Silvia G Motti1, Timothy Crothers1, Rong Yang2, Yu Cao2, Renzhi Li2, Michael B Johnston1, Jianpu Wang2, Laura M Herz1. 1. Department of Physics , University of Oxford, Clarendon Laboratory , OX1 3PU Oxford , United Kingdom. 2. Key Laboratory of Flexible Electronics (KLOFE) and Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM) , Nanjing Tech University , 30 South Puzhu Road , Nanjing 211816 , China.
Abstract
The addition of large hydrophobic cations to lead halide perovskites has significantly enhanced the environmental stability of photovoltaic cells based on these materials. However, the associated formation of two-dimensional structures inside the material can lead to dielectric confinement, higher exciton binding energies, wider bandgaps and limited charge-carrier mobilities. Here we show that such effects are not detrimental to the charge transport for carefully processed films comprising a self-assembled thin layer of quasi-two-dimensional (2D) perovskite interfaced with a 3D MAPbI3 perovskite layer. We apply a combination of time-resolved photoluminescence and photoconductivity spectroscopy to reveal the charge-carrier recombination and transport through the film profile, when either the quasi-2D or the 3D layers are selectively excited. Through modeling of the recorded dynamics, we demonstrate that while the charge-carrier mobility is lower within the quasi-2D region, charge-carrier diffusion to the 3D phase leads to a rapid recovery in photoconductivity even when the quasi-2D region is initially photoexcited. In addition, the blue-shifted emission originating from quasi-2D regions overlaps significantly with the absorption spectrum of the 3D perovskite, allowing for highly effective "heterogeneous photon recycling". We show that this combination fully compensates for the adverse effects of electronic confinement, yielding quasi-2D perovskites with highly efficient charge transporting properties.
The addition of large hydrophobic cations to lead halide perovskites has significantly enhanced the environmental stability of photovoltaic cells based on these materials. However, the associated formation of two-dimensional structures inside the material can lead to dielectric confinement, higher exciton binding energies, wider bandgaps and limited charge-carrier mobilities. Here we show that such effects are not detrimental to the charge transport for carefully processed films comprising a self-assembled thin layer of quasi-two-dimensional (2D) perovskite interfaced with a 3D MAPbI3 perovskite layer. We apply a combination of time-resolved photoluminescence and photoconductivity spectroscopy to reveal the charge-carrier recombination and transport through the film profile, when either the quasi-2D or the 3D layers are selectively excited. Through modeling of the recorded dynamics, we demonstrate that while the charge-carrier mobility is lower within the quasi-2D region, charge-carrier diffusion to the 3D phase leads to a rapid recovery in photoconductivity even when the quasi-2D region is initially photoexcited. In addition, the blue-shifted emission originating from quasi-2D regions overlaps significantly with the absorption spectrum of the 3D perovskite, allowing for highly effective "heterogeneous photon recycling". We show that this combination fully compensates for the adverse effects of electronic confinement, yielding quasi-2D perovskites with highly efficient charge transporting properties.
Metal halide perovskite semiconductors
have recently emerged as promising materials for photovoltaic devices,
whose efficiencies have reached over 23%.[1] However, a significant obstacle to commercial application is the
poor stability of this class of materials, in particular upon exposure
to moisture.[2−4] One strategy to overcome this challenge is the addition
of large hydrophobic organic cations to the perovskite precursors
as part of the film fabrication process, which has proven to enhance
the moisture resistance and the environmental stability of the material.[5,6] Since these molecules are too large to fit into the perovskite octahedra,
they instead form interlayers that induce the formation of a two-dimensional
(2D) structure. While these hydrophobic spacers thus reduce moisture
permeability, they also form a dielectric barrier between adjacent
layers of the metal halide perovskite. Such dielectric confinement
may result in higher exciton binding energies, wider bandgap, and
limited charge-carrier diffusion lengths[7,8] which are unfavorable
characteristics for photovoltaic applications.To mitigate the
adverse effects of charge confinement upon the
addition of hydrophobic molecules, quasi-2D compositions have been
fabricated for which the ratio between the small cation incorporated
into the perovskite lattice and the large hydrophobic cation is carefully
tuned. Depending on the exact processing conditions, the resulting
films contain various distributions of n semiconducting
perovskite layers, and consequently different levels of electronic
confinement. In addition, hydrophobic interlayers may be placed in
a random or gradient (low to high n) arrangement
across the film depth. Such mixed-phase materials can combine the
enhanced stability of 2D perovskites with the superior charge-transport
properties of their 3D counterpart, as has been demonstrated by their
successful implementation in light-emitting diodes[9−12] and photovoltaic devices.[13−20]Many fundamental and practical questions arise from the presence
of such chemical and electronic heterogeneity inside these mixed-phase
perovskites. For instance, it has recently been explored how the nature
of charge-carriers and their interaction with the lattice differ from
what is encountered in the more conventional bulk 3D perovskite semiconductors.[7,8,21−23] For the optimized
operation of electronic devices, knowledge of how energy and charge
transfer occur between different domains within mixed-phase materials
is particularly important. Although a few studies have investigated
electronic interactions between neighboring perovskite sheets and
short-scale transfer mechanisms,[24−26] an understanding of
how these heterogeneities affect charge transport throughout a film’s
depth is urgently required for optimization of charge conduction on
the device scale.In this study, we address this issue by investigating
mixed-phase
quasi-2D/3D lead-iodide perovskite films using a combination of time-resolved
photoluminescence (PL) and optical-pump terahertz-probe (OPTP) spectroscopy.
We demonstrate that for the deployed processing conditions, the film
contains a layer of quasi-2D domains on the side interfacing the substrate,
and a predominantly 3D region near the outer side of the film. We
find that the mobility of charge-carriers inside the quasi-2D region
is on average ∼25% lower than for those present in the 3D (bulk)
layer of the film. However, this seemingly detrimental effect of low
dimensionality appears to be short-lived, as the OPTP dynamics reveals
a transient enhancement of photoconductivity over a time scale of
∼1 ns after primarily the quasi-2D region has been photoexcited.
By modeling the charge-carrier dynamics in these films, we demonstrate
that this photoconductivity boost results from charge-carriers transferring
efficiently from quasi-2D regions to 3D layers, where the charge mobility
is higher. We show that such transfers are not only aided by charge-carrier
diffusion but also by photon recycling of higher-energy photons emitted
from the quasi-2D domains that are particularly efficiently recaptured
by the absorption profile of the 3D bulk phase. Our findings therefore
reveal that the presence of dielectric confinement in such mixed phase
films may be far less detrimental to photovoltaic performance than
is commonly assumed. In particular, charge-carrier transfer from quasi-2D
to 3D domains with higher mobility can be sufficiently rapid to outcompete
recombination and is aided by the upshift in emission energy resulting
from electronic confinement, which yields particularly effective photon
reabsorption by the 3D region. Hence, we find that for suitable film
morphology the enhanced stability of 2D perovskites can be combined
with the favorable charge-transport properties of 3D semiconductors.Mixed phase quasi-2D/3D lead iodide perovskite thin films were
fabricated on quartz substrates, based on the smaller methylammonium
(MA) cation for incorporation into the lead iodide perovskite lattice,
and the larger 3-bromobenzylammonium cation as a spacer (3BBA). Full
details of the film fabrication and characterization are provided
in the SI. A similar film fabrication method has recently been successfully
applied to yield active layers for efficient solar cells with a peak
power conversion efficiency of 18.2% and excellent stability in moist
environment.[6] The morphology of such films
can be examined in Figure a, which shows the cross-section of a perovskite film recorded
through aberration-corrected scanning transmission electron microscope
(STEM, see Supporting Information for details).
Although the top surface of the film appears homogeneous on the substrate
side, elongated crystallites can be identified which are oriented
perpendicular to the substrate. Grazing-incidence wide-angle X-ray
scattering (GIWAXS) measurements previously performed on such films[6] have revealed that the outer surface is constituted
mostly by 3D MAPbI3 crystallites, while additional peaks
associated with 2D-phase perovskite could be observed for higher incidence
angle (when the full depth of the films was being probed). Moreover,
these measurements indicated a predominant orientation of the layered
structures within the quasi-2D phase perpendicular to the substrate.
Previous reports suggest that such preferential formation of quasi-2D
domains on the substrate side may be linked to specific parameters
such as the solubility of the precursors, the substrate temperature,
and surface energies.[7,9−11] On the basis
of our experimental evidence, we conclude that the present mixed-phase
films comprise two distinct regions, as depicted schematically in Figure b. The top layer
on the outer surface consists of large 3D MAPbI3 crystallites
whereas the substrate-side layer constitutes a blend of smaller 3D
crystallites and quasi-2D domains, whose preferential orientation
is perpendicular to the film surface.
Figure 1
(a) Cross-section of a mixed phase quasi-2D/3D
lead iodide perovskite
film recorded by STEM (see Supporting Information for details). (b) Schematic illustration of the film morphology
showing 3D MAPbI3 crystallites on top and orientated quasi-2D
crystallites at the substrate side. (c) Absorption (dashed line, light
blue) and PL spectra taken in reflection geometry with excitation
at 3.1 eV photon energy either from the front (dark blue) or the back
side (red) of the perovskite film.
(a) Cross-section of a mixed phase quasi-2D/3D
lead iodide perovskite
film recorded by STEM (see Supporting Information for details). (b) Schematic illustration of the film morphology
showing 3D MAPbI3 crystallites on top and orientated quasi-2D
crystallites at the substrate side. (c) Absorption (dashed line, light
blue) and PL spectra taken in reflection geometry with excitation
at 3.1 eV photon energy either from the front (dark blue) or the back
side (red) of the perovskite film.To probe the optoelectronic properties of each region, we
illuminated
450-nm thick films either from the front or the back side with 3.1
eV light and measured the PL spectra in reflection mode (Figure c). At this excitation
energy, light is strongly absorbed by the lead iodide perovskite with
an associated penetration depth shorter than 100 nm (see Figure S2) which means that the initially generated
charge-carrier distributions will be located either in the 3D MAPbI3 or the quasi-2D layers. We find that, as expected, front
side photoexcitation produces a symmetric narrow-band emission consistent
with conventional 3D MAPbI3 spectra,[27] whereas photoexcitation on the back (substrate side) of
the film, however, results in a higher energy shoulder in the emission
which is in agreement with the presence of quasi-2D perovskite domains.To further investigate how the charge-carrier distribution evolves
through the film, we measured the PL dynamics following photoexcitation
from either the front (Figure a,b) or back side of the film (Figure d,e). We find that when the film is excited
from the back side, the PL spectrum at early times carries the fingerprint
of the quasi-2D region, which decays with a lifetime of only 4 ns.
This broad-band emission spectrum is superimposed onto the long-lived,
narrower emission spectrum of the 3D MAPbI3 region with
lifetime >1 μs (see Figure S4 for
component analysis). We note that the high-energy emission of the
quasi-2D region is centered around 1.74 eV, in contrast to that reported
for strongly confined 2D perovskites (n = 1) of similar
composition which have exhibited emission in the 2.2–2.5 eV
spectral region.[28] In addition, there is
no strong presence of sharp higher-energy bandgap phases in the absorption
spectrum of the film (Figure c, dashed blue line). Although the broad PL emission observed
from the present samples does not allow for accurate determination
of the n composition, it suggests a predominance
of n > 4 quasi-2D domains. The exciton binding
energies
for such a level of dielectric and electronic confinement are not
expected to be so significantly elevated as to be detrimental for
photovoltaic applications.[29,30] Nonetheless, even such
a low level of confinement apparently has a dramatic effect on the
radiative recombination rates of charge-carriers, as evidenced by
the high relative intensity and fast decay of the high energy emission
originating from the quasi-2D perovskite. Such high emission decay
rates could potentially be a limiting factor for photovoltaic devices,
where long carrier lifetimes (i.e., long diffusion lengths) are desirable
to promote efficient charge extraction. However, these short lifetimes
could alternatively be associated with charge and energy transfer
dynamics to the lower bandgap domains, which would be beneficial,
given that where these are likely to exhibit higher charge-carrier
lifetimes and mobilities, and lower exciton binding energies.
Figure 2
Maps of the
time-resolved PL originating from a 3D/quasi-2D lead
iodide perovskite film measured in reflection geometry with photoexcitation
from the front (a) or the back (d) of the films, taken with an excitation
energy of 3.1 eV (500 kHz, fluence ∼10 nJ/cm2);
PL decays (point spacing ∼3 ns) at 1.59 eV (red) and 1.9 eV
(dark blue) taken with photoexcitation from the front (b) or the back
(e) of the films; insets show the matching PL spectra at different
decay times. OPTP THz photoconductivity transients (plotted as −ΔT/T ∝ σ; time resolution ∼50
fs, excitation at 3.1 eV, repetition rate 5 kHz) taken with photoexcitation
incident on the front (c) or back (f) of the films; dots are experimental
data points and solid lines are fitted dynamics (which account for
charge diffusion and photon reabsorption and assume heterogeneous
PL emission).
Maps of the
time-resolved PL originating from a 3D/quasi-2D lead
iodide perovskite film measured in reflection geometry with photoexcitation
from the front (a) or the back (d) of the films, taken with an excitation
energy of 3.1 eV (500 kHz, fluence ∼10 nJ/cm2);
PL decays (point spacing ∼3 ns) at 1.59 eV (red) and 1.9 eV
(dark blue) taken with photoexcitation from the front (b) or the back
(e) of the films; insets show the matching PL spectra at different
decay times. OPTP THz photoconductivity transients (plotted as −ΔT/T ∝ σ; time resolution ∼50
fs, excitation at 3.1 eV, repetition rate 5 kHz) taken with photoexcitation
incident on the front (c) or back (f) of the films; dots are experimental
data points and solid lines are fitted dynamics (which account for
charge diffusion and photon reabsorption and assume heterogeneous
PL emission).To investigate such interplay
between confinement effects and the
charge transport properties of the mixed-phase films we performed
OPTP spectroscopy, which allows us to probe the transient photoconductivity
of the film in a contactless manner. The measurements were performed
with 3.1 eV pulsed photoexcitation incident either on the front or
back of the films, and the transients obtained are shown in Figure c,f. The photoinduced
differential transmission of terahertz (THz) radiation (ΔT/T) is proportional to the photoconductivity
(σ) of the film, which is in turn linearly dependent on the
charge-carrier population density and the effective charge-carrier
mobility (μ). From the −ΔT/T amplitude immediately after photoexcitation (i.e., before
charge-carrier recombination has occurred), μ can then be extracted
under knowledge of the absorbed photon density (see Section 1.5 in Supporting Information for details).[31,32] We find that while photoexcitation from the back side of the film
resulted in an initial charge-carrier mobility of 17.4 ± 0.9
cm2/(V s), this value increased to 23.9 ± 0.9 cm2/(V s) for excitation from the front side. The ∼25%
lower charge-carrier mobility measured when probing the back side
of the films is consistent with the presence of quasi-2D domains and
the higher concentration of dielectric barriers in this region.[7]The OPTP measurements further allow us
to investigate the subsequent
dynamics of charge-carriers following the initial photoexcitation.
We note that unlike the PL transients discussed earlier, which tend
to overemphasize the contributions from carrier recombination in strongly
confined regions that are associated with high radiative efficiencies,
the OPTP photoconductivity measurements are particularly sensitive
to carriers that are mobile, thus highlighting the electronic response
from regions of lower confinement. Figure c,f shows that both for back and front side
photoexcitation the photoconductivity lifetimes decrease with increasing
fluence (for full fluence dependence see Figure S5 in the Supporting Information). This behavior can be described
by the typical recombination dynamics of free charge-carriers observed
in perovskite semiconductors, which may recombine through a monomolecular
trap-assisted mechanism, combined with bimolecular radiative recombination
and third order Auger-like processes whose contribution become significant
at higher carrier densities.[31,33] At the lowest fluences,
transients are generally expected to be flat, as bimolecular and Auger
recombination become negligible, and the remaining trap-mediated recombination
may occur over a time scale much longer than the observation window
of 1 ns. However, while the low-fluence dynamics for front-side excitation
of the film indeed appear mostly flat, the transients taken after
photoexcitation of the back side of the film show a rise in photoconductivity
(Figure a). Because
of the short penetration depth (<100 nm) of the excitation light,
the ΔT/T signal immediately
after photoexcitation arises exclusively from the volume of the thin
films in which light is absorbed and where the charge-carriers are
initially concentrated. The THz probe beam on the other hand has a
penetration depth much longer than the sample thickness and is detected
in transmission geometry, therefore responding to mobile charge-carriers
present anywhere within the full volume of the film. In consideration
of the lower charge-carrier mobilities that we have observed in the
quasi-2D region of the films, we can credit the rise in the OPTP dynamics
following substrate-side photoexcitation to the transfer of charge-carriers
from the low-mobility quasi-2D region to the higher-mobility 3D region.
By analyzing the resulting photoconductivity enhancement, we are thus
able to investigate the mechanisms underpinning such rapid transfer
of charge-carriers.
Figure 3
(a) OPTP dynamics measured with illumination incident
on the front
(red) or back (dark blue) side of the thin film, with fluence 1 μJ/cm2. In order to account for different photoexcitation densities
that result from the different reflectivity of the perovskite (front)
or substrate (back) surfaces, the amplitudes have been plotted as
−ΔT/T* = (−ΔT/T)/N0, where N0 is the predicted initial density of photoexcited
carriers (see Figure S6 for unnormalized
data). (b) Schematic illustration of the charge-carrier transfer and
recombination mechanisms operating in a thin metal halide perovskite
film made of quasi-2D, higher bandgap domains near the substrate side,
and a 3D, lower bandgap region near the front (vacuum) side.
(a) OPTP dynamics measured with illumination incident
on the front
(red) or back (dark blue) side of the thin film, with fluence 1 μJ/cm2. In order to account for different photoexcitation densities
that result from the different reflectivity of the perovskite (front)
or substrate (back) surfaces, the amplitudes have been plotted as
−ΔT/T* = (−ΔT/T)/N0, where N0 is the predicted initial density of photoexcited
carriers (see Figure S6 for unnormalized
data). (b) Schematic illustration of the charge-carrier transfer and
recombination mechanisms operating in a thin metal halide perovskite
film made of quasi-2D, higher bandgap domains near the substrate side,
and a 3D, lower bandgap region near the front (vacuum) side.Figure b schematically
illustrates the mechanisms by which charge-carriers may be transferred
from quasi-2D to 3D domains in the film. Here, we do not account for
the transfer of excitons but rather focus on the movement of free
charge-carriers. Although exciton transfer has been observed in layered
perovskites,[26] it has been found to dominate
at much shorter time scales (∼100 fs) and distances than we
explore here and in the presence of higher exciton binding energies
in strongly confined 2D layers, which are not present in our samples.
We therefore focus on two main transfer mechanisms, which are diffusion
of free charge-carriers and photon recycling.The diffusion
of free charge-carriers from the quasi-2D to the
3D domains will be aided by the slight downward slope in bandgap energy
(Figure ) and the
strong gradient in charge-carrier density resulting from the short
penetration depth of the photoexcitation, which will cause both electrons
and holes to diffuse preferentially away from the illuminated area.
As we discuss further below, given the measured values for charge-carrier
mobilities, such diffusion should indeed occur within the nanosecond
time scales of our observations. We note that because the photoconductivity
probed by OPTP represents a sum of the electron and hole contributions,
we cannot distinguish between the individual dynamics of electrons
and holes. However, recent ultraviolet photoelectron spectroscopy
(UPS)[9,34] measurements of quasi-2D lead iodide perovskites
have revealed that the energetic positions of the valence band maxima
(VBM) show little variation with layer thickness n, while the conduction band minima (CBM) show more pronounced steps,
thus forming an energy cascade for electrons (see Figure ). Therefore, while such a
gradient in CBM will promote the transfer of electrons to lower-bandgap
3D domains toward the front side of our films, the alignment of the
VBM should allow free movement of holes into any direction. Such hole
transfer to higher band gap domains has indeed been previously observed
by transient absorption spectroscopy.[26,35−37] This characteristic has important implications for solar cells fabricated
with mixed-phase quasi-2D perovskites, as it allows for facile charge
separation of electrons and holes toward opposite electrodes when
a gradient of 2D effects through the depth profile is present.The second effective mechanism for the transfer of charges that
needs to be considered is the reabsorption of photons that have been
emitted following radiative charge-carrier recombination. Such photon
recycling is known to have significant effects on the excited state
dynamics over the nanosecond time scale of our measurements.[38] As we show below, this process will be particularly
efficient for the case of high-energy photons originating from the
highly emissive quasi-2D domains, which have strong energetic overlap
with the absorption spectrum of the lower-bandgap 3D perovskite.To evaluate the relative importance of each of these mechanisms,
we modeled the photoconductivity dynamics based on a modified version
of our previously reported approach that accurately described the
observed OPTP dynamics in 3D perovskite films.[38] As before, we account for the effects of the charge-carrier
diffusion and photon reabsorption as well as carrier recombination,[38] but in addition now also consider the heterogeneous
distribution of morphology and electronic properties through the film
profile. Briefly, the initial charge-carrier population after a short
pulse of photoexcitation is determined according to Beer’s
Law of absorption and decays exponentially away from the illuminated
surface. At any given depth of the film, the carrier population evolves
over time from its initial value, as a result of carrier recombination,
carrier diffusion, and reabsorption of photons originating from radiative
recombination that is tracked through the film. The mixed-phase morphology
of the films, with the presence of both quasi-2D and 3D layers, requires
us to account for the heterogeneous charge-carrier mobilities and
spectral shape of PL emission. On the basis of film profilometry,
STEM and spectroscopic data (see Section 4.1 in Supporting Information for details), we modeled the mixed-phase
films as comprising two layers: one on the substrate side, consisting
of a quasi-2D region of 150 nm thickness with effective mobility μ
= 17.4 cm2/(V s), on top of which resides a 3D perovskite
layer with 300 nm thickness and μ = 23.9 cm2/(V s)
(Figure S9). The characteristic PL emission
spectra associated with each layer were obtained from the PL spectra
measured at early times after photoexcitation from either side (see
insets in Figure b,e),
which were corrected to account for self-absorption effects (Figure S12). A full description of the model
is provided in Supporting Information.Our model simulates the diffusion of charge-carriers based on the
mobility and thickness of each layer and traces the photon reabsorption
according to the absorption and PL spectra and the radiative rate.
Simultaneously, the recombination rate constants are globally fitted
to the fluence dependence of the experimental transients. First, we
are able to determine the intrinsic value of the bimolecular recombination
rate constant accurately from fits of the transients, shown in Figure c,f for both front
and back photoexcitation and find a value similar to the one we have
recently reported[38] for MAPbI3 at room temperature (see Section S5 of the Supporting Information). Second, we are able to concentrate on a careful
examination of the photoconductivity transients collected at lower
excitation fluences to investigate the relative importance of the
individual contribution of charge diffusion and photon reabsorption. Figure b shows an example
for such transients, which exhibit a slow rise in photoconductivity
for excitation from the back side (quasi-2D region) but a decay for
excitation from the front side (3D layer). In the former case, importantly,
initial excitation of the quasi-2D region leads to a crossing in the
photoconductivity transient at later times. This observation is surprising,
given that for similar charge recombination rates the redistribution
of charge-carriers would eventually result in a uniform population
throughout the film giving equivalent photoconductivity regardless
of where carries are initially photoexcited. Alternatively, higher
radiative losses in quasi-2D domains could ultimately result in lower
photoconductivity values. However, such crossing in the dynamics instead
shows that the photoconductivity attained at long times after excitation
of the 2D phase exceeds that observed for direct excitation of the
3D phase. To understand the origin of this enhancement of photoconductivity
and the relative contributions of charge-carrier diffusion and photon
reabsorption, we applied the model to fit these transients with either
or both of these mechanisms omitted.
Figure 4
(a) PL spectra (dashed line, corrected
for self-absorption) of
the quasi-2D and 3D lead iodide perovskite regions of the thin film.
The highlighted area indicates the spectral overlap with the absorption
spectrum. The calculated photon recapture probabilities are 40% for
3D emission and 60% for quasi-2D emission. (b) OPTP dynamics measured
with illumination incident on the front (red) or back (dark blue)
side of the thin film, with fluence 16 μJ/cm2. Dots
represent experimental data and solid lines in (c) are simulated transients
(accounting for charge diffusion and photon reabsorption under the
assumption of heterogeneous PL emission; recombination rate constants
were obtained from the fits to experimental data). (d) Simulated OPTP
photoconductivity dynamics for photoexcitation incident on the front
(red) or back (dark blue) of the thin film, both accounting for charge
diffusion and photon reabsorption, but considering either homogeneous
(dotted lines) or heterogeneous (solid lines) PL emission. In order
to account for different photoexcitation densities that result from
the different reflectivity of the perovskite (front) or substrate
(back) surfaces, the amplitudes have been plotted as −ΔT/T* = (−ΔT/T)/N0, where N0 is the predicted initial density of photoexcited
carriers (see Figure S8 for unnormalized
data). Simulated transients in (c,d) were obtained for a fixed value
of N0 on both sides (see Section S6 in Supporting Information for full details of the
analysis).
(a) PL spectra (dashed line, corrected
for self-absorption) of
the quasi-2D and 3D lead iodide perovskite regions of the thin film.
The highlighted area indicates the spectral overlap with the absorption
spectrum. The calculated photon recapture probabilities are 40% for
3D emission and 60% for quasi-2D emission. (b) OPTP dynamics measured
with illumination incident on the front (red) or back (dark blue)
side of the thin film, with fluence 16 μJ/cm2. Dots
represent experimental data and solid lines in (c) are simulated transients
(accounting for charge diffusion and photon reabsorption under the
assumption of heterogeneous PL emission; recombination rate constants
were obtained from the fits to experimental data). (d) Simulated OPTP
photoconductivity dynamics for photoexcitation incident on the front
(red) or back (dark blue) of the thin film, both accounting for charge
diffusion and photon reabsorption, but considering either homogeneous
(dotted lines) or heterogeneous (solid lines) PL emission. In order
to account for different photoexcitation densities that result from
the different reflectivity of the perovskite (front) or substrate
(back) surfaces, the amplitudes have been plotted as −ΔT/T* = (−ΔT/T)/N0, where N0 is the predicted initial density of photoexcited
carriers (see Figure S8 for unnormalized
data). Simulated transients in (c,d) were obtained for a fixed value
of N0 on both sides (see Section S6 in Supporting Information for full details of the
analysis).Focusing first on the differences
in the OPTP transients observed
at early times, we find that exclusion of photon reabsorption from
the dynamical model still allows us to reproduce the dynamics with
good accuracy (see Figures S13 and S14).
Charge diffusion from quasi-2D domains with lower carrier mobility
to the high-mobility 3D region therefore appears to be the main mechanism
influencing the early transient enhancement of the photoconductivity
following excitation of the quasi-2D region. We observed that such
a rise cannot be reproduced when only photon reabsorption is used
to redistribute carriers across the film. However, when considering
both mechanisms, reabsorption results in prolonged charge-carrier
lifetimes and a further enhancement of photoconductivity at later
times with respect to the effect of diffusion alone (see Section S6.2 in Supporting Information).Finally, we are able to relate the crossing of the transients observed
at elevated excitation fluences (Figure b) for front and back excitation to the heterogeneous
nature of the PL emission spectra in these films. We observed that
such crossing can only be reproduced when accounting for photon reabsorption.
We then evaluate how the sample heterogeneity affects the efficiency
of photon recapture. Here, we simulated the OPTP dynamics incorporating
both charge diffusion and photon reabsorption, but now consider two
different spectral scenarios for photon reabsorption. In the first
case, we considered heterogeneous PL, where the emission of the quasi-2D
region has two components centered at 1.59 and 1.74 eV (as derived
from back-surface excitation spectra) whereas the emission of the
3D region is centered at 1.59 eV (as illustrated in Figure a). In the second case, we
considered homogeneous PL across the film, that is, both regions exhibit
emission centered at 1.59 eV (spectral shape of 3D MAPbI3, as observed for front-surface excitation), and its overlap with
the absorption spectrum of the film that is dominated by 3D MAPbI3 near the onset (Figure c). As Figure a illustrates, for the case of heterogeneous PL the high energy
photons emitted by the quasi-2D domains overlap much better with the
absorption coefficient spectrum of the 3D domains, resulting in a
60% probability of photon recapture, compared with a 40% probability
for the case of 3D MAPbI3 emission (see Section S6.2.1 in Supporting Information for full details
of calculation). Such improved spectral overlap between absorption
and emission enables the quasi-2D PL emission to contribute to a stronger
enhancement of photoconductivity over time (Figure S21) as a consequence of more efficient photon reabsorption
by the 3D MAPbI3 layer. As Figure d shows, the modeled OPTP transients for
front photoexcitation (red) and back photoexcitation (dark blue) will
only cross at later times if heterogeneous PL is considered at this
fluence, whereas they approach each other at long times for the case
of homogeneous PL. The experimentally observed crossing of these transients
(Figure b) thus provides
clear evidence that photon reabsorption, boosted by the higher-energy
emission of the quasi-2D region, augments capture and retention of
charge-carriers in the 3D perovskite layer.Our modeling of
photon reabsorption effects in these mixed-phase
perovskite films thus reveals two favorable effects. First, we find
that photon recapture minimizes radiative losses, even when charge-carriers
recombine relatively rapidly in the quasi-2D phase of the material,
because of efficient photon recapture that prolongs the effective
charge-carrier lifetime. As a second effect, photon reabsorption leads
to somewhat faster redistribution of charge-carriers from quasi-2D
to 3D domains than would be expected from charge diffusion alone.
These two effects are able to compensate, respectively, the increased
charge-carrier recombination rate and reduced mobility that characterize
quasi-2D perovskites. Because radiative recombination is a bimolecular
process, photon reabsorption appears to affect the dynamics more strongly
at higher excitation fluences (Figure S7). At low excitation fluences, charge-carrier diffusion is the dominant
mechanism and the measured THz photoconductivity reaches the same
amplitude for both front and back excitation (Figure a), because the charge-carrier density becomes
evenly spread through the film which compensates for the differences
in charge mobilities between regions of the film. At higher fluences
(Figure b), on the
other hand, the contribution of radiative recombination increases,
making photon reabsorption particularly effective and leading to the
observed crossing of transients. Therefore, at the radiative limit the more highly
optimized photon reabsorption resulting from better spectral overlap
between the quasi-2D emission and the 3D perovskite absorption ultimately
results in slightly longer charge-carrier lifetimes and increased
photoconductivity when the quasi-2D side is illuminated. We also note
that the efficiency of photon recapture is not greatly affected by
the total thickness of the film for values typically implemented in
perovskite solar cells (see Section 6.3 in the Supporting Information). This boost in lifetime and photoconductivity
promoted by the higher PL energy of the quasi-2D phase suggests that
light-harvesting devices fabricated with such mixed-phase perovskite
films could benefit from illumination being incident on the side containing
the quasi-2D material. In addition, we note that the presence of quasi-2D
domains should contribute to a decrease of nonradiative losses. The
passivation of grain boundaries by the large organic cation can decrease
the trap-assisted recombination rates, whereas the high radiative
rates in the quasi-2D domains result in higher PL quantum efficiencies.[7,9] Therefore, the heterogeneous photon recycling we observe here will
be particularly effective.In conclusion, we have investigated
the charge-carrier transport
in lead iodide perovskite films with a self-assembled graded structure
comprising quasi-2D domains on the substrate side, topped with a layer
of 3D MAPbI3. We find that, as expected, the presence of
electronic confinement results in lower charge-carrier mobility and
significantly higher radiative recombination rates. However, through
analysis of the photoconductivity dynamics following photoexcitation,
we show why these effects still present no obstacle to the implementation
of these materials in photovoltaic cells. First, the rapid diffusion
of charge carriers to 3D perovskite domains with higher charge-carrier
mobility leads to a strong recovery of photoconductivity in the semiconductor
even after initial illumination of mostly the quasi-2D material. Second,
the efficient reabsorption of photons originating from charge-carrier
recombination inside the quasi-2D domains results in a further boost
in photoconductivity associated with prolonged charge-carrier lifetimes.
Such heterogeneous photon recycling is particularly effective because
the emission spectrum of the quasi-2D domains is blue-shifted beyond
the absorption onset of the 3D perovskite. Thus, the effects of charge
diffusion and photon recycling are able to compensate for the less
favorable aspects of dielectric confinement for the graded structures
under investigation here. Such morphologies may therefore offer the
best of both worlds, combining enhanced moisture resistance and surface
passivation through the incorporation of the large hydrophobic cations
with excellent charge transporting properties needed for highly efficient
solar cells.
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