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<sec id="jpenergyacc892s1">
  <label>1.</label>
  <title>Introduction</title>
  <p> Halide perovskite solar cells (PSCs) were introduced in 2009, with demonstrated
  efficiencies just below 4% [ <xref ref-type="bibr" rid="jpenergyacc892bib1">1</xref> ].
  Since then, PSC efficiencies have grown rapidly, reaching over 25% for single junction
  cells [ <xref ref-type="bibr" rid="jpenergyacc892bib2">2</xref> ], and over 30% for
  tandem perovskite-on-silicon devices [ <xref ref-type="bibr" rid="jpenergyacc892bib3">3</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib4">4</xref> ]. Scalability
  potential towards PSC modules has been demonstrated, with pilot outdoor small scale
  photovoltaic (PV) systems already being made [ <xref ref-type="bibr" rid="jpenergyacc892bib5">5</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib6">6</xref> ]. Past experience based on organic PV device stability testing protocols
  has accelerated the understanding of degradation and stability towards more stable PSC
  devices [ <xref ref-type="bibr" rid="jpenergyacc892bib7">7</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib8">8</xref> ]. </p>
<p> The path towards commercialisation of perovskite technology also relies on accurate
  and reliable power rating of PSC devices. Relevant to power measurements, one of the
  characteristic features of PSCs is the metastability that is observed when acquiring
  electrical measurements due to hysteretic behaviour and/or light-soaking effects [ <xref ref-type="bibr" rid="jpenergyacc892bib9">9</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib10">10</xref> ]. Metastability profiles vary between different
  PSC architectures and materials [ <xref ref-type="bibr" rid="jpenergyacc892bib11">11</xref> ], making it challenging to distinguish between metastability and
  degradation when measuring the performance of such devices. This presents challenges
  when applying measurements to accurately determine the power and efficiency of PSC
  samples, where the choice of <italic>I</italic> – <italic>V</italic> measurement method may affect results [ <xref ref-type="bibr" rid="jpenergyacc892bib12">12</xref> ]. </p>
  <p> Several methods have been proposed recently to handle metastability during
  measurements, and allow accurate and repeatable electrical performance characterisation
  of PSCs. A dynamic <italic>I</italic> – <italic>V</italic>
  curve acquisition approach has been reported, as a straightforward initial approach for
  more accurate <italic>I</italic> – <italic>V</italic>
  acquisition of PSC devices [ <xref ref-type="bibr" rid="jpenergyacc892bib13">13</xref> ,
  <xref ref-type="bibr" rid="jpenergyacc892bib14">14</xref> ]. Asymptotic and maximum
  power point tracking methods have also been demonstrated as routes towards accurately
  determining the maximum power ( <italic>P</italic>
  <sub>max</sub> ) and efficiency of PSCs devices [ <xref ref-type="bibr" rid="jpenergyacc892bib15">15</xref> ], with an asymptotic <italic>P</italic>
  <sub>max</sub> scan method presented for performance calibration of perovskite and other
  emerging PV devices [ <xref ref-type="bibr" rid="jpenergyacc892bib16">16</xref> ]. A
  protocol where the sweep direction and repeatability of the <italic>P</italic>
  <sub>max</sub> measurement are considered has been proposed recently by the European
  Solar Test Installation, which makes it possible to distinguish metastability from
  degradation [ <xref ref-type="bibr" rid="jpenergyacc892bib17">17</xref> ]. Regarding
  standardised documentation, the IEC TR 63228:2019 serves as a best practice document to
  provide some guidance for reliable measurements for PSC devices [ <xref ref-type="bibr" rid="jpenergyacc892bib18">18</xref> ]. </p>
  <p> The hysteretic behaviour of PSC devices observed in <italic>I</italic> –
  <italic>V</italic> measurements has also been observed in
  photoluminescence (PL) spectroscopy measurements during voltage changes, attributed to a
  combination of the electrostatic screening effect and nonradiative recombination effect
  of ion migration under external electric field [ <xref ref-type="bibr" rid="jpenergyacc892bib19">19</xref> ]. Slow ion migration along with the interactions
  of these ions with interfaces in PSC devices has been reported as the cause of
  hysteretic behaviour under applied electric fields [ <xref ref-type="bibr" rid="jpenergyacc892bib9">9</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib20">20</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib21">21</xref> ]. Voltage
  dependent PL (PL-V) measurements have shown that PL intensity mirrors the
  current–voltage ( <italic>I</italic> – <italic>V</italic> )
  measurements in the power-generating range, which allows the study of the correlation
  between radiative and nonradiative recombination losses [ <xref ref-type="bibr" rid="jpenergyacc892bib22">22</xref> ]. PL spectroscopy has also been demonstrated as a
  useful technique for the analysis of various steps of PSC device fabrication process and
  for monitoring crystallisation stages [ <xref ref-type="bibr" rid="jpenergyacc892bib23">23</xref> , <xref ref-type="bibr" rid="jpenergyacc892bib24">24</xref> ]. In addition
  to bulk PL spectroscopy and PL micro-spectroscopy mapping of PSCs, large area PL imaging
  has been demonstrated as a fast technique for characterisation of spatial uniformity and
  stability of PSCs [ <xref ref-type="bibr" rid="jpenergyacc892bib25">25</xref> – <xref ref-type="bibr" rid="jpenergyacc892bib27">27</xref> ]. PL imaging presents the
  advantage of fast measurement speed and the capability to image large areas, full cells
  and even mini-modules [ <xref ref-type="bibr" rid="jpenergyacc892bib28">28</xref> ], and
  has been used to analyse the spatially inhomogeneous progression of PSC device
  performance changes after light-soaking [ <xref ref-type="bibr" rid="jpenergyacc892bib29">29</xref> ]. Routes towards quantitative PL imaging of PSC
  devices have been demonstrated [ <xref ref-type="bibr" rid="jpenergyacc892bib30">30</xref> ]. As an example, PL imaging at different light or voltage bias levels for
  PSCs devices has been used to infer spatial charge collection characteristics of
  transport layers in such devices [ <xref ref-type="bibr" rid="jpenergyacc892bib31">31</xref> ]. </p>
  <p> In previous studies reported above, PL imaging has been used for spatial
  characterisation of PSCs, however without taking into account spatial metastability
  variations of samples, while transient effects or hysteresis have been studied either
  globally or at specific points of the sample though microscopy methods. In this work, we
  present for the first time spatial macroscopic metastability effects of PSCs using PL-V
  imaging. In addition, PL-V imaging is used to investigate spatial metastability effects
  that take place specifically during maximum power ( <italic>P</italic>
  <sub>max</sub> ) and current–voltage ( <italic>I</italic> – <italic>V</italic> ) measurement protocols. This provides a better understanding
  of what considerations need to be taken during PSC device electrical testing towards
  standardised measurements. To demonstrate the broad applicability of the approach taken
  here, measurements have been applied to different types of PSC devices, planar PIN and
  NIP devices, as well as triple-mesoscopic-layer carbon PSCs. Especially the latter
  devices demonstrate a very slow response to voltage changes, in the order of seconds,
  which makes accurate electrical characterisation challenging. <italic>I</italic> – <italic>V</italic> parameters of such devices are measured,
  and PL-V imaging is used to monitor the temporal and spatially local PL response of the
  samples during different voltage steps. Lateral variation of metastability of PSC
  devices is demonstrated through PL-V measurements, showing that local non-uniformities
  and defects influence local metastability in PSC devices. Such features can affect
  reliable <italic>I</italic> – <italic>V</italic> acquisition
and also challenge common assumptions used in quantitative PL imaging, such as voltage
bias uniformity across a sample or lack of lateral currents. The combination of imaging
methods with measurement of electrical characteristics offers more accurate electrical
characterisation of PSC, and also provides insights into how different local defects and
non-uniformities impact ion kinetics and thus device metastability. </p>
</sec>