Carrier Recombination and Diffusion in Wet-Cast Tin Iodide Perovskite

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C: Energy Conversion and Storage; Energy and Charge Transport

Carrier Recombination and Diffusion in Wet-Cast Tin Iodide Perovskite Layers under High Intensity Photoexcitation Patrik Scajev, Ramunas Aleksiejunas, Paulius Baronas, Džiugas Litvinas, Marek Kolenda, Chuanjiang Qin, Takashi Fujihara, Toshinori Matsushima, Chihaya Adachi, and Saulius Jursenas J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03226 • Publication Date (Web): 18 Jul 2019 Downloaded from pubs.acs.org on July 23, 2019

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The Journal of Physical Chemistry

Carrier Recombination and Diffusion in Wet-Cast Tin Iodide Perovskite Layers Under High Intensity Photoexcitation Patrik Ščajev,† Ram¯unas Aleksiej¯unas,∗,† Paulius Baronas,† Džiugas Litvinas,† Marek Kolenda,† Chuanjiang Qin,‡,¶ Takashi Fujihara,§ Toshinori Matsushima,k,‡,¶ Chihaya Adachi,k,‡,¶ and Saulius Jurš˙enas† †Institute of Photonics and Nanotechnology, Physics Faculty, Vilnius University, Sauletekio Ave. 3, LT-10257, Vilnius, Lithuania ‡Center for Organic Photonics and Electronics Research (OPERA), Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan ¶Adachi Molecular Exciton Engineering Project, Japan Science and Technology Agency (JST), ERATO, 744 Motooka, Nishi, Fukuoka 819-0395, Japan §Innovative Organic Device Laboratory, Institute of Systems, Information Technologies and Nanotechnologies (ISIT), Fukuoka Industry-Academia Symphonicity (FiaS) 2-110, 4-1 Kyudai-shinmachi, Nishi, Fukuoka 819-0388, Japan kInternational Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan E-mail: [email protected]

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The Journal of Physical Chemistry 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

Abstract Tin iodide perovskite CH3NH3SnI3 is often considered as a replacement for toxic lead halide perovskites. Tin iodide is not only suitable for production of solar cells, but also it emits in the near infrared spectral region, which is unique among the metal halide perovskites. On the downside, the CH3NH3SnI3 layers tend to be of high unintentional p-type doping, which significantly limits the solar cell efficiency. On the other hand, it is little known how this doping could affect other optical and electrical properties, important for light-emitting applications. Here, we present an optical study of carrier diffusion and recombination pathways by time-resolved photoluminescence, differential transmission, and light induced transient grating techniques at excitations close to the lasing regime. We investigate several CH3NH3SnI3 layers formed by solvent bathing method and using different anti-solvents, causing different structural quality and doping level of the layers. We observe the amplified spontaneous emission with a threshold excitation as low as 5 µJ/cm2 ; however, the threshold is sensitive to structural quality and increases significantly in the layers with larger surface roughness. We present an all-optical method to determine the equilibrium density of holes, which varies in the range of (0.7–5.0)×1018 cm−3 , depending on the anti-solvent used for production of a particular layer. Finally, we observe band-like diffusion of carriers with high values of ambipolar diffusion coefficient: it grows from 0.5 to 1.5 cm2 /s with excitation due to carrier degeneracy. High diffusivity, large quantum yield even at low densities, and low stimulated emission threshold allow us to argue that unintentional p-type doping can be beneficial for light emitting applications.

Introduction Interest in the metal halide perovskites soared up after discovering the qualities necessary for cheap and efficient solar cells: the long diffusion length of carriers, a direct and easily tunable band gap in the visible and near infrared regions, and the possibility to produce the perovskite layers from the solution. 1,2 While the photovoltaics remains the main driving 2


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force behind the interest in perovskites, other applications can also employ their unique properties. In particular, the metal halide perovskites demonstrated good light emission efficiency making them an attractive active material for the light emitting diodes (LED) or even lasers. 3–6 On the downside, two major problems obstruct their usage: low device durability 7,8 and toxicity. The toxicity is related to the presence of lead in the most popular lead halide perovskites, 9 which also offer the best efficiency of solar cells so far. Therefore, a replacement for lead is being actively sought after and several less-toxic candidates are being considered, including tin. 10–14 Tin halide perovskites, both fully-inorganic and organic-inorganic, were shown to be a suitable absorber material in the solar cells. 15,16 Even more, tin iodide perovskites were demonstrated to emit light in the near-infrared, which is rare among wet cast materials and, thus, makes them an attractive candidate for near infrared LEDs; 17 a tin iodide LED based on perovskite multiple quantum wells has also been demonstrated recently. 18 The most pressing issue with the tin perovskites is the instability of Sn2+ ions that are easily oxidized to Sn4+ state leaving Sn2+ vacancies, which results in unintentional p-type doping up to 1019 cm−3 . 11,19 High unintentional doping is unwanted in photovoltaics since it causes fast band-to-band recombination of carriers (with characteristic lifetimes of hundreds of picoseconds) 11,20 and, consequently, short diffusion lengths (tens of nanometers). This is believed to be among the main reasons behind the relatively low efficiencies of the lead-free perovskite solar cells (efficiency typically does not exceed 6%). 16 On the other hand, high unintentional doping of the active material might turn beneficial for light emitting applications, at least in some aspects. One can speculate that high equilibrium carrier densities close to the threshold of degeneracy might result in high emission efficiency at low electron injection level or low threshold of amplified spontaneous emission (ASE). Indeed, a notoriously low ASE threshold of 6 µJ/cm2 has been reported for inorganic perovskite CsSnI3, 21 which is unattainable in lead halide perovskites. 22 Low ASE threshold carrier density of 8×1017 cm−3 was also reported for formamidinium tin triiodide. 23 On the 3



other hand, fast nonradiative recombination was reported in CH3NH3SnI3, which would limit the emission efficiency. 24 However, the impact of carrier transport and different recombination pathways to emission efficiency is little studied in CH3NH3SnX3 perovskites, in contrast to CH3NH3PbX3, where optical and electrical properties have been addressed in a number of publications. In this work, we investigate in detail the optical performance and charge transport in several CH3NH3SnI3 layers under high photoexcitation close to the lasing regime. We employ a number of optical techniques, including time-resolved photoluminescence (PL), spectrallyresolved differential transmission (DT), and light-induced transient gratings (LITG). To study the impact of layer quality to the optical properties, we use several CH3NH3SnI3 layers grown by the solvent bathing method and using various anti-solvents, which results in different structural quality and also the level of unintentional doping. 25 We demonstrate that background doping indeed results in a very low ASE threshold and rather high quantum yield at low carrier densities. Even more important, we observe band-like diffusion of carriers with suprisingly high diffusion coefficient.

Experimental Materials The studied CH3NH3SnI3 layers were prepared using the solvent bathing method. 25 Before use, glass substrates were cleaned by general ultrasonication followed by ultraviolet-ozone treatment. The precursor solution was prepared by dissolving methyl ammonium iodide (MAI), tin(II) iodide (SnI2), and tin(II) fluoride (SnF2) in dimethyl sulfoxide (DMSO) in a molar ratio of 1.0:0.8:0.2. The precursor solution was then filtered through a 0.45 µm membrane filter and spin-coated onto the cleaned glass substrate at 6000 rpm for 30 s; then the sample was dipped into a beaker full of anti-solvent for 2 min to form the perovskite structure. We used a 1:1 vol mixture of toluene and hexane (TH), toluene (T), or hexane (H) 4


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as the typical anti-solvents. This solvent ratio is the optimized one; other ratios decreased the film quality. Subsequently, the perovskite film was dried and annealed on a hot plate at 100 °C for 5 min. During dipping, the temperature of the anti-solvent was controlled by a cooling plate. For the sample S2, the temperature was set to 9 °C, for other samples - to 13 °C. We note that the sample S1 is identical to the sample S3, only thicker. The detailed description of the growth procedure together with the structural characterization of the layers can be found in Ref. 25 The stationary absorption spectra of the samples are shown in the Figure 1,

5

-1

)

10

(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


Sample: 4

10

S1 low S2 low S3 low S4 mod

3

S5 high

10

1.2

1.4

1.6

1.8

2.0

2.2

E (eV)

Figure 1: Stationary absorption spectra of the investigated layers. while the Table 1 lists the main parameters of the layers like the thickness, roughness, and peak position of spontaneous PL emission. The samples are organized and labeled according to the determined doping density p0 ; we describe the method of p0 determination further on. The labels in the sample names stand for low doping ("low"), moderate doping ("mod"), and high doping ("high"). Table 1: Parameters of the studied layers Sample S1 (low) S2 (low) S3 (low) S4 (mod) S5 (high)

Anti-solvent Thickness, Roughness, PL peak, nm nm eV TH 252 10 1.260 TH 130 8 1.260 TH 126 7 1.260 T 195 41 1.280 H 214 19 1.291

5



Techniques Femtosecond time-resolved DT measurements were carried out using Harpia spectrometer (Light Conversion) pumped with Pharos-SP (Light Conversion) laser emitting 190 fs pulses at 1030 nm and operating at 10 kHz repetition rate. White light continuum pulses were generated by focusing the fundamental harmonic onto the sapphire crystal. These spectrally broad but short pulses were delayed at mechanical translation stage with retroreflector and used as an optical probe. The probe pulses were recorded using the CCD linear sensor (Hamamatsu) coupled to a monochromator (Andor). Excitation wavelength was set to 840 nm using the optical parametric amplifier Orpheus (Light Conversion). Time-resolved PL measurements in a picosecond time domain were carried out using the Streak Scope C10627 detector (Hamamatsu) coupled with the same laser system. For LITG measurements, a pulsed picosecond laser PL2243 (Ekspla) emitting 10 ps duration pulses at 1054 nm with 10 Hz repetition rate was used. Transient diffraction gratings were recorded by the second harmonics pulses of this laser (wavelength 527 nm) that were used to project an image of a holographic beam splitter onto the sample. The period of the transient grating was varied between 1.24, 1.26, and 3.5 µm by choosing the appropriate holographic beam splitter. The probing of the transient grating was performed by the pulses of fundamental harmonics, delayed in the mechanical translation stage with the retroreflector. The procedure of determining the diffusion coefficient and carrier lifetime was the same as we used previously in other lead perovskite measurements. 22,26 All measurements were performed at room temperature.

6


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Results and Discussion Differential transmission, impact of carrier heating To better understand the nature of electronic transitions, we begin with the analysis of time-resolved differential transmission (DT) data. Spectrally and temporally-resolved DT spectra provide an insight into the occupation dynamics of all states, in contrast to photoluminescence measurements, where only the transitions from the lowest emitting electronic states are visible. Figure 2 shows the temporal evolution of DT spectra in the sample S3 (low) at two excitations, below and above the ASE threshold. We note that the oscillations 1000

a) 11

J/cm

1000

DT (mOD)

2

b) 110

J/cm

DT (mOD)

2

-6

-0.9

100

-0.6

Time (ps)

Time (ps)

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


-0.3

10 0 0.3

1

100

-4 -2

10 0 2

1

0.6

0.1 1.1

4

0.1

0.9

1.2

1.3

1.4

1.5

1.1

6

1.2

Energy (eV)

1.3

1.4

1.5

Energy (eV)

Figure 2: Time-resolved spectra of differential transmission in the sample S3 (low) at excitations below (a) and above (b) the ASE threshold. decorating the DT spectra is an experimental artifact caused by a narrow band filter used for blocking the fundamental 1030 nm laser radiation. The DT spectra are dominated by a broad signal with a negative sign. The DT signal is defined as DT = log10 (I0 /IT ), where I0 and IT is the intensity of incident and transmitted beams, respectively. Negative DT signal represents the laser-induced absorption bleaching that is related to partial occupation of the probed states. At low excitation, we observe cooling of carriers in the initial stage of DT signal decay represented by a fast shift of DT maxima from 890 - 900 nm to 950 nm (1.30 eV), where the DT peak then remains throughout the entire delay range. We note that this red shift is much larger than that due to band gap renormalization, obscuring the latter 7



from being visible in the DT data. We determine from the DT transients that carrier cooling takes place within first 1–2 ps, i.e. is much faster than carrier recombination and thus does not impact photoluminescence properties. The peak at 1.3 eV agrees well with the band gap value determined from the ASE peak position. Therefore, we attribute the dominant DT signal to the absorption bleaching of the states in the bottom of the bands. With delay, the DT signal decays without spectral shifting, i.e. we observe no redistribution from free to localized states. We also note that the occupation of the localized states, which are seen in the DT signal down to 1.1 eV, changes with the same decay time as the main states without the presence of any long living defect states. Above the ASE threshold, an additional fast DT component with the decay time of few picoseconds appears in the spectra. This component reflects the rapid deoccupation of the band states due to amplified spontaneous emission. Again, all DT spectral components decay with similar time constants marking the absence of long lived localized states, at least not in large quantities. This proves that PL emission is dominated by free carrier recombination and the role of localized states is very small, if any at all.

Optical determination of doping density It is important to know the density of equilibrium holes p0 (i.e. the doping level) as it plays an important role in emission properties of the investigated layers. Having in mind the sensitivity of tin halide perovskites to moisture and oxygen, it is reasonable to perform the measurements on encapsulated samples by adopting an all-optical approach. We discuss a way of obtaining p0 from the recombination coefficients and the quantum yield QY measured using an integrating sphere; here, QY is defined as the ratio between the photoluminescence and excitation intensities QY = IPL /I0 . Figure 3 shows the QY as a function of photoexcited carrier density in all samples. The dependencies exhibit two components: the low excitation region, where QY is almost constant, and the high excitation region, marked by a steep rise in QY in all samples but S4 (mod). The high excitation part reflects the ASE onset, 8


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which enhances QY up to ∼ 0.8 − 0.9 in the samples S2 (low) and S3 (low). In contrast, QY drops with excitation in the S4 (mod) due to the onset of non-radiative Auger process. The contribution of Auger recombination seen as QY decline before the ASE onset can be detected in other samples as well (the samples S5 (high) and S1 (low) in Figure 3). The relative impact of Auger process depends on the ASE threshold, being much smaller in the samples with the lower threshold. The radiative ASE is a much faster process than nonradiative Auger recombination: we estimate the characteristic decay times of ASE and Auger processes as 1 − 2 ps and ∼ 100 ps at given carrier densities, respectively (the estimations are based on DT transients and calculated Auger coefficient, as is discussed further on). The very different rates of these two processes cause the domination of radiative recombination pathway and, thus, high QY once ASE is initiated. 10

0

S1 low S2 low S3 low S4 mod

QY

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


S5 high

10

-1

1E16

1E17

1E18 N (cm

-3

1E19

)

Figure 3: Quantum yield QY as a function of photoexcited carrier density ∆N in the samples. QY in the low excitation region is determined by an interplay between the radiative and non-radiative recombination pathways. In this region, QY is independent on excitation, which we attribute to high p-type doping when the equilibrium density of holes p0 exceeds the photoexcited carrier density ∆N . Indeed, for band-to-band recombination of free carriers the PL intensity is proportional to B(n0 + ∆n)(p0 + ∆p), where B is the bipolar recombination coefficient, n0 and p0 are the equilibrium densities, while ∆n and ∆p - the densities of photoexcited electrons and holes, respectively. In heavily p-doped samples n0 ≈ 0. Also, for excitation we use the photon energy exceeding the band gap, thus the densities of photoex9



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cited electrons and holes are equal: ∆n = ∆p = ∆N . Under such experimental conditions, IP L ∝ B∆N 2 in an intrinsic semiconductor, but IP L ∝ Bp0 ∆N in a heavily p-doped one, provided p0 >> ∆N . This leads to dependencies on excitation IPL ∝ I02 in intrinsic and IPL ∝ I01 in heavily doped semiconductors, respectively; or, in terms of QY one obtains QY = IPL /I0 =const for highly doped semiconductor. With this in mind, we express QY using the relation:

QY =

Bp0 , Bp0 + 1/τNR + Cp20

(1)

here τNR - nonradiative recombination time and C - the Auger recombination coefficient. To extract p0 from the equation (1), in addition to QY one needs to know the recombination coefficients 1/τNR , B, and C; these parameters can be estimated directly from the timeresolved measurements. However, to decrease the number of variable parameters we calculate the non-degenerate radiative recombination coefficient B0 from the following relation: 27 3 −13 cm

B0 = 5.8 × 10

s

m∗h m∗e + m0 m0

−3/2 3/2 2 m0 m0 300K EG 1+ ∗ + ∗ nr , mh me T 1eV

(2)

here m0 is the electron mass, me = 0.28m0 and mh = 0.13m0 - effective masses of electron and hole, 28 and nr = 2.2 is the refractive index of the CH3NH3SnI3 at the PL peak wavelength. Equation (2) provided the value B0 = 9.6 × 10−11 cm3 /s, which is very close to that B = 1.3 × 10−10 cm3 /s in CH3NH3PbI3. 26 To account for carrier degeneracy and saturation of radiative recombination at high densities, we also use the relation B(∆N ) = B0 /(1 + (p0 + ∆N )/Nb ) , where Nb is the material-specific density parameter. 29 Assuming similar value Nb = 6 × 1018 cm−3 as in lead iodide perovskites, 26 we obtained the density-dependent B values that are listed in Table 2. To determine the non-radiative recombination lifetime τNR and Auger recombination coefficient C, we recorded the time-resolved PL decay traces at various excitations; a representative example of such traces in the sample S3 (low) are shown in Figure 4(a). The 10


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Table 2: Recombination parameters of the studied layers Sample

p0 , 18

×10 S1 (low) S2 (low) S3 (low) S4 (mod) S5 (high)

cm 0.7 0.9 0.9 2.3 5.0

−3

QY, % 13 5 5 8 12

τNR , ns 2.0 0.6 0.6 0.5 0.4

B, ASE threshold, 3 ×10 cm /s µJ/cm2 9.0 21.5 9.0 8.1 9.0 5.4 7.4 124 6.0 35 −11

instantaneous PL decay time τ , which is determined from an exponential fit of the measured transient IPL (t) ∝ exp(−2t/τ ), represent the cumulative action of several recombination pathways and is usually expressed as: 1 1 = + B(p0 + ∆N ) + C(p0 + ∆N )2 . τ τNR

(3)

The coefficients τNR and C are then obtained by fitting equation (3) to the dependence of τ on photoexcited carrier density ∆N with the previously determined doping-dependent B. Figure 4(b) shows the fits, while the obtained values are listed in the Table 2. Again, the extracted C values of (9 − 10) × 10−29 cm6 /s are very close to those in lead iodide mixed perovskite. 26 We note, however, that in tin iodide perovskites the Auger recombination is manifested at lower photoexcitation due to high residual p-type doping. Finally, the doping t ~ 140 ps

b)

a)

t ~ 210 ps

10

3

10

2

(ps)

PL (arb. u.)

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


52

t ~ 480 ps

S1 low

t ~ 570 ps

S3 low S4 mod S5 high

10

17

Time (ns)

10

18

N (cm

-3

10

19

)

Figure 4: (a) PL transients recorded in the sample S3 (low) at several excitations at 680 nm. (b) Instantaneous decay time τ as a function of photoexcited carrier density ∆N . The points show experimental values, the solid lines - theoretical fits according to equation (3). 11



level was calculated by fitting equation (1) to the low-excitation QY values in Figure 3 with p0 as a varying parameter and using the obtained recombination coefficient values; the extracted p0 values together with the non-radiative recombination time τNR for each sample are listed in the Table 2. It is informative to analyze what parameters lead to high QY values at excitations below the ASE threshold. Since nonlinear recombination coefficients B and C are rather similar in all the samples, then according to equation (1) the differences in QY must be caused by different non-radiative recombination rate 1/τNR and doping p0 . Indeed, low excitation QY is the highest (12–13%) in two samples S1 (low) and S5 (high) with the lowest and highest doping, respectively. When compared to the other three samples, it can be concluded that high QY in S5 (high) is caused by high doping, while in S1 (low) high efficiency stems from long τNR . The long non-radiative lifetime of 2.0 ns in S1 was achieved by increasing the layer thickness (compare to the similarly grown but thinner sample S3 with τNR = 0.6 ns). On the other hand, S5 (high) have the comparable thickness to S1, but the lifetime remains 5 times shorter. This data proves that even low structural quality and highly doped tin iodide perovskite layers can yield relatively high QY values in spite of fast non-radiative recombination. This can turn beneficial for light emitting applications since decreasing of non-radiative rate can be a formidable task, while higher p-type doping is easily achieved in tin perovskite layers.

Determination of ASE threshold In all the samples, a narrow line of amplified spontaneous emission (ASE) appears in the PL spectra after reaching a certain threshold excitation, which is different for each layer. Figure 5 shows the PL spectra in all samples at two excitations, below (a) and above (b) the ASE threshold. Below the threshold, the PL spectra consist of broad band-to-band recombination lines with peak emission occurring within the 1.25–1.28 eV range. Assuming that the low energy side is governed by thermal distribution of carriers within the band, we 12


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determined thermal energy of the carriers to be around 28 meV, which proves a negligible influence of heating effects. The position of PL peak differs from sample to sample, as it is listed in Table 1. The relative PL peak position between the samples is mirrored by the relative position of the absorption edge, as it can be seen in Figure 1. The observed differences in spectra position of up to ∼50 meV can be explained by the Burstein-Moss effect, which accounts for the increase in the effective band gap due to phase state filling by free carriers; the similar effect is responsible for the strong dependence of the absorption edge on unintentional n-type doping in InN. 30 It can be seen by comparing p0 and PL peak position (Table 1) that higher unintentional doping leads to emission and absorption spectra shifted further toward the higher photon energies. The amount of the blue shift together with the surface roughness of the layers indicate that the samples prepared using the toluenehexane mix as an anti-solvent ("low" doped layers S1–S3) have better structural quality and lower unintentional doping if compared to those fabricated using the pure hexane (sample S5 (high)) or toluene (sample S4 (mod)) anti-solvents. 10

4

a) 3.2

mJ/cm

2

10

6

b) 50 m J/cm

2

c)

S1 low S2 low

10

3

PL (arb.u.)

10

2

10

1

1.1

10 1.2

1.3 Energy (eV)

1.4

1.5

10

S3 low S4 mod

10

10 10

5

4

S5 high

3

PL (arb.u.)

10 PL (arb.u.)

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


10

1

1.2

10

1.3

1.4

1.5

Energy (eV)

6

g

10

2

7

~ 1.03

5

4

0.1

1

10

100 2

Excitation ( mJ/cm )

Figure 5: Photoluminescence spectra recorded in the samples at (a) low (3.2 µJ/cm2 ) and (b) high (50 µJ/cm2 ) excitation. (c) The dependence of photoluminescence intensity on excitation. γ indicates the slope coefficient of this dependence. With increasing excitation and after the threshold of amplified spontaneous emission is reached, narrow ASE line appears in all the samples. Figure 5(b) shows the PL spectra at 50 µJ/cm2 excitation where the ASE peaks are visible. We note that the ASE peak in all samples appears on the low energy side of spontaneous PL line, which indicates that the majority of emission comes from the mobile states and not from the recombination of localized carriers, as the ASE position marks the mobility edge of carriers. 31 To determine 13



the ASE threshold, we measured the dependence of the integrated PL intensity IPL on excitation I0 , as it is shown in Figure 5(c). The onset of ASE is marked by a steep increase in the slope of these dependencies; the determined ASE threshold values are listed in the Table 2. The lowest threshold values of 5.4 and 8.1 µJ/cm2 were found in two "low" doped samples S3 and S2, respectively; 5.4 µJ/cm2 corresponds to the photoexcited carrier density of ∆N = 1.3 × 1018 cm−3 . The latter value is calculated as ∆N = (1 − R)αI0 /2hν, here R and α are the coefficients of reflection and absorption, respectively, and hν is the photon energy. Factor 1/2 represents the fact that photoexcitation is non-homogeneous towards sample depth, so an averaged ∆N value is used. This value of threshold ASE carrier density agrees with the calculated effective density of states (0.7 − 1.2) × 1018 cm−3 , obtained using the modeled reduced effective masses from the range of 0.09 − 0.13 m0 , 28 and is close to that measured in FASnI3. 23 The data in the Table 2 clearly shows that the value of ASE threshold strongly depends on the surface roughness of a particular layer, increasing for the rougher samples. This result can be interpreted assuming that surface roughness represents the overall crystallinity of the sample; this assumption is confirmed by SEM images, reported previously. 25 Hence, the rougher surface indicates poorer ordering and cohesion of perovskite crystallites and, therefore, stronger light scattering and larger ASE threshold. We conclude that high doping close to the degeneracy limit generally facilitates the ASE process providing one type of carriers to the process, but the ASE threshold is even more sensitive to optical quality of a layer, i.e. further increase in doping while sacrificing the layer quality is not beneficial and increases the ASE threshold. To analyze the evolution of ASE line with excitation, Figure 6(a) shows the PL spectra measured at various excitations below and well above the ASE threshold in the layer S3 (low). Above the threshold, the ASE peak appears and with increasing excitation keeps broadening due to band filling and shifts toward the lower energies due to band gap renormalization. The change in peak PL position with photoexcited carrier density is shown in Figure 6(b). We use this dependence to determine the band gap renormalization parameter RF of CH3NH3SnI3. 14


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10

6

S3 low

a)

I

0

(

mJ/cm

2

b)

):

10

5

ASE PL peak (eV)

0.5

PL (arb.u.)

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


2 5

10

10

10

10

4

from

3

to

7

110 2

1.25

1.24

1.23 1

1.2

1.3

1.4

1.5

10

18

Energy (eV)

DN (cm

-3

10

19

)

Figure 6: (a) PL spectra in the layer S3 (low) measured for different excitations approximately from 0.2 µJ/cm2 to 200 µJ/cm2 . (b) Dependence of ASE peak position on the photoexcited carrier density in the S3 (low). We fit the data in Figure 6(b) to the following formula (valid for ∆N >> p0 ): 32 ∆EG = EG0 − RF × (∆N [cm−3 ])1/3 .

(4)

From the fitting, we determined the band gap at low carrier density EG0 = 1.27 ± 0.01 eV and the renormalization parameter RF = (1.3 ± 0.1) × 10−8 eV·cm of CH3NH3SnI3. The later value is similar to that in GaN: 2 × 10−8 eV·cm. 32 Also, the obtained band gap is typical for CH3NH3SnI3 and agrees well with the mobility edge energy of 1.27 eV determined from the ASE peak position (Figure 5(b)).

Optical measurement of carrier diffusion coefficient Now we discuss the possible impact of doping impurities toward the transport properties of charge carriers. To measure the lifetime and diffusion coefficient, we carried out the LITG measurements at various excitations. Figure 7 shows the measured carrier lifetime and diffusion coefficient in all the samples as a function of photoexcitation. We note that LITG data is available starting from excitation of 10 µJ/cm2 , which corresponds to the average density of photoexcited carriers of 2.4 × 1018 cm−3 . This excitation is already above the ASE threshold for the samples S2 (low) and S3 (low), which results in a considerably shortened 15



S1 low

a)

b) 1.6

S2 low S3 low S4 mod S5 high

1.2

2

100

D (cm /s)

(ps)

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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S1 low 0.8

S2 low S4 mod

10

S5 high

0.4

10 I

0

2

100

10

30

( J/cm )

I

0

50

2

( J/cm )

Figure 7: The dependencies of carrier lifetime τ (a) and diffusion coefficient D (b) as functions on photoexcitation I0 in the investigated layers. carrier lifetime in latter layers; very short lifetime prevented the measurement of D in the sample S3. On the other hand, the lifetime determined from the TRPL agrees rather well with the LITG data in the rest of the samples with the larger ASE thresholds. A noteworthy finding is the high values of diffusion coefficient D in the studied samples, which is demonstrated in Figure 7(b). D values are similar in all the samples and vary from 0.5 to 1.5 cm2 /s within the used excitation range. The latter values are considerably higher than those in wet-wast CH3NH3PbI3 layers 22 and approach the diffusivity in vapordeposited CH3NH3PbI3 and CH3NH3PbBr3 26 samples under similar conditions. Similarly as in the latter samples, D dependence on carrier density displays the band-like diffusion character and the increase in D with excitation can be explained by the modified Einstein relation: 33 kB T F1/2 (η) D = , µ e F−1/2 (η)

η=

E − EF . kB T

(5)

The LITG data suggest that the carrier diffusion coefficient, i.e. carrier mobility is barely affected both by doping and structural quality, at least at high densities in the vicinity of ASE. This leads to a conclusion that carrier scattering by ionized impurities and by grain boundaries do not play a determining role in defining carrier mobility at room temperature.

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Conclusions CH3NH3SnI3 layers demonstrate the optical and electrical parameters that can be useful for light emitting applications. We observe an extremely low threshold of amplified spontaneous emission, down to ∼ 5 µJ/cm2 at 950 nm. Low ASE threshold allows obtaining the quantum yield as high as 90 % at relatively low excitations. On the other hand, the ASE threshold is sensitive to layer optical quality and increases by ∼ 50 times in the layer with the largest surface roughness. The ambipolar diffusion coefficient exhibits high values within 0.5–1.5 cm2 /s range, which is much higher than those in wet cast lead halide perovskites. The dependence of ambipolar diffusion coefficient on excitation shows that carrier diffusion has a band-like character. This fact together with the PL and DT properties confirm that free carriers in extended states dominate the optical properties of CH3NH3SnI3 perovskite layers. Also, the diffusion coefficient was found to be independent on both doping and structural quality, which suggests that carrier scattering on grain boundaries and ionized impurities was not of critical importance at given experimental conditions. All these properties together make CH3NH3SnI3 layers potentially attractive for light emitting applications.

Acknowledgements Vilnius University team acknowledges the financial support provided by Research Council of Lithuania under the project No. S-MIP-17-71. Additionally, this work was supported by the Japan Science and Technology Agency (JST), ERATO, Adachi Molecular Exciton Engineering Project (grant number JPMJER1305), JSPS KAKENHI (grant numbers JP15K14149 and JP16H04192), and The Canon Foundation.

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Carrier Recombination and Diffusion in Wet-Cast Tin Iodide Perovskite

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