Double Charged Surface Layers in Lead Halide Perovskite Crystals

Transcription

1 upporting Information Double Charged urface Layers in Lead Halide Perovskite Crystals mritakshi P. armah, 1 Victor. Burlakov, Emre Yengel, 1 Banavoth urali, 1 Erkki Alarousu, 1 Ahmed. El-Zohry, 1 Chen Yang, 1 ohd. Alias, 3 Ayan A. Zhumekenov, 1 akhsud I. aidaminov, 1 Namchul Cho, 1 Nimer Wehbe, 4 omak itra, 5 Idris Ajia, 5 ukumar Dey, 1 Ahmed E. ansour, 1 aged Abdelsamie, 1 Aram Amassian, 1 Iman. Roqan, 5 Boon. Ooi, 3 Alain Goriely, Osman. Bakr, 1 Omar F. ohammed 1 * 1 King Abdullah University of cience and Technology, KAUT olar Center, Division of Physical ciences and Engineering, Thuwal , Kingdom of audi Arabia athematical Institute, University of Oford, Woodstock Road, Oford OX 6GG, United Kingdom 3 King Abdullah University of cience and Technology, Photonics Laboratory, Computer, Electrical and athematical ciences and Engineering Division, Thuwal , Kingdom of audi Arabia 4 King Abdullah University of cience and Technology, Imaging and Characterization Laboratory, Thuwal , Kingdom of audi Arabia 5 King Abdullah University of cience and Technology, emiconductor and aterial pectroscopy Laboratory, aterial cience & Engineering Division, Thuwal , Kingdom of audi Arabia These authors contributed equally to this work. Corresponding Author * omar.abdelsaboor@kaust.edu.sa 1

2 aterials and ethods: Chemicals and reagents. Lead bromide ( 98%), lead iodide (99.999% trace metal basis), DF (anhydrous, 99.8%) and GBL ( 99%) were purchased from igma-aldrich. ABr, FABr, AI and FAI were purchased from Dyesol Limited (Australia). All salts and solvents were used as received without any further purification. ingle Crystal ynthesis. APbBr 3, FAPbBr 3, APbI 3 and FAPbI 3 single crystals were grown by Inverse Temperature Crystallization (ITC) technique from 1 solution of PbBr /ABr in DF, 1 solution PbBr /FABr in DF:GBL (1:1 v/v), 1 solution PbI /AI in GBL and.8 solution of PbI /FAI in GBL, respectively, as it was previously reported elsewhere. 1- easurement and characterization: teady-state photoluminescence (PL) measurements. All room temperature photoluminescence (PL) measurements were conducted using Ti: apphire laser. The fundamental output came from a Ti: apphire femtosecond regenerative amplifier operating at 8 nm with 35 fs pulses and a repetition rate of 1 khz. pectrally tunable (4 6 nm) femtosecond pulses were generated by an Optical Parametric Amplifier. We ecited with 4 nm pump for one photon (1p) and 8 nm pump for two-photon (p) measurements for APbBr 3 and FAPbBr 3 crystals. Pump pulses at 4 nm were obtained in a straightforward manner by the second harmonic of the fundamental beam, where 1 μj of the laser output was focused on a 1-μm BBO nonlinear crystal, and 8 nm pump was obtained directly by using the fundamental beam. We ecited with 65 nm for 1p and 13 nm for p measurements for the APbI 3 and FAPbI 3 crystals, and these pulses were generated by the optical parametric amplifier. The temperature-dependent steady-state PL measurements were performed using micro-pl (Horiba LabRA ARAI) ecited by a Cobalt laser emitting at 473 nm (for APbBr 3 and FAPbBr 3 ) and 65 nm (for APbI 3 and FAPbI 3 ) with an optical power of.6 mw. The objective lens of 5 having a numerical aperture of.5 is used to obtain -5 µm spot size. All temperature measurements were set at 5 temperature points of 98, 318, 38, 358 and 368 K. Time Resolved Photoluminescence (TRPL) measurements. TRPL spectra were recorded using a high-resolution streak camera system (Hamamatsu C191) where the pump beam is generated using the fundamental (8 nm) and the second harmonic (41 nm) of the pectra-physics aitai ehp for p and 1p-ecitation. Repetition rates were selected using an APE

3 Pulse elect pulse picker as 1 Hz and 1 khz, which corresponds to the ecitation fluence of 1 nj/cm and 5 nj/cm for 1p and p ecitation, respectively. The temperature-dependent TRPL were taken using a micro-pl system with an objective lens of X. The pump beam is generated the fundamental (8 nm) of a mode-locked Ti:apphire laser (Coherent ira 9D) where 3 µj/cm and 118 µj/cm fluence is applied for APbBr 3 and FAPbBr 3, respectively. For comparison, 1p ecitation is also applied using the second harmonic (4 nm) of the fundemantal beam. During the measurements, emission of the samples was detected by a monochromator attached to a Universal Hamamatsu C686 streak camera with a temporal resolution of ps and the temperature is chosen in the range between 98 K and 363 K. econdary ion mass spectrometry (I) measurements. Depth profiling eperiments were performed on a Dynamic I instrument from Hiden analytical company (Warrington-UK) operated under ultra-high vacuum conditions, typically 1-9 Torr. A continuous Ar + beam of kev energy was employed to sputter the surface while the selected ions were sequentially collected using a AXI spectrometer equipped with a quadrupole analyzer. In order to avoid the edge effect, the I data were etracted from a small area of 5 5 µm centered in the middle of the sputtered area estimated to be 5 5 µm using an adequate electronic gating. The conversion of sputtering time to sputtering depth scale was carried out by measuring the depth of the crater generated at the end of the depth profiling eperiment using a stylus profiler from Veeco. Emission Correction: The emitted signal by the perovskite samples at 1p and p ecitations were corrected using the following equation 3 to reconsider the self-re-absorption of emission by perovskites; I cor em = I obs em (ep(( αd ) )erfc(( αd 1 ))) where α is the absorption coefficient, and d is the diffusion coefficient value of the material. This equation is implemented into a script using ATLAB. ore details about this procedure will be epanded into an ongoing manuscript. Theoretical analysis: patial variation of the electric field in the surface layer. In our model, we assume that the halide ions are placed on the surface with concentration n forming a charged plane, while the vacancies are distributed in the neighboring surface layer screening the electric 3

4 field produced by the ions. At thermal equilibrium, the distribution of vacancies is steady meaning that there is a balance between the diffusion and drift currents of vacancies dn e V D E nv, E n nv ydy nv ydy d where e is the charge associated with vacancy, nv (1) is the concentration of vacancies, D is the diffusion coefficient of vacancies, is their mobility, and is the static dielectric constant of the material. Taking into account charge conservation, we have n y dy n n y n n y dy, V V V which gives e E n nv y dy moreover, using the Einstein relation between the diffusion coefficient and mobility Eq. (1) can be rewritten as dnv e n nv ydy nv d kt () This is equivalent to d z e dz dz z, z n nv ydy, nv d kt d d The relevant solution to this equation is of the form a kt that for =, we have z b e b (3) n and ubstituting this solution into Eq (3), we obtain ktn e n nv y dy n, n e kt e n kt V d d V e n kt n n y dy The electric field is defined as kt n e a z b with a kt / e. Taking into account n y dy kt V we obtain b. e n (4) 4

5 e e n ekt n E n e n kt e n kt If the band gap of the material hence the PL frequency shift is proportional to the squared average electric field (note that it does not depend on the field direction) then 1 e n ekt n kt n dy e kt n E d e n kt (6) y kt e n kt where, is the characteristic penetration depth of light. This epression indicates that the blue shift of the PL line can be relatively high for 1p ecitation, which is characterized by a small light penetration depth, and much lower for the p ecited PL due to much higher light penetration depth. The equilibrium concentration of halide ions on the surface. (5) An equilibrium value of n is obtained by analyzing the free energy of the system n V ln V V V V V G n kt n n d E d e nv E d N V n n kt n ln N n ln 1 N N where, V is the vacancy formation energy measured relative to the energy of halide ions on the surface, and N is the surface concentration of available sites for halide ions and N V is the bulk concentration of available sites for halide vacancies. The first term in Eq. (7) describes the free energy of vacancies, the second and third terms describe the electrostatic energy of the field and of the vacancies in the field. The last term corresponds to free energy of ions on the surface taking their internal energy as a reference level. This epression for free energy is written in the mean-field approimation neglecting small repulsive interactions between individual ions on the surface and between individual vacancies in the bulk. inimization of the free energy with respect to n gives dgv d nv V kt nv ln nv d dn dn N V ekt n V V d e d d n n n y dy d dn e n kt dn n kt ln N n (8) Calculating each derivative in this equation using Eq. (4) we obtain (7) 5

6 d kt nv ln nv / NV nv d dn kt n e 8 kt n e kt ln dy kt ln, 3 N N V y kt y kt V kt 3 e kt n kt e n d dn e n kt e n kt d 3 d kt, 3 e d e d kt n e nv n nv ydy d d kt. 3 dn dn e n kt The derivative in the first line is approimated taking into account that the logarithm is a slow-varying function at the distances where the other factor is not too small. Therefore the log function is taken at y= when calculating the integral. Finally, the equation for n and its approimate solution take the form n V n e n kt ln kt kt ln, N kt N n V 1/3 kt NV N V kt ep e 3kT (1) where we assumed that n N. ubstituting Eq. (1) into Eq. (6) obtain for the blue shift (9) /3 kt N N 4kT V V e kt 5/3 ep V 3 kt ep e kt 3kT 1/3 1/3 V kt NV N V kt C kt ep kt e ep kt 3kT 3kT e where the constant C depends on a particular material. (11) 6

7 upporting Figures: Figure 1. Corrected Photoluminescence spectra of single crystals XPbY 3 for X= A (a), X=FA (b) and Y= I - obtained under 1p and p ecitations as indicated on each panel. Figure. Thickness dependent PL spectra of APbBr 3 after 1p ecitation. 7

8 Figure 3. E images of APbBr 3 with thicknesses of 1 µm (a), 115 µm (b), 19 µm (c) and 5 µm (d). E images of FAPbBr 3 with thicknesses of 71 nm (e) and 5 µm (f). Figure 4. PL decay of APbBr 3 and FAPbBr 3 with 1p ecitation. 8

9 Figure 5. Temperature-dependent PL spectra of single crystals APbI 3 and FAPbI 3 under 1p ecitations as indicated on each panel. Figure 6. Temperature-dependent absorption spectra of single crystals APbBr 3 (a) and FAPbBr 3 (b). 9

10 Figure 7. Effect of temperature variation on the absorption spectra of FAPbBr 3 (a) and APbBr 3 (b) at 5 C (black), and 9 C (red) and on the emission spectra of FAPbBr 3 (c) and APbBr 3 (d) at 5 C (blue), and 9 C (red) with corresponding shifts in nm. The dotted emission spectra correspond to the epected emission upon bandgap change only. 1

11 Figure 8. Arrhenius plot as a function of temperature derived from the impedance spectroscopy. References: (1) aidaminov,. I.; Abdelhady, A. L.; urali, B.; Alarousu, E.; Burlakov, V..; Peng, W.; Dursun, I.; Wang, L.; He, Y.; aculan, G.; Goriely, A.; Wu, T.; ohammed, O. F.; Bakr, O.. Nat. Commun. 15, 6, () aidaminov,. I.; Abdelhady, A. L.; aculan, G.; Bakr, O.. Chem. Commun. 15, 51, (3) Niesner, D.; chuster, O.; Wilhelm,.; Levchuk, I.; Osvet, A.; hrestha,.; Batentschuk,.; Brabec, C.; Fauster, T. arxiv preprint arxiv: