Short Photoluminescence Lifetimes Linked to Crystallite
Dimensions, Connectivity, and Perovskite Crystal Phases
Time-correlated single photon counting has been conducted to gain further insights into the short photoluminescence lifetimes (nanosecond) of lead iodide perovskite (MAPbI3) thin films (∼100 nm). We analyze three different morphologies, compact layer, isolated island, and connected large grain films, from 14 to 300 K using a laser excitation power of 370 nJ/cm2. Lifetime fittings from the Generalized Berberan-Santos decay model range from 0.5 to 6.5 ns, pointing to quasi-direct bandgap emission despite the three different sample strains. The high energy band emission for the isolated-island morphology shows fast recombination rate centers up to 4.8 ns–1, compared to the less than 2 ns–1 for the other two morphologies, similar to that expected in a good quality single crystal of MAPbI3. Low-temperature measurements on samples reflect a huge oscillator strength in this material where the free exciton recombination dominates, explaining the fast lifetimes, the low thermal excitation, and the thermal escape obtained.
Introduction<!>Sample Preparation and Description<!><!>Sample Preparation and Description<!>352
nm-CL<!>550
nm-CS and 103 nm-IS<!>Experimental Setup1,4<!>Time-Resolved Photoluminescence
Measurements
Depending on Temperature<!><!>Time-Resolved Photoluminescence
Measurements
Depending on Temperature<!><!>Continuous Distribution of Characteristic
Times: Generalized Berberan-Santos Decay<!><!>Continuous Distribution of Characteristic
Times: Generalized Berberan-Santos Decay<!>Thermal Excitation and Thermal Escape<!>Distribution of Recombination Rate Constants<!><!>Distribution of Recombination Rate Constants<!><!>Distribution of Recombination Rate Constants<!>Conclusions<!>
<p>Over the past years, a large number of studies have shown the technological
versatility of lead halide perovskites due to their remarkable physical
properties.1−4 These compounds have allowed obtaining an unprecedented progress
in light-to-energy conversion efficiencies5−7 and efficient
materials for light-emitting diodes (LEDs).8</p><p>Despite the huge number of implementations in a multitude
of applications,
there is a lack of understanding of the origin of the remarkable properties
of perovskites.9−11 For example, it is known that the photon emission
process (photoluminescence, PL) is more efficient in a direct bandgap
semiconductor than in an indirect bandgap semiconductor (in this case,
a phonon is required to emit a photon).12,13 Hence, the
long carrier lifetime (τ) measured in perovskites is not complete
understood if we assume them to be direct bandgap semiconductors with
efficient absorption.14−20 That is to say, there is a contradictory behavior in the properties
that the perovskites exhibit if we consider that the absorption and
emission of photons are ruled by the same transition matrix element.</p><p>Since long lifetimes often indicate materials with long diffusion
lengths (),
one of the main intensively explored
topics is the preservation of carrier diffusion length in perovskite
materials.21−26 It has been shown that the lead iodide perovskite film has a diffusion
length about two times longer than that of the lead bromide perovskite
film.21 Even between the same perovskite
material, the diffusion length depends on the sample preparation method,21 as each deposition/growth method comes with
some characteristic defects in a microscale. As it might influence
the results, these characteristic defects, due to the preparation
method, are typically determined using static/lifetime photoluminescence
mapping,27 or at least by proving the reproducibility
of results on multiple samples. For routing testing of the carrier
diffusion length, a laser grating technique has been proposed, instead
of joint measurements of mobility and photoluminescence lifetime.21</p><p>Taking into account that the diffusion
coefficient (D) is an intrinsic property of a crystal,
the most common standard
model among the scientific community to determine D is to assume perfect extraction or Dirichlet contour conditions n = 0 at the position x, where the selective
contact is located.28 Recently, it was
reported that a model with three slabs of different thicknesses of
the same material (the same D) suffer different direct
electron population detection decays.29 The different recombination kinetics due to their different thicknesses
(concentrations of carriers) showed that thinner slabs have shorter
lifetimes than thicker areas, and their dependence on thickness is
remarkable.</p><p>In order to get further insights into short photoluminescence
lifetimes,
we have investigated the dynamics of the recombination pathways of
the same material (therefore having the same D) in
three different morphologies of lead iodide perovskites films at different
temperatures ranging from 14 to 300 K and at a laser excitation power
of 370 nJ/cm2. With the aim of avoiding an arbitrary number
of exponential functions to describe the time-resolved PL (TRPL) spectra
decay, the Generalized Berberan-Santos decay equation (GBSe) was used.30 The distribution of recombination rate constants
(k) depending on the probability density function
(H) has allowed obtaining both qualitative and quantitative
information, such as the fast recombination centers and the FWHM,
which has shown that at the high energy band emissions for the isolated-island
configuration, the fast recombination rate centers are up to 4.8 ns–1, which explain the fast lifetimes, the low thermal
excitation, and the thermal escape obtained. Our observations corroborate
that the isolated-island configuration behaves as a semiconductor
with low density of impurities that inhibit bound exciton recombination.
In fact, its behavior at low temperatures would be comparable to that
expected in a good quality single crystal of MAPbI3, and the PL kinetics
measured is clearly associated with the "O"-phase free
exciton recombination.</p><!><p>The three different
morphologies of CH3NH3PbI3 lead iodide
perovskites (hereafter MAPbI3) films
are as follows: (i) 550 nm-thick continuous multilayers of small grains
(hereafter 550 nm-CS); (ii) 352 nm-thick continuous one layer of large
grains (hereafter 352 nm-CL); and (iii) low density of isolated 103–200
nm-thin islands of small grains (hereafter 103 nm-IS).</p><p>The size
of the small grain of 550 nm-CS and 103 nm-IS is 103 ± 9 nm,
while the size of the large grain of 352 nm-CL is 352 ±38 nm
(see Figure 1). The
length of each isolated island is approximately 1 Î¼m (1000 nm
±120 nm), and although most of the isolated islands are only
formed by a monolayer of small grains, a second layer of small grains
could not be ruled out.</p><!><p>Morphological characterizations by SEM of the
three selected morphologies
and their corresponding PL spectra to show the low energy band (LEB)
and the high energy band (HEB) at two different temperatures (40–50
K dashed line and 135–140 K solid line) and at a laser excitation
power of 370 nJ/cm2. (Green) one layer of large grains
(352 nm-CL), (red) multilayers of small grains (550 nm-CS), and (black)
one layer of islands of small grains (103 nm-IS).</p><!><p>Samples have been grown using a spin-coating solution processing
method. The details of the process can be found in refs (1) and (4):</p><!><p>An approximately 40 nm-thick
layer of TiO2 was deposited on the substrate fluorine-doped
tin oxide-coated glass. A 200 nm TiO2 mesoporous layer
was placed on this TiO2 buffer layer. MAPbI3 "cuboid-like" films of 352 nm thickness were deposited
inside a glovebox by spin-coating 30 Î¼L of a 1.082 M solution
of PbI2 in dimethylformamide at 500 rpm for 5 s. The PbI2 film was then dipped for 1 min in a CH3NH3I solution in isopropanol (0.044 M).</p><!><p>The structure
of the samples consists of a substrate of SiO2 (2 Î¼m),
a TiO2 layer (40 nm), an active layer of MAPbI3 (550 nm for 550 nm-CS and 100–200 nm for 103 nm-IS), and
a poly-methyl methacrylate (PMMA) capping layer (1 Î¼m) in order
to protect the sample from oxidation. 103 nm-IS was achieved by diluting
to 10% (w/w) the spin-coated perovskite solution of 40% used for the
other two morphologies 550 nm-CS and 352 nm-CL.</p><!><p>The cold finger
of a commercial closed-cycle compressed helium
cryostat (ARS DE-202) was used to characterize the samples. This cryo-generator
has a heating resistance and a thermometer, with which the temperature
can be controlled from 10 K to room temperature. For time-integrated
PL measurements, we used a continuous wave laser diode at 405 nm.
In time-resolved PL (TRPL) experiments, we used for excitation a 200
fs pulsed Ti:sapphire (Coherent Mira 900D, 76 MHz of repetition rate)
laser doubled to 400 nm with a BBO crystal. The backscattered PL signal
was dispersed by a double 0.3 m focal length grating spectrograph/spectrometer
(1200 g/mm with 750 nm blaze) and detected by an Andor Newton 970
EMCCD camera (for time-integrated PL spectra) and by a Si Micro Photon
Device (MPD) single photon avalanche diode (SPAD) photodetector connected
through a multimode optical fiber to the monochromator (for time-resolved
PL spectra); the SPAD was attached to a time correlated single photon
counting electronic board (TCC900 from Edinburgh Instruments).</p><!><p>To give new insights into the connection
between the morphology of the lead halide perovskites' absorber
layer/islands and their photophysical properties,31 we have measured the time-resolved photoluminescence (TRPL)
for both the low-energy (LEB) and the high-energy (HEB) band emissions
(see Figure 1). These
bands have been associated to exciton recombination in tetragonal
and orthorhombic phases, respectively.32−34 These bands coexist
in a certain temperature range, the HEB dominating at low T and the LEB at high T, as defined by
the phase transitions/discontinuities. Only for 103 nm-IS, there is
no coexisting crystallographic phases. The details of the PL spectra
can be found in refs (1) and (4). Figure 2a–f shows
the representative groups of normalized PL transients registered under
relatively high excitation fluencies (370 nJ/cm2) for the
three types of morphologies studied: 550 nm-CS, 352 nm-CL, and 103
nm-IS. This high excitation fluency of 370 nJ/cm2 was chosen
because most of the defective tetragonal-phase sites of the continuous
samples (550 nm-CS and 352 nm-CL) are filled (see Figure 3). In this way, the continuous
samples (550 nm-CS and 352 nm-CL) exhibit a similar temperature dependence
on the lifetime for "O"-excitons to the island-like
sample (103 nm-IS).1 The normalized TRPL
of the LEB (HEB) band is presented in the left (right) column.</p><!><p>(a–f)
Temperature dependence of the time-resolved photoluminescence
(PL) emission measured for the three different morphologies: (a, b)
one layer of large grains (352 nm-CL), (c, d) multilayers of small
grains (550 nm-CS), and (e, f) one layer of islands of small grains
(103 nm-IS) at 370 nJ/cm2. The blue curves represent the
evolution of the emission by increasing the temperature, which is
different in the HEB and LEB.</p><p>Low-temperature
recombination channels in MAPbI3 for
the three morphologies: (a) one layer of large grains (352 nm-CL),
(b) multilayers of small grains (550 nm-CS), and (c) one layer of
islands of small grains (103 nm-IS). At low temperatures, the grain
size of the layer of large grains is responsible for the appearance
of the dual emission (see Figure 1 and ref (4)). As the island morphology does not exhibit strain inhomogeneities
related to the formation of different tetragonal-defective domains,
a high excitation fluency of 370 nJ/cm2 was chosen to fill
most of these defective tetragonal-phase sites of the continuous samples
(550 nm-CS and 352 nm-CL). This ensures a similar temperature dependence
on the lifetime for "O"-excitons for the three morphologies.</p><!><p>In general, it is observed that the time-resolved
normalized PL
intensity is strongly dependent on the different morphologies (550
nm-CS, 352 nm-CL, and 103 nm-IS). For example, the PL intensity of
103 nm-IS (see Figure 2e,f) exhibits shorter lifetimes than the other two configurations
(see Figure 2a–d).
On the other side, the LEB band of the 352 nm-CL morphology (Figure 2a) exhibits the longest
lifetime. It should also be mentioned that only Figure 2a,f follows an exponential function (straight
line in a logarithmic scale). In particular, it is observed that for
the HEB, the two polycrystalline layers (550 nm-CS and 352 nm-CL)
(see Figure 2b,d) move
further and further away from an exponential behavior (i.e., from
a straight line in a logarithmic scale) by decreasing the temperature.
This might be related to the possible distortions or limitations of
the movement of the anions or cations that constitute our perovskite,
and it should be understood more deeply.</p><p>In order to explain
the differences of the temporal evolution of
each PL contribution/band, we have deduced the "continuous
distribution" of characteristic times or lifetimes (see Figure 3 and Figure 4a) that fits the experimental
decay curve (Figure 2) by using the Generalized Berberan-Santos decay equation35 (see Section 3.2). This characteristic time is an average time of the
entire transient extracted from the Berberan-Santos model. Therefore,
there is a unique scaling parameter for each PL transient. In the
second step, the thermal excitation and the thermal escape were also
calculated from the PL intensity plotted in Figure 4b (see Section 3.3). Finally, two fundamental parameters
were obtained from the distributions of recombination rate constants:
(i) the fast recombination center (kFAST) and (ii) its dispersion (FWHM). These parameters have provided
simple and relevant information to compare the TRPL data for these
three morphologies (see Section 3.4).</p><!><p>(a) Lifetime as a function of temperature for 352 nm-CL
(τLG), 550 nm-CS (τL), and 103 nm-IS
(τI). Closed symbols correspond to the data of the
LEB and the
open symbols to the HEB. (b) Time-integrated PL intensity as a function
of temperature for 352 nm-CL (ILG), 550 nm-CS and (IL), and 103 nm-IS (II). Closed symbols correspond
to the data of the LEB and the open symbols to the HEB.</p><!><p>Assigning an arbitrary
number (more than two) of exponential functions to explain the different
physical mechanisms involved in carrier recombination can be a speculation.
2-τ exponential fitting can stem from coupled rate equations,
but a multi-exponential decay fitting with 3-τ or more or even
a non-exponential decay is already very complicated to be supported
by an appropriate physical model. Although the use of an arbitrary
number of exponential functions is common, it has more physical sense
to set the mechanisms and translate them into the appropriate rate
equations, whose solution should describe the experimental decay curve.
Hence, we have find the "continuous lifetime (τ) distribution"
that fits the experimental decay curves by using the Generalized Berberan-Santos
equation (GBSe):30where
the scaling parameter τ has dimensions
of time. This characteristic time or lifetime is an average time of
the entire transient extracted from the GBSe. The shape-determining
parameters α and β are dimensionless, with 1 ≥
α > 0 and 1 ≥ β ≥ 0 (see Table 1). If β = 0, a compressed
hyperbola function is recuperated, whereas a stretched exponential
function is obtained for large values of α and for long times
if β > 0. Finally, the Berberan-Santos model behaves as an
exponential
function for small values of α and/or for values of β
near unity. Therefore, this Berberan-Santos relaxation function merges:
(i) the compressed hyperbola (or Becquerel36) function, which has been used for the description of decays of
experimental systems with inorganic solids, and (ii) the stretched
exponential (or Kolrausch37) function,
used for systems with organic molecules.</p><p>Our perovskite has both an inorganic framework
({PbI3}−) and an organic cations MA+.</p><p>From Table 1, it
follows that, for the HEB, i.e., in the orthorhombic phase, the polycrystalline
layers (550 nm-CS and 352 nm-CL) behave as a compressed hyperbola
(40–120 K). This is consistent with the fact that, for the
HEB, the MA+ cation becomes fixed, whereas the {PbI3}− anion becomes distorted by decreasing
the temperature.7,38−40 However, the
PL transients of the island (103 nm-IS) configuration follow an exponential
function (30–95 K), which could be expected in a good quality
single crystal of MAPbI3. It could be attributed to the strain relaxation
for this morphology and the dominantly free exciton recombination.1</p><p>On the other hand, the stretched exponential
is the predominantly
fitting type obtained for the LEB for the two configurations, in which
small grains are involved (layer (120–140 K) and islands (120–160
K)). At typical LEB temperatures, the MA+ cation shows
free rotation, and there exist eight disordered MA+ states,
whereas the {PbI3}− anion becomes less
distorted by increasing the temperature.4,38−40 Hence, the organic molecules are responsible for this behavior and
the phase transitions are linked to the ordered-disordered state of
the MA+ cation.41 However, the
PL transients of the configuration of large grains (352 nm-CL) follow
an exponential function, which could be due to the large size of the
grains. A possible explanation could be, as reported previously, the
fact that increasing the grain size from 80 to 352 nm could cause
a low density of subgap states at the phase boundaries.42−44 This would allow the MA+ cations to show free rotation
even at low temperatures for larger grains (Figure 2a). However, for the smaller grain size (Figure 2c,e), the temperature
should be increased for the PL transient to show an exponential behavior.
Therefore, it is expected to obtain the orthorhombic–tetragonal
phase transition for the larger grains at a lower temperature rather
than for a smaller grain size, as we have found (see Figure 4b). The importance of the grain
size has already been demonstrated, for example, to enhance the tetragonal
band versus the orthorhombic band4,43 or even to
produce duplication of bands in other kinds of structures when the
periodicity is of the order of 250 nm.45−47</p><!><p>The emission with the longest lifetime,
τLG, on the order of several to 10 ns is dominant
in the configuration of large grains (352 nm-CL, see Figure 3 and solid green triangles
in Figure 4a). This
is due to the fact that a large grain size has a smaller amount of
grain boundaries where nonradiative recombination can take place.51,52 As a result, a long lifetime is induced by a reduction of nonradiative
recombination channels, which is due to a reduced number of trap states
at the grain boundaries.35,53,54</p><p>The lifetime τL (in
between 1.3 and 5 ns) is related to recombination channels associated
to defective-"T" states originated by possible strain
inhomogeneities (see Figure 3 and solid red circles in Figure 4a).1</p><p>A fast lifetime τI = 0.5–1.3 ns was observed only at the low-density dispersive
isolated-island configuration 103 nm-IS (see Figures 3 and 4a). In this
case, the strain relaxation isolated-islands have no traces of shallow
electronic levels due to defective-"T" states.1 We can refer the reader here to a previous work
for a better understanding of the role of strain relaxation, "trap
states", etc. in these samples.1 Additionally, as observed in Figure 4a, the shortest photoluminescence lifetime was obtained
for individual isolated MAPbI3 islands as a result of great
separation between the islands.</p><!><p>To sum
up, the lifetime differences are due to changes in a nonradiative
mechanism relative to the boundaries of the grain, whose surface is
the one that defines its contribution with respect to radiative recombination.
Hence, a long lifetime, τLG, is obtained in the configuration
of large grains (352 nm-CL) due to a reduction of the nonradiative
recombination as a result of a reduced number of trap states at the
grain boundaries. Moreover, the lifetime is also due to the levels
of carrier capture, which are responsible for the increase in time
with temperature. Hence, even though the layer (550 nm-CS) and the
island (103 nm-IS) films have the same small grain size (103 ±
9 nm) and therefore the same boundaries of the grain, only the layer
(550 nm-CS) configuration has defective-"T" states originated
by strain inhomogeneities.</p><p>Thus, the observed differences in
the photoluminescence lifetimes
(ranging from 0.5 ns to few nanoseconds for 370 nJ/cm2)
are due to the boundaries of the grain and the levels of carrier capture.
Hence, the island (103 nm-IS) configuration has smaller lifetimes
due to the small grain size (or large boundaries of the grain) and
its lack of connectivity (avoiding diffusion) that causes the strain
relaxation. A general picture of the mechanisms explaining carrier
recombination dynamics in MAPbI3 can be found in Figure
2 of ref (55).</p><!><p>In Figure 4b, we examine
the phase transition regime more closely by plotting the time-integrated
PL intensity of a normalized decay against temperature for the two
energy bands. By increasing the temperature for an energy band, at
least one peak of the time-integrated PL intensity is obtained. This
fact has been linked to a phase transition.</p><p>For the high energy
band (orthorhombic phase), a low temperature phase transition/discontinuity
is observed at around 50 K (for 550 nm-CS and 352 nm-CL).1,4 The increase in intensity from 15 to 50 K of almost one order of
magnitude should be noted. For 103 nm-IS, two (30 and 110 K) phase
transitions/discontinuities below the expected orthorhombic–tetragonal
phase transition (see black, red, and green lines in Figure 4b) were observed. Note that
the HEB is observed from 15 to 140 K for this configuration. Although
there are some experimental data, a great difference in intensity
is again appreciated, especially for the second maximum between the
data at 95 K and the one at 120 K.</p><p>For the low energy band (tetragonal
phase), we have obtained the
characteristic orthorhombic–tetragonal phase transitions at
145 K for 550 nm-CS and around 127 K for 352 nm-CL (see Section 3.2), but also,
another phase transition/discontinuity at a higher temperature (180
K for 103 nm-IS) than the typical orthorhombic–tetragonal phase
transition (127–140 K) has been obtained for the polycrystalline
layers (550 nm-CS and 352 nm-CL).</p><p>The three different morphologies
show maximum emission centered
at different (transition) temperatures for the same laser excitation,
where this temperature is mainly determined by the speed of the process.56−63 Interestingly, the configuration that exhibits shorter lifetimes
than the other configurations for the PL intensity, as it is the case
of the 103 nm-IS, is the first one to undergo the phase transitions
(by decreasing the temperature). This can be understood if we consider
that the phase transformation will be more homogeneous in the case
of 103 nm-IS because of the strain relaxation isolated islands. Thus,
from a broader perspective, our study shows that the less extensive
the limits of grain and subgrains and the less connected the morphologies,
the faster the process of phase transformation.1,4,64 Hence, only in the case of 103 nm-IS that
no crystallographic phases coexist,1 which
has been observed in the other two configurations (550 nm-CS and 352
nm-CL)1,4 as well as in several inorganic perovskite
materials.65−70 Despite the fact that in our two polycrystalline layers (550 nm-CS
and 352 nm-CL), the HEB and the LEB seem to coexist in an intermediate
temperature range, the decrease in the HEB could be at the expense
of the increase in the LEB, if we assume that both phases have thermal
connection, and it could be considered as a non-radiative decrease
instead of as the peak of the phase transition (50 K).</p><p>The representation
of the log component PL intensity versus temperature
(Figure 4b) allows
us to calculate both the activation energies for the thermal escape
(Eact) and thermal excitation (Elow) for each of the two energy bands since
the PL intensity can be described as follows:48,49where B and C are the proportionality factors. The estimated Elow and Eact values of the
HEB and LEB are presented in Table 2.</p><p>The first phase transition/discontinuity
(20–60 K) has energy
values of the order of the tens of meV and the second phase transition
(96–150 K) of the hundreds. The thermal escape energy (Eact) is less than three times larger than the
thermal excitation energy (Elow). The
isolated-island configuration, in which PL transients follow an exponential
function instead of a compressed hyperbola function, has lower values
at the first phase transition, possibly consistent with the small
lifetimes. Its behavior at low temperatures would be that expected
in a good quality single crystal of MAPbI3.71</p><p>The estimated Elow and Eact of the LEB have lower values
at the orthorhombic–tetragonal
phase transition for the configuration of large grains (352 nm-CL),
in which the PL spectra follow an exponential function instead of
a stretched exponential function, but at that time, it exhibits long
lifetimes. Hence, this promising result of our work clearly shows
that the isolated-island (103 nm-IS) configuration is the first to
undergo the O–T phase transition by decreasing the temperature,
with shorter lifetimes; meanwhile, the large grain configuration (352
nm-CL) undergoes the O–T phase transition at a lower temperature,
with longer lifetimes. Thus, this is consistent with the fact that
the less extensive the limits of grain and subgrains and the less
connected morphologies, the faster the process of phase transformation.
These results give further insights into the photoluminescence response
to the crystallite dimensions, connectivity, and perovskite crystal
phases.</p><!><p>The experimental time-resolved photoluminescence emission curve I(t), plotted in Figure 2, has been normalized such that the area
under it is equal to 1. By directly inverting (k =
1/τ) the I(t)/area, we can
obtain the normalized area probability density function H (ns) as a function of the distribution of recombination rate constants
(k (ns–1)), as shown in Figure 5.35 Two fundamental parameters can be obtained: (i) its dispersion
(FWHM), as if H(k) was a single
band, without considering the narrow contribution of the islands (103
nm-IS) configuration and (ii) the fast/slow recombination center (kFAST and kSLOW),
defined as:</p><!><p>(a–f)
Distributions of the recombination rate constants
of the three different morphologies: (a, b) one layer of large grains
(352 nm-CL), (c, d) multilayers of small grains (550 nm-CS), and (e,
f) one layer of islands of small grains (103 nm-IS). The areas of
the distribution of recombination centers are normalized to 1. The
diamonds, squares, and circles represent the slow and fast recombination
centers of 352 nm-CL, 550 nm-CS, and 103 nm-IS, respectively.</p><!><p>These definitions provide simple and relevant information
to compare
the three perovskite morphologies, as well as for LEB and HEB PL contributions
(see Figure 5a–f).
Considering that the areas of the distribution of recombination centers
are normalized to 1, it can be deduced from Figure 5 that the three samples are not only distinguished
due to different (small/bigger) grain size ratios since the maximum
of the probability density function (HMAX) does not match that at the same k(HMAX) for a given temperature. Additionally, HMAX is smaller for the LEB than for the HEB, especially
for large grains, 352 nm-CL, where the HMAX is significantly smaller for the LEB (<0.3 ns for all temperatures)
and the fast recombination centers (kFAST) are larger (Figure 5a,b). If we take a closer look at these parameters (see Figure 6a–f), we observe
that the three samples are almost identical in their behavior at long
lifetimes (small k, kSLOW). In addition, at low temperatures, they present smaller kSLOW. However, the 550 nm-CS sample (at HEB)
and the 352 nm-CL sample (at LEB) have fewer slow recombination centers
in absolute number compared to the other two samples, with 103 nm-IS
being the sample that presents more slow recombination centers (kSLOW).</p><!><p>Comparison of slow and fast recombination centers
(kSLOW and kFAST) in absolute
number for the three configurations as a function of (a, b) H(1/e), (c, d) FWHM, and (e, f) k(HMAX). The diamonds, squares,
and circles represent the slow and fast recombination centers of 352
nm-CL, 550 nm-CS, and 103 nm-IS, respectively.</p><!><p>The behavior at short lifetimes (large k, kFAST) is clearly different for the three samples.
A large number of fast recombination centers for the LEB and for the
HEB are obtained in the configuration in which Elow and Eact are lower: (i) At
the LEB, the largest number of fast recombination centers (kFAST) has been observed for 352 nm-CL (Figure 6a,e) and (ii) at
the HEB, a very large number of widely dispersed fast recombination
centers (kFAST) for sample 103 nm-IS in
comparison to the other two polycrystalline samples have been observed
(Figures 6b,f).</p><p>These two configurations (103 nm-IS and 352 nm-CL) are also the
only ones that follow an exponential function, as seen in Section 3.2.</p><p>To sum
up, for the isolated-island configuration at the HEB, (i)
the PL transients follow an exponential function instead of a compressed
hyperbola function, (ii) it has the lowest thermal excitation (Elow) and the thermal escape (Eact) values at the first phase transition, (iii) it has
the smallest lifetime, (iv) it has the largest H(1/e), and (v) the fast recombination rate centers are up to
4.8 ns–1, compared to less than 2 ns–1 for the other two configurations. This represents a clear break
in the behavior of the isolated-island configuration (see Figure 5f). All these results
are consistent with each other and stem from the strain relaxation
that prevents shallow electronic levels from arising due to defective-"T"
states.</p><!><p>PL measurements
for the three morphologies in polycrystalline thin
film configuration at varying temperatures (14–300 K) evidenced
characteristic differences on the electronic properties of lead iodide
perovskite. In this work, we applied the Generalized Berberan-Santos
model to analyze the PL decay to account the short photoluminescence
lifetimes (nanosecond) since the models of quantum confinement or
surface chemistry cannot completely explain our results. We found
that the PL transient of the high energy band (HEB) in the orthorhombic
phase of polycrystalline layer morphology decayed as a compressed
hyperbola (40–120 K), consistent with the fact that the MA+ cation becomes fixed, whereas the {PbI3}− octahedral anion becomes distorted by decreasing the temperature.
Instead, PL transients of the island configuration follow an exponential
function decay attributed to strain relaxation and dominantly free
exciton recombination as expected in a good quality single crystal
of MAPbI3. On the other hand, the low energy band (LEB)
decayed following the stretched exponential function only if the sample
contained small crystallites. The island morphology-type film implies
larger boundaries of the grain with an increased number of trap states
on boundaries compared to larger crystallite morphologies. Then, faster
recombination rate centers are numerous and widely dispersed producing
short photoluminescence lifetimes, low thermal excitation, and thermal
scape due to this characteristic broken connectivity between grains.</p><!><p>The authors declare no
competing financial interest.</p>