Magnetic field effects in hybrid perovskite devices ... · Magnetic Field Effects in Hybrid...

1

Supplementary Information

for Manuscript

Magnetic Field Effects in Hybrid Perovskite Devices

C. Zhang1,†, D. Sun1,†, C-X. Sheng1,2,†, Y. X. Zhai1, K. Mielczarek3, A.

Zakhidov3, and Z. V. Vardeny1,*

1 Department of Physics & Astronomy, University of Utah, Salt Lake City, UT 84112,

USA 2 School of Electronic and Optical Engineering, Nanjing University of Science and

Technology, Nanjing, Jiangsu 210094, China

3 Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA

†These authors have made equal contributions to the work.

*Author to whom correspondence should be addressed; e-mail: [email protected].

Magnetic field effects in hybrid perovskite devices

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS3277

NATURE PHYSICS | www.nature.com/naturephysics 1

© 2015 Macmillan Publishers Limited. All rights reserved

http://www.nature.com/doifinder/10.1038/nphys3277

2

Fig. S1. SEM of two different perovskite PV devices used in this work. a, PV type; b, LED type where the perovskite layer is more disordered. The lesser quality perovskite film facilitates charge recombination, resulting in lower PCE but higher EL efficiency1.

1 µm1 µm

b

a

Al electrode

ITO electrode

Perovskite

PCBM

PEDOT:PSS

a

3

Fig. S2. Details on various PV device performance that are summarized in Table I. a, J-V device characteristic under AM 1.5G illumination. b, EL emission intensity vs. current that show enhanced EL intensity in low PCE devices. c, MPC(B) response in Devices 1 and 2 that show broad response beyond 160 mT. d, MPC(B) in Devices 3 and 4 that show a pronounced low-field component.

0.0 0.2 0.4 0.6 0.8 1.0-20

-15

-10

-5

0

J (m

A c

m-2)

Applied Voltage (V)0.0 0.2 0.4 0.6 0.8 1.0

0.1

1

10

100

Elle

ctro

lum

ines

cenc

e (m

V)

Current (mA)

ba

-160 -80 0 80 160

-0.15

-0.10

-0.05

0.00

MP

C (%

)

Magnetic Field (mT)

dc

-160 -80 0 80 160

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

Device 1

Device 2

Device 3Device 4

Device 1

Device 2

Device 3Device 4

Device 1

Device 2

Device 3

Device 4

2 NATURE PHYSICS | www.nature.com/naturephysics

SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3277



2

Fig. S1. SEM of two different perovskite PV devices used in this work. a, PV type; b, LED type where the perovskite layer is more disordered. The lesser quality perovskite film facilitates charge recombination, resulting in lower PCE but higher EL efficiency1.

1 µm1 µm

b

a

Al electrode

ITO electrode

Perovskite

PCBM

PEDOT:PSS

a

3

Fig. S2. Details on various PV device performance that are summarized in Table I. a, J-V device characteristic under AM 1.5G illumination. b, EL emission intensity vs. current that show enhanced EL intensity in low PCE devices. c, MPC(B) response in Devices 1 and 2 that show broad response beyond 160 mT. d, MPC(B) in Devices 3 and 4 that show a pronounced low-field component.

0.0 0.2 0.4 0.6 0.8 1.0-20

-15

-10

-5

0

J (m

A c

m-2)

Applied Voltage (V)0.0 0.2 0.4 0.6 0.8 1.0

0.1

1

10

100

Elle

ctro

lum

ines

cenc

e (m

V)

Current (mA)

ba

-160 -80 0 80 160

-0.15

-0.10

-0.05

0.00

MP

C (%

)

Magnetic Field (mT)

dc

-160 -80 0 80 160

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

Device 1

Device 2

Device 3Device 4

Device 1

Device 2

Device 3Device 4

Device 1

Device 2

Device 3

Device 4





4

Fig. S3. MPC(B) response up to 1 Tesla using below-gap laser excitation. The MPC(B) response when using 1.6 eV excitation in Device 2 (a) and Device 4 (b). The broad component, MPCB(B) in Device 4 disappears when illuminated the device with below-gap photon energy (compare to that of above-gap excitation, Figs. 3 and 4 in the text); whereas the narrow MPCN(B) component is robust. In this case the photogenerated electrons are delocalized, whereas the photoexcited holes are trapped in the VB localized states in the density-of-states tail, which may carry spin ½ when empty. However, the non-geminate e-h pairs that yield the MPCN(B) component still exist even with below-gap excitation.

-1000 -500 0 500 1000-0.6

-0.3

0.0

0.3

MP

C (%

)

Magnetic Field (mT)

ωL=1.6 eV

-1000 -500 0 500 1000

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

ωL=1.6 eV

B1/2≈15mT

a b

5

Fig. S4. Excitation intensity dependence of PC and MPC(B) in Device 2. Typical MPC(B) responses and excitation intensity dependence of PC and MPC, respectively excited with a diode laser at 3.1 eV (a,b) and 1.6 eV (c,d). This device shows a linear dependence of PC on the excitation intensity, IL, implying that carrier recombination kinetics is dominated by monomolecular processes. MPC with above gap laser excitation remains approx. unchanged (~0.15%) with increasing IL; whereas MPC with below gap excitation is negligibly small (<0.02%).

-160 -80 0 80 160

-0.15

-0.10

-0.05

0.00

5 mW 10 mW 20 mW 25 mW

MP

C (%

)

Magnetic Field (mT)0 10 20 30

0

4

8

12

Jsc (

mA

cm

-2)

Laser Power (mW)

0.0

-0.1

-0.2

-0.3

MP

C (%

)

-160 -80 0 80 160

-0.06

-0.03

0.00

1 mW 10 mW 47 mW 90 mW

MP

C (%

)

Magnetic Field (mT)0 20 40 60 80

0

5

10

15

20

Jsc (

mA

cm

-2)

Laser Power (mW)

0.0

-0.1

-0.2

-0.3

MP

C (%

)

ωL=3.1 eV

ωL=1.6 eV

ωL=3.1 eV

ωL=1.6 eV

a b

c d





6

Fig. S5. Excitation intensity dependence of PC and MPC(B) in Device 4. Typical MPC(B) responses and excitation intensity dependence of PC and MPC excited with a diode laser at 3.1 eV (a,b) and 1.6 eV (c,d). The PC of this device saturates at intermediate IL indicating that carrier recombination in the perovskite layer here is dominated by bimolecular e-h recombination kinetics. MPC also increases with IL at low excitation intensity, since the relative formation of e-h SP increases at higher IL. However, MPC changes very little with IL when IL>10 mW, indicating that the formed e-h pairs and their MFE do not depend on the PC saturation and the recombination dynamics.

0 20 40 60 800

20

40

60

Jsc (A

cm

-2)

Laser Power (mW)

0

-1

-2

-3

-4

MP

C (%

)

-160 -80 0 80 160

-3

-2

-1

0

0.5 mW 2 mW 5 mW 25 mW

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160

-3

-2

-1

0

0.5 mW 1 mW 10 mW 90 mW

MP

C (%

)

Magnetic Field (mT)

0 10 20 300

1

2

3

4

Jsc (A

cm

-2)

MP

C (%

)

Laser Power (mW)

0

20

40

60ωL=3.1 eV

ωL=1.6 eV

a b

c d

ωL=3.1 eV

ωL=1.6 eV

7

Fig. S6. Various MPC(B) responses obtained in different PV cells used to compile the ‘universal plot’ presented in Fig. 3d. We note that the MPC(B) width is narrower when the amplitude increases from a to h.

-160 -80 0 80 160

-1.5

-1.0

-0.5

0.0

MP

C (%

)

Magnetic Field (mT)-160 -80 0 80 160

-1.2

-0.8

-0.4

0.0

MPC

(%)

Magnetic Field (mT)

-160 -80 0 80 160

-0.2

-0.1

0.0

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160-0.06

-0.04

-0.02

0.00

MP

C (%

)


-0.8

-0.4

0.0

MP

C (%

)


-0.15

-0.10

-0.05

0.00

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

a b c d

e f g h





6

Fig. S5. Excitation intensity dependence of PC and MPC(B) in Device 4. Typical MPC(B) responses and excitation intensity dependence of PC and MPC excited with a diode laser at 3.1 eV (a,b) and 1.6 eV (c,d). The PC of this device saturates at intermediate IL indicating that carrier recombination in the perovskite layer here is dominated by bimolecular e-h recombination kinetics. MPC also increases with IL at low excitation intensity, since the relative formation of e-h SP increases at higher IL. However, MPC changes very little with IL when IL>10 mW, indicating that the formed e-h pairs and their MFE do not depend on the PC saturation and the recombination dynamics.

0 20 40 60 800

20

40

60

Jsc (A

cm

-2)

Laser Power (mW)

0

-1

-2

-3

-4

MP

C (%

)

-160 -80 0 80 160

-3

-2

-1

0

0.5 mW 2 mW 5 mW 25 mW

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160

-3

-2

-1

0

0.5 mW 1 mW 10 mW 90 mW

MP

C (%

)

Magnetic Field (mT)

0 10 20 300

1

2

3

4

Jsc (A

cm

-2)

MP

C (%

)

Laser Power (mW)

0

20

40

60ωL=3.1 eV

ωL=1.6 eV

a b

c d

ωL=3.1 eV

ωL=1.6 eV

7

Fig. S6. Various MPC(B) responses obtained in different PV cells used to compile the ‘universal plot’ presented in Fig. 3d. We note that the MPC(B) width is narrower when the amplitude increases from a to h.

-160 -80 0 80 160

-1.5

-1.0

-0.5

0.0

MP

C (%

)


-1.2

-0.8

-0.4

0.0

MPC

(%)

Magnetic Field (mT)

-160 -80 0 80 160

-0.2

-0.1

0.0

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160-0.06

-0.04

-0.02

0.00

M

PC

(%)


-0.8

-0.4

0.0

MP

C (%

)


-0.15

-0.10

-0.05

0.00

MP

C (%

)

Magnetic Field (mT)

-160 -80 0 80 160

-2

-1

0

MP

C (%

)

Magnetic Field (mT)

a b c d

e f g h





8

Fig. S7. Various MPL(B) responses obtained in different PV cells used to compile the ‘universal plot’ presented in Fig. 3d. We note that the MPL(B) width is narrower when the amplitude increases from a to f.

-200 -100 0 100 200

-0.2

-0.1

0.0

103 M

PL

Magnetic Field (mT)

-200 -100 0 100 200-0.6

-0.4

-0.2

0.0

103 M

PL

Magnetic Field (mT)

-200 -100 0 100 200

-0.4

-0.2

0.0

103 M

PL


-0.4

-0.3

-0.2

-0.1

0.0

103 M

PL

Magnetic Field (mT)

-200 -100 0 100 200-1.0

-0.5

0.0

10-3

MPL


-0.6

-0.4

-0.2

0.0

103 M

PL

Magnetic Field (mT)

a

d

b

e

c

f

9

Fig. S8. Temperature dependence of MPCN(B) response in perovskites compared to that of the magneto-current (MC) response in an OLED based on the polymer MEH-PPV. a, The MPCN(B) response measured with 3.1 eV excitation up to 50 mT at various temperatures as denoted. The HWHM here substantially decreases at low temperature (b), indicating that this response cannot be ascribed as due to spin-mixing related to the HFI. c, MC(B) response of an OLED based on MEH-PPV that was ascribed to HFI measured at various temperatures. d, The HWHM value of MC(B) as a function of temperature, which contrasts the temperature dependence of the MPC response in perovskite devices.

Surprisingly we found that MPCN(B) response in the perovskite-based PV device becomes narrower at low temperatures. In fact B1/2 of the MPCN(B) response decreases from ~14 mT at 300K to 2.5 mT at 125K. In contrast to the MPCN (B) response in the perovskite, the HWHM of MC(B) in the MEH-PPV based device is temperature independent. The MC(B) response of the MEH-PPV based OLED device is dominated by spin-mixing due to the HFI. We thus conclude that the MPC response in the perovskite- based devices cannot be ascribed as due to the HFI.

100 150 200 250 3000

3

6

MC

HW

HM

(mT)

Temperature (K)

-50 -25 0 25 50

Magnetic Field (mT)

MP

C (%

)

-50 -25 0 25 50

Magnetic Field (mT)

MC

(%)

c d300 K

190 K

100 K

150 200 250 3000

5

10

15

MP

C H

WH

M (m

T)

Temperature (K)

300 K

225 K

150 K

a bPerovskite Perovskite

MEH-PPVMEH-PPV





10

776 780 784 7880.8

0.9

1.0

Nor

mal

ized

PL

Wavelength (nm)

0T 1T 2T 3T 4T 5T

Fig. S9. Normalized PL emission spectra of a perovskite film measured at 10K and various magnetic field strengths, B. The PL emission spectrum shows a strong dependence on the applied field, including broadening due to the ‘Δg effect’, and red-shift caused by the diamagnetic dependence of the e-h SP energy with B (See Eq.(1) in the main text)2.

11

Fig. S10. Calibration of the sample temperature, Θ in the cryostat under laser illumination. In order to check Eq.(2) we plotted 1/P at a fixed field, B=5 T vs. the environment temperature, T. This dependence is nonlinear, since Θ>T due to the laser induced heating. We therefore used a fitting procedure for obtaining Θ vs. T, [Θ(T)] with a fixed, Δg. a, The experimental data of P at various temperatures measured at B=5 T and constant laser power, plotted as 1/P vs. T showing that it cannot be fitted by a linear dependence: P≈ΔgµBB/4kBT, especially at low T. This shows that the perovskite film in the cryostat is heated by the excitation laser, and consequently the sample temperature, Θ > T at low T. b, At constant laser excitation power we assume that Θ=T+IL/cΘ3=T+aΘ-3, when we consider that the sample heat capacity is proportional to Θ3 at low temperature (Debye model). The temperature dependence of the circular polarized PL can be now fitted with P≈ΔgµBB/4kBΘ with Θ(T). Consequently we get from this linear expression the function Θ(T) (sample temperature vs. the ambient temperature), that shows an obvious increase for T<25 K.

0 25 50 75 1000

100

200

300

Experiment Linear fitting

1/P

Chamber Temperature (K)0 25 50 75 100

0

25

50

75

100

Sam

ple

Tem

pera

ture

(K)

Chamber Temperature (K)

a b





12

S11. The underlying mechanism for Δg dependence on B2

The electrons and holes are subjected to strong SOC in the hybrid perovskites, and therefore the spin quantum number may not be well defined. In this case the total angular momentum operator, J=S+L is the correct description of the quantized electron angular momentum. Using band theory calculation that includes e-e interaction and SOC it was found that the holes in the VB of these materials are quasi-particles with angular momentum eigenvalue j=1/2 whereas the electrons in the CB have j=3/2. This is similar but opposite compared to the case of the electrons and holes in III-V semiconductors such as GaAs, where the hole has j=3/2 and electron has j=1/2. The g factor of an electron in a solid differs from the bare electron g factor of ge~2.002 due to the spin orbit interaction. Furthermore, the electron g factor is not constant, but changes with the electron energy in the continuum band, and also with an applied magnetic field, B. This could be simply expressed as g(B)=g(0)+g(2)B2, where g(0) is the zero order component, and g(2) is the second order component3. Therefore Δg between

electron and hole that comprises the SP species can be expressed as: Δg(B)=Δg(0)+B2,

where is the difference in the second order component of the electron and hole g-factors. Consequently, P(B) dependence may be written as following:

P = (Δg(0)+B2)µBB/4kBΘ, (S1) This is the underlying mechanism of having a small component of B3 in the obtained P(B)

dependence. From a close inspection of the measured P vs. B (Fig. 4c) we discovered that

there is a small but unambiguous B3 component. In Fig. S9-a, a better fit to the measured

P vs. B data has been achieved using Eq. (S1) instead of Eq. (2) in the text. In order to

find the nonlinearity of Δg vs. B, we plot the data as P(B)/B vs. B2 as shown in Fig. S9-b.

From this plot we obtain for the non-linear component, = -0.00150.0008 (Tesla)-2.

13

Fig. S11. The estimation of the B3 component in P vs. B based on Eq. (S1). a, The circular polarization, P vs. B obtained from P=(+--)/(++-). The blue line through the data points is a fit using Eq. (S1), P=(Δg(0)+B2)µBB/4kBΘ, where Θ is the sample local temperature; a small B3 component is clearly seen (see discussion above). b, The circular polarization data plotted as P(B)/B vs. B2. The red line through the data points is a linear fit for estimating , the strength of the B3 component; we get = -0.00150.0008 (Tesla)-2.

-5.0 -2.5 0.0 2.5 5.0-4

-2

0

2

4

Experiment g=g(0)+B2

P (%

)

Magnetic Field (Tesla)

a b

0 5 10 15 20 25

0.6

0.7 Experiment Linear fitting

P/B

(% T

-1)

B2 (T-2)





14

Fig. S12. SEM images of various perovskite films for MPL and ps dynamics characterization. a-d, Microscopic morphology of films 1-4 (corresponding to Fig. 5c and 5d in the text), which were annealed at 90-130 ⁰C respectively. The change of crystal quality and grain size can be clearly observed. This may serve as an explanation for the structure-property relation between the perovskite film morphology and the e-h pair lifetime, which is the underlying mechanism for the obtained ‘universal plot’ in Fig. 3d.

a b

c d

5 µm 5 µm

5 µm 5 µm

15

S13-16. Control experiments In addition to the existence of MPL and the ‘universal plots’ that we found in the perovskites, we also performed the following control experiments to confirm the intrinsic MFEs in these compounds. (i) We measured the MPC response in perovskite devices that lack an ‘electron transport’ PCBM layer. We found that MPC(B) response of these devices are similar to MPCB(B) or MPCN(B) response components depending on the film quality (Fig. S13). This indicates that MPC(B) is not related to a possible charge transfer e-h pair between the perovskite and PCBM as in OPV blends19. In addition, the MC response of charge transport layers here is negligibly small (Fig. S14). These two control experiments along with the MPL response that we have obtained in pristine films show that the MFE in the perovskite devices originates from the perovskite layer. (ii) We also measured MC(B) response in Devices 2 and 4 at forward bias voltages (Fig. S15). In Device 2 MC(B) measured at 1.2 V bias is negligibly small. In Device 4 we obtained MC(B) of ~0.08% at 1.2 V bias, which, importantly has the same response as MPCN(B). This shows that MPCN(B) is related with non-geminate e-h pairs that are formed from the initially free photogenerated charge excitations in the perovskite active layer. We note that MC(B) response can be also explained by the formation of e-h SP from the injected charges that are subjected to the same ‘Δg mechanism’ as that of the photogenerated e-h SP species. This conclusion is also in agreement with the intensity dependent PC and MEL response of Device 4 that shows bimolecular recombination kinetics. This recombination does not originate from ‘aging’ of the perovskite layer exposed to the air, although there is significantly decrease in the photocurrent density (Fig. S16) that is caused by excess traps. From these additional experiments, and the existence of MEL with the same properties as MPC, we conclude that the MPC response in the perovskite PV cells is an intrinsic property of the perovskite active layer.





16

Fig. S13. Control experiments with simplified PV perovskite devices. a,b, MPC(B) response measured in two different perovskite PV devices that do not contain a PCBM layer measured under 3.1 eV laser excitation. The PC is small (<100 nA) due to lack of an electron transport layer in the device, resulting in low S/N ratio for the obtained MPC response. However, both broad and narrow responses are still obtained, indicating that the MPC in perovskite PV devices is intrinsic to the perovskite layer.

-200 -100 0 100 200

-0.06

-0.04

-0.02

0.00

MPC

(%)


-0.06

-0.04

-0.02

0.00

MPC

(%)

Magnetic Field (mT)

a b

17

Fig. S14. Magneto-current (MC) measurements in devices having only charge transport layers. a,b, The MC(B) response in a ITO/PEDOT:PSS/Al device and a ITO/PCBM/Al device; without a perovskite layer. Both MC(B) responses are smaller than 0.01%, showing that the charge transport layers are not the reason for the MPC(B) response in the PV perovskite devices presented in this work.

-200 -100 0 100 200

-0.02

0.00

0.02

MC

(%)


-0.02

0.00

0.02

MC

(%)

Magnetic Field (kGauss)

PEDOT:PSS PCBMa b





18

Fig. S15. Magneto-current (MC) response in perovskite PV devices. a, MC(B) response measured at 1.2 V bias (black squares) and MPC(B) photogenerated using 3.1 eV excitation (blue circles) in Device 1. b, MC(B) measured at 1.2 V bias (black line) and MPC(B) photogenerated using 1.6 eV excitation (red line) in Device 4. In Device 1, MC at 1.2 V bias voltage is negligibly small (<0.005%). In contrast, in Device 4 MC(B) is ~0.08% at 1.2 V bias, which shares the same line-shape as MPCN(B). This shows that MPCN(B) cannot be due to photogenerated geminate pairs in the perovskite active layer, since the MC(B) response does not come from geminate pairs, by definition.

-160 -80 0 80 160

-0.04

-0.02

0.00

MC

(%)

Magnetic Field (mT)

-0.15

-0.10

-0.05

0.00

MP

C (%

)ωL=3.1 eVBias=1.2 V

-160 -80 0 80 160

-0.08

-0.04

0.00

MC

(%)

Magnetic Field (mT)

-3

-2

-1

0

MP

C (%


a bDevice 2 Device 4

19

Fig. S16. Control experiment where the perovskite layer was exposed to air for four hours before fabricating the PV device. a, J-V device dependence and b, MPC(B) response in the ‘aging’ perovskite device excited at 3.1 eV. The PC decreases dramatically due to degradation of the perovskite layer. In contrast the MPC response is not eliminated indicating that the narrow MPC(B) response in Device 2 is intrinsic to the perovskite rather than due to the aging effect, which is considered to be an extrinsic effect.

0.0 0.4 0.8-2

-1

0

J (m

A c

m-2)

Voltage (V)

4 hours in air

a b

-300 -150 0 150 300

0.0

0.1

0.2

0.3

0.4

MP

C (%

)

Magnetic Field (mT)





18

Fig. S15. Magneto-current (MC) response in perovskite PV devices. a, MC(B) response measured at 1.2 V bias (black squares) and MPC(B) photogenerated using 3.1 eV excitation (blue circles) in Device 1. b, MC(B) measured at 1.2 V bias (black line) and MPC(B) photogenerated using 1.6 eV excitation (red line) in Device 4. In Device 1, MC at 1.2 V bias voltage is negligibly small (<0.005%). In contrast, in Device 4 MC(B) is ~0.08% at 1.2 V bias, which shares the same line-shape as MPCN(B). This shows that MPCN(B) cannot be due to photogenerated geminate pairs in the perovskite active layer, since the MC(B) response does not come from geminate pairs, by definition.

-160 -80 0 80 160

-0.04

-0.02

0.00

MC

(%)

Magnetic Field (mT)

-0.15

-0.10

-0.05

0.00

MP

C (%


-160 -80 0 80 160

-0.08

-0.04

0.00

MC

(%)

Magnetic Field (mT)

-3

-2

-1

0

MP

C (%


a bDevice 2 Device 4

19

Fig. S16. Control experiment where the perovskite layer was exposed to air for four hours before fabricating the PV device. a, J-V device dependence and b, MPC(B) response in the ‘aging’ perovskite device excited at 3.1 eV. The PC decreases dramatically due to degradation of the perovskite layer. In contrast the MPC response is not eliminated indicating that the narrow MPC(B) response in Device 2 is intrinsic to the perovskite rather than due to the aging effect, which is considered to be an extrinsic effect.

0.0 0.4 0.8-2

-1

0

J (m

A c

m-2)

Voltage (V)

4 hours in air

a b

-300 -150 0 150 300

0.0

0.1

0.2

0.3

0.4

MP

C (%

)

Magnetic Field (mT)





20

Table S1

Device No.

Excitation Photon Energy ωL (eV)

MPC(B) (%)

HWHM B0

(mT)

Lifetime, τ (ps) from MPC(B)

Lifetime, τ (ps) from PA(t) decay

2 3.1 ~0.45% 325±11 28±3 22

4 1.6 ~1.6% 15±1 563±80 505

3.1 ~0.4%

~1.8%

183±12

16±1

49±6

537±50

22

465

Table S1: MPC(B) response and its comparison to ps dynamics On the one hand the obtained MPC(B) response in the perovskite PV cells could be very well fitted with Lorentzian functions. On the other hand MFE(B) response in the ‘Δg mechanism’ is a Lorentzian with HWHM, B0=ħ/(2µBΔgτ), where τ is an average lifetime of the e-h SP species that is determined by the SP dissociation and/or recombination rates. By comparing B0 to the measured MPC(B) HWHM we can obtained the SP lifetimes using the measured Δg=0.65 value, as summarized Table S1. Two time constants, namely τ1≈60 ps and τ2 ≈500 ps, could be obtained from the MPC(B) response of Device 4 excited at 3.1 eV; but SP species having only one time constant, τ2 survive when excited at 1.6 eV. This agrees very well with the lifetimes of excited e-h pairs in the ps transient spectroscopy.

21

References

1. Schmidt, L. C. et al. Nontemplate Synthesis of CH3NH3PbBr3 Perovskite Nanoparticles. J. Am. Chem. Soc. 136, 850-853 (2014).

2. Terent'ev, Y. V. et al. Magneto-photoluminescence of InAs/InGaAs/InAlAs quantum well structures. Appl. Phys. Lett. 104, 101111 (2014).

3. van Bree, J., Silov, A. Y., Koenraad, P. M., Flatté, M. E. & Pryor, C. E. g factors and diamagnetic coefficients of electrons, holes, and excitons in InAs/InP quantum dots. Phys. Rev. B 85, 165323 (2012).





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