Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)
Article
Normal and Inverted Hysteresis in Perovskite Solar Cells George Alexandru Nemnes, Cristina Besleaga, Viorica Stancu, Daniela Emilia Dogaru, Lucia Nicoleta Leonat, Lucian Pintilie, Kristinn Torfason, Marjan Ilkov, Andrei Manolescu, and Ioana Pintilie J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 11 May 2017 Downloaded from http://pubs.acs.org on May 14, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
∗†‡ ¶
¶ ¶
§∥
¶ ¶
§
∗ † ‡ ¶ § ∥
ACS Paragon Plus Environment
§ ∗¶
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
2
3
3
3−x
x
Voc
ACS Paragon Plus Environment
Page 2 of 23
Page 3 of 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
3 2
2
3
Vpol Vpol < 0
0 < Vpol < Voc
ACS Paragon Plus Environment
Vpol > Voc
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
FTO/TiO2
Spiro/Au
Page 4 of 23
FTO/TiO2
Spiro/Au
Vs Vs
Bias pre−poling
Vpol > Voc
Bias pre−poling
FTO/TiO2
Spiro/Au
FTO/TiO2
Spiro/Au
Ic
Reverse scan
Vpol < 0 Ic
V Voc Vpol < 0
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 23
Pnl τ
∂I −Rs C0 ∂t
!
q(V +IRs ) nkB T
"
−1 = Is e ! " Rs + +1 I Rsh V ∂V ∂Pnl + + C0 +A − Iph , Rsh ∂t ∂t
Pnl (t) − Pnl,∞ (Uc (t)) ∂Pnl =− , ∂t τ I(t = 0) = I0
Pnl (t = 0) = P0
J I
A
ACS Paragon Plus Environment
Rs
Page 7 of 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Rsh
n
Iph
Is C0
Pnl
τ
Pnl,∞ = (Uc /Voc )P∞
Uc = V +IRs
V
P∞
Uc = Voc
τ
P0 Pnl (nl)
Ic
= A × ∂Pnl /∂t
I = Iph − Id − Ish − Ic ,
Id
(l)
Ish
(nl)
Ic = Ic + Ic (l)
Ic
C0
(nl)
Ic
Pnl Vs
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Rs ≈ 0
Uc = V + IRs ≈ V
Pnl,∞ = (V /Voc )P∞
Vs = χs
Vbi
Page 8 of 23
Pnl Voc − Vbi , P∞
χs
Pnl χs = 1
dVs /dt = −[Vs − (V − Vbi )]/τ Pnl (t) Vs Vs
χs
Vpol = χs (P0 /P∞ )Voc
χs
χs
P0 χs
Vpol
P0
Vs
Vs
Voc
ACS Paragon Plus Environment
Page 9 of 23
(a)
20
(b)
NH
IH
16
16
2
2
J [mA/cm ]
12
J [mA/cm ]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
12
8
8
Experiment: Vpol = 1.2V
Experiment: Vpol = -1V
Theory: P0 = 9P∞
Theory: P0 = -7P∞
4
4
0
0
0.2
0.4
V [V]
0.8
0.6
0
1
0
0.2
0.4
V [V]
Vpol = 1.2
0.6
0.8
tpol = P0 = 9P∞
Vpol = −1V P0 = −7P∞ 0.23V < V < Voc
Iph = 1.11 V < 0.23 Voc
Vpol Vpol > Voc
0 < Vpol < Voc
Vpol < 0
2
3
3
3−x
x
ACS Paragon Plus Environment
tpol
1
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 10 of 23
x = 0.4
Vpol = 1.2V
Iph = 1.42
tpol =
Rs = 95Ω n = 1.53
Rsh = 3kΩ Is = 0.1
ϵr = 100
C0
2
P∞ = 18 Voc = 0.9
τ =9
P0 = 9P∞ A = 0.09
2
P0
P0 = −7P∞ Vpol = −1 Iph = 1.11
∼
Isc Vpol
ACS Paragon Plus Environment
Page 11 of 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Voc
Pnl (t)
Pnl (t = 0) = P0 ≫ P∞ τ
Pnl Pnl,∞ (Uc (t))
P0 < 0
Voc
Pnl
τ Pnl
Pnl,∞ = Pnl (nl)
Pnl (t)
Jc
P0
P0
Vpol
ACS Paragon Plus Environment
The Journal of Physical Chemistry
180
40 180
P∞ 0
0.2
0.4
0.8
0.6
-20
1
0
V [V]
0.2
0.4
0.6
0.8
1
V [V]
-60
-30
20
P∞
15 2
0
[mA/cm ]
-15
30
-40
Pnl
-80 -100
-60 -90 -120
-120
40
-150
R F
20 0
0
10
20
P∞
30
40
Pnl,∞
50
70
60
80
90
-180
-160
100
-180
5
0
-140
P∞
10
(nl)
-10
-20
Jc
2
Pnl [mC/cm ]
2
60
0
Pnl
60
-5
(nl)
90
30
80
Pnl,∞
2
[mA/cm ]
120
Jc
2
Pnl[mC/cm ]
2
100
R F
0
140 120
(b) IH
20
0 150
Pnl[mC/cm ]
(a) NH 160
Pnl [mC/cm ]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 23
0
0.2
0.4
0.6
0.8
1
0
V [V] 0
10
20
30
time [s]
40
0.2
0.4
0.6
0.8
1
V [V] 50
60
70
80
90
100
time [s]
Pnl Pnl,∞ (nl) Jc = ∂Pnl /∂t
Pnl
Pnl
0 < P0 < P∞
Isc Rsh Isc ≈ Iph Iph
P0 = −7P∞
P0 = −10P∞
Vpol
V
Voc
ACS Paragon Plus Environment
Voc
(a) Simulated J-V (P0)
10
10
10
-0.5P∞
0 20 10
0 20
0
0.2
0 20 10
-0.1V
0 20 -0.5V -1.0V
0 20
0.4
0.6
V [V]
0.8
1
2 1 0 -1 0
0 -1
-1.5V
10 0
0
-1
10
-10P∞
10
0
0.6V
0 20
-7P∞
10
1V
1
10
10
-3P∞
0 20
0
0 20
3P∞
0 20
1.2V
(c) Vs(V)
1
10
2
2
10
1
0 20
5P∞
0 20
(b) Measured J-V (Vpol)
10
9P∞
0 20
0
20
J [mA/cm ]
20
J [mA/cm ]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
(Vs+Vbi) / |Vpol|
Page 13 of 23
0
0.2
0 0.4
0.6
V [V]
0.8
1
-1
0
0.2
0.4
0.6
V [V]
0.8
1
Vpol P0
P0 Vs
Vbi
Vpol |Vpol | = χs Voc |P0 |/P∞ Vs
Isc Isc
Vs
(Vs + Vbi )/|Vpol | = Pnl /|P0 | Vs
Pnl P0
Pnl /|P0 | Vbi χs = 0.2 ± 0.05
Vbi ≈ 0.8 Vs = 0.4
ACS Paragon Plus Environment
Vpol = 1.2
The Journal of Physical Chemistry
8
P0 = -9.5 P∞
20 mV/s 40 mV/s 100 mV/s 1000 mV/s
2
J [mA/cm ]
6 4 2 0 -2
(a) 0
0.2
0.4
V [V]
0.8
0.6
1
8
Vpol = -1.4V
6
20 mV/s 40 mV/s 100 mV/s 1000 mV/s
2
J [mA/cm ]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 14 of 23
4 2 0 -2
(b) 0
0.2
0.4
V [V]
0.8
0.6
1
P0 = −9.5P∞ Isc
Isc (nl)
Pnl
Vpol = −1.4
Jc
= ∂Pnl /∂t
P0 = −9.5P∞ Isc Iph = 0.6
τ = 30
Isc Pnl
P0
(nl)
Jc
ACS Paragon Plus Environment
= ∂Pnl /∂t
∂Pnl /∂V
Page 15 of 23
20
15
2
J [mA/cm ]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
10 NH : P0 = 9P∞ IH : P0 = -9P∞ P0 = P∞ Steady state: P0=P∞=0
5
0
0
0.2
0.4
V [V]
0.8
0.6
1
P∞ P∞
Isc
P0 = 9P∞
P0 = −9P∞
P0 = P∞
P∞ = 0 [0, Voc ]
Voc P∞ ̸= 0
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 16 of 23
Voc
Vpol > Voc Vpol < 0
0 < Vpol < Voc
Vpol Isc
ACS Paragon Plus Environment
tpol
Page 17 of 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
∗
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment
Page 18 of 23
Page 19 of 23
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment
Page 20 of 23
Page 21 of 23
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment
Page 22 of 23
Page 23 of 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Spiro-OMeTAD - - - - MAPI Pinitial + + TiO2
+
+
+
J -
Spiro-OMeTAD + + + + + + MAPI Pinitial - TiO2
-
-
-
Normal hysteresis
+
-
V
J
Inverted hysteresis V
ACS Paragon Plus Environment
