C. Zhng 1,, D. Sun 1,, C-X. Sheng 1,2,, Y. X. Zhi 1, K. Mielczrek 3, A. Zkhidov 3, nd Z. V. Vrdeny 1, * 1 Deprtment of Physics & Astronomy, University of Uth, Slt Lke City, UT 84112, USA 2 School of Electronic nd Opticl Engineering, Nnjing University of Science nd Technology, Nnjing, Jingsu 2194, Chin DOI: 1.138/NPHYS3277 Mgnetic field effects in hyrid perovskite devices 3 Deprtment of Physics, University of Texs t Dlls, Richrdson, Texs 758, USA These uthors hve mde equl contriutions to the work. *Author to whom correspondence should e ddressed; e-mil: vl@physics.uth.edu. NATURE PHYSICS www.nture.com/nturephysics 1
DOI: 1.138/NPHYS3277 Al electrode PCBM Perovskite ITO electrode PEDOT:PSS 1 µm 1 µm Fig. S1. SEM of two different perovskite PV devices used in this work., PV type;, LED type where the perovskite lyer is more disordered. The lesser qulity perovskite film fcilittes chrge recomintion, resulting in lower PCE ut higher EL efficiency 1. 2 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277 J (ma cm -2 ) c -5-1 -15-2. -.5 -.1 -.15 Device 4 Device 3 Device 2 Device 1..2.4.6.8 1. Applied Voltge (V) Device 1 Device 2 Ellectroluminescence (mv) d 1 1 1.1..2.4.6.8 1. Current (ma) -1-2 Device 4 Device 3 Device 2 Device 1 Device 3 Device 4-16 -8 8 16-16 -8 8 16 Fig. S2. Detils on vrious PV device performnce tht re summrized in Tle I., J-V device chrcteristic under AM 1.5G illumintion., EL emission intensity vs. current tht show enhnced EL intensity in low PCE devices. c, MPC(B) response in Devices 1 nd 2 tht show rod response eyond 16 mt. d, MPC(B) in Devices 3 nd 4 tht show pronounced low-field component. NATURE PHYSICS www.nture.com/nturephysics 3
DOI: 1.138/NPHYS3277.3 ω L =1.6 ev ω L =1.6 ev. -1 B 1/2 15mT -.3-2 -.6-1 -5 5 1-1 -5 5 1 Fig. S3. MPC(B) response up to 1 Tesl using elow-gp lser excittion. The MPC(B) response when using 1.6 ev excittion in Device 2 () nd Device 4 (). The rod component, MPCB(B) in Device 4 disppers when illuminted the device with elowgp photon energy (compre to tht of ove-gp excittion, Figs. 3 nd 4 in the text); wheres the nrrow MPCN(B) component is roust. In this cse the photogenerted electrons re deloclized, wheres the photoexcited holes re trpped in the VB loclized sttes in the density-of-sttes til, which my crry spin ½ when empty. However, the non-geminte e-h pirs tht yield the MPCN(B) component still exist even with elowgp excittion. 4 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277. ω L =3.1 ev 12 ω L =3.1 ev -.3 c -.5 -.1 -.15. -.3 -.6 5 mw 1 mw 2 mw 25 mw -16-8 8 16 ω L =1.6 ev 1 mw 1 mw 47 mw 9 mw -16-8 8 16 Jsc (ma cm -2 ) d Jsc (ma cm -2 ) 8 4 -.2 -.1. 1 2 3 Lser Power (mw) 2 15 1 5 ω L =1.6 ev 2 4 6 8 Lser Power (mw) -.3 -.2 -.1. Fig. S4. Excittion intensity dependence of PC nd MPC(B) in Device 2. Typicl MPC(B) responses nd excittion intensity dependence of PC nd MPC, respectively excited with diode lser t 3.1 ev (,) nd 1.6 ev (c,d). This device shows liner dependence of PC on the excittion intensity, IL, implying tht crrier recomintion kinetics is dominted y monomoleculr processes. MPC with ove gp lser excittion remins pprox. unchnged (~.15%) with incresing IL; wheres MPC with elow gp excittion is negligily smll (<.2%). 5 NATURE PHYSICS www.nture.com/nturephysics 5
DOI: 1.138/NPHYS3277 ω L =3.1 ev 6 4 c -1-2 -3.5 mw 2 mw 5 mw 25 mw -16-8 8 16-1 -2 ω L =1.6 ev -3.5 mw 1 mw 1 mw 9 mw -16-8 8 16 Jsc ( A cm -2 ) d Jsc ( A cm -2 ) 4 2 1 2 3 Lser Power (mw) -4 6 4 2 ω L =3.1 ev ω L =1.6 ev 2 4 6 8 Lser Power (mw) 3 2 1-3 -2-1 Fig. S5. Excittion intensity dependence of PC nd MPC(B) in Device 4. Typicl MPC(B) responses nd excittion intensity dependence of PC nd MPC excited with diode lser t 3.1 ev (,) nd 1.6 ev (c,d). The PC of this device sturtes t intermedite IL indicting tht crrier recomintion in the perovskite lyer here is dominted y imoleculr e-h recomintion kinetics. MPC lso increses with IL t low excittion intensity, since the reltive formtion of e-h SP increses t higher IL. However, MPC chnges very little with IL when IL>1 mw, indicting tht the formed e-h pirs nd their MFE do not depend on the PC sturtion nd the recomintion dynmics. 6 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277.. c. d. -.2 -.4 -.5 -.1 -.15 -.6-16 -8 8 16-16 -8 8 16-16 -8 8 16-16 -8 8 16 e f. g h. -.1 -.2 -.4 -.8 -.4 -.8 -.5-1. -1-1 -2-1.2-1.5-2 -16-8 8 16-16 -8 8 16-16 -8 8 16-16 -8 8 16 Fig. S6. Vrious MPC(B) responses otined in different PV cells used to compile the universl plot presented in Fig. 3d. We note tht the MPC(B) width is nrrower when the mplitude increses from to h. NATURE PHYSICS www.nture.com/nturephysics 7
DOI: 1.138/NPHYS3277.. c. 1 3 MPL -.1 1 3 MPL -.1 -.2 1 3 MPL -.2 -.2 -.3 -.4 d -2-1 1 2. e -.4-2 -1 1 2. f. -2-1 1 2 1 3 MPL -.2 -.4 1 3 MPL -.2 -.4 1-3 MPL -.5 -.6-2 -1 1 2 -.6-2 -1 1 2-1. -2-1 1 2 Fig. S7. Vrious MPL(B) responses otined in different PV cells used to compile the universl plot presented in Fig. 3d. We note tht the MPL(B) width is nrrower when the mplitude increses from to f. 8 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277 3 K Perovskite 15 Perovskite 225 K 15 K MPC HWHM (mt) 1 5 c MC (%) -5-25 25 5 3 K MEH-PPV 19 K 1 K d MC HWHM (mt) 6 3 15 2 25 3 Temperture (K) MEH-PPV -5-25 25 5 1 15 2 25 3 Temperture (K) Fig. S8. Temperture dependence of MPC N (B) response in perovskites compred to tht of the mgneto-current (MC) response in n OLED sed on the polymer MEH-PPV., The MPCN(B) response mesured with 3.1 ev excittion up to 5 mt t vrious tempertures s denoted. The HWHM here sustntilly decreses t low temperture (), indicting tht this response cnnot e scried s due to spin-mixing relted to the HFI. c, MC(B) response of n OLED sed on MEH-PPV tht ws scried to HFI mesured t vrious tempertures. d, The HWHM vlue of MC(B) s function of temperture, which contrsts the temperture dependence of the MPC response in perovskite devices. Surprisingly we found tht MPCN(B) response in the perovskite-sed PV device ecomes nrrower t low tempertures. In fct B1/2 of the MPCN(B) response decreses from ~14 mt t 3K to 2.5 mt t 125K. In contrst to the MPCN (B) response in the perovskite, the HWHM of MC(B) in the MEH-PPV sed device is temperture independent. The MC(B) response of the MEH-PPV sed OLED device is dominted y spin-mixing due to the HFI. We thus conclude tht the MPC response in the perovskitesed devices cnnot e scried s due to the HFI. 9 NATURE PHYSICS www.nture.com/nturephysics 9
DOI: 1.138/NPHYS3277 1. Normlized PL.9 T 2T 4T 1T 3T 5T.8 776 78 784 788 Wvelength (nm) Fig. S9. Normlized PL emission spectr of perovskite film mesured t 1K nd vrious mgnetic field strengths, B. The PL emission spectrum shows strong dependence on the pplied field, including rodening due to the Δg effect, nd redshift cused y the dimgnetic dependence of the e-h SP energy with B (See Eq.(1) in the min text) 2. 1 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277 1/P 3 2 1 Experiment Liner fitting 25 5 75 1 Chmer Temperture (K) Smple Temperture (K) 1 75 5 25 25 5 75 1 Chmer Temperture (K) Fig. S1. Clirtion of the smple temperture, Θ in the cryostt under lser illumintion. In order to check Eq.(2) we plotted 1/P t fixed field, B=5 T vs. the environment temperture, T. This dependence is nonliner, since Θ>T due to the lser induced heting. We therefore used fitting procedure for otining Θ vs. T, [Θ(T)] with fixed, Δg., The experimentl dt of P t vrious tempertures mesured t B=5 T nd constnt lser power, plotted s 1/P vs. T showing tht it cnnot e fitted y liner dependence: P ΔgµBB/4kBT, especilly t low T. This shows tht the perovskite film in the cryostt is heted y the excittion lser, nd consequently the smple temperture, Θ > T t low T., At constnt lser excittion power we ssume tht Θ=T+IL/cΘ 3 =T+Θ -3, when we consider tht the smple het cpcity is proportionl to Θ 3 t low temperture (Deye model). The temperture dependence of the circulr polrized PL cn e now fitted with P ΔgµBB/4kBΘ with Θ(T). Consequently we get from this liner expression the function Θ(T) (smple temperture vs. the mient temperture), tht shows n ovious increse for T<25 K. NATURE PHYSICS www.nture.com/nturephysics 11
DOI: 1.138/NPHYS3277 S11. The underlying mechnism for Δg dependence on B 2 The electrons nd holes re sujected to strong SOC in the hyrid perovskites, nd therefore the spin quntum numer my not e well defined. In this cse the totl ngulr momentum opertor, J=S+L is the correct description of the quntized electron ngulr momentum. Using nd theory clcultion tht includes e-e interction nd SOC it ws found tht the holes in the VB of these mterils re qusi-prticles with ngulr momentum eigenvlue j=1/2 wheres the electrons in the CB hve j=3/2. This is similr ut opposite compred to the cse of the electrons nd holes in III-V semiconductors such s GAs, where the hole hs j=3/2 nd electron hs j=1/2. The g fctor of n electron in solid differs from the re electron g fctor of ge~2.2 due to the spin orit interction. Furthermore, the electron g fctor is not constnt, ut chnges with the electron energy in the continuum nd, nd lso with n pplied mgnetic field, B. This could e simply expressed s g(b)=g()+g (2) B 2, where g() is the zero order component, nd g (2) is the second order component 3. Therefore Δg etween electron nd hole tht comprises the SP species cn e expressed s: Δg(B)=Δg()+ B 2, where is the difference in the second order component of the electron nd hole g-fctors. Consequently, P(B) dependence my e written s following: P = (Δg()+ B 2 )µbb/4kbθ, (S1) This is the underlying mechnism of hving smll component of B 3 in the otined P(B) dependence. From close inspection of the mesured P vs. B (Fig. 4c) we discovered tht there is smll ut unmiguous B 3 component. In Fig. S9-, etter fit to the mesured P vs. B dt hs een chieved using Eq. (S1) insted of Eq. (2) in the text. In order to find the nonlinerity of Δg vs. B, we plot the dt s P(B)/B vs. B 2 s shown in Fig. S9-. From this plot we otin for the non-liner component, = -.15.8 (Tesl) -2. 12 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277 4 2.7 Experiment Liner fitting P (%) -2 Experiment g= g()+ B 2 P/B (% T -1 ).6-4 -5. -2.5. 2.5 5. 5 1 15 2 25 Mgnetic Field (Tesl) B 2 (T -2 ) Fig. S11. The estimtion of the B 3 component in P vs. B sed on Eq. (S1)., The circulr polriztion, P vs. B otined from P=( + - - )/( + + - ). The lue line through the dt points is fit using Eq. (S1), P=(Δg()+ B 2 )µbb/4kbθ, where Θ is the smple locl temperture; smll B 3 component is clerly seen (see discussion ove)., The circulr polriztion dt plotted s P(B)/B vs. B 2. The red line through the dt points is liner fit for estimting, the strength of the B 3 component; we get = -.15.8 (Tesl) -2. NATURE PHYSICS www.nture.com/nturephysics 13
DOI: 1.138/NPHYS3277 5 µm 5 µm c d 5 µm 5 µm Fig. S12. SEM imges of vrious perovskite films for MPL nd ps dynmics chrcteriztion. -d, Microscopic morphology of films 1-4 (corresponding to Fig. 5c nd 5d in the text), which were nneled t 9-13 ⁰C respectively. The chnge of crystl qulity nd grin size cn e clerly oserved. This my serve s n explntion for the structure-property reltion etween the perovskite film morphology nd the e-h pir lifetime, which is the underlying mechnism for the otined universl plot in Fig. 3d. 14 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277 S13-16. Control experiments In ddition to the existence of MPL nd the universl plots tht we found in the perovskites, we lso performed the following control experiments to confirm the intrinsic MFEs in these compounds. (i) We mesured the MPC response in perovskite devices tht lck n electron trnsport PCBM lyer. We found tht MPC(B) response of these devices re similr to MPCB(B) or MPCN(B) response components depending on the film qulity (Fig. S13). This indictes tht MPC(B) is not relted to possile chrge trnsfer e-h pir etween the perovskite nd PCBM s in OPV lends 19. In ddition, the MC response of chrge trnsport lyers here is negligily smll (Fig. S14). These two control experiments long with the MPL response tht we hve otined in pristine films show tht the MFE in the perovskite devices origintes from the perovskite lyer. (ii) We lso mesured MC(B) response in Devices 2 nd 4 t forwrd is voltges (Fig. S15). In Device 2 MC(B) mesured t 1.2 V is is negligily smll. In Device 4 we otined MC(B) of ~.8% t 1.2 V is, which, importntly hs the sme response s MPCN(B). This shows tht MPCN(B) is relted with non-geminte e-h pirs tht re formed from the initilly free photogenerted chrge excittions in the perovskite ctive lyer. We note tht MC(B) response cn e lso explined y the formtion of e-h SP from the injected chrges tht re sujected to the sme Δg mechnism s tht of the photogenerted e-h SP species. This conclusion is lso in greement with the intensity dependent PC nd MEL response of Device 4 tht shows imoleculr recomintion kinetics. This recomintion does not originte from ging of the perovskite lyer exposed to the ir, lthough there is significntly decrese in the photocurrent density (Fig. S16) tht is cused y excess trps. From these dditionl experiments, nd the existence of MEL with the sme properties s MPC, we conclude tht the MPC response in the perovskite PV cells is n intrinsic property of the perovskite ctive lyer. NATURE PHYSICS www.nture.com/nturephysics 15
DOI: 1.138/NPHYS3277.. -.2 -.4 -.2 -.4 -.6 -.6-2 -1 1 2-2 -1 1 2 Fig. S13. Control experiments with simplified PV perovskite devices.,, MPC(B) response mesured in two different perovskite PV devices tht do not contin PCBM lyer mesured under 3.1 ev lser excittion. The PC is smll (<1 na) due to lck of n electron trnsport lyer in the device, resulting in low S/N rtio for the otined MPC response. However, oth rod nd nrrow responses re still otined, indicting tht the MPC in perovskite PV devices is intrinsic to the perovskite lyer. 16 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277.2 PEDOT:PSS.2 PCBM MC (%). MC (%). -.2 -.2-2 -1 1 2-2 -1 1 2 Mgnetic Field (kguss) Fig. S14. Mgneto-current (MC) mesurements in devices hving only chrge trnsport lyers.,, The MC(B) response in ITO/PEDOT:PSS/Al device nd ITO/PCBM/Al device; without perovskite lyer. Both MC(B) responses re smller thn.1%, showing tht the chrge trnsport lyers re not the reson for the MPC(B) response in the PV perovskite devices presented in this work. 17 NATURE PHYSICS www.nture.com/nturephysics 17
DOI: 1.138/NPHYS3277. Device 2 Device 4.. MC (%) -.2 -.4 Bis=1.2 V ω L =3.1 ev -.5 -.1 MC (%) -.4 Bis=1.2 V ω L =1.6 ev -1-2 -16-8 8 16 -.15 -.8-3 -16-8 8 16 Fig. S15. Mgneto-current (MC) response in perovskite PV devices., MC(B) response mesured t 1.2 V is (lck squres) nd MPC(B) photogenerted using 3.1 ev excittion (lue circles) in Device 1., MC(B) mesured t 1.2 V is (lck line) nd MPC(B) photogenerted using 1.6 ev excittion (red line) in Device 4. In Device 1, MC t 1.2 V is voltge is negligily smll (<.5%). In contrst, in Device 4 MC(B) is ~.8% t 1.2 V is, which shres the sme line-shpe s MPCN(B). This shows tht MPCN(B) cnnot e due to photogenerted geminte pirs in the perovskite ctive lyer, since the MC(B) response does not come from geminte pirs, y definition. 18 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277.4.3 J (ma cm -2 ) -1 4 hours in ir.2.1. -2..4.8 Voltge (V) -3-15 15 3 Fig. S16. Control experiment where the perovskite lyer ws exposed to ir for four hours efore fricting the PV device., J-V device dependence nd, MPC(B) response in the ging perovskite device excited t 3.1 ev. The PC decreses drmticlly due to degrdtion of the perovskite lyer. In contrst the MPC response is not eliminted indicting tht the nrrow MPC(B) response in Device 2 is intrinsic to the perovskite rther thn due to the ging effect, which is considered to e n extrinsic effect. NATURE PHYSICS www.nture.com/nturephysics 19
DOI: 1.138/NPHYS3277 Tle S1 Device Excittion MPC(B) HWHM Lifetime, τ Lifetime, τ No. Photon Energy (%) B (ps) from (ps) from ω L (ev) (mt) MPC(B) PA(t) decy 2 3.1 ~.45% 325±11 28±3 22 4 1.6 ~1.6% 15±1 563±8 55 3.1 ~.4% 183±12 49±6 22 ~1.8% 16±1 537±5 465 Tle S1: MPC(B) response nd its comprison to ps dynmics On the one hnd the otined MPC(B) response in the perovskite PV cells could e very well fitted with Lorentzin functions. On the other hnd MFE(B) response in the Δg mechnism is Lorentzin with HWHM, B=ħ/(2µBΔgτ), where τ is n verge lifetime of the e-h SP species tht is determined y the SP dissocition nd/or recomintion rtes. By compring B to the mesured MPC(B) HWHM we cn otined the SP lifetimes using the mesured Δg=.65 vlue, s summrized Tle S1. Two time constnts, nmely τ1 6 ps nd τ2 5 ps, could e otined from the MPC(B) response of Device 4 excited t 3.1 ev; ut SP species hving only one time constnt, τ2 survive when excited t 1.6 ev. This grees very well with the lifetimes of excited e-h pirs in the ps trnsient spectroscopy. 2 NATURE PHYSICS www.nture.com/nturephysics
DOI: 1.138/NPHYS3277 References 1. Schmidt, L. C. et l. Nontemplte Synthesis of CH3NH3PBr3 Perovskite Nnoprticles. J. Am. Chem. Soc. 136, 85-853 (214). 2. Terent'ev, Y. V. et l. Mgneto-photoluminescence of InAs/InGAs/InAlAs quntum well structures. Appl. Phys. Lett. 14, 11111 (214). 3. vn Bree, J., Silov, A. Y., Koenrd, P. M., Fltté, M. E. & Pryor, C. E. g fctors nd dimgnetic coefficients of electrons, holes, nd excitons in InAs/InP quntum dots. Phys. Rev. B 85, 165323 (212). NATURE PHYSICS www.nture.com/nturephysics 21