SUPPORTING INFORMATION. and Nanotechnologies (ISIT), Fukuoka Industry-Academia Symphonicity (FiaS) 2-110, 4-1

Transcription

1 SUPPORTING INORMATION Diffusion Enhancement in Highly Excited MAPbI 3 Perovskite Layers with Additives Patrik Ščajev, Chuanjiang Qin,3, Ramūnas Aleksiejūnas, Paulius Baronas, Saulius Miasojedovas, Takashi ujihara 4, Toshinori Matsushima,3,5, Chihaya Adachi,3,5, and Saulius Juršėnas Institute of Photonics and Nanotechnology, Vilnius University, Sauletekio al. 3, LT 057, Vilnius, Lithuania Center for Organic Photonics and Electronics Research (OPERA), Kyushu University 744, Motooka, Nishi-ku, ukuoka , Japan 3 Adachi Molecular Exciton Engineering Project, Japan Science and Technology Agency (JST), ERATO, 744 Motooka, Nishi, ukuoka , Japan 4 Innovative Organic Device Laboratory, Institute of Systems, Information Technologies and Nanotechnologies (ISIT), ukuoka Industry-Academia Symphonicity (ias) -0, 4- Kyudaishinmachi, Nishi, ukuoka , Japan 5 International Institute for Carbon Neutral Energy Research (WPI-I CNER), Kyushu University, 744 Motooka, Nishi, ukuoka , Japan Corresponding author: R. Aleksiejūnas ramunas.aleksiejunas@ff.vu.lt S

2 Light induced transient grating technique Light induced transient gratings (LITG) is a type of pump-probe technique, which employs an interference light field to photoexcite a sample under study. The interference field is created by two coherent laser beams that are made to overlap in the sample at an angle A period of the resulting interference field is determined by the angle and wavelength of the pump beam p = p /(sin()). A convenient way of controlling is to use a set of phase diffraction gratings of different periods Gr. In this case, is determined by Gr and focal lengths f and f of the lenses serving as a telescope: = Gr / f /f. In this study,. m,.4 m, and. m periods were used. ree carriers are photoexcited in the illuminated areas of the interference field and, consequently, the refractive index is altered. or excitation, we used a Nd:YL laser emitting 0 ps duration pulses at 0 Hz. The wavelength of pump pulses was 57 nm. In the spectral range far from the electronic resonances, the index change n(t) is proportional to the density of free carriers N(t): n(t) = n eh N(t), where n eh is the index change induced by one electron-hole pair. According to the Drude model: n eh e, (S) n m p 0 eh p where m - eh = m - e + m - h is the reduced effective mass, m e and m h are the effective masses of electron and hole, e is the electron charge, 0 vacuum electrical permittivity, n p the refractive index, and p is the angular frequency at the probe wavelength. or probing, we used the pulses from the same laser at 053 nm. The samples were transparent at this wavelength, which enabled investigation of the entire excited thickness of the layers. S

3 Time evolution of carrier density in LITG experiment is monitored by measuring a diffraction efficiency (t) as a function of delay between the pump and probe pulses (i.e. LITG transients). Diffraction efficiency is defined as an intensity ratio of diffracted I D (t) and transmitted I T (t) beams: (t) = I D (t)/i T (t). Assuming an exponential decay, (t) can be related to photogenerated carrier density N(t) as: * * * d n t d n 0 eh N t d neh N t t exp, (S) G where d * =/ is the thickness of excited area, absorption coefficient, N 0 = I 0 /h initial free carrier density at the end of the pump pulse, I 0 excitation energy fluency, probe wavelength, and G grating decay time. was measured using a Perkin Elmer spectrometer for the wavelengths 57 nm and 680 nm and was equal to cm - and cm -, respectively. Once recorded, the grating decays due to (i) carrier recombination with the rate / R (here R stands for the carrier lifetime) and (ii) carrier diffusion along the grating vector with the rate / D. The rate of diffusive erasure depends on while that of recombination does not, which allows for distinguishing between these two processes. Hence, the ambipolar diffusion coefficient D and lifetime R can be determined from a set of LITG transients recorded for different according to the relation: G R D R 4 D. (S3) Ambipolar diffusion coefficient is related to the monopolar diffusion coefficients of electrons (holes) D e,(h) as D = D e D h /(D e + D h ). This relation is valid when the densities of S3

4 electrons and holes are equal. Latter requirement is fulfilled when electrons and holes are generated in pairs during band-to-band photoexcitation. igure S. (a) Normalized LITG transients recorded at different transient grating periods of.,.4, and. m in one of the samples at 4 J/cm excitation. The lines are guides to the eye. The inset illustrates the determination of diffusion coefficient and lifetime at different excitation intensities, according to Eq. (S3). (b) Dependence of LITG signal versus excitation intensity I 0 at short time delay after the pump. Dots show the experimental data for all the samples, the lines indicate the exponential fits at low and high excitations. To determine R and D at various carrier densities, we carried out LITG measurements while changing pump intensity and transient grating period. igure S(a) shows the LITG transients recorded at three grating periods in TCNQ sample. These transients are typical and resemble those in other samples under study. It can be seen that the decay is faster at smaller grating periods, which indicates the measurable impact of diffusion. The inset in igure S(a) shows the / G dependences on / plot for different excitations. The slope of the latter S4

5 function yields D, while the offset yields the carrier lifetime, according to Eq. (S3). The inset shows that both the diffusion coefficient and recombination rate increase with excitation. igure S(b) shows the dependence of diffraction efficiency on excitation energy fluence (I 0 ) at short delay time (just after the end of pump pulse). Photon energy of pump pulse (.35 ev) is above the band gap of MAPbI 3 (.68 ev), thus photoexcited carriers are generated in pairs and condition N I 0 is fulfilled. Therefore, at the end of pump pulse should be proportional to N, according to Eq. (S). This is indeed the case for low excitations up to ~50 J/cm, which is seen from the slope of of (I 0 ) (igure S(b)). At even higher excitations, the slope drops below. We attribute this to the onset of amplified spontaneous emission. S5

6 Diffraction efficiency (arb. u.) Diffraction efficiency (arb. u.) Experimental verification of perovskite layer stability It is well known that the prolonged exposure to light can change the characteristics of perovskite layers and devices. 3 To ensure that perovskite degradation or photomodification does not alter our results, we verified the stability of samples under the prolonged exposure to laser irradiation. We measured the stability of LITG signal for hour at high excitation energy fluence; this is ~4 times longer than it takes to measure a LITG transient. Also, LITG transients were recorded before the exposure and after it at identical experimental conditions. igure S (a) and (b) present the test results; no noticeable impact of degradation or photomodification has been observed TCNQ 40 J/cm 0 0 WO 40 J/cm After Before TCNQ.6 (a) Time (min) (b) Delay (ps) igure S. (a) LITG signal as a function of exposure time in TCNQ layer. (b) LITG transients recorded before (red line) and after (black line) the prolonged exposure to laser irradiation in TCNQ and WO layers. S6

7 SEM images and XRD spectra WO BQ HQ TCNQ igure S3. SEM images of WO, BQ, HQ, and TCNQ samples. Grain size varies from 00 nm to nm, an average grain size is ~0 nm in TCNQ and nm in other samples. S7

8 igure S4. XRD spectra of the studied samples. Model of diffusion coefficient dependence on excitation To numerically model the dependence of diffusion coefficient D on carrier density N, we used the model described Ref. 4 and adopted it for the degenerate case. According to this model, the density of localized (i.e. not contributing to diffusion) carriers n L can be expressed as: n L NL fl, fl, nl NL exp x, E EC. (S4) exp E E / k T L B Here = T/T 0, T 0 is the Urbach temperature, E U = k B T 0 is the Urbach energy, N L is the density of localized states, and f L is the occupation probability of the localized states, which depends on excited carrier density N (n L = N L in the case of E > E C ). E and E C are the ermi level and conduction band energies, respectively. The density of free carriers n C and their derivative by ermi level are: 5 S8

9 n C i N 0 C f /, i x dx, n E f C nc k T B / / exp x x., (S5) Here, N C is the density of states, while f is the ermi distribution function that is valid for arbitrary degeneracy, x = (E E C )/k B T, x = (E (N) E C )/k B T, and E (N) is the carrier density dependent ermi level, which was obtained by Nilsson approximation 6 with a few percent precision, according to the relation: x w 3/ 4 w ln 3/ w, w / 3 C w. (S6) 3 3/ 4 w NC n Assuming that equilibrium carrier density is low, which is typical for perovskites, the total density of nonequilibrium carriers is: x N exp x N nc nl NC / L (S7) Latter equation is solved analytically or numerically to obtain x. The electron diffusion coefficient in the studied system then will be: 4 D n D L 0 C. (S8) n n n C Here, D 0 is the diffusion coefficient of free carriers. or the degenerate case, we derive: D n N D0 nc nl n C / /. (S9) S9

10 Equation S9 was solved numerically and provided good fits for the measured D(N) dependences with the following fitting parameters: E U = 78 mev, N L = cm -3 for TCNQ, E U = 78 mev, N L = cm -3 for BQ, E U = 65 mev, N L = cm -3 for WO and HQ. S0

11 PL Intensity (arb. u.) Time-resolved differential transmission and photoluminescence measurements igure S5. Time-resolved differential transmission spectra in TCNQ sample for 680 nm (a) and 55 nm (b) pump wavelengths. ast thermalization of carriers within the bands is visible at nm during the first few picoseconds. The fast component at ~ 800 nm is attributed to the exciton screening laser 50ps 00ps 00ps 500ps ns ns 5ns 0ns 0ns Wavelength (nm) igure S6. Time-resolved PL spectra in WO sample at indicated delay times. No changes in the PL spectra shape with excitation are visible. S

12 ASE spectra in BQ sample igure S7. (a) PL spectra in BQ sample at different excitations, pump wavelength is 680 nm. (b) Integrated PL intensity as a function of excitation energy fluence. Green and blue symbols show the PL intensity at 770 nm and 800 nm, respectively; the black points indicate the overall PL intensity. Note the redshifted ASE spectral position (800 nm) if compared to that in WO, HQ, and TCNQ samples (785 nm). S

13 Quantum yield (%) Quantum yield in the samples 0 WO BQ HQ TCNQ N (cm -3 ) igure S8. Quantum yield in the samples as a function of carrier density. The higher yield correlates with the longer carrier lifetime at low carrier densities. The obtained QY values can be rationalized using the typical band-to-band and Auger recombination rates in MAPbI 3. S3

14 References () Eichler, H. J.; Gunter, P.; Pohl, D. W. Laser-Induced Dynamic Grattings; Springer-Verlag: New York, 986. () Malinauskas, T.; Jarašiunas, K.; Miasojedovas, S.; Juršenas, S.; Beaumont, B.; Gibart, P. Optical Monitoring of Nonequilibrium Carrier Lifetime in reestanding GaN by Time-Resolved our- Wave Mixing and Photoluminescence Techniques. Appl. Phys. Lett. 006, 88, 009. (3) Li, X.; Tschumi, M.; Han, H.; Babkair, S. S.; Alzubaydi, R. A.; Ansari, A. A.; Habib, S. S.; Nazeeruddin, M. K.; Zakeeruddin, S. M.; Grätzel, M. Outdoor Performance and Stability under Elevated Temperatures and Long-Term Light Soaking of Triple-Layer Mesoporous Perovskite Photovoltaics. Energy Technol. 05, 3, (4) Bisquert, J.; Vikhrenko, V. S. Interpretation of the Time Constants Measured by Kinetic Techniques in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells. J. Phys. Chem. B 004, 08, (5) Young, J..; Driel, H. M. Ambipolar Diffusion of High-Density Electrons and Holes in Ge, Si, and GaAs: Many-Body Effects. Phys. Rev. B 98, 6, 47. (6) Nilsson, N. G. An Accurate Approximation of the Generalized Einstein Relation for Degenerate Semiconductors. Phys. Status Solidi Appl. Mater. Sci. 973, 9, K75. S4