Solar Cells 2
shoomoosh
class08SolarCells2020-08Carriertransport2.pptxCarrier transport (2)
Prof. Richard R. King
Solar Cells
EEE 565
Arizona State University
‹#›
Thank you !
Many thanks to
Prof. Steve Goodnick
for his slides on solar cells which appear throughout this class
‹#›
In solar cells, surface recombination and grain boundary recombination play an important role: Both are “surface” phenomena rather than bulk
Interruption of the crystal lattice at a surface results in formation of interface states, or traps
Surface and/or interface recombination results in a flux of carriers towards the boundary due to diffusion. Surface recombination is treated as a boundary condition on np or pn in terms of a surface recombination velocity, Sn
Surface recombination rate depending on treatment of Si surface typically lies in the range between 102 - (6-8)·104 cm/s
The surface recombination rate on the Si-SiO2 interface can be as small as ≤ 0.5 cm/s (passivation)
Surface recombination
‹#›
Dominant recombination mechanism in direct gap semiconductors
Recombination rate is proportional to the product of the population of electrons and holes
Most important mechanism for light emitting devices
Primarily spontaneous emission until population inversion reached
Br is the band-to-band recombination coefficient (cm3/s)
For low level injection in n-type, with nno = ND :
Radiative recombination
‹#›
Cn,p are increasingly larger for narrower bandgaps
Under low level injection:
Strong doping dependence
Auger recombination
High level injection:
‹#›
• Suppose that we have uniform illumination in an n-type material, with a generation rate, GL. The spatial derivative is zero, and the diffusion equation under low level injection becomes:
• Assume now steady state conditions (time derivative zero). Then the excess minority carrier density is:
Example: Uniform illumination
‹#›
• Suppose now that the light has been on for a long time, and at time t = 0, it is turned off:
• The solution just decays with a time constant p
Example: Uniform illumination
‹#›
• Assume that light is absorbed in a narrow, infinitesimal surface layer at x = 0, in a p-type material, such that the minority carrier density there is np(0) >> np0 . Under low level injection in steady state:
where Ln is the minority carrier diffusion length
• Boundary conditions:
Example: Steady state injection
‹#›
• The solution is an exponential decay in space with a characteristic decay length given by the minority carrier diffusion length.
The minority carrier diffusion length can be thought of as the average distance a minority carrier travels before it recombines with a majority carrier.
Example: Steady state injection
‹#›
(
)
po
p
n
p
n
n
n
S
dx
dn
D
-
=
(
)
2
i
r
r
r
sp
n
np
B
R
np
B
R
-
=
=
(
)
(
)
pr
no
n
no
no
n
no
r
pr
p
p
p
n
p
n
B
R
t
-
=
-
»
ts
Coefficien
Auger
,
2
2
=
=
=
p
n
p
CHHL
n
CCCH
C
np
C
R
p
n
C
R
type
p
N
C
type
n
N
C
A
p
auger
D
n
auger
-
=
-
=
2
2
1
1
t
t
(
)
2
1
n
C
C
p
n
auger
D
+
=
t
(
)
p
no
n
L
n
p
p
G
t
p
t
-
-
=
¶
¶
p
L
n
no
n
G
p
p
p
t
=
D
=
-
(
)
p
p
t
p
L
t
n
n
p
n
n
e
G
e
p
p
dt
p
p
d
t
t
t
t
/
/
0
1
-
-
=
D
=
D
-
=
D
D
(
)
(
)
p
L
n
p
no
n
n
G
p
p
p
t
p
t
t
=
D
-
-
=
¶
¶
0
;
(
)
n
n
n
L
x
L
x
p
n
n
p
p
n
po
p
p
n
D
L
Be
Ae
n
D
n
x
n
n
n
x
n
D
n
n
t
t
t
=
+
=
D
=
D
-
¶
D
¶
=
-
-
¶
¶
-
;
0
;
0
/
/
2
2
2
2
(
)
(
)
(
)
A
n
n
n
B
n
po
p
p
p
=
-
=
D
=
=
¥
D
0
0
;
0
,
0
(
)
(
)
(
)
(
)
n
n
L
x
p
po
p
L
x
p
p
e
n
n
x
n
or
e
n
x
n
/
/
0
0
-
-
+
=
D
=
D
