Sungyun Kim
May 26, 2020
140

# Upper limit to the photovoltaic efficiency of imperfect crystals

The upper limit to the photovoltaic efficiency of imperfect crystals.

May 26, 2020

## Transcript

1. Upper limit to the photovoltaic eﬃciency of
imperfect crystals
&
Sunghyun Kim
김성현 (金聖鉉)
Imperial College London

2. London, 2017
2

3. 3 years of hard work
at Imperial College London
3

4. Acknowledgement
4
Prof. Aron Walsh
Dr. Ji-Sang Park
Dr. Samantha N. Hood
Dr. Thomas Unold
Dr. José A. Marquez
ICL HZB

5. Solar Cell 101
☀ ♨

P.T. Landsberg and G. Tonge, J. Appl. Phys. (1980)
Light in, electricity out
(XX. YY. 200Z) Thermodynamics 101

6. Thermodynamics of Heat Engine
!"#\$%&
= 1 − '!"#\$%
'&'(
= 95%!
The efficiencies of commercial solar cells
are much below 30%.
High temperature of sun enables
extremely efficient engines
when irreversible loss has not existed.
The losses from irreversible heat transfer
are significant in solar cells.
(XX. YY. 200Z) Thermodynamics 101

7. Solar Cell: Efficiency Matters
7
If you were here?
?

8. When is it time to stop?
8

9. Seriously, when?
9
Upper bound of photovoltaic efficiency
defined by laws of physics and chemistry

10. Theory of Solar Cells 1/3: SQ limit
10
J. Appl. Phys. 32, 510 (1961)
recombination

11. Theory of Solar Cells 2/3: SRH statistics
11
Phys. Rev. 87, 835 (1952)
Phys. Rev. 87, 387 (1952)

12. Theory of Solar Cells 3/3: Carrier Capture
12

13. We have/know (almost) everything.
But, can we predict something?
13
Theory Experiment
SQ limit
SRH statistics
MPE process
Eﬃciency
Capture cross-section
Empirical parameters?
η = max η(Eg
, NT
, ET
, Cn/p
,…) ?

14. I have a dream.
14
Structure in, Efficiency out

15. What can a computational [physicist] do?
15
“It’s time to see what I can do,
to test the limits and break through”
- Queen Elsa of Arendelle

16. Getting parameters for a certain material:
The equation of (almost) everything
16
“Oh, I performed DFT
calculations”

17. Maximum Photovoltaic Efficiency of Real Materials
from First-Principles
17
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)
C
p
C
n
E
gap
VB CB
E
gap
Energy
Configuration coordinate
p
0
n
0
ΔE
f
E
F
E
F
E
T
N
V
p
0
+Δn
n
0
+Δn
DOS
N
C
μ
A
μ
B
B AB
A
E
F,p
qV
E
F,n
J
V
C
n
: Electron
capture
C
p
: Hole
capture
V
B
+
V
A

V
B
VA
E
F
h+
e−
J
SC
J
0
B
T−1) qR
SRH
W η
max
Band
structure
E
gap
N
C
N
V
ro t
condition
μ
ormation
energy
E
f
, E
T
Configuration
coordinate
Capture
coe cient
C
n/p
Se consistent
ermi e e
E
F
N
T
n
0
p
0
recom ination rate
R
SRH
J
SC
J
0
1
1 2
3
3
4
5 6
6 7 8
5
5
4
Take no empirical parameters!

18. You know where to ﬁnd them.
18
CarrierCapture.jl: https://github.com/WMD-group/CarrierCapture.jl
SC-Fermi: https://github.com/jbuckeridge/sc-fermi
(a)TLC; Wannier_alpha: https://github.com/WMD-group/TrapLimitedConversion
DefectwithTheBoys: https://github.com/kavanase/DefectsWithTheBoys
CPLAP
CarrierCapture.jl
Wannier_alpha
SC-Fermi
(a)TLC
DWTF

19. Why am I doing this?
19
If only we have known the limit before we spend
too much time and money…

20. Kesterites: We put much effort into but…
20
By other's faults wise men correct their own.

21. Ga

Brief (alternative) history of kesterites
Si
Cd Te
Cu In Se
Cu Zn Sn
S/
Se
2−
2+
3+
4+
2+
1+

22. Can it absorb light?

23. Of course, it can, but how well?
23
0 1 2 3 4 5
Energy (eV)
101
102
103
104
105
106
107
Absorption coe cient (cm−1)
0
0.1
0.2
0.3
0.4
0.5
0.6
Solar
spectrum
Solar
spectrum
Absorption
coe cient
an ap
Spectral irra iation ( m−2eV−1)
For 2 µm-thick CZTS,
α = 104 cm−1 corresponds to a = 98%.
Very well

25. Two Common Characteristics of “Killer” Centers
Deep level Large lattice relaxation
“… So-called killer centers, with fast
nonradiative transitions, … we list four
examples:

2. Defect with favorable vibrational
properties, that is, with large-
amplitude modes promoting the
transitions, and large-energy modes
to take up the electronic energy
…”
- A. M. Stoneham in Defects and Defect
Processes in nonmetallic Solids
25
Park, J.-S., Kim, S., Xie, Z. & Walsh, A.,
Nat. Rev. Mater. 3, 194 (2018)
Which defects exhibit both deep levels and large la5ce relaxa6on?
Lone-pairs!

26. Redox Activity of Cation Lone-pairs
Large lattice relaxation
Inert-pair effect: ineffective screening by
d and f orbitals
The large ionization energy for ns orbitals
leads to a deep donor levels.
Deep level
[Kr] 4d10 5s0 5p0
R = 71 pm
[Kr] 4d10 5s2 5p0
R = 112 pm
The reduction and oxidation may lead to a
large change in the structure of defect
Sn(IV)
Sn(II)
The defects involving the oxida6on and reduc6on of lone-pairs
can act as killer centers.

27. Lone-pairs in VS
, VS
-CuZn
and SnZn
9
6
9
6

&X
=Q
í
6Q
=Q

9
6
&X
=Q

9
6
6Q
=Q

D E F
Defect wave functions are well localized around Sn 5s orbitals.
27
J. Mater. Chem. A 7, 2686 (2019)

28. Deep Donor Levels of VS,
SnZn
, and Complexes
28
Energy (eV)
a b c d
0.0
0.5
1.0
1.5
(+/0)
(+/0)
(2+/+)
(+/0)
(0/ )
(0/ )
(0/+)
(0/ )
V
e
n
n
V
e n
n
n n
n
n
V
E
F
(0/ )
(+/0)
(+/0)
(2+/+)
(+/0)
(0/ )
(0/ )
(0/+)
(+/ )
V
n
n
V
n
n
n n
n
n
V
E
F
(0/ )
(+/0)
(+/0)
(+/0)
(2+/+)
(+/0)
(0/ )
(0/ )
(0/+)
(0/ )
V
e
e
n
V
e n
e
n n
n
n
V
E
F
(0/ )
(+/0)
(2+/+)
(+/0)
(+/0)
(+/0)
(2+/0)
(0/ )
(0/ )
(0/+)
(0/ )
V
e
n
n
V
e
g
n
n
n
g
n
n
g
g
n
V
g
E
F
/
E
F
e e e
The forma8on of lone-pair in Sn-related defects
introduces deep levels.
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)

29. Large lattice distortion
2 4 6
−2 0 2 4 6
−2 0
Sn
Zn
2++h++e−
Sn
Zn
1++h+
Sn
Zn
2+
Ge
Zn
2++h++e−
Ge
Zn
1++h+
Ge
Zn
2+
0
2
1
Q (am 1 2 Q (am 1 2
ne (e
a b
E
b
E
b
(QHUJ\ H9
1HXWUDO
WUDS
5HSXOVLYH
WUDS
*LDQW
WUDS
9
6
&X
=Q
9
6

6Q
=Q

6Q
=Q

&X 6Q
í
7 .
ıQ FP

í
í
í
í
í
í
í
D E
The lone-pair leads to large lattice distortions
and large capture cross-sections.
J. Mater. Chem. A 7, 2686 (2019)
S. Kim, J. A. Márquez, T. Unold and A. Walsh,
Energy Environ. Sci. 13, 1481 (2020)

30. Can we remove SnZn
2+?
SnZn
2+
- Sn poor
- Zn rich
- hole poor (n-type)
30

31. Phase diagram
31
ZnSe is too stable with respect to the formation of CZTSe.
μSn
(eV)
−1
−2
0
o Zn-rich
o Sn-poor
The Cu-rich secondary phases are
conductive.
o hole poor (n-type)
The acceptor (CuZn
) are too many.
Ag
8
SnSe
6
Ag
Ag
2
SnSe
3
ZnSe
SnSe
SnSe
2
Se
CuSe
Cu
2
Se
Cu
Cu
2
SnSe
3
Se
ZnSe
SnSe
SnSe

μSn
μZn
μ Cu
0
−2
−2 −

−2
0
0
μSn
μZn
μ Ag
0
−2
−2 −

−2
0
0
Se
Se
a b
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)
(eV)
(eV)

32. Best Scenario: Anion-rich
32
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)

33. Trap Limited Conversion Eﬃciency
2 4 6
−2 0 2 4 6
−2 0
Sn
Zn
2++h++e−
Sn
Zn
1++h+
Sn
Zn
2+
Ge
Zn
2++h++e−
Ge
Zn
1++h+
Ge
Zn
2+
0
2
1
Q (am 1 2 Q (am 1 2
ne (e
a b
E
b
E
b
33
Energy (eV)
a b c d
0.0
0.5
1.0
1.5
(+/0)
(+/0)
(2+/+)
(+/0)
(0/ )
(0/ )
(0/+)
(0/ )
V
e
n
n
V
e n
n
n n
n
n
V
E
F
(0/ )
(+/0)
(+/0)
(2+/+)
(+/0)
(0/ )
(0/ )
(0/+)
(+/ )
V
n
n
V
n
n
n n
n
n
V
E
F
(0/ )
(+/0)
(+/0)
(+/0)
(2+/+)
(+/0)
(0/ )
(0/ )
(0/+)
(0/ )
V
e
e
n
V
e n
e
n n
n
n
V
E
F
(0/
(+/0
(2+/+)
(+/0)
(+/0)
(2+/0)
(0/ )
(0/ )
(0/+)
V
e
n
n
V
n
n
n
g
g
n
V
g
0 0.4 0.8
0
50
40
30
20
10
SQ limit
N
d
= 1020 cm–3
w/o doping
a
Current den it (m /cm2)
Voltage (V)
NT
Cn
ET
SnZn
: high concentration, deep level, and
high capture coefficient
Loss
T = 300K
W = 2µm
31.6%
20.3%
Energy Environ. Sci. 13, 1481 (2020)

34. Bad News: All Kesterites are not good.
E
g
(eV) E
g
(eV)
0
20
40
60
J
SC
(mA/cm2)
a b
c d
0.5
1.0
1.5
2.0
V
OC
(V)
0.5 1.0 1.5 2.0
0
25
50
75
100
FF (%)
0.5 1.0 1.5 2.0
0
10
20
30
PCE (%)
CZGSe
AZTSe
CZTSSe
SQ
lim
i
SQ
limi
SQ limi
SQ
lim
i
E g
High concentration of
recombination centers limits the
open-circuit voltage and
efficiency of kesterite solar cells
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)

35. You Get What You Paid For
Cu Zn Sn
S/
Se

Killer centers
Many killer centers
Ga
3+
4+
2+

36. To p or Not To p, That is the Question!
36
p-type:
High hole concentration promotes the formation of native donors.
not p-type:
Low hole concentration reduces the p-type conductivity.
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)

37. n-type Doping in p-type GaN
37
Rev. Mod. Phys. 87, 1139 (2015)

38. Codoping in Kesterites
38
Low hole concentration:
Low donor concentration
Post annealing in
a H-free environment:
High hole concentration
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)

39. Eﬀect of H-doping
E
g
(eV) E
g
(eV)
0
20
40
60
J
SC
(mA/cm2)
a b
c d
0.5
1.0
1.5
2.0
V
OC
(V)
0.5 1.0 1.5 2.0
0
25
50
75
100
FF (%)
0.5 1.0 1.5 2.0
0
10
20
30
PCE (%)
CZGSe
AZTSe
CZTSSe
SQ
lim
i
SQ
limi
SQ limi
SQ
lim
i
E g
J.-S. Park, S. Kim, Z. Xie, and A. Walsh, Nat. Rev. Mater. 3, 194 (2018)
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)
To access the true limits of solar cells,
we need to take into account of
thermodynamics of light, electron,
and crystal.

40. Optimal thickness of CZTS
40
0 2 4 6 8 10
Thickness (μ
0
10
1
20
2
0
icienc (
aTLC
Max
W
(aTLC)
li it

41. Not-hands-on session
(a)TLC: https://github.com/WMD-group/TrapLimitedConversion/blob/master/atlc/aTLC.ipynb
41

42. Summary:
From Theory to “Measurables”
42
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I’m developing the first-
principles method to calculate
the theoretical maximum
photovoltaic efficiency of
real materials without
empirical parameters.
The simulations can
complement the experiments
and bridge the gap between
macroscopic properties of
materials and microscopic
processes underneath.
J.-S. Park, S. Kim, Z. Xie, and A. Walsh, Nat. Rev. Mater. 3, 194 (2018)
S. Kim, J. A. Márquez, T. Unold and A. Walsh, Energy Environ. Sci. 13, 1481 (2020)

43. Making Good Solar Cells: a No-win Scenario.
A lesson I’ve learned for 3 years.
We can not change the laws of physics and chemistry.
43

44. Making Good Solar Cells: a No-win Scenario.
Do not go gentle into that good night
Dylan Thomas
Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.
Though wise men at their end know dark is right,
Because their words had forked no lightning, they
Do not go gentle into that good night.

44

45. “I don’t believe in the no-win scenario.”
Do not go gentle into that good night
Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the nonradiative recombination.
Though wise men at their end know dark is right,
Because their words had forked no lightning, they
Do not go gentle into that good night.

45
- James T. Kirk

46. Finally!
46