Advanced Characterization of Perovskite Thin Films for Solar Cell Applications Using Time‐Resolved Microwave Photoconductivity and Time‐Resolved Photoluminescence

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# Advanced Characterization of Perovskite Thin Films for Solar Cell Applications Using Time-Resolved Microwave Photoconductivity and Time-Resolved Photoluminescence

## _Emmanuel V. Péan,* Jiashang Zhao, Alexander J. Doolin, Rodrigo García-Rodríguez,_ _Tom J. Savenije, and Matthew L. Davies*_

Thanks to their direct band-gap, high absorption coefficient, low manufacturing
cost, and relative abundance of component materials, perovskite
materials are strong candidates for the next generation of photovoltaic
devices. However, their complex photochemistry and photophysics
are hindering their development. This is due, in part, to the complex charge
carrier recombination pathways in these materials, as well as their instability
during measurements. Here, a new characterization methodology is detailed
that allows the measurement, with high certainty, of the intrinsic parameters
of a single perovskite sample, such as the trap state concentration and carrier
~~mobilities. This methodology is based on a combination of time-resolved~~
microwave photoconductivity (TRMC) and time-resolved photoluminescence
(TRPL) spectroscopy. Compared to TRPL only, this methodology is faster, does
not lead to significant changes in the perovskite properties over time, and
increases the certainty of the parameters retrieved. Using this methodology,
green solvent systems are studied to replace the traditional harmful
solvents usually used when spin–coating perovskites. Although devices made
using the greener solvents presented lower efficiencies, TRMC and TRPL
measurements highlighted that the perovskites made with these solvents can
achieve the same performance compared to the traditional solvent system.

1. Introduction

E. V. Péan, A. J. Doolin, R. García-Rodríguez, M. L. Davies
SPECIFIC IKC
Materials Research Centre, College of Engineering
Swansea University Bay Campus
Fabian Way, Swansea SA1 8EN, UK
[E-mail: emmanuel.pean@swansea.ac.uk;](mailto:emmanuel.pean@swansea.ac.uk) [m.l.davies@swansea.ac.uk](mailto:m.l.davies@swansea.ac.uk)
J.Zhao,T.J.Savenije
Department of Chemical Engineering
Delft University of Technology
van derMaasweg 9,Delft 2629 HZ,TheNetherlands
M.L.Davies
School of Chemistry andPhysics
University of KwaZulu-Natal
PrivateBag X54001, 4000 Durban,South Africa

The ORCID identification number(s) for the author(s) of this article
[can be found under https://doi.org/10.1002/smtd.202400818](https://doi.org/10.1002/smtd.202400818)

© 2025 The Author(s). Small Methods published by Wiley-VCH GmbH.
[This is an open access article under the terms of the Creative Commons](http://creativecommons.org/licenses/by/4.0/)
[Attribution License, which permits use, distribution and reproduction in](http://creativecommons.org/licenses/by/4.0/)
any medium, provided the original work is properly cited.

DOI: 10.1002/smtd.202400818

Perovskite solar cells (PSCs) have
emerged as a promising technology for
the development of low-cost and highly
efficient photovoltaic devices. Over the
past decade, PSCs have advanced rapidly,
and their energy conversion efficiency
has increased from ca. 4% in 2009 to
26.1% in 2024. [1] This is comparable
to traditional silicon-based solar cells
and higher than other emerging, lowcost, photovoltaic technologies such as
quantum dots solar cells, dye-sensitized
solar cells, and organic solar cells. This
progress has largely been achieved
through materials and manufacturing
developments, as well as a better understanding of the underlying physics
of PSCs. [2] One of the key advantages
of PSCs is their potential low cost of
production. [3] Unlike traditional siliconbased solar cells, which require expensive
and energy-intensive manufacturing processes, PSCs can be manufactured using
solution-processing techniques, which
are relatively simple and inexpensive. [4] Additionally, PSCs can be
made using a range of materials, including lead, which is abundant and inexpensive [5,6] (although the use of lead can lead to
other problems, some of which are addressed in). [7] Lead-based
PSCs have demonstrated high power conversion efficiencies, in
part, thanks to their high absorption coefficient. [8] The band gap
of perovskites can be tuned by varying their composition (e.g.,) [9]

making them useful candidates for tandem solar cells with, e.g.,
silicon solar cells. [10,11]

Decreasing the open-circuit voltage ( _V_ OC) loss is crucial to further improve the efficiency of perovskite solar cells in the future. These are usually due to non-radiative recombination pathways, within the bulk of the perovskite layer or at the charge
transport layer/perovskite interfaces. It is therefore essential
to understand and quantify the impact of the recombination
pathways in perovskite materials. Time-resolved photoluminescence (TRPL) and time-resolved microwave photoconductivity
(TRMC) allow the study of charge carrier recombination processes in organic and inorganic materials. However, perovskites
have been shown to have complex photophysics which makes the

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ing the photoluminescence of a sample after a short (typically ps)
excitation pulse. TRPL intensity is proportional to the bimolecular recombination rate:

_ITRPL_ ( _t_ ) ∝ _kB_ Δ _ne_ ( _t_ ) [ Δ _nh_ ( _t_ ) + _p_ 0]

(4)

Figure 1. Schematic representation of the Bimolecular-Trapping–
Detrapping model in the case of a _p_ -type material. Photoexcited electrons
(concentration Δ _ne_ ) in the conduction band (CB) and holes (concentration Δ _nh_ ) in the valence band (VB) undergo bimolecular recombination
at rate constants _kB_ . Electrons get trapped in trap states (concentration
_NT_ ) at a rate constant _kT_ . Trapped electrons (concentration _nt_ ) can then
detrap back to the VB at a rate constant _kD_ .

investigation of their recombination pathways convoluted. [12–14]

This is partly due to the low exciton binding energy in lead-based
perovskite materials, compared to organic materials used in organic solar cells, leading to a dependence of the recombination
process rates on the charge carrier concentration. [12,13] Because
electrons and holes are uncoupled, their direct recombination requires one entity of each species to happen and is, therefore, a bimolecular process. Similarly, trapping and detrapping can be respectively considered as bimolecular processes between the free
electrons and the available trap states, and between the trapped
electron and the free hole concentration [12,13] ( Figure 1 ).

In the case of a _p_ -type material, the rate equations describing the variations of the photoexcited electron (Δ _ne_ ), photoexcited
hole (Δ _nh_ ) and trapped electron ( _nt_ ) concentrations are: [13,14]

TRPL can be used to characterize organic compounds, allowing to extract carrier lifetime, recombination rate, and carrier
extraction rate relatively easily thanks to their excitonic nature.
However, as we previously discussed in, [12] fitting the TRPL of
perovskite materials is a complex task. First, it is essential to
allow most charge carriers to recombine between two consecutive excitation pulses to avoid unwanted carrier accumulation
during measurements. However, since most detrapping usually
happens after the TRPL has reached zero, determining the minimum excitation repetition period preventing carrier accumulation is a complex task. Second, due to the complexity of the charge
carrier recombination model (Equations 1–4), multiple TRPL decays measured over a wide range of excitation fluences are required to determine with accuracy the different parameter values.
Due to their long carrier lifetime and low emission rate, the acquisition of TRPL decays of perovskite can take multiple hours
or days. A full set of TRPL decays measured at different excitation fluences can therefore be time-consuming. Furthermore,
long TRPL measurements can lead to changes of the perovskite
properties through their interaction with light, oxygen, and moisture amongst others which subsequently affects the TRPL decay
shape during the measurements.

TRMC consists of monitoring the sample conductivity
changes through the interaction of the photoexcited carriers with
microwaves after a short excitation pulse. The variation of the
conductivity measured is equal to the sum of the photoexcited
electron and hole concentrations multiplied by their respective
mobilities (μ _X_ ):

_ITRMC_ ( _t_ ) = _?e_ Δ _ne_ ( _t_ ) + _?h_ Δ _nh_ ( _t_ )

_N_ 0

(5)

] − _kT_ Δ _ne_ ( _t_ ) [ _NT_ - _nt_ ( _t_ )] (1)

_d_ Δ _ne_ = _G_ ( _t_ ) − _kB_ Δ _ne_ ( _t_ ) [ Δ _nh_ ( _t_ ) + _p_ 0

_dt_

Δ _ne_ = _G_ ( _t_ ) − _kB_ Δ _ne_ ( _t_ ) [ Δ _nh_ ( _t_ ) + _p_ 0

_dt_

_dndtt_ = _kT_ Δ _ne_ ( _t_ ) [

- _kDnt_ ( _t_ ) [

Δ _nh_ ( _t_ ) + _p_ 0

_dnt_

_NT_ - _nt_ ( _t_ ) ]

]
(2)

] − _kDnt_ ( _t_ ) [Δ _nh_ ( _t_ ) + _p_ 0

]
(3)

where _N_ 0 is the photoexcited carrier concentration. Contrary
to TRPL, which reaches zero when either carrier concentration
is zero, the TRMC intensity only reaches zero when both carrier concentrations are zero. TRMC is thus a more sensitive
technique to measure non-radiative recombination than TRPL.
TRMC is also much faster than TRPL and only requires hundreds
to thousands of averages to measure a single trace, implying a
sample can be fully measured in less than an hour. TRMC usually
uses a very low repetition rate excitation source (≈10 Hz) which
allows to assume negligible carrier accumulation between excitation pulses. [13] Finally, thanks to the short measurement time and
low excitation repetition rate, little to no change or degradation
is usually observed in the properties of samples during TRMC
measurements if the sample is kept in an inert atmosphere. [13]

Using the parameters retrieved from TRMC or TRPL fitting,
it is possible to calculate the quasi-Fermi level splitting μ _F_ as
defined by: [14]

_d_ Δ _nh_ = _G_ ( _t_ ) − _kB_ Δ _ne_ ( _t_ ) [ Δ _nh_ ( _t_ ) + _p_ 0

_dt_

Δ _nh_ = _G_ ( _t_ ) − _kB_ Δ _ne_ ( _t_ ) [ Δ _nh_ ( _t_ ) + _p_ 0

_dt_

where _kB_ is the bimolecular recombination rate constant, _kT_ is
the trapping rate constant, _kD_ is the detrapping rate constant, _p_ 0
is the dark hole concentration, _NT_ is the trap state concentration
and _G_ is the carrier generation rate. It is assumed that the carrier
concentrations are all zero before photoexcitation, which can be
achieved by keeping the sample in the dark. Note that this model
can be adapted for _n_ -type materials by simply inverting the notation. In comparison, because of their higher exciton binding energy, recombinations in organic materials tend to be monomolecular, therefore significantly simplifying the above model. [12,13]

TRPL is a powerful and popular characterization technique to
investigate charge carrier recombinations. It consists of measur

) ( _p_ 0 + Δ _nh_

_n_ 2 _i_

(6)

⎞
⎟
⎟
⎟⎠

( _np_ 02 _i_ + Δ _ne_

)

_?F_ = _kT_ ln

_q_

⎛
⎜
⎜
⎜⎝

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where _k_ is the Boltzmann constant, _T_ is the temperature, _q_
is the elementary charge and _ni_ is the intrinsic carrier concentration in the sample. The quasi-Fermi level splitting corresponds to the upper limit of the solar cell open-circuit voltage and therefore can indicate if the latter can be improved
or not.

Although TRMC is more suitable than TRPL to measure perovskite materials and then calculate the quasi-Fermi level splitting, we show here that the high complexity of charge carrier
recombination in perovskite materials requires TRPL measurements to extract meaningful quantities. In, [15] the authors created
a setup capable of measuring TRPL and TRMC at the same time
and under the same measurement conditions, while controlling
the measurement temperature, and employ a model that, they
claim, can reproduce both the TRPL and TRMC behavior. They
used their setup to compare three different perovskite compositions: MAPbI3, CsPbBr3, and a mixed-cation, mixed-anion perovskite. However, their experimental setup was in the high fluence regime (10 16 to 10 18 cm −3 ) and therefore may have overlooked non-radiative recombinations. In, [16] TRMC and TRPL
were used to evaluate the effect of 2D layers in a 2D/3D perovskite mixture and employed the mobilities for TRMC and a
biexponential fitting for TRPL to conclude that the addition of
these 2D perovskites passivates defects on the surface of the perovskite. Here we present a novel methodology that allows one to
determine the sample properties, including its quasi-Fermi level,
with high certainty and combines the advantage of quick TRMC
measurements and fitting while requiring fewer TRPL measurements than needed when measuring and fitting TRPL alone. Furthermore, it does not require the fitting of TRPL decay curves,
which can be computationally costly, when done properly for perovskite materials, due to the necessity to account for carrier accumulation. We then apply this methodology to investigate alternative green solvents to replace the traditional harmful dimethylsulfoxide (DMSO) / dimethylformamide (DMF) solvent system, and
ethyl acetate (EA) antisolvent, employing the selection criteria
described in previous work; [17] namely dimethylpropyleneurea
(DMPU), ethanol (EtOH), 2-methyltetrahydrofuran (2-MeTHF)
and dimethyl carbonate (DMC). While DMPU is still not ideal,
it is a significant improvement on the use of DMF and through
this approach, the volume of DMPU can be minimized through
the use of solvent blends.

2. Experimental Section

2.1. Sample Fabrication

All fabrication of triple cation perovskite was undertaken with
reference to the method reported in. [17]

_2.1.1. Precursor Solution_

The Cs0.066(MA0.17FA0.83)0.934Pb(I0.83Br0.17)3 precursor solution was manufactured at a molar ratio of 1:1.1:0.2:0.2:0.08
FAI:PbI2:PbBr2:MABr:CsI using 22.4 mg of methylammonium
bromide (Sigma Aldrich, ≥99%), 73.4 mg of lead bromide
(Sigma Aldrich, 99.999%), 172 mg of formamidinium iodide

(Sigma Aldrich, 99%, anhydrous), and 507.1 mg of lead iodide
(TCI Chemicals, 99.99%). For the DMF/DMSO solution, 987 μL
of DMF (Acros Organics extra dry, 99%) and DMSO (Acros
Organics extra dry, 99%) were added in a 4:1 v/v ratio. The A01
samples include 40 vol% DMSO, 30 vol% DMPU and 30 vol%
comprising EtOH and 2-MeTHF - with 34 vol% 2-MeTHF to
66 vol% EtOH. The B01 formulation includes 40 vol% DMSO,
30 vol% DMPU and 30 vol% DMC. Subsequently, 53 μL of
caesium iodide (Sigma Aldrich, 99.999%) was added using
a stock solution (390 mg mL −1 in DMSO - Acros Organics
extra dry, 99%), which had been previously heated to 100 °C
and then cooled to STP. This represents 6.6% Cs addition in a
1.25 m solution. Previous studies have shown high performance
for compositions between 5% and 10%. [18] This composition
includes a PbI2 excess.

_2.1.2. Films for TRMC and TRPL Measurements_

All films were deposited in a freshly purged N2 glovebox (GB).
GB temperature was regulated to between 22 and 27 °C. Film
characterization utilized 2.5 × 1.2 cm 2 quartz substrates. The
quartz substrates were sonicated in acetone and IPA for 10 min
respectively, prior to a 10 min UV–ozone treatment. After transfer to an N2 GB, 38.4 μL of perovskite precursor was spun at
4000 rpm and 4000 acceleration for 30 s with 96 μL of the antisolvent EA or DMC dropped dynamically onto the center of the
sample 12 seconds from the start of the spin cycle. A01 and B01
solvent formulations utilized a 2-step spin coating cycle with 10
seconds at 2000 rpm and 200 rpm m −1 acceleration followed
by 6000 rpm and 2000 rpm m −1 acceleration for 30 seconds
with the anti-solvent added 5 s from the end of the spin cycle
(96 μL of anti-solvent). All films were then annealed on a hot
plate at 100 °C for 30 min. All films characterized are coated
with poly(methyl methacrylate) (PMMA - Sigma Aldrich, average molecular weight ≈120000 by GPC) under N2. PMMA was
applied from a 1 m solution in toluene (heated to 80 °C for 12 h),
with 100 μL spun at 3000 rpm.

_2.1.3. Full Devices_

ITO substrates, pre-cut chemically etched 2.8 cm 2 pieces of
Kintec polished glass (1 mm thick) were first cleaned with 2%
Hellmanex solution, before being sonicated for 30 min at STP,
followed by 5 min sonication in deionized water. Substrates were
transported to a class VI clean room environment for 10 min
of sonication in acetone and IPA respectively prior to drying
with a nitrogen flow. A 10 min treatment in a plasma cleaner
at maximum power using oxygen at 0.3 mbar was conducted
before coating. A tin oxide solution was prepared from 15% tin
(IV) oxide colloidal solution (Alfa Aesar) which was diluted by a
ratio of 3:1 with deionized water and subsequently filtered using
0.2 μm PTFE. This is anticipated to reduce the concentration
below 5% but is required to remove agglomerates prone to cause
poor surface contact and pinholes. 150 μL of tin oxide solution
was spin-coated onto substrates at 3000 rpm and 3000 acceleration for 30 s. A swab was then used to remove a strip of the SnO2
down the middle of the sample, before annealing at 130 °C for

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Figure 2. Example of the grid fitting analysis to find local minima based on a model with two parameters. The associated _R_ 2 value is displayed in the
background to show which parameter values yield a good fit. a) A grid of guess values is created as shown by the white dots. b) The fitting optimization
is carried out with each set of guess values. Here, 3 and 5 fits converge toward two distinct solutions while the remaining optimizations yield incorrect
solutions as indicated by their low _R_ 2 . Due to the high computational cost of this method, we did not perform a formal convergence test for the grid
points. However, the fact that most optimizations converged toward 2–3 distinct solutions suggests that our grid was likely sufficient.

30 min. A ceramic hotplate was used, with the samples left to
cool to room temperature before removal. A 10 min UV–ozone
treatment was applied to the substrate prior to perovskite deposition. The one-step deposition method was used to spin–coat
perovskite onto the ETL substrates with an anti-solvent drip
of either EA or DMC. For the DMF/DMSO formulation spin
coating settings of 4000 rpm, 4000 rpm m −1 acceleration for 30 s
were used. 250 μL of EA or DMC was dropped onto the sample
12 s from the start of the spin cycle. The A01 and B01 devices
were fabricated using a 2-step spin coating cycle with 10 s at
2000 rpm and 200 rpm m −1 acceleration followed by 6000 rpm
and 2000 rpm m −1 acceleration for 30 s with the anti-solvent
added 5 s from the end of the spin cycle (250 μL of anti-solvent).
Devices were then placed on a hot plate at 100 °C for 30 min
to anneal. For the HTL, 85 mg of 2,2′,7,7′-tetrakis-(N,N-di-4methoxyphenylamino)-9,9′-spirobifluorene (Spiro-OMeTAD Merck Millipore - Sigma Aldrich) was dissolved in 996 μL of
chlorobenzene (anhydrous, 99.8%) 34 μL 4-tertbutylpyrridine,
20 μL of bis(trifluoromethane)sulfonimide lithium salt (LiTFSI) in acetonitrile (520 mg Li-TFSI in 1 mL acetonitrile
(anhydrous, 99.8%)), and 8 μL of tris(2-(1H-pyrazol-1-yl)−4-tertbutylpyridine)-cobalt(III)tris(bis(trifluoromethylsulfonyl)imide))
(FK-209) were subsequently added. The completed hole transport layer (HTL) solution was then filtered with 0.2 μm PTFE
filter before deposition. 100 μL of Spiro-OMeTAD solution was
spread onto the PAL, with a 30 s spin cycle at 4000 rpm. Oxidation of the HTL was achieved by leaving the device in a dark
environment for 12–24 h. Finally, gold wire (Au, 99.99% purity
1.0 mm thick Sigma Aldrich) was used to deposit top contacts on
all devices using an Edwards bell jar evaporator at a pressure of
10 −5 mbar.

2.2. Sample Characterization

TRPL was measured using an Edinburgh Instruments Lifespec
time-correlated single photon counting and an EPL405 laser
(405 nm excitation wavelength, 100 kHz repetition rate, 80 ps
pulse width).

TRMC was measured using an in-house setup. Excitation was
provided by an Ekspla Nd:YAG pulsed laser with a 650 nm excitation wavelength, a 3.5 ns pulse width with a 10 Hz repetition rate.
High excitation fluence measurements were carried out using an
open-cell microwave cell, while low fluence measurements used
a resonant cavity microwave cell with a response time of 18 ns.
Both cells are air-tight and allow to keep the samples in nitrogen atmosphere during the measurements, to prevent reaction
with oxygen and moisture. The combination of both cells allows
laser intensity variation over more than 3 orders of magnitude. A
8.5 GHz –100 mW voltage-controlled oscillator was used to generate the microwaves. [13]

Film thickness was measured using a Dektak profilometer
(model Veeco).

Sample absorptance was measured using a Perkin-Elmer
UV/Vis spectrophotometer (Lambda 1050) fitted with an integrating sphere.

2.3. TRMC and TRPL Simulations

The Bimolecular-Trapping–Detrapping model discussed above
was used to fit the TRMC data and simulate TRPL. For TRMC, a
Gaussian pulse is used for the generation rate _G_ :

where _A_ is the amplitude, _t_ 0 is the centre of the Gaussian and _w_
is the pulse width. For resonant cavity measurements, the simulated TRMC intensity was reconvolved with the cavity response
function defined by:

_IRF_ ( _t_ ) = _e_ − _?_ _t_ (8)

where _?_ is the response time of the cavity.

For TRPL simulations, thanks to the much shorter excitation
pulse (≈80 ps), it is simply assumed that the charge carriers are
instantaneously generated at _t_ = 0. The photoexcited concentration after a certain excitation pulse _p_ is thus equal to the sum of

_G_ ( _t_ ) = _Ae_ −

4 log(2)( _t_ - _t_ 0) 2

_w_ 2 (7)

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the photoexcited carriers by the pulse _N_ 0, and any carrier present
in the system just before the pulse: [12]

Δ _n_ _p_ _e_

_p_ _e_ ( _t_ = 0) = _N_ 0 + Δ _n_ _e_ _p_ −1

_p_ _h_ ( _t_ = 0) = _N_ 0 + Δ _n_ _h_ _p_ −1

_e_ _p_ −1 ( _t_ = _T_ ) (9)

Δ _n_ _p_ _h_

_h_ _p_ −1 ( _t_ = _T_ ) (10)

Δ _n_ _p_ _t_

_p_ _t_ ( _t_ = 0) = Δ _n_ _t_ _p_ −1

_t_ _p_ −1 ( _t_ = _T_ ) (11)

_G_ ( _t_ ) = 0 (12)

where _T_ is the excitation repetition period. The photoexcited concentration _N_ 0 was calculated from the laser fluence _I_ 0 the sample absorptance _A_ at the excitation wavelength, and the sample
thickness _d_ : [12]

_N_ 0 = _I_ 0 _A_ (13)

_d_

Using the above equations, it is possible to simulate the TRPL
after multiple excitation pulses, thus allowing carrier accumulation to be accounted for in the sample. As discussed in a previous paper, experimental TRPL decays resulting from billions of
excitation pulses can be simulated with only a few hundred by
defining a stabilized pulse after which the carrier concentration
variations are similar: [12]

Figure 3. TRMC decays of a triple cation perovskite thin film measured at
different excitation fluences.

where _SStotal_ is defined as the sum of the squared difference between each point and the average of all curves _̄ y_ :

∑ _Ni_

_j_

_S Stotal_ =

∑ _M_

_i_

( _yi,j_ - _̄ y_ )2 (18)

||| _nXp_ −1

_p_ (14)

_X_ ( _t_ )|| | ≤ 10−6 _N_ 0

_Xp_ −1 ( _t_ ) − _n_ _p_ _X_

Since a 10 Hz excitation repetition rate was used for TRMC
measurements, it is assumed that carrier accumulation is negligible during these measurements and therefore the TRMC intensity was calculated with a single excitation pulse. In both cases,
the carrier concentrations are assumed zero before excitation.

The quasi-Fermi level μ _F_ was calculated at room temperature
and the intrinsic carrier concentration was taken from [19] and
measured from a similar perovskite composition ( _ni_ = 1.26 ×
10 5 _cm_ −3 ).

2.4. Data Fitting

TRMC fitting was carried out using a non-linear least square optimization. For a dataset containing _M_ curves, each curve _i_ containing _Ni_ datapoints, the optimization residue _SSres_ is:

∑ _Ni_

_j_

_S Sres_ =

∑ _M_

_i_

( _yi,j_ - _F_ ( _ti,j, Ai_

))2
(15)

where _yi_, _j_ is the experimental TRMC intensity at the time _ti_, _j_ of
point _j_ of curve _i_ . _Ai_ are the model parameters associated with
curve _i_, and _F_ is the fitting model given by:

_F_ ( _t,_ …) = _ITRMC_

( _t, Gi, kiB_ _,_ …) (16)

where _ITRMC_ are calculated using the above model. The quality of
the fit is estimated from the coefficient of determination _R_ 2 :

_R_ 2 = 1 − _SSres_

_SStotal_

(17)

The least-square optimization was solved using a trust region
reflective algorithm as implemented by the SciPy package. [20]

Each set of TRMC decays measured at different excitation fluences was fitted using a global approach by using the same set of
parameter values, only varying the generation rate _G_ .

In order to find all the local minima of the fitting optimization, a grid of guess values are generated using _kB_ =
10 −11,10 −10 _cm_ 3 / _s_, _kT_ = 10 −9,10 −8 _cm_ 3 / _s_, _kD_ = 10 −11,10 −10 _cm_ 3 / _s_,
_NT_ = 10 12, 10 13 _cm_ −3, _p_ 0 = 10 12, 10 13 _cm_ −3, μ _e_ = 1, 10 _cm_ 2 /( _Vs_ )
and μ _h_ = 1, 10 _cm_ 2 /( _Vs_ ). Fitting is then carried out using each
set of guess values. Only good fits are then considered (i.e., _R_ 2 _>_
0.9), and fits converging toward the same minimum are merged
into one. An example of the “grid fitting” analysis is shown in
Figure 2 for a model with two parameters.

3. Results & Discussion

Figure 3 shows the TRMC decays of a triple-cation thin film measured at different excitation fluences, generating between 1.3 ×
10 13 _cm_ −3 and 3.6 × 10 16 _cm_ −3 charge carrier concentrations (see
Table S1 for the sample thickness, Figure S1 for its absorptance,
and Figure S2 for its XRD pattern, Supporting Information). As
predicted by the model, as the laser fluence is decreased, the decay lifetime increases due to the lower bimolecular recombination contribution and the higher contribution of trapping and detrapping.

In order to find all the sets of recombination parameters able
to fit these data, we fitted these data using the BimolecularTrapping–Detrapping model previously discussed with a wide
range of guess parameter values. For each parameter, two guess
values were considered, yielding 128 combinations. Each combination of guess values was then used to fit the data. Out of 128 fitting optimizations, 116 were considered good fits which parameters are displayed in a parallel coordinate graph ( Figure 4 a).

The fitting optimizations converged toward two distinct solutions (Figure 4b,c). Both solutions fit the data well as shown by

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Figure 4. Results of the grid fitting analysis. a) Parallel coordinate plot showing the different optimized parameter values obtained. b) & c) Comparison
of the two fitting solutions obtained and their residues. d) & e) Comparison between the experimental TRPL and the TRPL simulated using the two sets
of variables fitting the TRMC traces well.

their small residue. We note that the residue spikes at high excitation fluences likely originate from fluctuations of the laser
power during the measurements. Both solutions have very similar bimolecular recombination rate constant _kB_ but significantly
differ for other parameters (Figure 4a). To determine the correct solution, the TRPL intensity was simulated from these two
solutions and was compared to experimentally measured TRPL
(Figure 4d,e). For each solution, the model parameters were kept
the same, except for the excitation fluence which was changed to
account for the much shorter TRPL pulse (Equation 12). Furthermore, we also accounted for charge carrier accumulation due to
the higher excitation repetition rate of TRPL, by simulating the
carrier concentration after multiple excitation pulses. As shown
in Figure 4d, the TRPL simulated from the first solution matches
well the experimental TRPL at low fluence but starts to differ at
higher fluence. On the contrary, the simulated TRPL from the
second solution does not match the experimental TRPL except at
one fluence (Figure 4e). It is worth mentioning that based on the

Saha equation, not all photons yield charge carriers at high excitation fluences. [21] We know that this phenomenon is not happening for the fluences used during our TRMC measurements
as the measured carrier mobility sum did not change depending on the fluence. However, we are potentially overestimating
the charge carrier concentration at the highest excitation fluence
used to measure TRPL, which is higher than the highest fluence
used during TRMC measurements. This would therefore explain
why the simulated TRPL from Fit 1 decays faster compared to the
experimental TRPL.

We can therefore say with high certainty that Fit 1 represents our triple-cation perovskite sample whose parameters are
shown in Table 1 . A similar trap state concentration was previously calculated in [14,22] for a similar perovskite composition
((Cs0.06FA0.79MA0.15)Pb(I0.85Br0.15)3). However, the values previously reported showed a higher carrier mobility sum (μ _e_ + μ _h_ ≈
40 _cm_ 2 /( _Vs_ )) and bimolecular recombination rate constant ( _kB_ =
40 × 10 −10 _cm_ 3 / _s_ ). It is also worth mentioning that the charge

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Table 1. Parameter values extracted from the TRMC and TRPL measurements.

Parameter Value

_kB_ 2.1 × 10 −10 _cm_ 3 / _s_

_kT_ 4.2 × 10 −9 _cm_ 3 / _s_

_kD_ 9.2 × 10 −10 _cm_ 3 / _s_

_NT_ 8.4 × 10 14 _cm_ −3

_p_ 0 3.2 × 10 13 _cm_ −3

μ _e_ 10.3 _cm_ 2 /( _Vs_ )

μ _h_ 7.2 _cm_ 2 /( _Vs_ )

carrier recombination model used here does not differentiate between _n_ -type and _p_ -type doping. It is therefore possible that the
doping concentration would correspond to _p_ -type doping instead
of the _n_ -type doping previously mentioned (in which case, we
would consider hole trapping).

Our methodology is schematically summarized in Figure 5 .
Analysis of fitting solution one shows that, although a significant number of trapped electrons and holes are left in the trap

Figure 5. Schematic representation of our new methodology.

states and Valence band before the next excitation pulse, carrier
accumulation here is very limited and leads to only 2% difference
between the TRPL decays obtained after a single excitation pulse
and multiple pulses ( Figure 6 a).

At the highest fluence used during the TRPL measurements,
the trap states are fully saturated, and carrier accumulation is
negligible (Figure 6b). Using a constant generation rate matching AM1.5 Direct illumination ( _G_ = 2.5 × 10 12 _cm_ −3 / _ns_ ) shows
that the trap states get quickly saturated and most recombination are direct (Figure 6c). Finally, we simulate the quasi-Fermi
level using Equation 6 and compare it to the value obtained
from devices made using our perovskite system (Figure 6d).
We note that we obtained a _V_ OC of 1.05 V, similar to the one
reported by Abdi-Jalebi in [22] for a similar perovskite composition (CsMAFAPb(I0.85Br0.15)3). To account for potential variations of the intrinsic carrier concentration in our sample compared to the one reported in, [19] we estimated the quasi-Fermi
level between 0.5 _ni_ and 2 _ni_ . Compared to the experimental
_V_ OC, we see a difference from 0.12 up to 0.2 eV with the
quasi-Fermi level. This shows that the efficiency of these devices could be significantly improved by, for example, passivating trap states at the transport layer interfaces, such as using

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Figure 6. Analysis of the fitting result. Variations of the carrier concentrations after multiple excitation pulses under a) medium ( _N_ 0 ∼ _NT_ ) and b) high
( _N_ 0 _> NT_ ) excitation fluence during TRPL measurements. c) Variation of the carrier concentrations under AM1.5 Direct illumination and d) calculated
quasi-Fermi level (μ _F_ ) for increasing generation rate compared to the experimental open-circuit voltage ( _VOC_ ). The area shows the error on μ _F_ dependent
upon the intrinsic carrier concentration between 6.25 × 10 4 _cm_ −3 and 25 × 10 4 _cm_ −3 .

K + passivation which showed a significant improvement of the
_V_ OC in. [14]

We used this method to investigate different solvent systems (DMF/DMSO, DMSO/DMPU/EtOH/2-MeTHF and
DMSO/DMPU/DMC herein referred as A01 and B01) and antisolvents (ethyl acetate and dimethyl carbonate – herein referred
to as EA and DMC) ( Figure 7 ; Figures S3–S15, Supporting
Information).

Perovskite films made using the DMC anti-solvent present
equal or lower electron and hole mobilities compared to EA
(Figure 7a,b). This is likely responsible for the lower shortcircuit current measured in devices made with this anti-solvent
(Figure 7e; Figure S15, Supporting Information). Although a
slight increase of the hole mobility is measured when using A01
and B01, the electron mobility significantly decreases compared
to DMF/DMSO. The mobility sum is therefore lower for A01
and B01 while the associated short-circuit current is higher than
DMF/DMSO. We hypothesize that the low hole mobility limits
the short-circuit current in the DMF/DMSO-DMC perovskite.
The lower discrepancy between the electron and hole concentrations as well as the higher hole mobility could therefore explain
the higher short-circuit current observed in these perovskites.
DMC perovskites also present a higher trap state concentration
compared to EA, consistent with the lower open-circuit voltage
(Figure 7d). Little to no difference in terms of trap state concentration is observed between the different solvent systems when
using DMC. Overall, a lower power conversion efficiency is mea

sured for devices made using the DMC anti-solvent compared to
EA (Figure 7f). A01 and B01 perovskites present similar efficiencies while being 2.3 points lower than DMF/DMSO.

Using the EA anti-solvent, while the hole mobility appears unaffected by the solvent system, a higher electron mobility is measured when using B01. However, this does not result in a higher
short-circuit current, which is consistent with the short-circuit
current being limited by the hole mobility. The trap concentration is 4 times higher in A01 and B01 compared to DMF/DMSO,
however, this does not seem to affect the open-circuit voltage significantly. The lower efficiency measured with A01 and B01 compared to DMF/DMSO can be explained by the lower fill factor in
these devices (Figure S16, Supporting Information).

Although the triple cation perovskite fabricated with the
greener solvent systems tends to present slightly lower performances than the more widely used DMF/DMSO solvent system with EA anti-solvent, our simulations show that the quasiFermi level does not significantly depend on the solvent system, or the anti-solvent used during manufacturing (Figure 7d).
In particular, while the A01 and B01 solvent systems, and the
DMC anti-solvent present a higher trap state concentration, it
is compensated by a lower trapping rate constant for these
(Figure S17, Supporting Information). This suggests that these
greener alternative solvents are therefore adequate replacement
for DMF/DMSO-EA and might simply need more refinement,
through tuning the solvent blends, to achieve similar performances. It is interesting to note that these solvent systems have

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Figure 7. Properties of perovskites made using the DMF/DMSO, A01, and B01 solvent solvents, and the Ethyl acetate (EA) and dimethyl carbonate DMC
anti-solvents. a) Electron and b) hole mobilities. c) Trap state concentration d) Quasi-Fermi level and open-circuit voltage ( _VOC_ ) of devices (dashed lines)
using the same solvent systems. e) Short-circuit current ( _JSC_ ) and f) power conversion efficiency (PCE).

matched the performance of DMF/DMSO solvent systems with
a MAPbI3 absorber layer and thus this implies there is a requirement to alter solvent blends to a particular perovskite precursor
to optimize the performance in the triple cation perovskite. [17]

4. Conclusion

We have presented a novel characterization methodology to confidently measure the intrinsic properties of perovskite thin films.
Our process starts with the measurement of the TRMC and TRPL
of the sample studied at different excitation fluences. The TRMC
decays are then fitted with a state-of-the-art charge carrier recombination model and a global fitting approach. Different sets of
guess values for the different parameters of the models are used,
allowing to find the different local minima of the optimization.
The fitting solutions are then curated and grouped up. Out of
the few solutions left, we simulate the TRPL decays based on the
experimental measurement parameters. We then compare the
simulated TRPL decays to the experimentally measured decays,
accounting for the different excitation conditions between TRPL
and TRMC, allowing us to determine the best solution representing the sample properties. This method offers many advantages
compared to traditional characterization methods such as TRMC
or TRPL measurements only. First, while measuring the TRPL
only would require exposing the sample to light for a long time
to acquire all the decays required, our method limits the exposure of the sample because of the low excitation repetition rate of
TRMC and the fact that we do not require to measure the TRPL
with as many fluences. Second, while carrier accumulation can

be assumed negligible during TRMC measurements, it is almost
unavoidable during TRPL measurements. Fitting TRPL considering carrier accumulation is computationally costly due to the
requirement to simulate hundreds of excitation pulses instead
of just one. Here, we fit TRMC data without considering carrier
accumulation and only consider it when simulating the TRPL,
thus greatly reducing the computational cost compared to fitting TRPL. Our method is therefore faster, less likely to induce
changes to the sample during the measurements, less computationally intensive, and increases the confidence in the parameter values retrieved compared to TRMC measurements only.
We have investigated potential green solvent replacements for
dimethyl formamide, dimethyl sulfoxide, and ethyl acetate. Our
findings showed that, although devices made using our greener
alternatives presented lower open-circuit voltages – and therefore
lower efficiencies, they could achieve the same potential maximum open-circuit voltage.

Supporting Information

Supporting Information is available from the Wiley Online Library or from
the author.

Acknowledgements

This work was made possible by support from the Engineering and
Physical Sciences Research Council (EP/S001336/1) and through the
funding of the SPECIFIC Innovation and Knowledge Centre by EPSRC

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(EP/N020863/1), Innovate UK [920036], and the European Regional Development Fund [c80892] through the Welsh Government. EVP is grateful for
funding through the IMPACT project. EVP and MLD are grateful for funding through the Super Solar project. MLD is also grateful for the funding of
the TEA@SUNRISE project, funded with UK aid from the UK government
via the Transforming Energy Access platform, and to funding from UKRI
and the EU Horizon Europe Framework Programme (101122277).

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

Keywords

perovskite, solar cells, TRPL, TRMC

Received: June 2, 2024

Revised: July 31, 2024
Published online: March 18, 2025

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