and its importance for Solar Cells

statementdizzyeyedSemiconductor

Nov 1, 2013 (3 years and 9 months ago)

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Concepts of Contact Resistance
and its importance for Solar Cells

-
Mehul

Raval
(
Phd

student)

Email


mehulmatrix@gmail.com

Outline


Theoretical model of Metal
-
Semiconductor
Interface


Practical condition for
Ohmic

Contacts


Concept of Contact Resistivity


Relation of Contact Resistance and Contact
Resistivity


Solar Cell Contact Resistance with an illustration


Summary

2

Theoretical model of Metal
-
Semiconductor Interface*










Figure.
Schottky

model for metal
-
semiconductor contacts


Schottky

model gives the barrier height for M
-
S interface as,


Φ
B

=
Φ
M

-

χ

,


where,
Φ
B

= Barrier Height,


Φ
M

= Metal work function &


χ

= Semiconductor electron affinity (
contd
…)

3

* D. K,. Schroder and D. L. Meier, “Solar cell contact resistance
-
A review,” IEEE Trans. Electron
Devices,
Vol

ED
-
31, No 5, May 1984,pp. 637
-
647.


Φ
B

doesn’t depend on the doping of semiconductor.


Good
ohmic

contact requires a low
Φ
B

indicated by ‘accumulation’
contact.


For measured
Φ
B

v/s
Φ
M,

slope ~0.3 for Si and ~0.06 for
GaAs
*.


The interfacial chemistry plays an important role and is difficult to control.


As a rule of thumb,
Φ
B

is roughly 2/3 times the band gap for n
-
type
material and 1/3 times for p
-
type material.**


Hence ‘accumulation’
ohmic

contacts is virtually impossible, especially for
n
-
type substrates.


4

* *C. A. Mead, “Physics of interfaces,” in
Ohmic

Contacts to
Semiconductors,B
. Schwartz, Ed.
New York:
Electrochem
. SOC.,1969, pp 3
-
16.

* J. L.
Freeouf
, “
Silicide

interface
stoichiometry
,” J. Vac.
Sci.Technol
., vol. 18, pp. 910
-
916, Apr.
1981.

Practical condition for
Ohmic

Contacts


Barrier Height engineering is not a realistic way of making
ohmic

contacts.


Only practical way is to deposit metal on a highly doped semiconductor.


Even if
Φ
B
is significant, narrow space
-
charge region due to heavily doped
semiconductor allows tunneling.


Various mechanisms for conduction:


-
>
Thermionic Emission:

Carriers gain sufficient


energy to cross the barrier.


Dominant for N
D

< 10
17

cm
-
3


-
>
Thermionic/Field Emission:

Carriers excited


to energy < full barrier height and then


tunneling takes place.


Occurs for 10
17

cm
-
3

< N
D

< 10
19

cm
-
3
.


-
>
Field Emission:

Carriers tunnel through the


barrier. Occurs for N
D

> 10
19

cm
-
3
.



Figure. Conduction mechanisms


with increasing d
oping


concentration

5

Concept of Contact Resistivity


Contact Resistivity(
ρ
c
) defined as,


ρ
c
= (
δ
J/

δ
V)
-
1

|V = 0

(ohm
-

sq.cm)


and
characterizes contact independent of contact area.


ρ
c
(TE) =
ρ
1 exp(q

Φ
B’/
kT
),
ρ
1 = constant inversely prop to temp.


ρ
c
(FE) =
ρ
1C
2
exp(q

Φ
B’/
Eoo
), C
2

= Function of N
D
, T &
Φ
B’.


Eoo

α

(N
D
)
1/2
.


ρ
c
(TFE) =
ρ
1C
1
exp(q

Φ
B’/
Eo
), C
1

= Function of N
D
, T &
Φ
B’.


Eo

=
Eoo.coth
(
Eoo
/
kT
).


For lightly doped semiconductors,
kT
/
Eoo

>> 1 and thermionic emission is
dominant.


For highly doped semiconductors,
kT
/
Eoo

<< 1 and field emission is
dominant.


For
kT
/
Eoo

≈ 1, Thermionic/Field Emission is dominant.


ρ
c

decreases sharply as the doping concentration increases.




6

Relation of Contact Resistivity and
Contact Resistance


Contact Resistance(
R
c
) important for device
behavior rather than
ρ
c
.


Tempting to divide
ρ
c

by the contact area to
obtain
R
c
(ohms).


This need not apply for contacts on diffused
layers as the current could flow only through
certain section under the contacts.



Transfer Length(L
T
) = (
ρ
c
/R
s
)
1/2



Approximate relation for V(x) under the contact


V(x) = V
o

exp(
-
x/L
T
)*.


Concept of L
T

holds true only for horizontal +
lateral current flow.




























7

* P. L.
Hower
, W. W. Hooper, B. B. Cairns, R. D.
Fairman
, and D. A.
Tremere
, “The
GaAs

field
effect transistor”
inSemiconductors

and Semimetals, vol. 7A, R. K.
Willardson

and A. C. Beer,
Eds. New York: Academic Press, 1971, pp. 147
-
200.

Fig. Current crowding at
contact edges with
voltage distribution


R
c

= (L
T
/Z)R
s

coth
(L/L
T
)
*, the expression is valid only for Z >> L & L
T

and for
negligible metal resistance.


Two limiting cases for
R
c

are,


For L ≥ 1.5 L
T,
R
c

≈ L
T
R
s
/Z =
ρ
c
/L
T
Z,


while for L < 0.5 L
T
,
Rc


ρ
c
/LZ.


Another useful term is
R
c
Z
(normalized contact resistance) and is shown in
figure 2 for different L and
ρ
c

values.


From
figure,it

can be observed that L
T

is few um regardless of L. So
decreasing L will not increase
R
c
, but will increase the grid resistance.

8

Fig 1. Dimensions of the finger pattern


for the contacts

* D. K,. Schroder and D. L. Meier, “Solar cell contact resistance
-
A review,” IEEE Trans. Electron
Devices,
Vol

ED
-
31, No 5, May 1984,pp. 637
-
647.

Fig 2.
R
c
Z

as a function of various


parameters

Solar Cell Contact Resistance


Series Resistance(
r
s
) of a solar cell is a combination of various components
as shown.


R
4

is the contact resistance.


P
out

= JV, where P
out
= O/P power density, J = current density & V =
voltage at max power point.


9

Figure. Components of solar cell


series resistance


P
loss
(due to series resistance) = J
2
A
2
r
s
≤ K
1

P
out
A
, where A = solar cell area
and K
1

= ratio of series resistance power loss/ O/P Power.


Hence,
r
s

≤ K
1

Pout/ J
2
A = K
1
V/JA.


Let
K
2

=
R
c
/
r
s

i.e. ratio of contact resistance to total resistance.


Also since metallization covers a fraction of total cell, let
K
3

= A
m
/A = ZL/A
.


So,
R
c

≤ K1 .K2.K3. V/JZL or
R
c
Z

≤ K1 .K2.K3. V/JL


An illustration: J = 30mA/ sq.cm, V = 0.5V, K
1

= 0.05(series resistance
power loss is 5%), K
2

= 0.1(contact resistance is 10% of series resistance),
K
3

= 0.05(contact area is 5% of total cell area) and L = 50um. Then


R
c
Z

= 0.83ohm
-
cm.


So from figure , for R
s

= 100 ohms/square,
ρ
c

≤ 2 x 10
-
3

ohm
-
sq.cm.


Similarly for back
-
side contacts, K
3

= 1 so
R
c
Z

≤ 17 ohm
-
cm and
ρ
c
≤ 0.1
ohm
-
sq.cm.


Allowable contact resistance is inversely proportional to J and hence
ρ
c
has
to reduce by the same order.


Example
-

For 100 suns,
ρ
c
(front) ≤ 2 x 10
-
5

ohm
-
sq.cm


10


What are the doping values for the desired contact resistivity?


Variations can be present due to variability in the measurements,
substrate doping not accurately known.



So for Si solar cells, for
ρ
c

< 2m ohm
-
sq.cm


N
D

> 10
19
cm
-
3

( for n
-
contact) and N
A

> 10
17
cm
-
3

(for p
-
type contact)


Relaxed criteria for p
-
type due to larger contact area and lower barrier
height.

11

Figures. Contact Resistivity for Al on Si data as a function of doping concentration

Summary


Accumulation mode
ohmic

contact is virtually impossible between a metal
and semiconductor due to lack of control over interfacial chemistry.


Heavily doped semiconductor allows tunneling of carriers and hence field
emission mode is required for low
ρ
c.


R
c

cannot be simply calculated by dividing
ρ
c
with contact area as the
transfer length(L
T
) is applicable for lateral current flow.


ρ
c
< 2 m ohm
-
sq.cm is a reasonable value for power loss is < 5% due to
front side metallization.



N
D

> 10
19
cm
-
3

( for n
-
contact) would be needed to achieve
ρ
c
< 2 m ohm
-
sq.cm.


In part 2 of presentation, ill take up methods for measurement of
ρ
c.

12


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