# Meeting Summarization with Pre-training and Clustering Methods

Andras Huebner
<EMAIL_ADDRESS>
Wei Ji
<EMAIL_ADDRESS>
Xiang Xiao
<EMAIL_ADDRESS>
###### Abstract

Automatic meeting summarization is becoming increasingly popular these days.
The ability to automatically summarize meetings and to extract key information
could greatly increase the efficiency of our work and life. In this paper, we
experiment with different approaches to improve the performance of query-based
meeting summarization. We started with HMNetZhu et al. (2020), a hierarchical
network that employs both a word-level transformer and a turn-level
transformer, as the baseline. We explore the effectiveness of pre-training the
model with a large news-summarization dataset. We investigate adding the
embeddings of queries as a part of the input vectors for query-based
summarization. Furthermore, we experiment with extending the locate-then-
summarize approach of QMSumZhong et al. (2021a) with an intermediate
clustering step. Lastly, we compare the performance of our baseline models
with BART, a state-of-the-art language model that is effective for
summarization. We achieved improved performance by adding query embeddings to
the input of the model, by using BART as an alternative language model, and by
using clustering methods to extract key information at utterance level before
feeding the text into summarization models.

The code of our experiments can be found in our github repository
https://github.com/wxj77/MeetingSummarization.

##  1 Introduction

Meeting summarization models aim to extract key information from video
records, audio records, or meeting transcripts that consist of utterances from
multiple people on multiple topics. Meeting is a common subject in everyday
life, and millions of meetings happen in the US and around the world every
day. An automatic meeting summarization model can help both meeting
participants and non-participants review key information of a meeting in a
shorter time and potentially save a significant amount of time by making the
usual manual note taking at least partly obsolete.

One essential challenge of meeting summarization is that the discussions in a
meeting are usually multi-faceted and different participants may hold
different opinions or focus on different facets of the same object, therefore,
it is challenging to compress or compose a short summary that contains all the
salient information. Zhong et al. (2021a) proposed QMSum, a new meeting
summarization pipeline that adopts a query-based summarization approach. QMSum
adopted a two-stage locate-then-summarize solution. Given a query, a Locator
model first locates the relevant text spans in the meeting according to the
query, then a Summarizer model summarizes the selected text spans based on the
query. This approach is more flexible and interactive, and caters to users’
diverse intents when generating summaries. In this paper, we aim to build on
top of QMSum and explore ways to make it generates better meeting summaries.

As our baseline model, we used the baseline model presented by Zhong et al.
(2021a). In our experiments, since we mainly focus on the Summarizer, we
directly used the provided relevant text spans for each query, published by
the authors. For the Summarizer, we experimented both with the HMNet modelZhu
et al. (2020) and the BART modelLewis et al. (2019). For the HMNet model, we
used a simplified versionLee (2020) and extended/changed the code as required
for our experiments. For the BART model, we used the Fairseq sequence modeling
toolkitOtt et al. (2019), which provides implementation of BART finetuned on
the CNN-DailyMail datasetSee (2018).

We used the provided relevant text spans of the Locator and the simplified
version of the HMNet Summarizer without query embedding as the baseline for
our experiments.

We performed the following experiments with the assumption that they might
help improving the performance of this model:

  * •

Adding query embedding into the code base of the simplified HMNet

  * •

Pre-Training the simplified HMNet model with CNN data

  * •

Pre-Training the simplified HMNet model with CNN data most related domain
knowledge to the QMSum dataset

  * •

Testing a locate-then-cluster-then-summarize approach (while the original
HMNet implementation uses a locate-then-summarize approach)

  * •

Testing an alternative language model (BART)

##  2 Related Work

Meeting summarization models can be grouped into two major categories:
extractive methods and abstractive methods. The extractive methods use words
picked from the original text to generate summaries and therefore has a higher
chance to maintain faithfulness of the original text. However, discussions in
meetings are usually multi-faceted and consist different opinions from
different people, thus, extractive methods may not capture all key information
of a meeting. On the other hand, the abstractive methods use language models
and encoding-decoding algorithms, which can generate better meeting summaries.
Because abstractive meeting summarization is the mainstream approach and is
more commonly discussed in recent papers, we focus on discussing recent
abstractive meeting summarization methods.

Zhong et al. (2021a) present an end-to-end learning network that leverages the
encoder-decoder transformer architecture. They introduce two major design
improvements to adapt the structure to meeting summarization: 1) employ a two-
level hierarchical structure: a word-level transformer to process the token
sequence of one turn (i.e., an utterance of a participant) in the meeting, and
a turn-level transformer to process the information of all m turns in a
meeting; 2) train a role vector for each meeting participant during encoding,
and append this role vector to the turn-level representation for later
decoding.

Zhang et al. (2021) perform a comprehensive study on long dialogue
summarization by investigating strategies to address the lengthy input
problem. The authors investigate the following models: 1) a retrieve-then-
summarize pipelineFeng et al. (2020); 2) end-to-end summarization models that
include BART (a transformer-based encoder-decoder model), HMNet (a
hierarchical type of model)Zhu et al. (2020), and Longformer (an extended
transformer model). The authors compare performance of these models in
generating summaries for long dialogue and find that the retrieve-summarize
pipeline results in the best performance, and BART-large performs worse than
HMNet when the input is beyond 512 tokens.

Shang et al. (2018) present a fully unsupervised, end-to-end meeting speech
summarization framework that composes 4 modules: 1) text preprocessing; 2)
cluster utterances that should be summarized by a common abstractive sentence;
3) generate a single abstractive sentence for each utterance community, using
an extension of the Multi-Sentence Compression Graph; 4) perform budgeted
submodular maximization to select the best elements from the generated
sentences to form the summarization. Advantages of the proposed approach are
that it is fully unsupervised and can be interactively tested.

Feng et al. (2020) explore dialogue discourse (i.e., relations between
utterances in a meeting) to model the utterances interactions for meeting
summarization. Specifically, the authors first convert meeting utterances with
discourse relations (6 types) into a meeting graph where utterance vertices
interact with relation vertices. Then, they design a graph-to-sequence
framework to generate meeting summaries using a standard LSTM decoder with
attention and copy mechanisms.

Besides introducing the QMSum dataset, Zhong et al. (2021a) also introduce a
baseline model for query-based meeting summarization. They adopted a two-stage
locate-then-summarize solution: first, a Locator model locates the relevant
text spans in the meeting according to the queries, and then a Summarizer
model summarizes the selected text spans based on the query. The authors
investigated variants of the model with different Locators and Summarizers.
They found that a Pointer Network and hierarchical ranking-based Locator and
the HMNet Summarizer generated the best summarization results.

##  3 Data

As the basis for our experiments, we use the AMI part of the QMSum dataset and
combine it with the extracted relevant spans for each query (published results
of the Locator part of the QMSum model) Zhong et al. (2021b). This was done by
using the original AMI data. In the original AMI data, each dataset represents
one meeting and the dataset contains overall 137 datasets, but for each
dataset, there exist multiple combinations of specific queries and reference
summaries (answers) for each query.

For our experiments, we generated for each combination of meeting
transcript/query (both for train and test meeting transcripts) a separated
dataset in the required input format which resulted in 894 training datasets
and 196 test datasets (each dataset representing a unique combination of
query/meeting transcript). Each meeting trancript appears multiple times (as
each meeting transcript has multiple queries with reference summaries included
in the QMSum dataset, but the combination of each query/summarization/meeting
transcript is unique).

For experiments including pre-training of the model with news summarization
data, we use parts of the CNN news summmarization data (which are part of the
CNN/DailyMail dataset) See (2018). The CNN/DailyMail dataset consists of 312k
news articles with reference summaries, the CNN subpart consists of 92.5k news
articles.

##  4 Our models

Motivated by locate-then-summarize methodZhong et al. (2021a) and unsupervised
graph-base multi-sentence compression (MSC) modelsShang et al. (2018), we
would like test whether we can combine benefit of the two approaches. We
proposed a approach of locate-then-cluster-then-summarize by adding a
unsupervised clustering layer between the locator and the summarizer. The
added clustering layer can help further extract the key information from each
utterance and reduce unrelated short utterances.

We build our baseline model based on the QMSum pipeline. The original QMSum
model consists of two parts: The Locator and the Summarizer. The Locator
recommended by the authors is a hierarchical ranking based Locator. The
authors also published the manually labeled relevant ’golden’ text spans for
each pair of summarized text and meeting script. We decided to use the
published relevant text spans as our input.

The authors of the QMSum model tested different models as the summarizer and
found HMNet to be the best performing summarizer. Therefore, we used a
simplified implementation of the HMNet model Lee (2020) as our baseline model.
The reason for choosing this simplified implementation was that the original
HMNet model requires more GPU resources than we had available.

The simplified version of HMNet consists, as the original implementation, of a
Word-level Transformer, followed by the Turn-level Transfomer and a Decoder.
In the original implementation, the inputs into the Word-level Transformer are
the encoded tokens of each turn, the encoded role of the speaker and two
embedding matrices to represent the part-of-speech (POS) and entity (ENT)
tags. The simplified version doesn’t use POS and entity tags.

For our baseline result, we used the simplified HMnet model with the AMI part
of the QMSum dataset with the original hyperparameters and no role vectors and
no positional encoding included. The training was performed with 30 epochs.

To get the clustering layer in between the locator and the summarizer, we
followed the clustering methods in Shang et al. (2018). The authors discussed
graph-based method to summarize text, in which a word-graph is first generated
and then is used to get the best paths in the graph as the summarized results.
We used four methods in the paper: Filippova (2010) in which a word graph is
generated by iteratively adding sentences to it and the shortest paths in word
graph is used as the result, Boudin and Morin (2013) in which a word co-
occurence network is built to generate the word-graph, Mehdad et al. (2013) in
which an entailment word-graph over the sentence communities is built, and
Tixier et al. (2016) in which a graph degeneracy-based approach is used to
decompose the word-graph to extract the central nodes that contain key
information in the word-graph.

We also explored an alternative language model as the summarizer, BARTLewis et
al. (2019), which is a de-noising pre-trained model for language generation,
translation and comprehension. BART is particularly effective when fine tuned
for text generation, and has achieved new state-of-the-art results on many
generation tasks, including summarization. We used the BART implementation
provided by FairseqOtt et al. (2019), and finetuned it on the CNN-Dailymail
summarization taskSee (2018).

We measured the performance of our models with ROUGE-1, ROUGE-2 and ROUGE-L
score Chin-Yew (2004). Rouge-N score is a recall metric which measures what
percentage of all n-grams in the human generated reference summary are
captured by the n-grams of the algorithmic generated summary. ROUGE-L measures
the overlap of the longest common sequence between the algorithmic generated
summary and the human generated reference summary, calculating both the recall
(number of words in the reference summary in denominator) and the precision
(number of words in generated summary in denominator).

##  5 Experiments

Model | ROUGE-1 F | ROUGE-2 F | ROUGE-L F
---|---|---|---
HMNet/Simp. in original form | 0.251 | 0.048 | 0.225
HMNet/Simp. query emb. | 0.259 | 0.054 | 0.233
HMNet/Simp. 10k pre-training | 0.246 | 0.044 | 0.224
HMNet/Simp. most sim. 15k / 15 epochs pre-training | 0.254 | 0.042 | 0.230
HMNet/Simp. most sim. 5k / 5 epochs pre-training | 0.205 | 0.027 | 0.187
BART | 0.252 | 0.061 | 0.222
Table 1:  Performance of the models when generating summaries that corresponds to the queries in the QMSum dataset.  Model | ROUGE-1 F | ROUGE-2 F | ROUGE-L F
---|---|---|---
HMNet/Simp. | 0.251 | 0.048 | 0.225
HMNet/Simp. + Clustering utterances | 0.263 | 0.052 | 0.233
HMNet/Simp. + Longest Sentences | 0.242 | 0.047 | 0.221
BART | 0.252 | 0.061 | 0.222
BART + Clustering utterances | 0.273 | 0.067 | 0.237
BART + Longest Sentences | 0.250 | 0.058 | 0.220
Table 2:  Performance of the models after clustering.  Model | ROUGE-1 F | ROUGE-2 F | ROUGE-L F
---|---|---|---
BART (summaries for queries) | 0.252 | 0.061 | 0.222
BART (summaries for entire meeting) | 0.227 | 0.047 | 0.205
Table 3:  BART performance when generating summaries that corresponds to the
queries vs. summaries for the entire meetings.

###  5.1 Baseline model

We used the code of the simplified HMNet model with QMSum data as input with
default settings (no speaker role vectors, no POS tagging) as our baseline.
For our first experiment, we embedded the query for each query/meeting
summarization dataset as the first utterance of a meeting, using the fictive
meeting role ”questioner”. The hyperparameters of the model remained unchanged
over all experiments if not specifically called out otherwise in the following
sections.

###  5.2 Pre-training with domain data

We used the model above and pre-training it on 10k randomly selected CNN news
from the CNN-DailyMail data set (5 epochs pre-training). To achieve this, we
expand the code of the simplified HMNet model to allow transforming and
loading the CNN news summarization data into a pseudo-meeting format. Then, we
perform a pre-training loop before fine-tuning the model on the QMSum training
data.

To further see whether the size of pre-training data could impact model
performance, we used the model above and increased the size of the pre-
training news summarization datasets to 15k. We wrote a custom logic to
identify the 15k news whose topics are most related to QMSum meetings, and
used them for pre-training purposes (in contrast to just choosing news
datasets randomly). The pre-training was again performed over 15 epochs. We
gain very small improvement by pre-training with 15k related news data.

In order to further evaluate the effect of pre-training, we ran another
experiment to fine-tune the model with only the 5k CNN news that are most
related to the AMI meeting topics (5 epochs). However, we observed a decrease
in performance. Results are shown in table 1.

###  5.3 Clustering utterances

Inspired by unsupervised meeting summarization methods Shang et al. (2018), we
first generated a short meeting script by using four different clustering
method in Filippova (2010); Boudin and Morin (2013); Mehdad et al. (2013);
Tixier et al. (2016) to cluster each utterance in given text span. We found
some utterances that we cannot find candidate results of clustering. These
sentences mostly consists of just stopping words, such as ’Hmm’, ’Right’. But
we also find some meaningful sentences also yield to no clustering results. We
think it could be because the length of the utterance is too short to generate
a word graph to be clustered. So we chose to use the longest sentence of that
utterance in the short meeting script. After clustering each utterance. we
combined the generated short meeting scripts from the four different
clustering methods and then used the combined short meeting script as the
input and pass it through Simple HMNet to compare with our baseline model.
Results are shown in table 2. We achieved improvement of ROUGE scores by this
method.

###  5.4 Longest sentences

To further explore the impact of reducing the length of the utterance, we
decided to generated a short meeting script by only using the longest sentence
of each utterance. Results are shown in table 2. We notice that the ROUGE
scores are comparable to that of the baseline model. This finding suggests
that a shorter utterances of extracted key information would yield to as good
result as long utterances.

###  5.5 BART

We performed the following experiments with the BART model:

  * •

Using BART to generate summaries that correspond to the queries in the QMSum
dataset

  * •

Using BART to generate summaries for the entire meeting transcripts in the
QMSum dataset

We first compared the performance of BART with that of the HMNet models. In
Zhang et al. (2021), the authors found that the overall performance of HMNet
is worst than BART. Therefore, we expect BART to perform better than the
simplified HMNet models explored. Second, we studied whether the performance
of BART is affected by the input length. In Zhang et al. (2021), the authors
found that the performance of the BART model decreases sharply when the
dialogue input becomes longer. They argue that this could be the result of
BART’s unique properties: pre-trained on the datasets with a limited length
(i.e., 1,024) and the input has to be truncated to fit the limitation. In the
QMSum dataset, the transcripts for the entire meeting are usually very long
(30 minutes to 1 hour meeting), while the relevant texts pans for each query
are much shorter. We expect to achieve similar results from Zhang et al.
(2021): BART performs better when generating summaries that correspond to the
queries (shorter input text) than generating summaries for the entire meeting
(longer input text).

##  6 Analysis

###  6.1 Query Embedding

We found that having the simplified HMNet model as the baseline, and embedding
queries into the model resulted in a slight improvement in the ROUGE scores.
Therefore, query embedding helps to improve performance of HMNet.

###  6.2 Pre-train with related data

We found that pre-training the model with randomly selected 10k CNN news
didn’t improve ROUGE scores. But pre-training the model with the most similar
15k CNN news with 15 epochs resulted in an improvement in the ROUGE scores.
However, the performance still didn’t beat the baseline. Pre-training the
model with the most similar 5k CNN news with 5 epochs, interestingly, led to a
significantly drop in ROUGE scores.

The fact that pre-training with CNN datasets didn’t help to improve HMNet
performance contradicts to our assumption. This might be caused by that the
size of the pre-training datasets was not large enough. Looking at the overall
results, it seems that ideally the pre-training would need to be performed
with a larger number of news articles but with only a small number of pre-
training epochs. When looking at the results of the different pre-training
data size/epoch combinations, the best combination was pre-training with the
most related 15k CNN news and 15 epochs of pre-training. The next logical step
would have been to use, for example, the most related 30k news and
experimenting with different numbers of pre-training epochs, which worth
further investigation.

Another reason why the pre-training approach didn’t work might be that the
authors of the original HMNet model took a different approach when setting up
the pre-training. They chose groups of each 4 news articles to build an
”artifical” meeting and in addition, shuffled the sentences of the news
articles. Furthermore, they performed the pre-training over the complete
CNN/Daily Mail and also XSum datasets with over 500k news articles.

###  6.3 Utterance-level information extraction

We found a performance improvement by using clustering methods to apply a
utterance-level information extraction and then apply the summarization model
over the meeting scripts. This finding confirmed that summarizing each
utterance first and then summarizing the summarized utterances could be give a
better meeting summarization result. The utterance-level summarization can
dropping unrelated stopping words from the scripts, and pick the most
important information from each utterance, and therefore lead to a better
result.

We tried another utterance-level information extraction by using the longest
sentence from each utterance as the input. We found that by simply using the
longest sentence from each utterance as the information extraction method
yield to a worse result. However, the result we got is still comparable to
that using the whole meeting scripts. We think this finding suggested that a
large portion of information is contained in the longest sentences of each
utterance, and therefore we got comparable results. However,because the key
information is not just included in the longest sentence but is contained
across the utterance, the overall performance is worse than the result using
the whole script. We think that to further confirm our finding, other
utterance-level information extraction methods are also worth trying to
further evaluate the impact of utterance-level information extraction.

###  6.4 BART as the summarizer

BART achieved a slightly better performance than the simplified HMNet model,
which is consistent as the observations in Zhang et al. (2021). When looking
at the performance of BART as the input length changes(table 3), our finding
is also consistent to Zhang et al. (2021): the performance of the BART model
is worse at generating summaries for the entire meeting (much longer dialogue
input) than generating summaries for text spans that correspond to queries
(shorter dialogue input).

##  7 Conclusion

In summary, we achieved small improvement of ROUGE scores by applying a
clustering algorithm to generate a word-graph of each utterance, condensing
the utterance into a shorter sentence by finding the best-path in the word-
graph, and using the shorter sentences as the transcript to be summarized.
This finding suggests that by using clustering algorithms to pick up the most
important words and phrases in each utterance, the performance of meeting
summarization would still be maintained or improved. This finding also
suggests that an additional first-stage clustering step over each utterance
would help yield better results for summarizing the whole meeting transcript.

We also found that pre-training the summarization model with related data in
the same domain could improve the performance of summarization. But this pre-
traing method requires a larger quantity of related data from the same domain
to show its effectiveness.

In addition, the performance of the BART model is affected by the input
length, and BART performs better at query-based meeting summarization with
QMSum than generating sumamries for the full meeting transcripts.

Also, despite the ROUGE scores, the generated texts still contain many
grammatical mistakes which result in poor readability.

## Acknowledgments

We would like to thank the staff of XCS224U course.

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# Lead Free Alloyed Double Perovskites: An Emerging Class of Materials from
Many-Body Perturbation Theory

Manjari Jain<EMAIL_ADDRESS>[MJ] Manish Kumar  Preeti Bhumla
Saswata Bhattacharya<EMAIL_ADDRESS>[

###### Abstract

The discovery of lead free all-inorganic alloyed double perovskites have
revolutionized photovoltaic research, showing promising light emitting
efficiency and its tunability. However, detailed studies regarding optical,
exciton, polaron and transport properties remain unexplored. Here, we report a
theoretical study on the variation of carrier-lattice interaction and
optoelectronic properties of pristine as well as alloyed Cs2AgInCl6 double
perovskites. We have employed many-body perturbation theory (G0W0@HSE06) and
density functional perturbation theory (DFPT) to compute exciton binding
energy (E${}_{\textrm{B}}$) and exciton lifetime of different alloyed double
perovskites. We find that phonon scattering limits charge-carrier mobilities
and thus, plays an important role in the development of high-efficiency
perovskite photovoltaics. In view of this, dominant carrier-phonon scattering
is observed via Fröhlich mechanism near room temperature. Moreover, we observe
a noticeable increase in hole and electron mobilities on alloying. We believe
that our results will be helpful to gain a better understanding of the
optoelectronic properties and lattice dynamics of these double perovskites.

+91-11-2659 1359 Indian Institute of Technology Delhi] Department of Physics,
Indian Institute of Technology Delhi, New Delhi, India

In a remarkably short period of time, lead halide perovskites have emerged in
an unprecedented way in the field of optoelectronics by virtue of their
exceptional properties like suitable optical band gap, long carrier diffusion
length, high carrier mobility and low manufacturing cost1, 2, 3, 4, 5, 6, 7,
8, 9. The power conversion efficiency of lead halide perovskites-based solar
cells has increased from 3.8% to 25.5% in the last decade10, 11. Despite their
great potential, there are two major challenges including Pb toxicity and
phase instability. The stability issues have been partly overcome by replacing
organic cation with inorganic cesium ion 12, 13. However, Pb toxicity is still
a drawback and dealing with this issue without compromising the efficiency is
of paramount importance.

Over the past few years, lead free all-inorganic double perovskites with
formula A2B′B′′X6 have emerged as possible contenders due to low toxicity,
intrinsic thermodynamic stability and small carrier effective mass 14, 15, 16,
17, 18, 19, 20, 21, 22, 23. In particular, the double perovskite Cs2AgInCl6
has been the subject of several studies, revealing excellent environmental
stability and promising optoelectronic properties. For example, Cs2AgInCl6
double perovskite exhibits a direct band gap as well as ultralong carrier
lifetime (6 $\mu$s), which are suitable for photovoltaic applications24, 25.
Moreover, Luo et al. reported that the alloying of Na cation in double
perovskite Cs2AgInCl6 increases the photoluminescence efficiency by three
orders and emits a warm white light with enhanced quantum efficiency 26. Also,
Cs2AgInCl6 has found to be successfully synthesized experimentally with the
direct band gap of 3.3 eV and good stability 27. However, the wide band gap of
Cs2AgInCl6 doesn’t show optical response in visible region. In order to reduce
its band gap and expand the spectral response in visible light region,
alloying with suitable elements could be the best solution. In one of our
recent works, we have done the sublattice mixing by partial substitution of
several metals M(I), M(II), M(III), and halogen X at Ag/In and Cl sites,
respectively, to reduce the band gap of Cs2AgInCl6 and hence, enhancing its
optical properties 28. We have found that sublattices with Br and I
substitutions at the Cl site, Cu(I) and Au(I) at the Ag site, Ga and Ir(III)
at the In site, and Zn(II) at the Ag and In sites simultaneously have tuned
the band gap in the visible region. In the present work, we have studied the
excitonic properties and the role of electron-phonon coupling in these
promising perovskites.

Formation of excitons in optoelectronic materials greatly influences the
charge separation properties. Hence, accurate estimation of excitonic
parameters viz. exciton binding energy, exciton radius and exciton lifetime is
of great importance in this class of materials. The excitons dissociate into
free charge carriers, which effect the solar cell performance. Moreover, in
order to explain multiple photophysical phenomena in perovskite materials, the
concept of polarons has been used. The polaronic effect plays a crucial role
in the excitaion dynamics and charge transport. The separation of free charge
carriers is also influenced by the carrier mobility, which in turn depends on
the electron-phonon (e-ph) coupling strength. Understanding the effect of
electron-phonon coupling in terms of polaron mobility is important. In view of
this, we attempt here to explore electronic and optical properties of
Cs2AgInCl6 and its alloyed counterparts using state-of-the-art many-body
perturbation theory. Various important aspects such as excitonic properties,
carrier mobility, the role of electron-phonon coupling have been studied
presumably for the first time in this class of materials. Using Fröhlich
model, we have also discussed the effect of electron-phonon coupling and
calculated the polaron mobility.

Figure 1: (a) Crystal structure of Cs2AgInCl6 double perovskite and (b)
bandstructure of Cs2AgInCl6 using G0W0@HSE06. E${}_{\textrm{f}}$ is fermi
energy level.

According to Wannier-Mott model 29, the exciton binding energy
(E${}_{\textrm{B}}$) for screened interacting electron-hole (e-h) pair is
given by:

$\begin{split}\textrm{E}_{\textrm{B}}=\left(\frac{\mu}{\epsilon_{\textrm{eff}}^{2}}\right)\textrm{R}_{\infty}\end{split}$
(1)

where, $\mu$ is the reduced mass, $\epsilon_{\textrm{eff}}$ is the effective
dielectric constant and R∞ is the Rydberg constant. In order to compute
E${}_{\textrm{B}}$, firstly we have calculated the effective mass of electrons
and holes using Wannier-Mott approach by plotting E-k dispersion curve (see
Fig. 1(b) for pristine Cs2AgInCl6 and for different alloyed compounds, see
section I of supplementary information (SI)). The conduction band minimium
(CBm) and valence band maximum (VBM) are obtained at high symmetry point
$\Gamma$ (0, 0, 0). We have done the parabolic fitting of the dispersion
curves for calculating the effective mass of the electrons and holes. Further,
we have taken the average of effective mass values from $\Gamma$ $\rightarrow$
L and $\Gamma$ $\rightarrow$ X directions. The effective mass can be
calculated by using expression:

$\begin{split}\textrm{m}^{*}=\frac{\hbar^{2}}{\frac{d^{2}\textrm{E}(k)}{dk^{2}}}\end{split}$
(2)

where m∗, E(k), k, and $\hbar$ are the effective mass, energy, wave vector and
reduced Planck’s constant, respectively. The calculated effective mass and
reduced mass in terms of rest mass of electron (m0) for pristine Cs2AgInCl6
double perovskite and different alloyed compounds are listed in Table 1. The
obtained values of effective mass and reduced mass for Cs2AgInCl6 double
perovskite are well in agreement with the previous findings 30.

Table 1: Effective mass of electron m${}_{\textrm{e}}^{\ast}$, hole m${}_{\textrm{h}}^{\ast}$ and reduced mass $\mu$ in terms of rest mass of electron m0. Compounds | ${\textrm{m}_{\textrm{e}}^{*}}$ | ${\textrm{m}_{\textrm{h}}^{*}}$ | ${\mu}$
---|---|---|---
Cs2AgInCl6 | 0.29 | 1.07 | 0.23
Cs2AgInBr0.04Cl5.96 | 0.28 | 0.80 | 0.21
Cs2AgInI0.04Cl5.96 | 0.26 | 0.67 | 0.19
Cs2Au0.25Ag0.75InCl6 | 0.25 | 0.80 | 0.19
Cs2Cu0.25Ag0.75InCl6 | 0.27 | 1.09 | 0.22
Cs2AgGa0.25In0.75Cl6 | 0.27 | 0.84 | 0.21
Cs2AgIr0.25In0.75Cl6 | 0.29 | 0.86 | 0.22
Cs2Zn0.50Ag0.75In0.75Cl6 | 0.28 | 0.83 | 0.21

Now, our next task is to compute $\epsilon_{\textrm{eff}}$ in order to find
the exciton binding energy of pristine Cs2AgInCl6 and different alloyed
compounds. As it is reported earlier that the E${}_{\textrm{B}}$ gets changed
due to the lattice relaxation 31 i.e., if $\omega_{\textrm{LO}}$ is the
longitudinal optical phonon frequency and
E${}_{\textrm{B}}$$<<$$\hbar\omega_{\textrm{LO}}$, then one needs to consider
lattice relaxation. Therefore, a value intermediate between the static
electronic dielectric constant at high-frequency
($\epsilon_{\textrm{$\infty$}}$) and the static ionic dielectric constant at
low frequency ($\epsilon_{\textrm{static}}$) should be considered for the
$\epsilon_{\textrm{eff}}$. However, if
E${}_{\textrm{B}}$$>>$$\hbar\omega_{\textrm{LO}}$ then the ionic contribution
to the dielectric screening is negligible and, hence does not alter the
E${}_{\textrm{B}}$ 32. In such cases, $\epsilon_{\textrm{eff}}$ $\rightarrow$
$\epsilon_{\textrm{$\infty$}}$, where $\epsilon_{\textrm{$\infty$}}$ is the
static value of dielectric constant at high frequency that mainly consists of
electronic contribution.

Figure 2: (a) Electronic contribution to the dielectric function and (b) ionic
contribution to the dielectric function of pristine Cs2AgInCl6 and different
alloyed compounds.

In Fig. 2(a), we have shown the electronic contribution of the dielectric
function calculated using G0W0@HSE06 and in Fig. 2(b), we have plotted the
ionic contribution to the dielectric function computed using DFPT approach.
The value of $\epsilon_{\textrm{$\infty$}}$ and $\epsilon_{\textrm{static}}$
for pristine Cs2AgInCl6 double perovskite are 2.05 and 9.63, respectively,
which are well in agreement with the obtained values in previous reports 28,
33. Also from Fig. 2(b), we have observed that the value of
$\epsilon_{\textrm{static}}$ for the alloyed compounds is less than the
pristine Cs2AgInCl6, which implies that the ionic contribution to the
dielectric constant in case of alloyed compounds is less prominent than the
pristine Cs2AgInCl6. Now, using reduced mass (provided in Table 1) and the
dielectric constants, we have determined the upper and lower bounds of
E${}_{\textrm{B}}$ using Eq 1, listed in Table 2.

Table 2: Upper bound (E${}_{\textrm{Bu}}$) and lower bound
(E${}_{\textrm{Bl}}$) on exciton binding energy E${}_{\textrm{B}}$ for double
perovskites.

Compounds $\epsilon_{\textrm{$\infty$}}$ E${}_{\textrm{Bu}}$ (eV)
$\epsilon_{\textrm{static}}$ E${}_{\textrm{Bl}}$ (eV) Cs2AgInCl6 2.05 0.74
9.63 0.03 Cs2AgInBr0.04Cl5.96 2.06 0.67 6.90 0.06 Cs2AgInI0.04Cl5.96 2.09 0.59
5.25 0.09 Cs2Au0.25Ag0.75InCl6 2.10 0.58 5.64 0.08 Cs2Cu0.25Ag0.75InCl6 2.07
0.70 3.71 0.21 Cs2AgGa0.25In0.75Cl6 2.05 0.68 4.71 0.12 Cs2AgIr0.25In0.75Cl6
2.09 0.87 3.72 0.27 Cs2Zn0.50Ag0.75In0.75Cl6 2.05 0.68 4.01 0.17

By knowing the exciton binding energy, dielectric function, and reduced mass,
we can calculate the various excitonic parameters such as exciton radius
(r${}_{\textrm{exc}}$) and the probability of a wavefunction
($|\phi_{\textrm{n}}(0)|^{2}$) at zero charge separation (given in Table 3).
The exciton radius ($\textrm{r}_{\textrm{exc}}$) is calculated as follows:

$\textrm{r}_{\textrm{exc}}=\frac{\textrm{m}_{0}}{\mu}\varepsilon_{\textrm{eff}}\,\textrm{n}^{2}\textrm{r}_{\textrm{Ry}}$
(3)

where $\textrm{m}_{0}$ is the free electron mass, $\mu$ is the reduced mass,
$\varepsilon_{\textrm{eff}}$ is the effective dielectric constant (here, the
electronic dielectric constant has been taken), n is the exciton energy level
(n=1 provides the smallest exciton radius) and
$\textrm{r}_{\textrm{Ry}}=0.0529$ nm is the Bohr radius. For electron-hole
pair at zero seperation, the exciton lifetime ($\tau$) is inversely
proportional to the probability of a wavefunction
($|\phi_{\textrm{n}}(0)|^{2}$). The $|\phi_{\textrm{n}}(0)|^{2}$ is determined
as follows:

$|\phi_{\textrm{n}}(0)|^{2}=\frac{1}{\pi(\textrm{r}_{\textrm{exc}})^{3}\textrm{n}^{3}}$
(4)

Table 3: Excitonic parameters of Cs2AgInCl6 and different alloyed compounds. Compounds | r${}_{\textrm{exc}}$ (nm) | |$\phi$${}_{\textrm{n}}$(0)|2 (1027m-3)
---|---|---
Cs2AgInCl6 | 0.47 | 2.96
Cs2AgInBr0.04Cl5.96 | 0.53 | 2.18
Cs2AgInI0.04Cl5.96 | 0.59 | 1.54
Cs2Au0.25Ag0.75InCl6 | 0.56 | 1.81
Cs2Cu0.25Ag0.75InCl6 | 0.50 | 2.54
Cs2AgGa0.25In0.75Cl6 | 0.53 | 2.13
Cs2AgIr0.25In0.75Cl6 | 0.49 | 2.87
Cs2Zn0.50Ag0.75In0.75Cl6 | 0.51 | 2.39

From Table 3, it is observed that the alloyed compounds have longer exciton
lifetime than the pristine Cs2AgInCl6 double perovskite. The longer exciton
lifetime corresponds to lower recombination, which leads to higher quantum
yield and conversion efficiency 34. Hence, the different alloyed compounds,
having longer exciton lifetime than the pristine Cs2AgInCl6, are good for
solar cells and photovoltaic devices.

In order to calculate the charge carrier mobility, we have used deformation
potential model proposed by Bardeen and Shockley 35. According to this model,
the charge carrier mobility ($\mu$) for 3D materials can be expressed as:

$\begin{split}\mu=\frac{2\sqrt{2\pi}e\hbar^{4}\textrm{C}_{\textrm{3D}}}{3(k_{\textrm{B}}\textrm{T})^{3/2}(\textrm{m}^{*})^{5/2}\textrm{E}_{l}^{2}}\end{split}$
(5)

where $k_{\textrm{B}}$ is the Boltzmann constant, T is the temperature, and e
is the elementary charge of electron (for more details, see section II of SI).
We can see from Eq. 5, the effective mass has a significant effect on the
carrier mobility. Due to the intrinsic cubic structure, the pristine
Cs2AgInCl6 and different alloyed compounds show an isotropic transport
character. From Table 1, it can be seen that the hole effective mass is nearly
3 times larger than that of the electron, which implies that electron
transport ability is better than hole transport ability.

Figure 3: (a) Relationship between total energy and the applied strain along
the transport direction (z-axis) (b) Band energy shifts of VBM and CBm under
uniaxial strain for Cs2AgInCl6. Table 4: Calculated deformation potential
constant ($\textrm{E}_{l}$), 3D elastic constant ($\textrm{C}_{\textrm{3D}}$),
and carrier mobility ($\mu$) for electrons and holes along the transport
direction (z-axis) of different configurations at 300 K.

Compounds Carrier type El (eV) C${}_{3\textrm{D}}$ (Nm-2) $\mu$ (cm2V-1s-1)
Cs2AgInCl6 electron 11.71 67.48 665.38 hole 10.66 67.48 30.68
Cs2AgInBr0.04Cl5.96 electron 11.69 70.81 730.98 hole 11.26 70.81 59.21
Cs2AgInI0.04Cl5.96 electron 11.83 76.72 965.19 hole 11.91 76.72 90.05
Cs2Au0.25Ag0.75InCl6 electron 11.57 67.25 909.88 hole 10.69 67.25 63.79
Cs2Cu0.25Ag0.75InCl6 electron 11.54 62.43 765.15 hole 9.78 62.43 31.98
Cs2AgGa0.25In0.75Cl6 electron 11.47 66.75 804.62 hole 10.36 66.75 59.06
Cs2AgIr0.25In0.75Cl6 electron 11.53 72.08 673.36 hole 8.57 72.08 88.10
Cs2Zn0.50Ag0.75In0.75Cl6 electron 11.38 58.97 672.35 hole 10.31 58.97 53.86

Further, along with effective mass, the carrier mobility also depends on 3D
elastic constant $\textrm{C}_{\textrm{3D}}$ and deformation potential
$\textrm{E}_{l}$. In order to compute $\textrm{C}_{\textrm{3D}}$ and
$\textrm{E}_{l}$, uniaxial strain has been applied along the lattice direction
(z-axis). The total energies and positions of the VBM and CBm are calculated
with respect to the uniaxial strain using PBE xc functional. These values are
also calculated using HSE06 xc functional for Cs2AgInCl6 and
Cs2Cu0.25Ag0.75InCl6, which are comparable with PBE xc functional (see section
III of SI for comparison). Therefore, we have used PBE xc functional as it is
computationally more cost effective. Now, $\textrm{C}_{\textrm{3D}}$ can be
obtained by fitting the energy vs strain curve and $\textrm{E}_{l}$ is
proportional to the band edge shift induced by applied strain along the
transport direction (see Fig. 3 for Cs2AgInCl6). Subsequently, based on the
obtained values of m∗, $\textrm{C}_{\textrm{3D}}$ and $\textrm{E}_{l}$, the
electron mobility comes out to be 665.38 cm2V-1s-1 and the hole mobility is
30.68 cm2V-1s-1 for Cs2AgInCl6. The obtained hole mobility is quite well in
agreement with the previous finding 36. Note that, the electron mobility is
about 20 times higher than that of the hole mobility. Further, for the alloyed
compounds, we have observed increment in carrier mobilities in comparison to
pristine Cs2AgInCl6 (see Table 4). This demonstrates excellent photovoltaic
properties for the alloyed compounds than the pristine (For more details of
$\textrm{C}_{\textrm{3D}}$ and $\textrm{E}_{l}$ for alloyed compounds, see
section IV in SI).

Table 5: Polaron parameters corresponding to electrons in pristine Cs2AgInCl6 and different alloyed compounds. Compounds |  $\omega_{\textrm{LO}}$ (THz) |  $\theta_{\textrm{D}}$ (K) | $\alpha_{\textrm{e}}$ |  $\textrm{m}_{\textrm{P}}$/$\textrm{m}^{*}$ | l${}_{\textrm{P}}$ (Å) |  $\mu_{\textrm{P}}$ (cm2V-1s-1)
---|---|---|---|---|---|---
Cs2AgInCl6 | 4.49 | 215 | 5.59 | 2.71 | 28.73 | 8.54
Cs2AgInBr0.04Cl5.96 | 5.86 | 281 | 4.26 | 2.16 | 40.48 | 13.44
Cs2AgInI0.04Cl5.96 | 5.85 | 280 | 3.48 | 1.88 | 45.09 | 21.42
Cs2Au0.25Ag0.75InCl6 | 5.60 | 268 | 3.62 | 1.93 | 42.75 | 21.17
Cs2Cu0.25Ag0.75InCl6 | 5.69 | 273 | 2.66 | 1.62 | 50.75 | 32.53
Cs2AgGa0.25In0.75Cl6 | 5.36 | 257 | 3.54 | 1.90 | 41.85 | 20.81
Cs2AgIr0.25In0.75Cl6 | 5.12 | 245 | 2.86 | 1.68 | 45.24 | 28.35
Cs2Zn0.50Ag0.75In0.75Cl6 | 3.07 | 147 | 4.13 | 2.11 | 25.56 | 21.60

The influence of electron-phonon coupling on physical/chemical properties of a
material remains an alluring paradox. It has been reported that in case of
polar semiconductors (e.g., halide perovskites), the interaction of carriers
with the macroscopic electric field generated by longitudinal optical (LO)
phonons, known as the Fröhlich interaction is the dominating scattering
mechanism near room temperature 37, 38. In order to find the reason behind the
discrepancy in mobility between theory and experiment, Fröhlich’s polaron
model is observed to be a remarkable model. Using this model, here we have
investigated the electron-phonon coupling in Cs2AgInCl6 and different alloyed
compounds and estimated an upper limit on the related charge carrier
mobilities. The dimensionless Fröhlich parameter $\alpha$ of dielectric
electron-phonon coupling which can be seen as a comparative measure of
Fröhlich coupling strength is given as

$\begin{split}\alpha=\frac{1}{4\pi\epsilon_{0}}\frac{1}{2}\left(\frac{1}{\epsilon_{\infty}}-\frac{1}{\epsilon_{\textrm{static}}}\right)\frac{{e}^{2}}{\hbar\omega_{\textrm{LO}}}\left({\frac{2\textrm{m}^{*}\omega_{\textrm{LO}}}{\hbar}}\right)^{1/2}\end{split}$
(6)

This parameter $\alpha$ is fully defined by the material specific properties,
specifically, optical ($\epsilon_{\infty}$) and static
($\epsilon_{\textrm{static}}$) dielectric constants, the carrier effective
mass ($\textrm{m}^{*}$), and a characteristic phonon angular frequency
($\omega_{\textrm{LO}}$). For a system with multiple phonon branches, an
average LO frequency can be calculated by considering all the infrared active
optical phonon branches and taking a spectral average of them 39.
$\epsilon_{0}$ is the permittivity of free space. We observe that due to an
increase in high frequency dielectric constant, the Fröhlich scattering
strength in alloyed compounds is reduced (see Table 5). Note that, the value
of $\alpha$ remains in the moderate strength range, and comparable to the
hybrid halide perovskite series 40. Further, the Debye temperature
($\theta_{\textrm{D}}$) of effective LO frequency comes out to be 215 K for
pristine Cs2AgInCl6. Similarly, for the different alloyed systems as well, the
Debye temperature is well below the room temperature and hence, suggests
dominant polaronic contribution to limit carrier mobility near room
temperature.

From the above discussion, we have found that these materials possess large
dielectric electron-phonon coupling. Polarons are dressed quasiparticles,
which are formed due to the interaction of electron and hole with the lattice.
Within Fröhlich’s polaron theory, as extended by Feynman, the polaron mass
renormalisation for polaron, ${\textrm{m}_{\textrm{p}}}$ 41 can be calculated
as

$\begin{split}{\textrm{m}_{\textrm{P}}}=\textrm{m}^{*}\left(1+\frac{\alpha}{6}+\frac{\alpha^{2}}{40}\right)\end{split}$
(7)

Further, the polaron radius can be calculated as

$\begin{split}\textrm{l}_{\textrm{P}}=\sqrt{\frac{h}{2\textrm{c}\textrm{m}^{*}\omega_{\textrm{LO}}}}\end{split}$
(8)

where, c is the speed of light. Our calculated polaron mass renormalisation
and the corresponding polaron radius are listed in Table 5. Notably, these
parameters can be used to estimate an upper limit on charge carrier mobilities
under the assumption that carriers are interacting only with the optical
phonons. Now, the polaron mobility according to the Hellwarth polaron model 39
is defined as follows:

$\begin{split}\mu_{\textrm{P}}=\frac{(3\sqrt{\pi}e)}{2\pi\textrm{c}\omega_{\textrm{LO}}\textrm{m}^{*}\alpha}\frac{\textrm{sinh}{(\beta/2)}}{\beta^{5/2}}\frac{w^{3}}{v^{3}}\frac{1}{\textit{K}}\end{split}$
(9)

where, $\beta$ = hc$\omega_{\textrm{LO}}$/$k_{\textrm{B}}$T, w and v
correspond to temperature dependent variational parameters. K is a function of
v, w, and $\beta$. Here, we have calculated w and v by minimizing the free
polaron energy (see section V in SI for details). The obtained upper limits on
the charge carrier mobilities at room temperature are listed in Table 5. From
Table 5, one can find that in case of pristine Cs2AgInCl6 and different
alloyed compounds, large polarons [$\textrm{l}_{\textrm{P}}$ $>>$ lattice
parameter] will be formed. This leads to increased carrier lifetime due to the
reduction in carrier-carrier and carrier-defect scatterings 42. Large polarons
can be effectively seen as quasicharge carriers possessing higher effective
masses than the original carriers, thus practically reducing the carrier
mobility. In case of pristine Cs2AgInCl6, our estimated polaron mobility is
8.54 cm2V-1s-1, which suggests the dominant role of electron-phonon coupling
here. We have also found polaronic mass to be 2.71 times of the effective mass
of electron, which confirms the increased carrier lattice interaction.
Further, in case of alloyed compounds, we have observed substantial reduction
in electronic effective mass and polaronic mass renormalization (see Table 5).
As such, the limit to the electron mobility increases almost 2-4 times, in
case of alloyed compounds. We have discussed the hole mobility as well (for
reference, see SI section VI). From the above discussion, we infer that the
reduction in effective mass and increase in dielectric constant will largely
improve the carrier mobility and ensure a better screening against ionized
impurities in different alloyed compounds compared to pristine Cs2AgInCl6.
This shows the higher overall carrier mobility in different alloyed compounds.

In summary, using first-principles calculation, the excitonic, and polaronic
properties of pristine Cs2AgInCl6 and different alloyed double perovskites are
investigated systematically. Initially, using Wannier-Mott approach, we have
computed the upper and lower bound of exciton binding energy. After that, from
the exciton lifetime calculation, we have found that the alloyed compounds
have longer exciton lifetime than the pristine Cs2AgInCl6. Further, the
deformation potential approach reveals substantial increase in the charge
carrier mobility on alloying. Using the Feynman polaron model, we have
discussed the carrier-lattice interaction in these materials. Careful analysis
of carrier effective mass, electronic and ionic dielectric constant and
effective LO frequency help us to address the electron-phonon coupling. The
detailed theoretical investigation presented in this work will surely help the
future studies to improve the overall performance of double perovskites.

##  1 Computational Methods

The density functional theory (DFT) 43, 44 calculations have been performed
using the Vienna ab initio simulation package (VASP) 45, 46. The ion-electron
interactions in all the elemental constituents are described using projector-
augmented wave (PAW) potentials 47, 46. The double perovskite Cs2AgInCl6 has a
cubic structure with space group Fm$\bar{3}$m. The corresponding sublattice is
composed of alternate octahedra of InCl6 and AgCl6 as shown in Fig. 1(a). All
the structures are optimized (the atomic positions are relaxed) using
generalized gradient approximation of PBE 48 as the exchange-correlation (xc)
functional until the forces are smaller than 0.001 eV/Å. The electronic self
consistency loop convergence is set to 0.01 meV, and the kinetic energy cutoff
is set to 600 eV for plane wave basis set expansion. A k-grid of $4\times
4\times 4$ is used for Brillouin zone integration, which is generated using
Monkhorst-Pack 49 scheme. Advanced hybrid xc functional HSE06 50 is used for
the better estimation of band gap. For determination of optical properties,
single shot GW (G0W0) 51, 52 calculations have been performed on top of the
orbitals obtained from HSE06 xc functional. The polarizability calculations
are carried out on a grid of 50 frequency points. The number of bands is set
to four times the number of occupied orbitals. Note that spin orbit coupling
was not taken into consideration here because it negligibly affects the
electronic structures of Ag/In halide double perovskites 25, 53. The ionic
contribution to dielectric function has been calculated using density
functional perturbation theory (DFPT) 54 with $7\times 7\times 7$ k-grid.
Carrier mobilities are simulated via implementing a temperature dependent
Feynman polaron model 55. A detailed description of the model along with the
necessary parameters needed can be found in Ref 55, 56, 57. MJ acknowledges
CSIR, India, for the senior research fellowship [grant no.
09/086(1344)/2018-EMR-I]. MK acknowledges CSIR, India, for the senior research
fellowship [grant no. 09/086(1292)/2017-EMR-I]. PB acknowledges UGC, India,
for the senior research fellowship [1392/(CSIR-UGC NET JUNE 2018)]. SB
acknowledges the financial support from SERB under core research grant (grant
no. CRG/2019/000647). We acknowledge the High Performance Computing (HPC)
facility at IIT Delhi for computational resources. Electronic bandstructure of
different alloyed compounds using G0W0@HSE06; Free charge carrier mobility
using deformation potential model; Comparison of charge carrier mobility using
PBE and HSE06 exchange-correlation (xc) functional; Deformation potential
constant ($\textrm{E}_{l}$) and 3D elastic constant
($\textrm{C}_{\textrm{3D}}$) for alloyed compounds; Polaron mobility using
Feynman polaron model; Polaron parameters for holes.

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