# Vision-driven Autocharacterization of Perovskite Semiconductors

###### Abstract

In materials research, the task of characterizing hundreds of different
materials traditionally requires equally many human hours spent measuring
samples one by one. We demonstrate that with the integration of computer
vision into this material research workflow, many of these tasks can be
automated, significantly accelerating the throughput of the workflow for
scientists. We present a framework that uses vision to address specific pain
points in the characterization of perovskite semiconductors, a group of
materials with the potential to form new types of solar cells. With this
approach, we automate the measurement and computation of chemical and
optoelectronic properties of perovskites. Our framework proposes the following
four key contributions: (i) a computer vision tool for scalable segmentation
to arbitrarily many material samples, (ii) a tool to extract the chemical
composition of all material samples, (iii) an algorithm capable of
automatically computing band gap across arbitrarily many unique samples using
vision-segmented hyperspectral reflectance data, and (iv) automating the
stability measurement of multi-hour perovskite degradation experiments with
vision for spatially non-uniform samples. We demonstrate the key contributions
of the proposed framework on eighty samples of unique composition from the
formamidinium-methylammonium lead tri-iodide perovskite system and validate
the accuracy of each method using human evaluation and X-ray diffraction.

Vision-driven Autocharacterization of Perovskite Semiconductors
Alexander E. Siemenn1,∗, Eunice Aissi1,∗, Fang Sheng1, Armi Tiihonen2, Hamide
Kavak3, Basita Das1, and Tonio Buonassisi1
1Department of Mechanical Engineering 2Department of Applied Physics
3Department of Physics Massachusetts Institute of Technology Aalto University
Cukurova University Cambridge, MA 02193, USA P.O. Box 11100, Aalto, Finland
Adana, 01330, Turkey<EMAIL_ADDRESS><EMAIL_ADDRESS>

##  1 Introduction

††∗ Corresponding authors; contributed equally.

Computer vision approaches have the potential to accelerate the
characterization process of novel alloys that are in demand for applications
ranging from solar to structural materials [14, 6]. Innovating new alloys is
challenging, in part because the composition space is vast, requiring numerous
cycles of synthesis and characterization [22, 23]. Furthermore, numerous
cycles of learning are time- and cost-prohibitive to perform manually. These
pain points in the domain of material synthesis can be targeted via laboratory
automation. Siemenn et al. [21] and MacLeod et al. [10] recently demonstrated
autonomous hardware systems capable of significantly accelerating the cycles
of learning for material synthesis. However, to realistically accelerate the
process of novel material discovery, one has to match the high-throughput
synthesis loop with equally as fast characterization. The scalability of the
pipeline is not only a matter of accelerating the characterization of
individual samples but depends also on the breadth of the pipeline, e.g., the
number of samples required to be characterized. Computer vision has the
capacity to scale to arbitrarily many samples without significantly increasing
the duration of each characterization step [5, 9, 17].

Thus, in this contribution, we propose an automated materials characterization
pipeline that is fully based on computer vision. We demonstrate this automated
vision-based characterization loop using (i) a computer vision tool for
scalable segmentation to arbitrarily many material samples, (ii) a tool to
extract the chemical composition of all material samples, (iii) an algorithm
capable of automatically computing band gap across arbitrarily many unique
samples using vision-segmented hyperspectral reflectance data, and (iv)
automating the stability measurement of multi-hour perovskite degradation
experiments with vision for spatially non-uniform samples. The accuracy of
each developed method is benchmarked against human evaluation and X-ray
diffraction.

Figure 1: The workflow for autocharacterization of perovskite semiconductors
using computer vision. From left to right: A fluid handling system mixes and
deposits each unique semiconductor material onto a plate. The vision system
captures images in RGB and hyperspectral channels (wavelengths
$\lambda\in[380\textrm{nm},1020\textrm{nm}]$), then segments the pixels of
each material deposit ($X,Y,\lambda$) from the background. The (i)
compositional information, (ii) direct band gap, and (iii) stability of each
unique sample are automatically characterized using the optical data segmented
by the vision system.

###  1.1 Related Work

Increasing levels of laboratory automation, machine learning, and other
algorithmic approaches enable the development of accelerated, integrated
approaches to investigate novel materials [14, 10, 6, 19]. Generally, there is
high interest in many use cases for parsing through large image data sets
using computer vision, for example, Garnot et al. [5] developed algorithms for
time series analysis of satellite images. Computer vision is gaining traction
specifically in rapid morphological material characterization and is
increasingly being used to analyze large sets of microscope images [17]. As
such, multiple analytical computer vision tools have been developed to access
material morphology, often focused on identifying microstructures of
materials. For example, Park et al. [18] created a semi-automated image
segmentation and analysis algorithm to extract the morphology of nano-
particles from image data. Likewise, Chowdhury et al. [3] utilized computer
vision and machine learning to detect dendritic microstructures from a
database of solder alloy micrographs. There is also extensive work surrounding
materials recognition in non-micrographic images using computer vision [2, 8].
In order to support the growing need for micrographs and other experimental
image analysis, advances like those made by Li et al. [9], Wang et al. [24],
and Neshatavar et al. [16] on object segmentation and denoising allow for
further use cases of computer vision in scientific research.

The development of autocharacterization methods of materials is not novel,
however, little literature exists on driving autocharacterization with
computer vision to accelerate throughput and increase algorithm scalability to
arbitrarily many samples. Escobedo-Morales et al. [4] design an automated band
gap calculation tool from reflectance data, however, their implementation does
not employ automatic vision segmentation, hence, the approach is limited to
single sample-by-sample processing. Furthermore, the process of band gap curve
fitting using inclination angles developed by Escobedo-Morales et al. [4]
produces numerical inconsistencies and is removed in our implementation in
favor of a simpler and more robust version of RMSE minimization. Keesey &
Tiihonen et al. [7] develop a procedure of optically extracting a figure of
merit to quantify the stability of perovskites but this methodology requires
the manual segmentation of samples one by one, which becomes infeasible for a
human researcher when the number of samples increases significantly. In this
paper, we build from these prior works by demonstrating the performance of
three autocharacterization methods that are scalable to arbitrarily many
samples using a computer vision-driven approach.

##  2 Methods

In this paper, we develop four processes for the autocharacterization of
perovskites: (i) a hyperspectral vision segmentation process, (ii) an
automatic composition extractor, (iii) an automatic band gap computation
algorithm, and (iv) an automatic stability measurement method. All the code
required for reproducing the autocharacterization results described in this
contribution will be made publicly available in full publication.

(a) Raw Image

(b) Vision-segmented Image

Figure 2: Vision segmentation of hyperspectral datacubes to locate the
reflectance pixel values for material deposits only. (a) Raw image that
contains reflectance information, $R$, for all pixels, $(X,Y)$, including the
background; (b) vision-segmented image that contains reflectance information
for only the target material deposit pixels with a unique feature index
assigned to each deposit $(\widehat{X},\widehat{Y})$. Through the segmentation
process described by Algorithm 1, background pixels are removed, illustrated
by the gray hatches in (b), such that only the circular material deposit
pixels and their corresponding $R$ remain. Furthermore, all material deposit
pixels are assigned a unique feature index, illustrated by the purple-to-
yellow colormap. Using this segmentation and unique index assignment, the
optical data in the $R$-domain is uniquely mapped onto the deposit it was
measured from. This process is equivalent for $\lambda$ values in both
Hyperspectral and RGB regimes.

###  2.1 Experiments

In this study, we synthesize $80$ unique perovskite compositions within the
formamidinium-methylammonium lead tri-iodide perovskite system, FA1-xMAxPbI3.
These $80$ materials are synthesized using a high-throughput liquid deposition
tool, as described in Siemenn et al. [21]. In brief, the perovskites are
deposited onto an amorphous glass slide by pumping fluid from two sources
containing the liquid-based precursors of methylammonium lead iodide (MAPbI3)
and formamidinium lead iodide (FAPbI3). The total time to deposit all $80$
samples is $16.5$ seconds and each pump runs at a rotational velocity that may
vary over this total time. Hyperpectral optical data is recorded across the
batch of $80$ samples as a single image for band gap analysis. The eighty
perovskite samples were degraded under 50∘C temperature, 35% air humidity, and
0.5 sun illumination (visible only) for 6 hours to assess stability via color
change, captured with RGB imaging. The hyperspectral data are acquired with
the Resonon, Inc. Pika L camera and the RGB data are acquired with the
Thorlabs, Inc. DCC1645C camera.

###  2.2 Hyperspectral and RGB Vision Segmentation

Figure 3: Automated extraction of chemical composition from vision-segmented
perovskite deposits synthesized using a high-throughput liquid deposition
system. From left to right: A liquid handling system rasters along the black
path, depositing perovskite semiconductors of varying composition by
temporally varying the two pump rotational velocities, $\omega_{\textrm{FA}}$
and $\omega_{\textrm{MA}}$; the rotational velocity $\omega_{\textrm{FA}}$
governs the proportion of FA in the deposit while the rotational velocity
$\omega_{\textrm{MA}}$ governs the proportion of MA in the deposit; these
time-dependent velocities are obtained directly from the pump microcontrollers
and are plotted as the black diagonal lines in the $t$ versus $\omega$
subplots; the integrals of the $\omega$’s over time for four vision-segmented
deposits are shown as the purple and yellow areas beneath the black curves;
computing the integral solves for $x$ to estimate the composition
FA1-xMAxPbI3. This method is validated by XRD measurement. The right panel
illustrates a peak shift of $+0.152^{\circ}$ in $2\theta$ from measured
deposits with a high expected FA proportion (purple) to measured deposits with
high expected MA proportion (yellow), which is the expected result.

The common thread across the composition, band gap, and stability
autocharacterization processes is the vision segmentation framework. The
desired output of the segmentation procedure is the segmented optical data
$\Phi$, a set of uniquely indexed optical data for each material deposit:

$\displaystyle\begin{split}\Phi&=(\widehat{X},\widehat{Y},R(\lambda)),\\\
\lambda&=\begin{cases}\\{a\>|\>380\leq a\leq 1020\\},&\textrm{if
Hyperspectral}\\\ \\{700,546,435\\},&\textrm{if RGB},\end{cases}\end{split}$
(1)

where $(\widehat{X},\widehat{Y},R(\lambda))$ is the 3D datacube of segmented
and indexed pixels, $(\widehat{X},\widehat{Y})$, for each material with the
corresponding reflectance intensity data, $R(\lambda)$, at the wavelengths
$\lambda$ in nanometers (nm).

1

2

Input : $(X,Y,R(\lambda))$: All image pixels and reflectance

$\Theta_{\textrm{min}}$: Minimum segmented feature size

$\Theta_{\textrm{max}}$: Maximum segmented feature size

Output : $(\widehat{X},\widehat{Y},R(\lambda))$: Segmented pixels and
reflectance

Let $\kappa$ be kernel size

3 img $\leftarrow(X,Y,R(\lambda))$

4 img $\leftarrow$ Crop(img)

5 img $\leftarrow$ Grayscale(img)

6 img $\leftarrow$ 255 - img

7 mask $\leftarrow$ Binarize(img)

8 mask $\leftarrow$ MorphGradient(mask, $\kappa=12$)

9 mask $\leftarrow$ Erode(mask, $\kappa=3$)

10 mask $\leftarrow$ MedianBlur(mask, $\kappa=7$)

11 mask $\leftarrow$ DistTransform(mask, $\kappa=3$)

12 mask $\leftarrow$ LabelFeatures(mask)

13 $(\widehat{X},\widehat{Y})$ $\leftarrow$ Watershed(img, mask)

14 $(\widehat{X},\widehat{Y})$ $\leftarrow$
Dilate($(\widehat{X},\widehat{Y})$, $\kappa=5$)

15 $(\widehat{X},\widehat{Y})$ $\leftarrow$
MedianBlur($(\widehat{X},\widehat{Y})$, $\kappa=7$)

16 for  _$\phi$ in Feature($(\widehat{X},\widehat{Y})$)_ do

17 if  _Size $(\phi)<\Theta_{\mathrm{min}}$ or
Size$(\phi)>\Theta_{\mathrm{max}}$_ then

18 $(\widehat{X},\widehat{Y})$.Prune$(\phi)$

19

20 end if

21

22 end for

23bool $\leftarrow$ Boolean($(\widehat{X},\widehat{Y})$)

24
$(\widehat{X},\widehat{Y},R(\lambda))\leftarrow\left(X,Y,R(\lambda)\right)$.Mask$\left(\textrm{bool}\right)$

Return $(\widehat{X},\widehat{Y},R(\lambda))$

Algorithm 1 Vision Segmentation

The raw image datacube without segmentation is $\Omega=(X,Y,R(\lambda))$. To
obtain $\Phi$, $(X,Y,R(\lambda))$ is passed through several filters to find
the edges of each feature and then index the features appropriately. In this
study, the input image dimensions are $(900,600)$ pixels and each feature has
an area of roughly $1000$ pixels. There are approximately 80 features in the
image area but their number and location vary from experiment to experiment.
Inputting images or features of different sizes may require tuning the kernel
sizes, $\kappa$, of the filters.

Algorithm 1 describes this segmentation process of
$(X,Y,R(\lambda))\rightarrow(\widehat{X},\widehat{Y},R(\lambda))$. First, the
input image is cropped and converted to greyscale, then it is passed through
several layers of thresholding and smoothing. By thresholding, eroding,
blurring, and then thresholding again, we capture the edges of each feature
while removing edge effects. The background is indexed as zeros, hence, all
features split by zeros are assigned a unique index using
LabelFeatures$(\cdot)$ and Watershed$(\cdot)$ [13]. Once segmented, the
features are smoothed, and any improperly segmented aberrations are pruned
with the user-selected hyperparameters $\Theta_{\textrm{min}}$,
$\Theta_{\textrm{max}}$. Finally, a boolean mask is created for all pixels
encoded with non-zero values to output $\Phi$, where each uniquely indexed
material deposit is directly mappable to the $R(\lambda)$ measured for that
deposit. Figure 2(a) shows the unprocessed, raw hypercube of perovskite
semiconductor reflectance intensity data, $R$, and Figure 2(b) shows the post-
processed, segmented hypercube, output by Algorithm 1.

Generating a clean segmented image mappable to optical reflectance data
provides a powerful foundation for further characterization of material
properties. In this paper, We use the output $\Phi$ to automatically extract
compositional, band gap, and stability information from each unique perovskite
deposit.

###  2.3 Automatic Composition Extraction

Figure 4: Automatic band gap computation from vision-segmented perovskite
deposits. From top to bottom: The reflectance intensities,
$R(\lambda),\lambda\in[380\textrm{nm},1020\textrm{nm}]$, are acquired for each
sample from the vision-segmented hypercube, $\Phi$ (obtained from a single
image of a hyperspectral camera); the Tauc curves are computed from the median
reflectance across all wavelengths for each deposit; each Tauc curve is
recursively segmented into small line segments and then iteratively fit with
linear regression lines; the regression line that minimizes the RMSE with the
Tauc curve is illustrated by the thick red line, which computes the band gap,
$E_{g}$.

In the perovskite semiconductor system, the performance metrics of band gap
and stability are largely governed by the chemical composition of the material
[23, 7]. However, since the $80$ samples are synthesized using the high-
throughput method described in Section 2.1, the exact composition of each
unique deposit (the value of $x$) is not known a priori. Traditionally, X-ray
photoelectron spectroscopy (XPS) is used to determine the chemical composition
but XPS is a time-consuming process. Here, we extract the compositional
information automatically and deterministically from the segmented image by
mapping it with the synthesis conditions of the liquid deposition tool over
space, as shown in Figure 3 and in the following expression:

$x(\Phi)=\int_{t_{a}(\Phi)}^{t_{b}(\Phi)}\frac{\omega_{\textrm{MA}}(\Phi)}{\left(\omega_{\textrm{MA}}(\Phi)+\omega_{\textrm{FA}}(\Phi)\right)}dt,$
(2)

where $\omega_{\textrm{MA}}(t)$ and $\omega_{\textrm{FA}}(t)$ are the
rotational velocities of the MA and FA precursor pumps, respectively, as a
function of time $t$. These time-dependent rotational velocities are acquired
directly from the pump microcontrollers and are visualized in the middle panel
in Figure 3. The time-dependent coordinates of the fluid deposition system’s
raster path are acquired directly from the system G-code and are visualized as
the black pathway beneath the deposits in the left panel of Figure 3. Hence,
the pump velocity timestamps and the raster coordinate timestamps are bi-
directionally mappable to each other: $t(X,Y)\leftrightarrow
t(\omega_{\textrm{MA}},\omega_{\textrm{FA}})$. Therefore, both the pump
velocities, $\omega_{\textrm{MA, FA}}(\Phi)$, and the integration time,
$t_{b}(\Phi)-t_{a}(\Phi)$, for each material deposit are obtainable from the
vision-segmented data, $\Phi$, and $x(\Phi)$ is computed using Equation 2 to
solve FA1-xMAxPbI3.

###  2.4 Automatic Band Gap Computation

Computing the band gap of a semiconductor material often requires laborious
manual curve fitting to Tauc plots [22] that result in human error and consume
time. Current band gap computing software from literature still requires each
sample to be processed one by one, which becomes infeasible for large numbers
of samples produced by high-throughput synthesis tools. We develop a band gap
computation tool that takes in the vision-segmented hyperspectral data,
$\Phi$, for each deposited sample and accurately computes each band gap
autonomously. This developed process is agnostic to the number of samples and
will scale up to higher numbers of samples, accelerating the material
characterization process.

Figure 5: Automatic degradation testing of vision-segmented perovskite
deposits. The aging test is started by taking a single image of a reference
color chart on the sample holder plate. The chart is swapped with the samples
that are continuously degraded under environmental stress for 6 hours and
photographed using an RGB camera with 10-second intervals. The segmented color
time series is averaged over the pixels in each sample, color calibrated, and
analyzed by calculating the instability index from the data.

Figure 4 illustrates the workflow of the automatic band gap computation
procedure. First, the hyperspectral reflectance, $R(\lambda)$, is acquired
from the vision segmentation output, $\Phi$, for each sample. The median
$R(\lambda)$ for all $(\widehat{X},\widehat{Y})$ per sample is taken to
minimize the influence of outlier pixels and edge effects on the reflectance.
Then, reflectance is transformed into a Tauc curve for each sample using the
following equation [11]:

$F(R(\lambda;\widehat{X},\widehat{Y}))=\left(\frac{620(1-R(\lambda;\widehat{X},\widehat{Y}))^{2}}{\lambda
R(\lambda;\widehat{X},\widehat{Y})}\right)^{\frac{1}{\gamma}},$ (3)

where $\gamma$ is a constant value of $\frac{1}{2}$ or $2$ for direct band gap
or indirect band gap, respectively. We compute the direct band gap for
FA1-xMAxPbI3 perovskites, hence, $\gamma=\frac{1}{2}$. The transformed Tauc
curves are then recursively segmented into linear segments that are split in
half until every segment achieves a coefficient of determination of $R^{2}\geq
0.990$. As shown in the bottom panels of Figure 4, the dark blue markers along
the Tauc curve have a higher density along curved regions, indicating a higher
segmentation rate is required to form straight line segments. Once the
recursion is complete, each pair of adjacent line segments is iteratively fit
with a linear regression line, as shown by the thin red lines in the bottom
panels of Figure 4. The root-mean-square error (RMSE) is computed between each
regression line and the Tauc curve within the range of the $x$-intercept and
the Tauc peak location minus one-half of the peak width. Enforcing the RMSE
computation within this range was shown to increase fitting accuracy. The band
gap, $E_{g}$, is the $x$-intercept point of the regression line that minimizes
the RMSE.

###  2.5 Automatic Stability Measurement

A helpful property in screening potential perovskite crystal structures is
their stability under relevant environmental conditions. For example, in solar
panels, the lifetime of the perovskite semiconductor under given illumination
conditions, humidity levels, and temperature are all deterministic of possible
applications. To determine stability, the perovskite semiconductors were
subject to an accelerated degradation chamber, and the three-channel RGB
approximation of the color change of the sample was recorded as a proxy to
sample stability. [7] The chamber, pictured in Figure 5, maintains a uniform
temperature, illumination, and humidity level around the samples, and obtains
real-time images of the perovskite semiconductors every time step $\Delta t$
for a duration of time $T$ resulting in $\Omega(\Delta t)$ images. [7] The
vision segmentation algorithm described in Algorithm 1 is applied to the first
droplet image, $\Omega$, to output the segmented locations and reflectance
data, $\Phi$, of each spatially-non uniform sample across the duration of the
experiment with a fixed camera position.

In order to use color as a reproducible and repeatable quantitative proxy for
degradation, color calibration needs to be applied because the illumination
conditions in the aging test chamber may vary over time. At the beginning of
the degradation study, an image of a reference color chart (X-Rite Colour
Checker Passport; 28 reference color patches), $I_{R}$, is taken under the
same illumination conditions as the perovskite semiconductor samples. Images
at each time step, $\Omega(\Delta t)$, are transformed into L*a*b and
subsequently to a stable reference color space (standard observer CIE 1931 2
degrees, standard illuminant D50) by applying a 3D-thin plate spline
distortion matrix $D$ [23, 12] defined by $I_{R}$ and known colors of the
reference color chart:

$D=\begin{bmatrix}V\\\ O(4,3)\end{bmatrix}{\begin{bmatrix}K&P\\\
P^{T}&O(4,4)\end{bmatrix}}^{-1}$ (4)

Here, $O(n,m)$ is an $n$x$m$ zero matrix, $V$ is a matrix of the color checker
reference colors in the stable reference color space, $P$ is a matrix of the
color checker RGB colors obtained from $I_{R}$, and $K$ is a distortion matrix
between the color checker colors in the reference space and in $I_{R}$.

Using the color-calibrated images and droplet pixel locations given by $\Phi$,
a final array, $R(t;\widehat{X},\widehat{Y})$ of the average color at time $t$
for perovskite semiconductor of composition FA1-xMAxPbI3 is created. The color
of each droplet is measured to determine a stability metric $I_{c}$ [23]:

$I_{c}(\widehat{X},\widehat{Y})=\sum_{R=\\{r,g,b\\}}\int_{0}^{T}|R(t;\widehat{X},\widehat{Y})-R(0;\widehat{X},\widehat{Y})|dt$
(5)

Here, the color is averaged over sample pixels and is collected from red
($r$), green ($g$), and blue ($b$) color channels.

##  3 Results

Combining the three vision-driven autocharacterization processes developed in
this paper accelerates the identification of perovskite semiconductors with
desirable properties relative to conventional human-evaluated
characterization. Using the segmented optical data, $\Phi$, of each sample
composition, band gap, and stability are all computed automatically. This
combination is a sufficient number of characterizations for a pipeline that
initially screens perovskite materials properties, which we demonstrate can be
implemented fully via computer vision techniques. In this section, we
visualize the characterization results output by each automated process and
benchmark them against human evaluation.

(a) Extracted Band Gaps

(b) Extracted Instability Index

Figure 6: The output (a) band gaps and (b) instability indices from the band
gap and stability autocharacterization methods. Each uniquely segmented
sample, $\Phi$, is plotted as a colored square marker with its color and
$x$-axis position corresponding to the proportion of MA in FA1-xMAxPbI3. (a)
The equation of the regression line fit to the $E_{g}(x)$ curve is displayed
in the chart area. (b) The $I_{c}$ is thresholded at a value of $10000$ to
indicate high degradation above the threshold and low or no degradation below.

Figure 6 shows the band gap and instability index as a function of sample
composition computed using autocharacterization. The computed band gap of each
composition is shown to have a linearly increasing trend with an increasing
proportion of MA. Furthermore, the computed band gap values fall within a
range of $1.45$eV–$1.52$eV. This eV range and linearly increasing trend align
with the anticipated results from literature as the MA proportion is increased
within the FA1-xMAxPbI3 system, for example, Weber et al. report a linear
trend within a range of 1.45eV–1.55eV [25, 22].

The computed instability index of each composition peaks at approximately
$25\%$ MA content, indicating more degradation occurs closer to the FA-rich
compositions, but not at purely FAPbI3 compositions. Through visual inspection
of the degradation results, we manually threshold the instability index at
$I_{c}>10000$ px $\cdot$min to classify samples with high degradation rates,
i.e., the samples with MA proportions between $10$%–$40$%. Patterns of high
stability in FA-pure perovskites that decrease as MA is added are seen within
literature, for example when the samples are degraded under high heat and
humidity [23], however, the trends in high-MA compositions are less clear from
literature [25, 1, 20]. The extracted instability index results are thus
further validated via pre- and post-aging XRD (shown in the Supplemental
Information). The post-aging XRD peaks of hexagonal FAPbI3 first increase with
increasing MA proportion but start to decrease after more than $50$% of MA is
added, which matches the degradation observed via the computer vision
approach. At the same time, the other possible major degradation route via
perovskite decomposition [23] can be ruled out based on XRD. As a result, we
link the color change to the transformation of cubic FA1-xMAxPbI3 to a
hexagonal crystal structure. The presence of the hexagonal FAPbI3 phase
indicates degradation from the more electrically favorable cubic FAPbI3 phase
[15].

To further validate the autocharacterization tools developed in this paper, we
benchmark the extracted results with human-evaluated results. To measure the
accuracy of each result, we take the difference between the set of human-
evaluated reference results, $\mathbf{Z}_{\textrm{ref}}$, and the set of
automatically extracted results, $\mathbf{Z}_{\textrm{ext}}$, and divide the
difference by the total maximum difference:

$\textrm{Acc.}=\left(1-\frac{|\mathbf{Z}_{\textrm{ref}}-\mathbf{Z}_{\textrm{ext}}|}{\texttt{Max}(\mathbf{Z}_{\textrm{ref}},\mathbf{Z}_{\textrm{ext}})-\texttt{Min}(\mathbf{Z}_{\textrm{ref}},\mathbf{Z}_{\textrm{ext}})}\right)\times
100$ (6)

For the band gap data, $\mathbf{Z}_{\textrm{ref}}$ is a set of numerical band
gap results in electronvolts (eV) acquired by a domain expert through manual
regression line fitting of Tauc plots to $\Omega$, who has not seen the set
$\mathbf{Z}_{\textrm{ext}}$ computed from $\Phi$. For the stability data,
$\mathbf{Z}_{\textrm{ref}}$ is a binarized set acquired by a domain expert
through manual regression line fitting of Tauc plots to the post-degradation
$\Omega$. If no band gap exists after degradation, this implies high
degradation has occurred and a value of $1$ is assigned, otherwise, a value of
$0$ is assigned. Similarly, for the stability data,
$\mathbf{Z}_{\textrm{ext}}$ is a binarized set acquired by thresholding
$I_{c}$ at $10000$ px $\cdot$ min, as shown in Figure 6(b), where
$I_{c}>10000$ implies high degradation has occurred and a value of $1$ is
assigned, otherwise, a value of $0$ is assigned. Finally, for the composition
data, no direct measure of composition was taken in this study, thus,
$\mathbf{Z}_{\textrm{ref}}$ is inferred by computing $x$ from the regression
line fit of the extracted band gap data, as shown in Figure 6(a), and the
error of the fit is propagated to the composition accuracy calculation.

Method | Accuracy (%)
---|---
Composition | $78.77\pm 9.4$
Band Gap | $\mathbf{89.08\pm 7.3}$
Stability | $87.84\pm 7.5$
Table 1: Results of the vision-driven autocharacterization methods relative to
a human evaluation reference. Accuracy is shown as a percentage with the $95$%
confidence interval shown in the error.

Table 1 shows the accuracy, computed using Equation 6, for each
autocharacteriztion method developed in this paper. The automatic band gap
extraction method demonstrates the highest accuracy of the three methods at
$89.1\%$, relative to its human-evaluation counterpart. The simple linear
relationship between $x$ and $E_{g}$ within the FA1-xMAxPbI3 system supports
the high performance of the automatic band gap extraction method. Conversely,
the trace of $I_{c}(x)$ is parabolic rather the linear, like $E_{g}(x)$,
implying that there are more complex chemical mechanisms at work during
stability testing. We note the automatic stability measurement method has an
accuracy of $87.8\%$, slightly lower than that of the automatic band gap
extraction. Finally, the composition extraction process has an accuracy of
$78.8\%$, which is significantly lower than the accuracies of the other
autocharacterization methods, due to error propagation in acquiring
$\mathbf{Z}_{\textrm{ref}}$ for composition in this study. Overall, each of
the three autocharacterization methods developed in this paper exhibits high
accuracy between $78\%$–$89\%$, compared to human evaluation. Furthermore, the
key contribution of the developed autocharacterization methods extends past
simply accelerating the throughput of sample-by-sample characterization and
more largely drives scalable characterization of arbitrarily many samples
through the use of computer vision, such that characterization is no longer
the bottleneck process in high-throughput materials screening.

##  4 Conclusions

In the modern-day exploration of novel materials, synthesis is no longer the
bottleneck process due to the paradigm shift towards autonomous and self-
driving laboratories [14, 10, 6, 19]. For example, in this paper, we
synthesize $80$ unique perovskite semiconductor materials along the
FA1-xMAxPbI3 sequence in only $16.5$ seconds. Instead, the bottleneck for
novel material discovery is now the manual characterization of each sample
individually [22]. Although strides have been made with some
autocharacterization methods of materials, there is a lack of scalability to
these methods to arbitrarily many samples, as produced by high-throughput
synthesis hardware, thus, inhibiting the throughput of materials discovery
[21]. Integration of computer vision in tandem with autocharacterization has
the promise of improving this throughput. However, conventional computer
vision approaches for materials-specific tasks have been used predominately
for morphological analyses in combination with specialized microscopy methods
[18, 3]. In this paper, we proposed the design of three autocharacterization
tools to compute (i) composition, (ii) band gap, and (iii) stability of
perovskite semiconductors and integrate each of these tools with computer
vision segmentation of optical reflectance data to further automate and
accelerate the characterization pipeline.

Through the use of high-fidelity computer vision segmentation, we demonstrate
the scalability of accurate and automatic characterization for $80$ unique
FA1-xMAxPbI3 perovskite samples. The developed vision segmentation method
avoids edge effects and removes aberrations to output a clean segmentation of
optical data. From the segmented optical data, the automatic band gap
computation is demonstrated to achieve an accuracy of $89.1\%$, the automatic
stability measurement is demonstrated to achieve an accuracy of $87.8\%$, and
the automatic composition extraction is demonstrated to achieve an accuracy of
$78.8\%$ across all $80$ perovskite samples, relative to a human evaluation
reference. Furthermore, the results extracted by the developed vision-driven
autocharacterization tools are validated to align with traditional x-ray
diffraction characterization. The results achieved by the methods developed in
this paper support the advancement of scalable, high-throughput novel
materials discovery by surmounting the obstacle of sample-by-sample
characterization.

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Supplemental Information:
Vision-driven Autocharacterization of Perovskite Semiconductors

Anonymous ICCV submission

##  S-1 Perovskite Sample Preparation

Figure S-1: Traces of pump speed over time for each precursor, MAPbI3 and
FAPbI3

Pure FAPbI3 and MAPbI3 precursor solutions are prepared in a nitrogen glovebox
environment at $0.6$M molarity and with a $4:1$ DMF:DMSO solvent ratio. A
2”$\times$3” amorphous glass slide is prepared using a three-step cleaning
process: (1) ultrasonication in a 2%vol. Hellmanex and deionized (DI) water
solution for 5 minutes, (2) ultrasonication in DI water for 5 minutes, (3)
ultrasonication in isopropyl alcohol for 5 minutes. The precursors are loaded
into their corresponding pumps and flowed through a Teflon tube at the pump
speeds indicated in Figure S-1.

Figure S-2: Output from the automatic composition extractor. The raw RGB image
of the deposits is input to the composition extractor and then the computed
composition labels of each deposit are returned superimposed onto the
centroids of each vision-segmented deposit. The segmented deposits are
illustrated as circular objects with a purple-to-yellow colormap. The raster
path of the fluid handling system is also shown along with its start and end
points.

Prior to running the motors at these speeds, all plumbing lines are purged for
$30$ seconds to remove air bubbles. Pumping the fluid forms droplets in-air
from the continuous flow of fluid by actuating a Precigenome, Inc. SwitchEZ
solenoid pinch valve at $30$Hz frequency and $11\%$ duty cycle that pinches
and perturbs the flow within a 1/32”ID$\times$3/32”OD silicone tube to form
discrete droplets. The print head rasters in a zig-zag pattern, shown in
Figure S-2 at $38$mm/s to deposit each material as a unique sample on the
prepared glass slide. Approximately $80$ unique samples are produced within
$16.5$ seconds and are then annealed on a hotplate at $150^{\circ}$C for $10$
minutes. Two identical plates of samples are synthesized, one for
hyperspectral data collection and degradation, and the other for X-ray
diffraction (XRD) analysis.

##  S-2 Characterization Methods

###  S-2.1 Hyperspectral Imaging

Immediately after the samples are synthesized, the samples are removed from
the glovebox and their hyperspectral images are taken using Resonon, Inc. Pika
L camera. Figure S-3 illustrates the reflectance trace of all $80$ samples.
One of the sample glass slides is measured using XRD, and the other undergoes
a degradation experiment and thereafter is measured using XRD post-
degradation.

Figure S-3: The reflectivity curves obtained from the vision-segmented
hyperspectral datacube of FA1-xMAxPbI3 samples prior to degradation. A general
decrease in reflectance intensity is noted as a function of increasing MA
proportion at about the $\lambda=830$nm (infrared).

###  S-2.2 X-ray Diffraction

The XRD degradation traces pre- and post-degradation are shown in Figure S-4.
Lead iodide (PbI2) peaks, which are a perovskite decomposition product [23],
are not detected at their expected $2\Theta=12.5^{\circ}$ location before or
after the aging test. Hence, this indicates that the samples went through just
the initial stages of degradation from cubic FAPbI3 to hexagonal FAPbI3 during
the degradation test, rather than degrading completely to
FAPbI${}_{3}\rightarrow$ FAI $+$ PbI2 or to MAPbI${}_{3}\rightarrow$ MAI $+$
PbI2.

(a) Pre-degradation XRD

(b) Post-degradation XRD

Figure S-4: (a) Pre-degradation XRD and (b) post-degradation XRD traces of the
FA1-xMAxPbI3 sequence. Post-degradation, the crystal coordination of high FA
concentration samples is shown to degrade from the favorable perovskite cubic
phase to the unfavorable non-perovskite hexagonal phase. The main XRD peak for
the hexagonal phase arises at $2\theta=26.284^{\circ}$. The reference peak
$2\theta$ locations of the degraded phase are indicated as red vertical lines
along the bottom $x$-axis of (b). The reference peak $2\theta$ locations of
the favorable, non-degraded cubic FAPbI3 and tetragonal MAPbI3 are indicated
as black vertical lines along the top and bottom $x$-axes of both (a) and (b).

###  S-2.3 Automatic stability measurement

The degradation experiment is conducted over the course of $6$ hours at steady
state conditions of $50^{\circ}$C, $35\%$ relative humidity, and $0.5$ suns
illumination of visible light. A timeseries of these conditions over the
course of the experiment is illustrated in Figure S-5. The exact construction
and operation of the degradation chamber setup is detailed in Keesey &
Tiihonen et al. [7] under the ”Second generation chamber at MIT (thin films)”
section. During the 6-hour degradation experiment, RGB images of the samples
are taken at $10$ second intervals, acquired with the Thorlabs, Inc. DCC1645C
camera.

After segmenting each sample across the entire time domain of the experiment,
the full matrix of degradation time-series is populated and color calibrated
automatically, as shown in Figure S-6(a). In this specific experiment, spatial
non-uniformity of the illumination was detected in the post-analysis which
does not affect the instability index calculation but gives rise to artificial
color differences in the films. These color differences are due to the
physical configuration of the environmental chamber. To counter these color
differences only in this specific experiment, an additional color correction
step initializes all the films to the same color. Color correction is used in
generating figures in which the color changes within and between the films are
easier to see. After the color correction, a fully calibrated matrix of
degradation time-series is acquired showing the color change over time of each
perovskite sample S-6(b).

Figure S-5: Steady-state temperature, humidity, and illumination conditions
for the 6-hour stability experiment. The purple binary switching curve
indicates the ON/OFF mode of a dry nitrogen line. When the humidity increases
past the set threshold, the dry nitrogen line turns on to decrease the water
vapor content in the air and maintain stable conditions.

(a) Stability Pre-color Correction

(b) Stability Post-color Correction

Figure S-6: Final stability timeseries matrix of all segmented droplets over
the course of a 6-hour degradation experiment (a) pre-color correction and (b)
post-color correction. All samples begin the experiment colored as dark gray
and over the course of degradation, samples with MA proportions between
10%–40% exhibit yellowing around the 100min–150min mark – indicating
degradation. The two lighter points at approx. 110 minutes are droplets of
water in the optical path of the camera and are excluded from the analysis as
such.

###  S-2.4 Full Readout of Results

Table LABEL:table4 contains the full readout of the characterization results
extracted from all $80$ droplets. We report the numerical values of band gap,
composition, and whether or not the sample degraded as extracted automatically
(using the methods described in the main paper) from the collected data. As a
comparison of how accurate our extracted band gap values are, we also report
the ”actual” band gaps computed manually by a domain expert by curve fitting
the Tauc plots obtained from the reflectance data. The proportion of MA is
extracted from the relative speed of the motors whereas the actual MA
proportion is calculated by fitting a straight line to the calculated band
gaps, given band gap is a linear function of the composition. The stability is
extracted from the RGB color analysis data by binarizing the calculation of
instability index, $I_{c}$, post-vision-segmentation. The actual stability is
determined by manual Tauc analysis by a domain expert using hyperspectral
reflectance data measured after the degradation experiment. If a band gap no
longer exists in a sample, it is assigned a value of $1$ to denoted
degradation, otherwise, it is assigned a value of $0$.

Table S-1: Data acquired from automated extraction and manual methods for each droplet | Bandgap (eV) | MA Proportion ($x$) | Degradation (0/1)
---|---|---|---
Drop Index | Extracted | Actual | Extracted | Actual | Extracted | Actual
$FA_{100}MA_{0}$ | $1.51$ | $1.5$ | $0$ | $0.74$ | $0$ | $0$
$FA_{100}MA_{0}$ | $1.47$ | $1.48$ | $0$ | $0$ | $0$ | $0$
$FA_{100}MA_{0}$ | $1.47$ | $1.51$ | $0$ | $0$ | $0$ | $0$
$FA_{100}MA_{0}$ | $-$ | $1.52$ | $0$ | $-$ | $0$ | $0$
$FA_{100}MA_{0}$ | $1.5$ | $1.52$ | $0$ | $0.54$ | $0$ | $0$
$FA_{98}MA_{2}$ | $1.5$ | $1.5$ | $0.02$ | $0.47$ | $0$ | $0$
$FA_{97}MA_{3}$ | $1.51$ | $-$ | $0.03$ | $0.80$ | $0$ | $0$
$FA_{97}MA_{3}$ | $1.5$ | $1.5$ | $0.03$ | $0.41$ | $1$ | $1$
$FA_{95}MA_{5}$ | $1.49$ | $1.5$ | $0.05$ | $0.31$ | $1$ | $1$
$FA_{93}MA_{7}$ | $1.49$ | $1.49$ | $0.07$ | $0.27$ | $1$ | $1$
$FA_{92}MA_{8}$ | $1.49$ | $1.49$ | $0.08$ | $0.14$ | $1$ | $1$
$FA_{92}MA_{8}$ | $1.49$ | $1.48$ | $0.08$ | $0.21$ | $1$ | $0$
$FA_{90}MA_{10}$ | $1.5$ | $1.5$ | $0.1$ | $0.34$ | $0$ | $0$
$FA_{88}MA_{12}$ | $1.45$ | $1.49$ | $0.12$ | $0$ | $0$ | $0$
$FA_{87}MA_{13}$ | $1.46$ | $1.46$ | $0.13$ | $0$ | $0$ | $0$
$FA_{85}MA_{15}$ | $1.48$ | $1.48$ | $0.15$ | $0$ | $0$ | $0$
$FA_{84}MA_{16}$ | $1.5$ | $1.5$ | $0.16$ | $0.34$ | $1$ | $1$
$FA_{83}MA_{17}$ | $1.5$ | $1.5$ | $0.17$ | $0.34$ | $1$ | $1$
$FA_{82}MA_{18}$ | $1.49$ | $1.49$ | $0.18$ | $0.04$ | $1$ | $1$
$FA_{80}MA_{20}$ | $1.49$ | $-$ | $0.2$ | $0.27$ | $0$ | $-$
$FA_{80}MA_{20}$ | $1.49$ | $1.5$ | $0.2$ | $0.21$ | $1$ | $1$
$FA_{78}MA_{22}$ | $1.49$ | $1.5$ | $0.22$ | $0.24$ | $1$ | $1$
$FA_{77}MA_{23}$ | $1.49$ | $1.5$ | $0.23$ | $0.27$ | $1$ | $1$
$FA_{75}MA_{25}$ | $1.5$ | $1.48$ | $0.25$ | $0.34$ | $1$ | $1$
$FA_{75}MA_{25}$ | $1.49$ | $1.5$ | $0.25$ | $0.21$ | $1$ | $0$
$FA_{73}MA_{27}$ | $1.49$ | $1.5$ | $0.27$ | $0.27$ | $0$ | $0$
$FA_{71}MA_{29}$ | $1.49$ | $1.5$ | $0.29$ | $0.31$ | $0$ | $0$
$FA_{70}MA_{30}$ | $1.49$ | $1.5$ | $0.3$ | $0.27$ | $0$ | $0$
$FA_{68}MA_{32}$ | $1.49$ | $1.5$ | $0.32$ | $0.11$ | $1$ | $0$
$FA_{67}MA_{33}$ | $1.5$ | $1.51$ | $0.33$ | $0.37$ | $1$ | $0$
$FA_{66}MA_{34}$ | $1.5$ | $1.5$ | $0.34$ | $0.37$ | $1$ | $1$
$FA_{64}MA_{36}$ | $1.49$ | $1.51$ | $0.36$ | $0.27$ | $1$ | $1$
$FA_{63}MA_{37}$ | $-$ | $1.52$ | $0.37$ | $-$ | $1$ | $0$
$FA_{62}MA_{38}$ | $1.5$ | $1.5$ | $0.38$ | $0.51$ | $1$ | $0$
$FA_{60}MA_{40}$ | $1.5$ | $1.5$ | $0.4$ | $0.47$ | $0$ | $0$
$FA_{58}MA_{42}$ | $1.5$ | $1.5$ | $0.42$ | $0.44$ | $0$ | $0$
$FA_{58}MA_{42}$ | $1.5$ | $1.5$ | $0.42$ | $0.37$ | $0$ | $0$
$FA_{57}MA_{43}$ | $1.49$ | $1.52$ | $0.43$ | $0.31$ | $0$ | $0$
$FA_{54}MA_{46}$ | $1.5$ | $1.5$ | $0.46$ | $0.34$ | $0$ | $0$
$FA_{53}MA_{47}$ | $1.5$ | $1.5$ | $0.47$ | $0.41$ | $0$ | $0$
$FA_{52}MA_{48}$ | $1.5$ | $1.5$ | $0.48$ | $0.51$ | $0$ | $0$
$FA_{50}MA_{50}$ | $1.5$ | $1.5$ | $0.5$ | $0.51$ | $1$ | $0$
$FA_{49}MA_{51}$ | $1.5$ | $1.52$ | $0.51$ | $0.47$ | $1$ | $0$
$FA_{47}MA_{53}$ | $1.5$ | $1.5$ | $0.53$ | $0.47$ | $1$ | $0$
Table S-2: Data acquired from automated extraction and manual methods for each droplet (continued) | Bandgap (eV) | MA Proportion ($x$) | Degradation (0/1)
---|---|---|---
Drop Index | Extracted | Actual | Extracted | Actual | Extracted | Actual
$FA_{45}MA_{55}$ | $1.51$ | $1.52$ | $0.55$ | $0.67$ | $0$ | $0$
$FA_{43}MA_{57}$ | $1.51$ | $1.52$ | $0.57$ | $0.70$ | $0$ | $0$
$FA_{42}MA_{58}$ | $1.51$ | $1.5$ | $0.58$ | $0.74$ | $0$ | $0$
$FA_{41}MA_{59}$ | $1.51$ | $1.52$ | $0.59$ | $0.74$ | $0$ | $0$
$FA_{40}MA_{60}$ | $1.51$ | $1.52$ | $0.6$ | $0.67$ | $0$ | $0$
$FA_{38}MA_{62}$ | $1.5$ | $1.52$ | $0.62$ | $0.60$ | $0$ | $0$
$FA_{37}MA_{63}$ | $1.51$ | $1.52$ | $0.63$ | $0.77$ | $0$ | $0$
$FA_{35}MA_{65}$ | $1.51$ | $1.52$ | $0.65$ | $0.74$ | $0$ | $0$
$FA_{33}MA_{67}$ | $1.51$ | $1.52$ | $0.67$ | $0.74$ | $0$ | $0$
$FA_{33}MA_{67}$ | $1.51$ | $1.52$ | $0.67$ | $0.77$ | $0$ | $0$
$FA_{30}MA_{70}$ | $1.51$ | $1.52$ | $0.7$ | $0.74$ | $0$ | $0$
$FA_{28}MA_{72}$ | $1.51$ | $1.52$ | $0.72$ | $0.80$ | $0$ | $0$
$FA_{27}MA_{73}$ | $1.51$ | $1.52$ | $0.73$ | $0.80$ | $0$ | $0$
$FA_{25}MA_{75}$ | $1.51$ | $1.52$ | $0.75$ | $0.67$ | $0$ | $0$
$FA_{24}MA_{76}$ | $1.51$ | $1.52$ | $0.76$ | $0.77$ | $0$ | $0$
$FA_{23}MA_{77}$ | $1.51$ | $1.52$ | $0.77$ | $0.67$ | $0$ | $0$
$FA_{21}MA_{79}$ | $1.51$ | $1.52$ | $0.79$ | $0.70$ | $0$ | $0$
$FA_{20}MA_{80}$ | $1.51$ | $1.52$ | $0.8$ | $0.74$ | $0$ | $0$
$FA_{18}MA_{82}$ | $1.51$ | $1.52$ | $0.82$ | $0.80$ | $0$ | $0$
$FA_{17}MA_{83}$ | $1.51$ | $1.52$ | $0.83$ | $0.80$ | $0$ | $0$
$FA_{16}MA_{84}$ | $1.51$ | $1.52$ | $0.84$ | $0.84$ | $0$ | $0$
$FA_{14}MA_{86}$ | $1.51$ | $1.52$ | $0.86$ | $0.87$ | $0$ | $0$
$FA_{13}MA_{87}$ | $-$ | $1.52$ | $0.87$ | $-$ | $0$ | $0$
$FA_{12}MA_{88}$ | $1.5$ | $1.5$ | $0.88$ | $0.41$ | $0$ | $0$
$FA_{10}MA_{90}$ | $-$ | $-$ | $0.9$ | $-$ | $0$ | $0$
$FA_{8}MA_{92}$ | $1.51$ | $1.52$ | $0.92$ | $0.97$ | $0$ | $0$
$FA_{7}MA_{93}$ | $1.51$ | $1.5$ | $0.93$ | $0.84$ | $0$ | $0$
$FA_{7}MA_{93}$ | $1.51$ | $1.52$ | $0.93$ | $0.93$ | $0$ | $0$
$FA_{5}MA_{95}$ | $1.52$ | $1.52$ | $0.95$ | $1$ | $0$ | $0$
$FA_{3}MA_{97}$ | $1.51$ | $1.5$ | $0.97$ | $1$ | $0$ | $0$
$FA_{2}MA_{98}$ | $1.52$ | $1.53$ | $0.98$ | $1$ | $0$ | $0$
$FA_{0}MA_{100}$ | $1.52$ | $1.53$ | $1.0$ | $1$ | $0$ | $0$
$FA_{0}MA_{100}$ | $1.52$ | $1.52$ | $1.0$ | $0.93$ | $0$ | $0$