . W e h a v e p r o d u c e d t h i n - f i l m I n P / C d S cells o n c a r b o n substrates. T h e efficiency of c u r r e n t p o l y c r y s t a l l i n e samples is 5 % . on V

o c

and J

expected

s c

However, based

of these e a r l y cells, efficiencies of at least 7 - 8 %

can be

(45).

F u t u r e efforts to p r o d u c e i n e x p e n s i v e solar cells w i l l go b e y o n d exist i n g m a t e r i a l s a n d processes.

F o r instance, a large n u m b e r of

semicon

d u c t o r s exist w h o s e b a n d g a p a n d c o n d u c t i v i t y h a v e n o t b e e n sufficiently c h a r a c t e r i z e d to p e r m i t a d e c i s i o n e v e n a b o u t t h e i r p o t e n t i a l usefulness i n solar cells ( 5 8 ) .

M a n y of these s e m i c o n d u c t o r s are c o m p o s e d of i n e x

p e n s i v e r a w m a t e r i a l s . P u r i f i c a t i o n to s o l a r - g r a d e s e m i c o n d u c t o r s , r e n t l y a n expensive methods.

step, w i l l h a v e to b e

c a r r i e d out b y

A n e x a m p l e is a u n i t c o m b i n i n g r e d u c t i o n of S i 0

2

cur

continuous to S i , r e a c

t i o n to S i F , d i s t i l l a t i o n of S i F , a n d d i s p r o p o r t i o n a t i o n to p u r e p o l y 2

2

c r y s t a l l i n e S i a n d to S i F

4

(59).

Conclusion W h i l e m u c h progress has b e e n m a d e i n a n a l y z i n g a n d i m p r o v i n g the p e r f o r m a n c e of solar cells, i t is not y e t possible to p r e d i c t m a t e r i a l s a n d processes for i n e x p e n s i v e converters.

T h e present s i t u a t i o n calls f o r

a n increase i n the n u m b e r of a v a i l a b l e options a n d f o r the of

new

production

techniques,

both

with

development

a substantial input

chemists.


from

130

SOLID STATE

CHEMISTRY

Nomenclature


A

diode factor

a, b, c

l a t t i c e p a r a m e t e r s ( c m or A )

D

n p

d i f f u s i o n coefficient of electrons i n p - t y p e m a t e r i a l ( c m s" )

D

p n

d i f f u s i o n coefficient of holes i n η-type m a t e r i a l ( c m s ' )

E

q

b a n d - g a p energy ( e V )

1

2

2

Ei

F e r m i level i n an intrinsic semiconductor ( e V )

E

n

F e r m i l e v e l i n a n η-type s e m i c o n d u c t o r ( e V )

E

p

1

F e r m i level i n a p-type semiconductor ( e V )

FF

f i l l factor, o r c u r v e f a c t o r

h

P l a n c k ' s constant ( 6.62 Χ 1 0 "

I

electrical current density ( A c m " )

Z

photocurrent density ( A c m " )

34

Js) 2

2

L

i p 0

/

operating current density ( A c m " ) 2

short c i r c u i t c u r r e n t d e n s i t y ( A c m " ) 2

8 C

ίο

reverse s a t u r a t i o n c u r r e n t d e n s i t y ( A c m " )

k

B o l t z m a n n ' s constant ( 1.380 Χ 1 0 "

2

23

J K" ) 1

L

diffusion length ( c m )

iV

c o n c e n t r a t i o n of i o n i z e d acceptors ( c m " )

N

A

0

3

effective d e n s i t y of states i n c o n d u c t i o n b a n d ( c m " ) 3

Ν

c o n c e n t r a t i o n of i o n i z e d donors ( c m " )

Ny

effective d e n s i t y of states i n v a l e n c e b a n d ( c m " )

iV t 8

d e n s i t y of surface r e c o m b i n a t i o n centers ( c m " )

iV

t

d e n s i t y of b u l k r e c o m b i n a t i o n centers ( c m " )

3

Ώ

3

2

3

η

c o n c e n t r a t i o n of electrons ( c m " )

Πι

carrier concentration i n an intrinsic semiconductor ( c m " )

tin

c o n c e n t r a t i o n of electrons i n η-type m a t e r i a l ( c m " )

P

3

i n

8

3

i n c i d e n t solar p o w e r flux ( W c m " ) 2

ρ

c o n c e n t r a t i o n of holes ( c m " )

PP

c o n c e n t r a t i o n of holes i n p - t y p e m a t e r i a l ( c m " )

q

e l e c t r o n i c c h a r g e ( 1.60 χ 1 0 "

Rex

e x t e r n a l l o a d resistance ( Ω )

R

3

3

8

i n t e r n a l series resistance ( Ω )

Re!,

i n t e r n a l s h u n t resistance ( Ω )

Τ V

19

C )

temperature ( Κ ) D

diffusion voltage ( V )

Voc

open-circuit voltage ( V )

V

o p e r a t i n g voltage ( V )

o p

ν

t h e r m a l v e l o c i t y of charge carriers ( c m s * ) 1

χ

distance ( c m )

α

o p t i c a l a b s o r p t i o n coefficient ( c m " )

Ε

e l e c t r i c field ( V c m " )

1

1


6.

W A G N E R

Sohr

131

Cells

c

r e l a t i v e d i e l e c t r i c constant

€o

p e r m i t t i v i t y of free space ( 8.86 Χ 1 0 "

λ

wavelength ( c m )

ν

f r e q u e n c y ( s" )

ρ

density of charge ( C c m ' )

σ

14

f cm

- 1

)

1

3

c a p t u r e cross s e c t i o n of a surface defect ( c m ) 2

β ί

a

c a p t u r e cross s e c t i o n of a b u l k defect ( c m )

τ

l i f e t i m e of a c h a r g e c a r r i e r ( s )

τι

l i f e t i m e d e t e r m i n e d b y r e c o m b i n a t i o n of t y p e i ( s )

2

t


Photovoltaic

τ

l i f e t i m e o f electrons i n p - t y p e m a t e r i a l ( s )

η ρ

τρη r

l i f e t i m e of holes i n η-type m a t e r i a l ( s ) l i f e t i m e d e t e r m i n e d b y surface r e c o m b i n a t i o n ( s )

e t

φι

w o r k function of semiconductor i ( e V )

χι

e l e c t r o n affinity o f s e m i c o n d u c t o r i ( e V )

Literature

Cited

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