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
13
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