Normal and Inverted Hysteresis in Perovskite Solar Cells - The Journal

May 11, 2017 - Hysteretic effects are investigated in perovskite solar cells in the standard FTO/TiO2/CH3NH3PbI3–xClx/spiro-OMeTAD/Au configuration...
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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

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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.

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∗†‡ ¶

¶ ¶

§∥

¶ ¶

§

∗ † ‡ ¶ § ∥

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§ ∗¶

The Journal of Physical Chemistry

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2

3

3

3−x

x

Voc

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3 2

2

3

Vpol Vpol < 0

0 < Vpol < Voc

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Vpol > Voc

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FTO/TiO2

Spiro/Au

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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

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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

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Rs

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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

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Rs ≈ 0

Uc = V + IRs ≈ V

Pnl,∞ = (V /Voc )P∞

Vs = χs

Vbi

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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

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(a)

20

(b)

NH

IH

16

16

2

2

J [mA/cm ]

12

J [mA/cm ]

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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

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tpol

1

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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

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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

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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

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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

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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 ]

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The Journal of Physical Chemistry

(Vs+Vbi) / |Vpol|

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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

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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

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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

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= ∂Pnl /∂t

∂Pnl /∂V

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20

15

2

J [mA/cm ]

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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

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Voc

Vpol > Voc Vpol < 0

0 < Vpol < Voc

Vpol Isc

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tpol

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The Journal of Physical Chemistry



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Spiro-OMeTAD - - - - MAPI Pinitial + + TiO2

+

+

+

J -

Spiro-OMeTAD + + + + + + MAPI Pinitial - TiO2

-

-

-

Normal hysteresis

+

-

V

J

Inverted hysteresis V

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