Claude Pasquier
email: claude.pasquier@univ-cotedazur.fr

Alain Robichon

Computational search of hybrid human/ SARS-CoV-2 dsRNA reveals unique viral sequences that diverge from other coronavirus strains

published or not. The documents may come

Introduction

Two restraint scale epidemics occurred already in the recent past caused by two coronaviruses: the severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS) [START_REF] Wu | A new coronavirus associated with human respiratory disease in China[END_REF][START_REF] Zhou | A pneumonia outbreak associated with a new coronavirus of probable bat origin[END_REF].

The third recent new viral outbreak causing a fast propagating pandemic is provoked by a new coronavirus, named SARS-CoV-2, that exhibits terrifying spread out of control. Metagenomic sequencing along with the phylogenetic analysis of the virus from a sample of broncho-alveolar lavage fluid of an infected patient have been performed [START_REF] Wu | A new coronavirus associated with human respiratory disease in China[END_REF][START_REF] Zhou | A pneumonia outbreak associated with a new coronavirus of probable bat origin[END_REF]. The high homology of the predicted protein of the RBD domain of the spike protein with the precedent SARS-CoV hints that the human angiotensin-converting enzyme 2 (ACE2) acts as a receptor for fixation and entry to human host cells [START_REF] Wrapp | Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation[END_REF][START_REF] Letko | Functional assessment of cell entry and receptor usage for SARS-CoV-2 and other lineage B betacoronaviruses[END_REF]. Inside mammal infected host cells, the role of RNAi machinerie to degrade virus is debated. In fungi, plants and invertebrates, the viral dsRNAs are trapped and cleaved by Dicer/Ago machinerie into small interfering RNAs (siRNAs) that degrade the targeted viral messenger RNAs within the RNA-induced silencing complex (RISC) [START_REF] Aliyari | RNA-based viral immunity initiated by the Dicer family of host immune receptors[END_REF]. In mammals/humans the detection of virus-derived small RNAs has been mainly undetectable upon RNA virus infection [START_REF] Umbach | The role of RNAi and microRNAs in animal virus replication and antiviral immunity[END_REF]. The unique Dicer in humans processed long double-stranded RNA (dsRNA) and hairpin dsRNA into small interfering RNAs (siRNAs) and microRNAs respectively but its role as producer of antiviral

RNAis is yet far to be admitted by many authors. However, mammalian viruses were successfully eliminated and replication inhibited in cultured host cells via synthetic small interfering RNAs (siRNAs) [START_REF] Umbach | The role of RNAi and microRNAs in animal virus replication and antiviral immunity[END_REF]. In mammals, a powerful and non-sequence-specific synthesis of interferon (IFN) appears the major molecular weapon to fight RNA viruses [START_REF] Sadler | Interferon-inducible antiviral effectors[END_REF]. This effector response might have overwhelmed the initial RNAi role, which is inferred by the rare accumulation of virus-derived small RNAs (vsRNAs) in few mammal host cells for which any specified functions have been found [START_REF] Sadler | Interferon-inducible antiviral effectors[END_REF][START_REF] Koshiba | Mitochondrial mediated antiviral immunity[END_REF][START_REF] Berkhout | RNAi-mediated antiviral immunity in mammals[END_REF]. The question whether RNA virus infection of mammalian cells can trigger an effective and powerful antiviral RNAi weapon remains unknown and little documented as no siRNAs of viral origin were experimentally found in mammal infected cells in contrast with the observations in plants and invertebrates [START_REF] Koshiba | Mitochondrial mediated antiviral immunity[END_REF][START_REF] Berkhout | RNAi-mediated antiviral immunity in mammals[END_REF]. The absence of virus specific siRNAs in mammal cells remains presently a puzzling observation for which an explanation could be the scarcity of intra RNA pairing offered by the virus genomes. In the past weeks we proceeded to a computational search of the SARS-CoV-2 full RNA sequence to explore whether short readings presenting perfect match in reverse complementary strand with RNA candidates from the full human transcriptome might exist.

We also examined the possibilities of intra pairing within the full SARS-CoV-2 RNA at a minimum 20 bases length. Comparative studies were conducted with the SARS-CoV, the MERS-CoV along with two non-virulent coronaviruses (HCoV-229E and HCoV-OC43). The purpose of this searching was guided by the hypothesis that hybrid duplex RNA (one strand from human transcriptome, the other from SARS-CoV-2) could be theoretically formed and consequently might lead to degradation of RNA targets not only in SARS-CoV-2 but more importantly, the other way around, in the human transcriptome.

Dicer can trap dsRNAs pairing over a 19-base length with at least a 2 nt overhang at the 3' ends and can then directly transfer the modified/unmodified siRNA to the Ago2 site [START_REF] Snead | Molecular basis for improved gene silencing by Dicer substrate interfering RNA compared with other siRNA variants[END_REF][START_REF] Snead | RNA Interference Trigger Variants: Getting the Most Out of RNA for RNA Interference-Based Therapeutics[END_REF][START_REF] Sun | Asymmetric RNA duplexes mediate RNA interference in mammalian cells[END_REF]. This mechanism has been further demonstrated with fluorometric dsRNA [START_REF] Bernard | Dicer-Argonaute2 Complex in Continuous Fluorogenic Assays of RNA Interference Enzymes[END_REF]. Some paired 19-mers with a dTdT overhang at the 3' end bind Dicer with high affinity; these sequences are not cleaved by Dicer, are fully transferred to Ago and trigger high-efficiency gene silencing activity [START_REF] Snead | Molecular basis for improved gene silencing by Dicer substrate interfering RNA compared with other siRNA variants[END_REF][START_REF] Snead | RNA Interference Trigger Variants: Getting the Most Out of RNA for RNA Interference-Based Therapeutics[END_REF].

Dicer also binds single RNAs at a specific site with high affinity, the function of which is to accelerate hybridization with a partner from the "soup" of RNA metabolism [START_REF] Kurzynska-Kokorniak | Revealing a new activity of the human Dicer DUF283 domain in vitro[END_REF]. Authors have also shown that the pairing length can be as short as 16 nt, with a several-base overhang at the 3' end to fully bind to Dicer and consecutively to activate Ago in the RISC context [START_REF] Snead | Molecular basis for improved gene silencing by Dicer substrate interfering RNA compared with other siRNA variants[END_REF][START_REF] Snead | RNA Interference Trigger Variants: Getting the Most Out of RNA for RNA Interference-Based Therapeutics[END_REF][START_REF] Sun | Asymmetric RNA duplexes mediate RNA interference in mammalian cells[END_REF]. In this study, a pairing length for computational searching was set minimally to 20 bases, which leads to 24 mers considering the 2nt overhang in both 3' extremities for Dicer cleavage specificity. Exact duplex at and/or above 20 bases length coming from intra annealing of viral RNA were not found although the possibilities of imperfect or very short pairing length exist. Inversely the computational search of hybrid pairing RNAs has retrieved few human genes related to ubiquitin metabolism and two long non coding RNAs. This observation validate the hypothesis that RISC/Ago might be fueled by diverse source of RNAi, byproducts of the action of Dicer, originated from hybrid and asymmetric RNA duplex, one strand coming from host and the other from the virus.

Results

List of human transcripts theoretically duplexing with SARS-CoV-2 RNA

Short segments of SARS-CoV-2 RNAs that are potential sources of siRNA by hybridization with human RNAs were computationally found, which identified the transcripts of 7 coding human genes that are complementary to a segment of SARS-CoV-2 RNA. Results are summarized in Table 1 and the full list of pairing transcript isoforms is shown in Table S1. Among the human genes, we noticed the presence of DNAJC13 (which regulates endosomal membrane trafficking [START_REF] Yoshida | Parkinson's disease-linked DNAJC13 mutation aggravates alpha-synucleininduced neurotoxicity through perturbation of endosomal trafficking[END_REF]), FBXO21 (a F-box protein that is one of the four subunits of ubiquitin protein ligase complex [START_REF] Yu | Lys29-linkage of ASK1 by Skp1-Cullin 1-Fbxo21 ubiquitin ligase complex is required for antiviral innate response[END_REF]), FLRT2 (encodes a fibronectin leucine rich transmembrane), ELP4 (encodes an histone acetyltransferase, a subunit associated with RNA polymerase type II), USP31 (an ubiquitin specific peptidase that has been described to activate transcription factor NF-kappaB that stimulates interferon synthesis [START_REF] Tzimas | Human ubiquitin specific protease 31 is a deubiquitinating enzyme implicated in activation of nuclear factor-kappaB[END_REF]) and USP30 (a mitochondrial ubiquitin specific peptidase [START_REF] Cunningham | USP30 and parkin homeostatically regulate atypical ubiquitin chains on mitochondria[END_REF]). The segment of USP30 RNA having a reverse complement in SARS-CoV-2 RNA was found exclusively in humans, which highlights the unexpected and intriguing specificity of this coronavirus. The viral pairing sequences are originating from 3 putative open reading frames (orf): orf1a/b, Spike and orf3b. In a recent study, Chan et al., show that there are no remarkable differences between orf1a/b in SARS-CoV-2 with the one in SARS-CoV [START_REF] Chan | Genomic characterization of the 2019 novel human-pathogenic coronavirus isolated from a patient with atypical pneumonia after visiting Wuhan[END_REF], the major distinction being located in orf3b, Spike and orf8. The authors note that orf3a encodes a completely novel short protein that may have a role in viral pathogenicity. Orf3a also includes the 20-base sequence that potentially targets the ubiquitin specific peptidase 30 (USP30). The complementary sequence segment of USP30 within the SARS-CoV-2 was found only in this coronavirus strain whereas the corresponding USP30 segment was not found in other mammal species.

List of human transcripts theoretically duplexing with RNA of other coronaviruses

The same type of analysis was conducted with other Coronaviridae for comparison: SARS-CoV (having caused the precedent China pandemic), MERS-CoV and two no virulent strains (HCoV-229E and HCoV-OC43). Results are shown in Tables 234and Table S1. We notice that each strain presents a unique set of sequences of 20 bases length matching in reverse complement with human transcripts and these unique sets target no human genes in common. Remarkably, SARS-CoV mostly targets ncRNAs (Table 2 andTable S1). MERS targets an histone methyltransferase (KMT2C) and a miscRNA included in this gene; a small GTPase of the Rho-subfamily (CDC42); an ubiquitin protein ligase (ARH1); a calcium activated chloride channels (ANO9); a voltage and calcium-sensitive potassium channel (KCNMA1) and finally an adhesion glycoprotein (THBS3) (Table 3 and Table S1). Regarding the no virulent coronavirus (HCoV-229E and HCoV-OC43), few human genes are potentially targeted by viral RNA sequences, among them few no coding RNAs for which a role in defense against viral infection is not documented. The few coding genes do not appear to qualify for GO annotation of cellular signaling susceptible to be altered by the virus infection (see NCBI database for information).

Theoretical hybrid human/ SARS-CoV-2 dsRNA are related to ubiquitin pathway and mitochondria

Upon RNA viral infection, the RNA helicases (RIG-I and MDA-5) binds virus-derived RNAs [START_REF] Takeuchi | Innate immunity to virus infection[END_REF][START_REF] Iwasaki | Regulation of adaptive immunity by the innate immune system[END_REF][START_REF] Fujita | RNA recognition and signal transduction by RIG-I-like receptors[END_REF]. The complexes then translocate at the outer mitochondrial membrane by binding with MAVS (mitochondrial antiviral signaling). The bound MAVS acting as scaffold protein recruits downstream effectors to form a "MAVS signalosome" of which the major function resides in drastically inducing the stimulation of the NF-κB and I B and IRF-3 factors; a molecular scenario well documented in viral infection of host mammal cells [START_REF] Sun | The specific and essential role of MAVS in antiviral innate immune responses[END_REF]. Mitochondria appear to constitute a hub of communication that implicates a cascade of effector molecules recruited for antiviral defense [START_REF] Sun | The specific and essential role of MAVS in antiviral innate immune responses[END_REF]. Regarding the humans genes targeted by SARS-CoV-2, we observe the presence of USP30 a deubiquitinase specific of mitochondria and FBXO21which is a subunit in an ubiquitin protein ligase complex. Remarkably FBXO21 ubiquitin ligase complex has been reported to be required for antiviral innate response [START_REF] Yu | Lys29-linkage of ASK1 by Skp1-Cullin 1-Fbxo21 ubiquitin ligase complex is required for antiviral innate response[END_REF]. The host ubiquitin system is known to be crucial in innate immunity, the host E3-ubiquitin ligase having clearly antiviral functions [START_REF] Rajsbaum | The host ubiquitin system in innate immunity and virus replication: proviral and antiviral functions of the host E3-ubiquitin ligase TRIM family[END_REF]. Putatively dsRNAs, hybrid forms with one strand coming from human transcriptome and the other from viral RNA might have the unfortunate role to direct the Dicer/ago/RISC defense system against its own host.

Philogenetic analysis of the 20 bases length of RNA sequences between coronaviruses strains and between mammal species

We conducted the comparison of the RNA segments within the ortholog genes of numerous vertebrate species with a particular emphasis placed on the class of primates. Results are shown in figure 1 and Supplemental data-Table S2-S8. In summary, one 20 bases sequence (FBXO21) presents 100% homology between human, gorilla and chimpanzee. One other sequence (USP30) is unique to human whereas the sequence (USP31) was found in human, gorilla, chimpanzee and capuchin. All these sequences were found to be phylogenetically distant in other mammal species. Overall the combinatorial setting of the 7 RNA segments in humans was unmatched with another primate species, which highlights that a pattern of gene targets might be unique for humans. The same type of analysis was conducted between different strains of coronaviruses (see figure 2 and Supplemental data-Tables S9-S15). In such case the conservation of the 20 bases sequences are weak with significant divergences. We note that Sars-Cov-2 and the bat coronavirus RaTG13 present 4 sequences on 7 identical or with one base change whereas the other coronaviruses known as causing the same clinical symptoms and physiopathology in humans than Sars-Cov-2 are highly divergent for the 7 sequences.

Discussion

Our observations lead to conclusions that i) segments presenting intra or inter RNA pairing above 20 bases length within the 5 coronaviruses RNAs are rare although pairing on very short length and/or pairing with mismatches are frequent, ii) the list of hybrid duplex coranoviruses/human RNAs was significantly more important in SARS-CoV-2 than in the other strains if we consider all the isoforms in the transcriptome, iii) regarding SARS-CoV-2, amazingly hybrid duplexing sequences were found in three important human genes: mitochondrial ubiquitin specific peptidase 30 (USP30), a subunit of ubiquitin ligase complex (FBXO21) and finally ubiquitin specific peptidase 31 (USP31). SARS-CoV-2 might affect mitochondria via ubiquitination alteration, which could be a plausible pathway of interference to explain the dramatic deteriorating conditions of many patients affected by this virus. SARS-CoV-2 might have a "stolen" piece of genetic information from homo sapiens and/or humanoids acquired along the co-evolution history over millions years or alternatively SARS-CoV-2 genome might have randomly drifted allowing the apparition of matching pieces of sequences with human genome; all these genetic innovations could have occurred with in fine the catastrophic result which consists to return the human immunity defense system against itself. This argues in favor of the idea that the immune defense Dicer/Ago/RISC system could work against its host upon viral infection. Not only RNA viruses over million years of co-evolution dodge the immune system of hosts but in some cases could trigger a "self destruction" or "programmed suicide" of infected mammal host cells. A recent reports documents that interferons molecule (type I,II and III) are little or not expressed in cells and tissues infected by SARS-CoV-2 whereas in contrast high level of chemokines and interleukin type 6, a pro inflammatory cytokine involved in innate immunity were observed [START_REF] Blanco-Melo | Imbalanced host response to SARS-CoV-2 drives development of COVID-19[END_REF]. The authors observed that the ongoing infection down regulated a large panel of genes among which are our genes making hybrid dsRNA. This puzzling transcriptomic picture regarding the classic immune responses to viral infection suggests a scenario for which SARS-CoV-2 induced molecular pathways in infected cells derailed from expected patterns. Recently, authors reports that they have retrieved the full catalogue of human proteins that bind with strong affinity to the 26 tagged SARS-CoV-2 proteins by double hybrid technology [START_REF] Gordon | A SARS-CoV-2 protein interaction map reveals targets for drug repurposing[END_REF]. The datasets outlines that 42 human proteins are strong candidates for high affinity with viral partners (corrected p value from 1.41E-29 to 0.00578) and other 280 human proteins show weak statistical evidence for interaction [START_REF] Gordon | A SARS-CoV-2 protein interaction map reveals targets for drug repurposing[END_REF]. Among this first group (n=42), 13 are mitochondrial proteins, each one interacting with different viral proteins and 6 are controsomal proteins interacting with a unique viral partner. Mitochondrial proteins are also heavily represented in the second group (n=280). In the full dataset of interacting human proteins, no protein linked to Dicer/ago pathways were found, which suggests that the RNAi process is not altered by the SARS-CoV-2 viral infection [START_REF] Gordon | A SARS-CoV-2 protein interaction map reveals targets for drug repurposing[END_REF]. All together these information hint that the physiopathology landscape provoked by SARS-CoV-2 infection might be multifactorial including inactivation of major host proteins by high affinity binding with a viral partner along with drastic degradation of host messenger by RNAi machinerie.

Method

Viral sequences

We obtained the sequences of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2);

Human transcriptome

RNA products annotated on the Genome Reference Consortium Human Build 38 patch release 13 (GRCh38.p13) were downloaded from NCBI FTP site (RefSeq accession: GCF_000001405.39).

Identification of potential double-stranded RNA fragments

Our previous published analysis, along with other published works, confirmed that the catalogue of siRNAs is far more complex and extensive than previously thought and that it encompasses larger sets of the transcriptome [START_REF] Pasquier | Transcriptome-wide-scale-predicted dsRNAs potentially involved in RNA homoeostasis are remarkably excluded from genes with no/very low expression in all developmental stages[END_REF][START_REF] Ghildiyal | Endogenous siRNAs derived from transposons and mRNAs in Drosophila somatic cells[END_REF][START_REF] Czech | An endogenous small interfering RNA pathway in Drosophila[END_REF][START_REF] Li | Global analysis of RNA secondary structure in two metazoans[END_REF]. A study has shown that an extensive presence of dsRNAs in the Drosophila and C. elegans obtained by high-throughput sequencing involves many categories of RNA including mRNAs in which miRNA and lncRNA populations appear a minority component [START_REF] Li | Global analysis of RNA secondary structure in two metazoans[END_REF]. Following the same approach as the one used by Pasquier et al. [START_REF] Pasquier | Transcriptome-wide-scale-predicted dsRNAs potentially involved in RNA homoeostasis are remarkably excluded from genes with no/very low expression in all developmental stages[END_REF], each virus sequence have been cut up into short overlapping sequences of 15 bases. These 15-bases sequences were extracted at intervals of 6 bases to ensure that any sequence of at least 20 bases belonging to the complete virus sequence includes at least one of the 15-base sequences. The potential pairing were computed by aligning short 15-base sequences on RNA sequences with the STAR RNA-seq aligner [START_REF] Dobin | STAR: ultrafast universal RNA-seq aligner[END_REF] and by retaining only perfect matches for which the short sequence was reverse complemented. We then extended the matches to obtain the maximum alignment length. We subsequently applied a second post-processing step to eliminate duplicate alignments and to remove sequences aligned over less than 20 bases. This procedure has been applied to compute the potential pairing between RNA viruses and human transcripts and also to identify the possible internal pairing within RNA virus sequences. Briefly regarding SARS-CoV-2, the pairing segment was observed in all the isoforms (2 known and 13 predicted) of the human transcripts of USP30.

The pairings were identified at the junction between exons 17 and 18 of DNAJC13, into exon 10 of ELP4, exon 12 of FBXO21, exon 2 of FLRT2, exon 13 of USP30, exon 16 of USP31 and exon 4 of ZNF443. The sequence of 20 bases, originating from orf3a of SARS-CoV-2 has the potential to target the sequence AAAGATAGAGAAAAGGGGCT which is shared by 15 predicted and/or found transcripts of USP30. On the other side, regarding USP30 gene, the data gathered by the "1000 genomes project" shows that this 20 bases sequence is present in all Homo Sapiens with the exception of 0,49 % of Han Chinese in Bejing that have a mutation A/T in 2nd position within this matching sequence [START_REF] Siva | Genomes project[END_REF]. Finally DNAJC13 is an endosome-related protein and believed to regulate endosomal membrane trafficking. Mutations provoke Parkinson disease and neurodegeneration [START_REF] Blanco-Melo | Imbalanced host response to SARS-CoV-2 drives development of COVID-19[END_REF].

In parallel the SARS-CoV-2 fragments that pair with USP31, FLRT2, FBXO21 were found in only 5, 4 and 5 isoforms (predicted or experimentally found) respectively. Regarding the MERS virus, the collection of hybrid dsRNA seems more disparate with the targeting of 2 ionic channels and a GTPase of Rho subfamily. The analysis of no virulent viruses (HCoV-229E and HCoV-OC43) did not reveal a targeting of essential genes except the coding genes: SSH1 (Protein tyrosine phosphatase involved in actin filament dynamics in cellular lamellipodia formation), PTP4A1 (Protein tyrosine phosphatase involved in progression G1-S mitosis), GCNA (protein with acidic domain involved in genome stability for which mutants accumulate DNA-protein crosslinks resulting in chromosome instability), COX11 (a component of the mitochondrial respiratory chain, that catalyzes the electron transfer from reduced cytochrome c to oxygen) and finally SRGAP1 (GTPase activator involved in neuronal migration) (see NCBI database for information).

Identification of intra double-stranded RNA sequences in Coronaviridae

In parallel, we also investigate whether the structure of the 5 tested coronaviruses RNAs permits the formation of intermolecular double-stranded structures. We computed the potential internal pairing minimally over 20 bases length and identified only one candidate in SARS-CoV, involving a sequence of 22 bases starting at position 25961 and located in orf3a. This highlights that coronaviruses, under pressure of selection, have evolutionary succeeded in escaping the vigilance of RNAi host defense strategy by minimizing internal dsRNA structure.

Assesment of the scope of hybrid duplexing against other species or viruses

To assess whether the sequences identified in SARS-CoV-2 could impact other species, we used BLAST to calculate the similarities between each human sequence and the following 12 other

  previously provisionally named 2019-nCoV, Middle East respiratory syndrome-related coronavirus (MERS-CoV), SARS coronavirus (SARS-CoV), Human coronavirus 229E (HCoV-229E) and Human coronavirus OC43 (HCoV-OC43) from NCBI GeneBank (RefSeq accession: NC_045512.2, NC_019843, NC_004718.3, NC_002645.1 and NC_006213.1) [1,2, 27-30].

  species : Gorilla gorilla, Pan troglodytes, Pongo abelii, Papio anubis, Macaca mulatta, Sapajus apella, Mus musculus, Rattus norvegicus, Pteropus vampyrus, Sus scrofa, Bos taurus and Felis catus. The potentiality of hybrid pairing depends on the species and on candidate mRNAs in the host (figure 1 and supplementary tables S2 to S8). USP30 features the only human-specific hybrid pairing. Conversely, using BLAST, we also calculated similarities of sequences originating from SARS-CoV-2 with the following viruses: Bat coronavirus RaTG13, SARS-CoV, MERS-CoV, HcoV-229E and HcoV-OC43. The results are presented in figure 2 and supplementary tables S9 to S15).

transcriptome and the other

  from HCoV-229E and HCoV-OC43The 4 first lines (*1888 to 25074) refers to HCoV-229E and the 6 last lines (°849 to 23025) to HCoV-OC43. The table shows the start position of the sequence in the RNA virus, the DNA sequence coding the human RNA and the corresponding features in human.The numbers in the column 'Human target' are specified using the format x(y) where x and y are the numbers of known and predicted transcripts respectively.

Figure 1

 1 Figure 1 Philogenetic comparison of the human strand of hybrid dsRNAs with other mammals species. The graph represents the comparison of the sequences within the ortholog genes between few mammal species. Results are plotted as a percentage of similarities with the human counterpart.

Figure 2

 2 Figure 2 Philogenetic comparison of the SARS-CoV-2 strand of hybrid dsRNAs with other coronaviruses. The graph represents the comparison of the 20 bases sequences between few coronaviruses strains. Results are plotted as a percentage of similarities with the SARS-CoV-2.

Table 1 : List of hybrid duplex RNA potentially formed with one strand from human transcriptome and the other from SARS-CoV-2 The

 1

	Start pos. in virus	Human sequence forming hybrid duplex RNA	length	Human target
	15256 AGAGGCCATTATCCTAAGCA	20	1 lncRNA of NUTM2B-AS1
	19102 AAACAAACAAACACCATCAG	20	0(3) ncRNAs of LOC101927871
	20547 TCAACATGTCCATCCTTACA	20	1 lncRNA of LRP1-AS
	20792 CAGAGCCAGCACCAAAGTGA	20	0(2) mRNAs of LOC102724965
	27270 AAGAGAATAATTTTCATGTT	20	0(5) lncRNAs of LINC02272

table

shows the position of the sequence in the RNA virus (start position and ORF name), the DNA sequence coding the human RNA and the corresponding features in human. The numbers in the column 'Human target' are specified using the format x(y) where x and y are the numbers of known and predicted transcripts respectively.

Table 2 : List of hybrid duplex RNA potentially formed with one strand from human transcriptome and the other from SARS-CoV The

 2 table shows the start position of the sequence in the RNA virus, the DNA sequence coding the human RNA and the corresponding features in human. The numbers in the column 'Human target' are specified using the format x(y) where x and y are the numbers of known and predicted transcripts respectively.

	Start pos. in virus	Human sequence forming hybrid duplex RNA	length	Human target
	9467 CAGCAGCAACAACAGCAATT 20	1(27) mRNAs, 0(1) miscRNA
				of KMT2C
	15455 TGCAGTGGTGGCATCTCCGCT 21	2(0) mRNAs of CDC42
	21230 TTAATAGTACCCAAGTAATT	20	1 mRNA of ARIH1
	22581 TCAACACCTTCAGCCTGTTC 21	2(5) mRNAs, 0(10) miscRNAs
				of ANO9
	23098 AAGCCAGCCACCACCTTCAA 20	6(12) mRNAs of KCNMA1
	25583 TTTGAGGATGCAGTGACCAA 20	0(2) mRNAs, 1 ncRNA of THBS3

Table 3 : List of hybrid duplex RNA potentially formed with one strand from human transcriptome and the other from MERS-CoV The

 3 table shows the start position of the sequence in the RNA virus, the DNA sequence coding the human RNA and the corresponding features in human. The numbers in the column 'Human target' are specified using the format x(y) where x and y are the numbers of known and predicted transcripts respectively.

	Start pos. in virus	Human sequence forming hybrid duplex RNA	length	Human target
	*1888 GTTCAACACGTGAAGATTTA	21	2 ncRNAs of GTF2IP4
	*9372 TATTATAGAAAAATTATGCA	21	1(6) mRNAs of GCNA
	*16936 TTGGCATTACAGGCATGAGC	20	2 mRNAs of SRGAP1 0(2) mRNAs of COX11
	*25074 AACTGAAGAATAACAATGAATA 22	0(1) ncRNA of LOC107986455
	°849 TCTTCAACTTTAAAATCATA	20	1 lncRNA of LINC01829
	°5404 CAAATCAACTTGACTAAACA	20	0(1) ncRNA of LOC107986018
	°12038 CCTCATCAAGATTTTTCTTA	22	0(1) mRNAs of SSH1
	°13797 TTCAACAAAATCATACCAAT	20	0(1) ncRNA of LOC105373593
	°21968 TTGATGGTGATTTTATAATT	20	1 mRNA of PTP4A1
	°23025 CACCAGTGTCTTTATTAAAA	20	0(1) ncRNA of LOC107985904

Table 4 : List of hybrid duplex RNA potentially formed with one strand from human

 4

Acknowledgments

This work was supported by the ANR grant "Methylclonome" ANR-12-BSV6-006-01 to Alain Robichon and Claude Pasquier. This work was also supported by the French National Research Agency (ANR) through the LABEX SIGNALIFE program (reference # ANR-11-LABX-0028-01).

Author contributions

C.P. did the bio-informatic analysis. C.P. and A.R. conceive the conceptual framework of this study and wrote the paper.

Competing interests

There is no conflict of interest to declare regarding the data provided in this article. S1 Hybrid dsRNAs between human transcriptome and SARS-CoV-2 RNA.

Supplemental Table

The table details hybrid duplexing RNA between SARS-CoV-2 and humans. The analysis detailed all human transcript isoforms for each targeted gene by the viral RNA. Four other coronaviruses were analyzed in comparison with SARS-CoV-2.

Supplemental Tables S2 to S15

Alignments of human and SARS-CoV-2 strands within the hybrid dsRNAs collection with respectively other mammal and virus species. The tables represent the alignments of the identified 20 bases length sequences between different mammal species and between different coronaviruses. These sequences correspond to the 7 genes identified by computational search as potentially generating hybrid dsRNA between SARS-CoV-2 and humans.

The alignment analysis was conducted with the human strand of hybrid dsRNA regarding the similarities with other mammal species. The viral strand regarding similarities with other coronaviruses was compared in parallel.


Dr Valentin Lacanau

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From Electronic Waste to Suzuki-Miyaura Cross-Coupling Reaction in Water: Direct Valuation of Recycled Palladium in Catalysis

come

Introduction

Palladium is a rare precious metal, well known for its numerous applications in catalysis. [START_REF] Tsuji | Palladium Reagents and Catalysts: New Perspectives for the 21st Century[END_REF] However, further development of Pd-catalyzed reactions at industrial scale suffers from the high cost of this metal, which now regularly exceeds that of gold. Although numerous efficient atom-economical reactions are available using homogeneous Pd catalysis, their cost is not competitive with classical synthesis, which often requires more steps and generates more effluents. [START_REF] Pagliaro | [END_REF] Recently, the boom in Pd-catalyzed reactions in water, thanks to micellar catalysis, [START_REF] Lipshutz | Transition-Metal-Catalyzed Cross-Couplings Going Green: In Water at Room Temperature[END_REF][START_REF] Lipshutz | [END_REF][5] opens a new chapter in the field of user-friendly chemistry, and the reduction of the Pd cost would definitely enable wider use of such reactions. The cost of Pd is mainly due to its rare occurrence in the earth's crust (ca. 15 µg/kg), accompanied by a narrow distribution of deposits: today more than 80% Pd is mined in South Africa (SA) and Russia, with most of the reserves located in SA. [6,7] Whatever the ore treated, Pd is obtained after thorough purification, as a by-product of nickel (Russia) or platinum (SA). Economical and geopolitical analyses of natural resources have led to the inclusion of platinum group metals (PGM, which include Pd) in lists of critical raw materials by the European Union (EU) and the United States Geological Survey (USGS). [8,9] As a consequence, especially for Western and Asian countries (Europe, United States, China, Japan…), Pd mining from the so-called 'urban mine' is nowadays more and more considered. [10,11] Already, Pd contained in automotive catalytic converters is widely recycled, along with Pt and Rh. [12] And although gold and copper remain the principal targets of studies related to valuable metal production from metallic waste, several solutions regarding Pd recovery from electronic waste have been proposed. [12][13][14][START_REF] Hao | Resources[END_REF] Whatever its source, natural ore or waste, Pd is separated from other metals and isolated via hydrometallurgy, combining selective precipitation and liquid-liquid (L/L) extraction steps. Liquid-liquid extraction (or solvent extraction) is an efficient technique which is widely employed at industrial scale for the refinement of metals obtained from natural ores, such as copper, nickel and PGM. [START_REF] Rydberg | Solvent Extraction Principles and Practice[END_REF][START_REF] Poirot | [END_REF][18] It enables metal separation and isolation through its selective extraction from an aqueous phase into an organic phase, based on specific complexing agents (extractants). Possible impurities contained in the organic phase are then removed by washing with water or dilute acid aqueous solution (scrubbing stage). The target metal remaining in the organic phase is afterwards back-extracted into a specific aqueous layer, and the organic phase is re-employed in a new extraction cycle. In the specific case of palladium, the metallic cation is back-extracted from the organic phase into a chloride aqueous phase, and usually precipitated as a Pd(II) salt ([Pd(NH 3 ) 4 ]Cl 2 ) with ammonia and hydrochloric acid, filtered and dried. [19] Pd sponge is eventually obtained after burning [Pd(NH 3 ) 4 ]Cl 2 , and metallic Pd can be further refined using electrowinning. [START_REF] Crundwell | Extractive Metallurgy of Nickel[END_REF] Recycled Pd and natural Pd both join the same industrial applications routes only after these extra steps. In order to avoid the tedious and effluent generating steps dedicated to Pd isolation and ultimate purification, we propose in the present work a simple process dedicated to the direct use of Pd contained in organic extraction phases into micellar catalysed reactions in water. This process is especially interesting as it enables the straightforward valuation of Pd recovered from waste, after its separation from other metals with L/L extraction. The key step in the process lies in the direct back-extraction of Pd from the organic phase into an aqueous micellar phase (Figure 1). We studied the resulting micellar phase, and demonstrated that it shows similar catalytic activity as conventional micellar media prepared from commercial Pd(II) salt (Pd(OAc) 2 ). Such a process skips steps required for Pd isolation, as well as inherent reduction-oxidation steps, and subsequent preparation of a well-defined Pd(II) intermediate.

Various sustainable approaches to catalysts have been proposed to overcome the limitations of the global supplies of precious metals. [START_REF] Ritter | [END_REF] The trash-to-resource approach has been proposed on model three-way catalysts prepared at the laboratory using Pd only: [22] Leaching of metallic Pd using organic reagents enables the formation of a Pd(II) complex, [22] which can be either decomposed into nanoparticles to obtain a heterogeneous catalyst, [23] or subject of ligand exchange to obtain molecular catalysts. [24,25] Harvesting Pd dispersed in the environment appears as an appealing complementary solution, thanks to phytoextraction, [26] considering the possible use of 'green' Pd recovered from plants directly into catalysed reactions. [27,28] But latter proof of concept was based on rhizofiltration of a synthetic solution containing solely Pd, [27] and levels of Pd accumulation in plants after phytoextraction from soil are below that required for active Pd-catalysts. [26] Thus, to our knowledge, the direct use of Pd recovered from a complex mixture of metals such as those found in wastes has never been evidenced so far.

The reprocessing of electronic waste is a very complex procedure, based on physical and chemical operations. [START_REF] Hao | Resources[END_REF][START_REF] Birloaga | Waste Electrical and Electronic Equipment Recycling[END_REF] Detailed analysis of available literature reveals that no satisfactory Pd isolation has ever been reported using processes based on waste grinding followed by complete digestion with aqua Regia (HCl/HNO 3 mixture). [19] Pd is mainly found in waste of electrical and electronic equipment (WEEE) as Ag/Pd alloy in multi-layer ceramic capacitors (MLCC). [START_REF] Prabaharan | [END_REF] Separation of components, including MLCC, from printed-circuit boards can be easily performed after dissolution of Sn/Pb solders. [31,32] We recently demonstrated that the Pd-based alloy found in so recovered MLCC is readily dissolved into 3 M aqueous nitric acid, without generation of NO x gases. [19] Thus, Pd present in WEEE can be available as Pd(II) in a relatively simple aqueous nitrate solution, which contains base metals such as Cu, Ni, Co, Zn, La, Fe or Al (Figure 1), and leaving most Au and Cu on the naked board. [19] We previously reported the selective extraction of Pd from this mixture, using either a sulfoxide (bis(2-ethylhexyl)sulfoxide, BESO) or a diamide (N,N'-dimethyl,N,N'-dibutyltetradecylmalonamide, MA) extractant (see Figure S1 in supplementary information for chemical structures). [13,19] Both molecules are available, stable, have extremely low water solubility, and have been employed in continuous pre-industrial extraction processes. The purpose of the present work is to evaluate the feasibility of the valuation of the organic phases obtained after Pd extraction.

Results and Discussion

The dissolution of Pd contained in MLCC isolated from boards recovered from various end of use electronic apparatus (see Figure S2 in supplementary information) was performed using 3 M aqueous nitric acid according to the process we developed recently. [19] A solution containing Pd along with Cu, Fe and Ni as major impurities was obtained (Table 1, see Table S1 in supplementary information for complete data). Pd extraction was studied in detail using two organic phases: a 0,5 M MA solution in toluene, and a 0,2 M BESO solution in n-heptane. The Pd distribution coefficient is higher than 50 with BESO, so that quantitative Pd extraction is obtained, even with a phase volume ratio of 3/1 (aqueous/organic), which enables Pd concentration in the organic phase (Table 1). With MA, the lower distribution ratio (D = 16) enables almost complete Pd extraction (99% yield) after a two-stage crosscurrent extraction step (Table 1). Little Cu is extracted with both systems, and relatively important Fe amount is co-extracted with MA (Table 1). Ni could not be detected in the organic phase; other metals also present in the leachate in lower amount (Ag, Pb, Sn, Zn, see Table S1 in supplementary information), have distribution coefficients much lower than that of Fe, [19] and could not be detected in the final organic phases. These results are in full agreement with previous results from our laboratory regarding BESO [13] and MA, [19] and prove the robustness of these extracting systems according to the variations of the composition of the initial leachate. Washing of the organic phase with a small amount of water (volume phase ratio organic/aqueous of 10) is possible without measurable loss of Pd from the organic layer (less than 1%), and enables to bring concentrations of unwanted metals below limit of detection (LoD) in the case of BESO (Table 1). In the case of MA, there is still a small amount of Fe and Cu (Table 1), which removal could be envisioned using a second washing with dilute nitric acid, albeit with 4% Pd loss, as observed during our previous studies, and which was not attempted here. [19] According to the extractant chosen, Pd(II) is stabilized in the organic phase mostly through coordination in the first sphere of the metallic cation, by the extractant and two nitrate anions, to ensure electro neutrality of the supramolecular species. [18,33] Our experimental results are in full agreement with previous data which suggest a higher stability of the Pd-sulfoxide complex in comparison with the Pdmalonamide complex, which (relative) stability was quite suprising. [START_REF] Poirot | [END_REF]18] Back-extraction into the aqueous layer relies either on poor stability of former coordination complex, or on formation of a more stable complex in the aqueous layer. BESO is more efficient than MA for extraction stage, but quantitative Pd back-extraction into aqueous phase requires aqueous Pd-stabilizing agents (ammonia, thiourea…). With MA, we previously proved that back-extraction can be almost quantitative without any added reagent, as long as the aqueous nitrate concentration is low. [13] Both organic phases containing Pd arising from WEEE processing are thus available, and were examined in the following Pd backextraction studies. Extraction yield (BESO) [a] >99 % 1% 1% NA [c] Extraction yield (MA) [b] 99% 2% 18% NA [c] Final organic concentration (mg/L, BESO) [d] [b] Organic phase: MA 0,2 M in toluene, two stages, aqueous/organic phase volume ratio of 2.

[c] NA: not applicable (the concentration of the metal was below the limit of quantification).

[d] After washing the organic phase with water, organic/aqueous phase volume ratio of 10. In order to use a surfactant in the proposed process of Pd recovery (Figure 1), several features are necessary. First of all, the surfactant should be water soluble and not leach into the organic phase.

SDS TPGS TAC

Moreover, during the back-extraction step, it should lead to clean phase separation and efficient Pd backextraction. Finally, the surfactant has to be efficient for micellar catalysis, i.e. it must enable to run Pd catalysed reactions in aqueous media. In a preliminary evaluation of employable surfactants, we screened several non-ionic or ionic amphiphiles previously described as suitable for micellar catalysis, [34] including sodium dodecyl sulphate (SDS), fatty alcohol polyglycol ethers (e.g. C 12 H 25 -(EO) 23 -H), alkyl or fluoroalkyl phosphate esters (e.g. fluorinated Zonyl UR). We also evaluated the vitamin-E based glycol ethers TPGS-750-M and TPGS-1000 (Structures given in Figure S3), classically employed to perform micellar catalysed reactions. [35] All of them led to the formation of a stable emulsion after contacting and shaking with n-heptane or toluene, even after centrifugation (Figure 2).

Only surfactants derived from a Tris-ACrylamide polymerizable monomer (TAC) allowed a clean phase separation (Figure 2). TAC surfactants are obtained in a single step by free radical polymerization of an acryloyl monomer derived from tris(hydroxymethyl)acrylamide-methane (THAM) in the presence of an alkane-or a perfluoroalkanethiol as a transfer reagent (telogen), and have been prepared at the gramscale. [36] These oligomers, perfectly water soluble for average degrees of polymerization (DPn ≥ 4), have been developed for variable applications from drug delivery [37,38] and theranostics [39] to extraction and stabilization of membrane proteins. [40] We focused in the present study on two molecules of this family (Figure 2), a fluorinated one (F-TAC, with a C 6 F 13 CH 2 CH 2 chain) and a hydrogenated one (H-TAC, with a C 12 H 25 chain). Both have hydrophobic chains of comparable molecular volume, and similar critical micellar concentration (CMC).

Before studying the back-extraction of Pd(II), we checked whether TAC surfactants can be employed in order to perform Pd-catalyzed reaction in micellar media. Latter reactions have been developed using vitamin-E derived surfactants such as TPGS-750-M as stated before, but good yields and conversion rates with various classical ionic or non-ionic surfactants have also been previously reported. [34] As a model reaction, a Suzuki-Miyaura [5,41] cross-coupling reaction was chosen (Scheme 1). Yields obtained with both fluorinated or hydrogenated TAC surfactants were very satisfactory, only slightly lower than those obtained with TPGS-750-M, in conditions optimized for TPGS-750-M (Table 2). These conditions are not trivial, as only 1,1 mol % Pd(II) is employed. Using a lower amount of Pd(II) led to a drastic drop in yield using TPGS-750-M. With both H-TAC and F-TAC, almost quantitative back-extraction could be observed when 1% surfactant was added in the aqueous phase (Figure 3). However, cruds (precipitates) were obse rved at the interphase from 1% weight surfactant concentration, especially with H-TAC. These cruds generally lead to decreased back-extraction yields on higher scale, and need to be avoided. We did not investigate their origin, but they seem related to the presence of ions in the system, as the phenomenon was independent of the choice of organic solvent and extractant, and as no phase separation issue was encountered without HNO 3 and Pd(II) in the aqueous phase. F-TAC appears as the optimal surfactant, although it is possible to work with 2 wt % H-TAC as long as stirring is not too vigorous. The Pd back extraction from a BESO organic phase is particularly striking, as no specific Pd(II) chelating moiety is grafted on the surfactant.

The exact coordination mode of Pd(II) will be studied later on, in order to determine the exact interactions between surfactant and metal. NMR analyses after back-extraction in a deuterated aqueous solution (see supplementary information, Figure S4) demonstrated that the quantities of n-heptane and BESO carried along into the aqueous phase with palladium are negligible compared to the total organic phase volume, so that it is possible that a Pd(II)-BESO complex is involved in the back-extraction as the BESO quantity is of same order of magnitude as the Pd quantity. We also checked that no TAC surfactant migrated into the organic phase during the process (Figure S5). Aqueous micellar solutions containing Pd(II) were then evaluated in the Suzuki-Miyaura reaction described beforehand. The only difference lies in the Pd(II) source, as well-defined solid Pd(OAc) 2 is replaced by a solution of Pd(II) in aqueous H-or F-TAC solution. The Pd concentration in latter solutions also depends on the initial Pd concentration in the aqueous solution arising from leaching of WEEE. The final concentration can be higher than the initial one, thanks to concentrating extractions performed with unequal volumes of aqueous and organic phases (Table 1). Starting from a model aqueous solution containing Pd (100 mg/L), Fe (1 000 mg/L) and Cu (2 000 mg/L), we were able to prepare aqueous H-or F-TAC solutions containing Pd(II) at concentrations between 650 and 900 mg/L (Table 3). No Cu nor Fe were detected in the final aqueous solutions, although (voluntarily) the Fe quantity in the initial model solution was set higher than that of real leachate solution.

Table 3. Composition of aqueous micellar solutions prepared from a 3 M aqueous HNO 3 solution containing Pd (100 mg/L),

Fe (1 000 mg/L) and Cu (2 000 mg/L) using BESO 0,2 M in n-heptane.

Entry Surfactant

(2 wt %)

Extraction conditions [a] Backextraction conditions [a] Final Pd(II) It is preferable to work at low aqueous to organic phase volume ratio for the extraction process, and high organic to aqueous phase volume ratio for the back-extraction process (Table 3, entries 1 and 3) as the Pd that remains in the organic phase after incomplete back-extration is not lost: it is possible to recycle the organic phase containing a small Pd hold-up, as it is not deleterious to its extraction properties. [19] When using recycled Pd, in order to keep the Pd quantity constant relative to cross-coupling reaction reagents, we needed to adapt the amount of surfactant solution employed in the cross-coupling reaction, i.e. we increased the volume of aqueous solution employed in order to reach the 1,1 mol% Pd amount required.

A 1 150 mg/L Pd solution would lead to exactly the same volume of aqueous surfactant solution employed in the cross-coupling reaction. As a consequence, with recycled Pd, there was a dilution of reaction medium by a factor 1,2 to 1,7. Yields obtained with both H-and F-TAC surfactant solutions are very satisfactory (Table 1); a 77% yield was obtained with the F-TAC solution (Table 3, entry 3), in comparison with the 85% yield obtained with commercial Pd(OAc) 2 . The nitric acid concentration in final F-TAC solution (Table 3, entry 3) was determined experimentally to be 0,1 M. This acid was neutralized using 1 extra equivalent of trimethylamine, and did not set any peculiar issue to the use of recycled Pd.

To our knowledge, this result represents the first proof of concept of a chemical reaction catalysed with palladium directly recovered from waste. In this work, the recovered Pd is purified through a solvent extraction process, and the presence of possible impurities was checked: after washing of the organic phase, Fe and Cu, the major impurities, were not detected in the organic solution. They were neither detected in the final aqueous Pd solution employed for catalysis: Pd purity is above 99% regarding Fe.

This purification is ensured by the selective Pd extraction with BESO. The use of a solvent extraction process has two further key features: it enables Pd concentration (up to 10-fold concentration between leaching solution and surfactant solution for catalysis) and separation of Pd from the nitric acid employed for leaching (initially 3 M aqueous solution). The extracting molecule (BESO) presents no peculiar health or environmental hazards according to its safety datasheet, the organic solvent employed (nheptane) is amongst the best possible according to green chemistry guidelines considering that water solubility has to be minimal. The surfactant employed in the system is easily accessible and has been developed for medical applications. Nitric acid is employed for the leaching operation, and it has to be mentioned that this reagent has a very low impact on human health and environment in comparison with available alternatives, especially considering that is it employed diluted in water. To our knowledge, leaching of Pd can also be envisioned using halide based reagents, which also set problems (chloride ions in oxidizing media lead to chlorine offgas, and iodine is very toxic to aquatic life and harmful according to ECHA). The amount of waste generated by the proposed process is very low (only 10% of the volume of the organic phase employed), and especially in comparison with previously performing processes developed at our laboratory, which are already very well positioned. [13,19] It is key to mention that backextraction of Pd from a BESO based organic phase is impossible without the use of a specific aqueous layer, which has then to be processed in order to isolate Pd. As mentioned before, Pd is usually isolated by precipitation after addition of ammonia then hydrochloric acid. A detailed life-cycle assessment would enable a more precise evaluation of the impact of waste reduction.

In the continuation of this work, we will pursue the study of impurities influence (metallic ions and acid)

and see how we can further simplify the process. We will also consider different reactions, including more demanding reactions which rely on sole Pd catalysis such as Buchwald-Hartwig reactions. [42] Suzuki-Miyaura reactions are indeed less sensitive to metallic impurities such as Fe, and it has even been recently proven that Fe nanoparticles containing only trace Pd can act as efficient catalyst for this reaction. [43] The system we propose in this work is also of interest considering the work-up at larger scale of cross-coupling reactions performed in micellar medium: there is no emulsion generated during the Pd back-extraction process with TAC-surfactants, and similarly we did not encounter any phase separation issue during extraction of reaction product in diethyl ether after reaction. The catalytic system remains in the aqueous layer and no Pd was detected in the final product.

Conclusion

As a conclusion, we propose an original combination of hydrometallurgic process dedicated to Pd recovery from electronic waste and surfactant aqueous formulation, which enables the direct use of recycled Pd in important chemical reactions. The selective Pd extraction process enables the straightforward preparation of a Pd aqueous solution employable as a reaction medium for Suzuki-Miyaura reaction. The co-extracted acid quantity is manageable, and the other metallic impurities, mainly Cu and Fe, eliminated using a small aqueous washing, so that the amount of generated waste is minimal. It is of course arguable that Suzuki-Miyaura reactions can be performed using lower amount of Pd, but the aim of this work is not to develop specific catalysts with very high turnover in specific conditions, but to replace simple commercial Pd(OAc) 2 using classical ligands in the simplest reaction medium: water. This novel approach is promising as it opens the door towards open cycles in circular economy, going from waste to valuable compounds, a key for a better use of our resources, and the emergence of performing sustainable chemical industry.

Experimental Section

Determination of metal concentration in solutions: Aliquots of aqueous phases (100-250 µL) were directly diluted into a 2% HNO 3 aqueous solution. Metals contained in the aliquots of the organic phases (100-200 µL) were back-extracted with 800 µL of an aqueous 0.1 M thiourea solution at 20-22°C for 1 h.

Both phases were separated, and 500 µL of the resulting aqueous solution were taken and diluted into a 2% HNO 3 aqueous solution. Concentrations of each metal in so-obtained 2% HNO 3 aqueous phases were determined by inductively coupled plasma atomic emission spectroscopy (ICP/AES, SPECTRO ARCOS ICP Spectrometer, AMETEK Materials Analysis). Given concentrations are calculated as the means of three replicates on three different wavelengths for each metal; relative standard deviations were determined and lie between 1 and 4%.

General experimental procedure for the preparation of organic Pd(II) solutions from aqueous mixtures of metallic cations: An aqueous nitrate phase containing the metallic cations, prepared either from electronic waste according to our previously reported procedure [19] (details are also given in supplementary material), or from the corresponding metallic salts (Pd(NO 3 ) 2 .xH 2 O, Fe(NO 3 ) 3 .9H 2 O, Cu(NO 3 ) 2 .3H 2 O) diluted in 3 M aqueous HNO 3 , was contacted to an organic phase (either MA 0,5 M in toluene or BESO 0,2 M in n-heptane) in 15 mL plastic tubes with a ratio of aqueous to organic phase volumes between 1 and 10 (see text for details). The mixture was vigorously shaken using an IKA-Vibrax VXR basic shaker at 1 200 rpm for 1 h at 20°C. The vials were removed and let to stand for 5 min and the phases were separated. The resulting organic phase was washed with water (ratio of organic to aqueous phase volumes equal to 10, contact time 15 min), and the phases were separated as described above. The resulting organic phase was aliquoted for analysis of metals with ICP/AES as described above.

General experimental procedure for the back-extraction with aqueous micellar solutions: An organic Pd(II) solution was contacted to an aqueous solution of surfactant of concentration between 0,5 and 2 wt %, with a ratio of organic to aqueous phase volumes between 1 and 2,5 (see text for exact values). The mixture was gently stirred using an IKA-Vibrax VXR basic shaker at 200 rpm for 1 h at 20°C. The vials were removed and let to stand for 5 min (or centrifuged for 5 min to achieve complete phase separation) and the phases were separated. The resulting aqueous phase was aliquoted for analysis of metals with ICP/AES as described above.

General experimental procedure for Suzuki-Miyaura coupling in micellar medium: Bromoanisole (1 equiv.), phenyl boronic acid (1,5 equiv.) and tri-tert-butylphosphonium tetrafluoroborate (4,4 mol %)

were weighed and placed in an 2 mL plastic vial. Using Pd(OAc) 2 : A 2 wt % solution of surfactant freshly prepared and previously degassed under argon containing palladium(II) acetate (1,1 mol %) was added to the solids (1 mL/mmol). Using recycled Pd: A 2 wt % solution of surfactant prepared after back-extraction of organic phase and previously degassed under argon was added to the solids (volume adjusted in order to reach 1,1 mol % Pd, i.e. 1,2 to 1,7 mL/mmol). The resulting mixture was homogenised and degassed with argon bubbling (5 min). Then triethylamine (3-4 equiv) was added, and the resulting mixture was stirred using an IKA-Vibrax VXR basic shaker at 1 200 rpm for 18 h at 20°C.

The mixture was extracted twice with 3 mL of diethyl ether. The combined organic layers were concentrated in vacuo and the crude residue was purified by flash chromatography on silica gel using cyclohexane and ethyl acetate as eluents.

On a fait la une !

Figure 1 .

 1 Figure 1. Principle for the direct use in micellar catalysis of Pd recovered from waste of electrical and electronic equipment (WEEE). L = bis(2-ethylhexyl)sulfoxide (BESO), or N,N'-dimethyl,N,N'-dibutyltetradecylmalonamide (MA). MLCC = multi-layer ceramic capacitors.

  Organic phase: BESO 0,2 M in n-heptane, one stage, aqueous/organic phase volume ratio of 3.

Figure 2 .

 2 Figure 2. Amphiphiles employed for back-extraction and micellar catalysis (Tris-Acrylamide based hydrogenated and fluorinated TAC surfactants), and phase separation after centrifugation (3 min at 5 000 rpm) of toluene and aqueous solutions of SDS, TPGS-750-M or F-TAC (concentration 20 mg/mL).

Scheme 1 .

 1 Scheme 1. Suzuki-Miyaura reaction employed as model reaction throughout the study.

  NA: Not applicablePd back-extraction studies were systematically conducted on model organic phases containing Pd(II) only, of similar concentration (about 200 mg/L), with a phase volume ratio of 1. With a diluted aqueous HNO 3 solutionpreferred to water in order to avoid hydrolysis of the Pd(II) cation -without surfactant, the back-extraction yield reaches 55% in the case of MA, and 23% with BESO (Figure3). To our delight, the sole addition of TAC surfactant to the aqueous phase increased the Pd back-extraction yield.

Figure 3 .

 3 Figure 3. Top: Back-extraction of Pd(II) from a 0,5 M MA in toluene organic phase into an aqueous H-or F-TAC based solution. Bottom: Back-extraction of Pd(II) from a 0,2 M BESO in n-heptane organic phase into an aqueous H-or F-TAC based solution. * denotes the presence of cruds at the interface.

  A/O = aqueous to organic phase volume ratio [b] O/A = organic to aqueous phase volume ratio

Table 1 .

 1 Preparation of organic phases after extraction of MLCC leachate (data for other metals not shown for clarity).

	Metal	Pd	Cu	Fe	Ni
	Initial aqueous
		87	2 140 740	520
	concentration (mg/L)

Table 2 .

 2 Effect of surfactant and palladium source on outcome of Suzuki reaction.

	Entry	Surfactant	Yield (%)	Yield (%)
			Pd(OAc) 2	Recycled
				Pd
	1	TPGS-750-M	95	NA [a]

Acknowledgements


Nicolas Cavassilas

Daniel Suchet

Amaury Delamarre

Jean-Francois Guillemoles

Fabienne Michelini

Marc Bescond

Michel Lannoo

Optimized operation of quantum dot intermediate-band solar cells deduced from the electronic transport modelling

So far physics of quantum electronic transport has not tackled the problems raised by quantum dot intermediate-band solar cells. Our study shows that this physics imposes design rules for the inter-subband transition. We developed an analytical model that correctly treats, from a quantum point-of-view, the trade-off between the absorption, the recombination and the electronic transport occurring in this transition. Our results clearly indicate that it is essential to control the transit rate between the excited state of the quantum dot and the embedding semiconductor. For that, we propose to assume the dot in a tunnel-shell whose main characteristics can be obtained by a simple analytical formula. Moreover, we show that in a realistic case, the energy transition only needs to be larger than 0.28 eV to obtain a quasi Fermi-level splitting. This quite small value designates the quantum dot solar cell as a serious candidate to be an efficient intermediate-band solar cell. This work gives a framework to design efficient inter-subband transitions and then opens new opportunities for quantum dot intermediate-band solar cells.

I. INTRODUCTION

Inter-subband transitions are widely used in infrared sensors [1] and in the concept of intermediate-band solar cells (IBSC) [2]. From an optical point-of-view these transitions have been the subject of numerous studies which show that the monochromatic absorption is maximal between the ground state and the first excited state if those two are well localized (bound-to-bound system) [3]. Nevertheless, whether in sensors or in solar cells, the objective is to recover excited electrons in an electric current. In case of sensors this current is the response to the absorption while in a solar cell it is at the origin of the generated power.

However, in the case where the electrons were excited on a very localized state, it will be difficult to withdraw them in an electrical contact. On the other hand, the reduction of the localization decreases the maximum of absorption, but also broadens it. This could be an advantage for a wide spectrum excitation. Finally, we understand that it will be necessary to find a compromise between absorption, recombination and extraction [4].

In this paper we propose an analytical model in which all these effects are considered rigorously from the point-of-view of quantum mechanics. We have developed this model based on the non-equilibrium Green functions (NEGF) formalism that allows to treat a quantum system with interactions [5][6][7][8][9]. The system, in this case a quantum dot with a tunnel-shell embedded in a 3D material, is simplified for computational concerns. The main simplifications are a perfectly selective contact, flat bands and the effective mass approximation.

This gives an effective model which, with a reduce number of parameters, favor the understanding of tricky but ultimately very important quantum transport phenomena. Moreover, even if such approaches are not so precise that fully numerical models, effective models are currently used to optimize devices assuming, for example, strongly confined system [10,11], tunneling modified by strain [12] or scattering in quantum well [13].

This analytical model is then applied to the inter-subband transition of an IBSC. The purpose of these concept is to exceed the Shockley-Queisser limit [14] by using an intermediateband in the band-gap of the absorbing semiconductor [15,16]. The idea is to use this intermediate-band to absorb photons having a lower energy than the energy gap. This absorption is then supposed to contribute to the current [17] without the full loss in voltage of a simple bandgap solar cell. To create an intermediate-band the use of nano-objects (usually dots) is often adopted [2,18,19]. Their lowest conduction state serves as an intermediateband while the second one is connected to the contact. But, this concept has not yet demonstrated performances beyond the Shockley-Queisser limit [19]. The main difficulty is that electronic populations in the intermediate-band and in the contact must not be allowed to equilibrate, in order to maintain a quasi-Fermi level splitting. Without this splitting, the IBSC is reduced to a simple solar cell with the bandgap defined by the energy between the valence-band and the first conduction state of the nano-objects. This is usually obtained experimentally. In this article, we deeply investigate this inter-subband transition, between the two first conduction states of the dot.

We have already reported a study dedicated to this transition [4], but conclusions were limited to a specific case (one set of parameters). With the present analytical model, it is henceforth possible to extend this study and to draw more general conclusions. We show that this transition must follow some rules, related to quantum electronic transport, in order to provide the efficiency higher than an equivalent single gap cell. To the best of our knowledge, none of these rules have ever been respected in quantum-dot IBSC proposed in the literature. Our findings, therefore, offer new perspectives by providing a framework for the design of IBSC.

II. MODEL AND SYSTEM

The system we model is schematically represented in Fig. 1. It is characterized by a discrete state |1 of energy E 1 filled with an energy-independent distribution f 1 which will be considered as an input parameter. This state represents the intermediate-band and f 1 the filling of this band. In an IBSC, f 1 is also relative to the transition between the valence-band and the intermediate-band. Even though this transition is another technological challenge involving the holes transport, here, we only consider it through this filling parameter. In addition to the first state |1 , which is perfectly located in the quantum dot, we consider an excited state |2 at E 2 (the transition energy is given by E t = E 2 -E 1 ) which has a coupling strength to the contact tuned via a tunnel barrier. The characteristics of this barrier result in a tunnel transfer rate σ T . Tunneling can occur in both ways, either extracting generated carriers from |2 to the contact, or injecting carriers from the contact into |2 for a retrapping.

As far as emission and absorption are concerned, both states |1 and |2 are linked by σ I and σ S the induced and spontaneous optical transition rates respectively. Moreover, as stated in the introduction, the states |1 , |2 and the contact do not share the same distribution. We then consider a second Fermi function for the contact f c . In an illuminated IBSC the two corresponding chemical potentials µ c and µ 1 must be split so that there is a gain compared to a single bandgap cell. In our model this quasi-Fermi level splitting, S = µ c -µ 1 , is an input parameter. Finally the contact is also defined by its energy band-edge E c and we will call in the following E r = E 2 -E c the ratchet energy [20][21][22][23][24]. In order to calculate the current generated by this transition we use detailed-balance model with radiative and tunnelling rates calculated with the NEGF formalism. It is very powerful since it allows to consider a quantum system with interactions. The interaction between photons and electrons is indeed processed by a self-energy which represents the central concept to describe inelastic scattering in the Green's functions. In the literature this is usually done numerically [5,7]. Here, by simplifying the description of the system (through the flat bands approximation in particular), we can include it analytically. For example it allows us to calculate the tunnel transit rate from state |2 through the tunnel barrier:

σ T = 8E 2 3 k r W cosh 2 (Lρ) (1)
with W = π/( 2Etm * 3 ) the side length of the cubic dot and L the thickness of the tunnel barrier. The wave vectors of the electron at energy E in the contact (with origin E 1 = 0) and the barrier are respectively given by k r = 2(E 2 -E c )m * / with m * the effective mass, and ρ = √ 2Bm * / with B the barrier energy related to E 2 . As expected this expression

shows that the tunnel transit rate σ T decreases exponentially with L. Moreover, it shows that when E 2 is close to E c (low k r ), an interference behavior increases the tunnel rate.

Note finally that this expression is original. It is indeed related, to the tunneling between a continuum and a quasi-continuum [25], and not to the tunneling between two continua or to a resonant tunneling on a bound state [26,27].

The analytical development, to obtain this expression, is exposed in the Supplemental Material (SM), like the development of the current formula resulting in the Eq. ( 4) of the present work. Before to expose this full expression, we present another formula, having a close form, but obtained with a simpler development based on rate model. This toy model helps to better understand the final formula of the current.

For this toy model, we assume discrete states for |1 , |2 and the contact. Moreover, σ T and both optical rates σ I and σ S are independent of the energy. It is then straightforward to write the variation in time of the distribution f 2 on the state |2 knowing f 1 and f c :

df 2 dt = σ T {f c (1 -f 2 ) -f 2 (1 -f c )} + σ I {f 1 (1 -f 2 ) -f 2 (1 -f 1 )} -σ S f 2 (1 -f 1 ). (2)
In steady state this variation vanishes. Assuming this condition, and knowing that the current at the contact is given by J = -eσ T (f 2 -f c ) (e the elementary charge) we then have for the current:

J = eσ T σ I (f c -f 1 ) + σ S f c (1 -f 1 ) σ T + σ I + σ S (1 -f 1 ) . ( 3
)
This expression shows that the current is a competition between induced absorption and spontaneous recombination (in the numerator). This competition is all the more favorable for absorption as f 1 is high and f c is low. The technological challenge is to have a higher generation than the recombination while having a higher chemical potential in the contact than in the state |1 . Concerning the trade-off between tunneling and optic, we note that numerator is given by the product of σ T with the summation of the optical rates, while the denominator equals the summation of all rates. Therefore, if σ T is strongly larger than the optical rates, the current is limited by the optical processes. In the opposite situation, the current is limited by the tunneling. This then confirms that current is a balance between all such interactions.

The main limit of this toy model is that the density-of-states of |2 is a simple Dirac peak. This state being linked to both state |1 and contact, lifetime is finite. This implies, according to the relation of uncertainty, that state |2 is broadened [5,[START_REF] Bastard | Wave mechanics applied to semiconductor heterostructures[END_REF]. We will see in the following that this broadening is the key element to obtain a maximum of efficiency. By considering the calculation of the transit rates via the NEGF formalism, as shown in the SM, we go beyond the previous toy model (Eq. ( 3)) and obtain for the current across the system presented in Fig. 1, the following expression:

J(S) = Em Ec J(S, E)dE = Em Ec (J A (S, E) + J R (S, E))dE = 2e h Em Ec σ T σ I (E)(f c (E) -f 1 ) + σ S (E)f c (E)(1 -f 1 ) ( E-E 2 ) 2 + (σ T + σ I (E) + σ S (E)(1 -f 1 )) 2 dE, (4)
The absorption current J A (S, E) is related to the induced optical rate σ I (E) =

M(E) (CΩ S b T S (E) + n r πb T R (E)), while the retrapping current J R (S, E) is related to the spontaneous optical rate σ S (E) = M(E) n r π. The electron-photon coupling is given by:

M(E) = E 8π 3 0 8e 3m * W 2 n c 3 (5)
with n the refractive index of the considered material, b T (E) = 1 exp E k B T -1 the Bose distribution, T S = 6000K and T R = 300K respectively the sun and the room temperatures, Ω S = 6.7 × 10 -5 the solid angle of absorption. We also have

f c (E) = 1 1+exp E-µc k B T R
. Concerning the sign convention for the current, power is produced when J < 0. For all calculations, we choose an initial state half-filled with f 1 = 0.5, involving µ 1 = E 1 . The upper limit E m is a numerical parameter defined in the SM. Finally, C is the sun concentration and n r a non-radiative coefficient that accounts for non radiative recombination: for one radiative recombination we have (n r -1) non-radiative ones. This parameter strongly depends on the materials, growing conditions and shape of the dots [START_REF] Gerardot | [END_REF]. In consequence, while experimental study shows results close to the radiative limit [START_REF] Gerardot | [END_REF]30], theoretical calculations suggest n r = 5 × 10 4 [31]. In the following, we generally assume n r = 10 2 but we extended our conclusions to the radiative limit and to the case where strong non-radiative processes occur.

The denominator of Eq. ( 4) looks like that of a Lorentzian centered on E 2 , while the numerator looks like that of Eq. (3). Indeed, in both Eqs. ( 3) and ( 4), the current is proportional to the tunnel transit rate σ T and is a competition between absorption and retrapping. But compared to Eq. ( 3), the denominator of Eq. ( 4) shows a broadening around E 2 which is given by the sum of the different transition rates. A fast analysis of this equation shows that J(0, E 2 ) is maximum when

σ T = σ I (E 2 ) + σ S (E 2 )(1 -f 1 ). If σ T is
lower, the current is limited by the tunneling, while if it is larger, the current is limited by the absorption. This condition does not involve that the current is maximal since the total current is the result of a summation over energy. However, as we will show in the following of this article, adjusting the design to fulfil this condition remains a good milestone.

We can note finally that this set of equations can easily be implemented in a few lines of code as shown in the SM. Using Eq. ( 4) we can calculate the current spectrum and the total current as a function of S for the junction shown in Fig. 1. If we consider this inter-subband transition as a solar cell, we can calculate the corresponding current J sc = J(S = 0), the quasi-Fermi level splitting canceling the current S oc and the maximum power P max .

III. RESULTS

Figure 2 shows current spectra at S oc for a realistic set of parameters and different tunnel barrier thicknesses. The negative (positive) component corresponds to absorption (retrapping). The narrower around E 2 these two components are, the thicker is the barrier. This reflects the effect of the lifetime on the broadening of |2 controlled by the tunnel rate. For recombination, in addition to this peak, there are also electrons injected from the contact band-edge at E c . This contribution is all the more important as the broadening of |2 is important. Indeed, a high density-of-states in the well at the energy E c promotes the injection from the contact. In the bound-to-continuum case (L = 0 nm) shown in Fig. 2a, the broadening is maximum and this band-edge injection is dominant. As a result, S oc is low since it is controlled by E c and not by E 2 . This band-edge also impacts the current absorption since, as shown Fig. 2a, the spectrum is cut-off at E c . Therefore, in case of large broadening of |2 , the effective energy transition is more defined by E c than by E 2 in sense that a low (high) E c means a high (low) J sc and a low (high) S oc . Figure 2b shows the current spectrum in the bound-to-bound case with a thick barrier, L = 10 nm. The broadening being small we just have a very weak injection from E c and consequently a higher S oc than in the bound-to-continuum case. We recover here the broadening effect introduced in a previous work [4] at the origin of S oc modification. Moreover, the excitation component being very narrow around E 2 , the absorption spectrum is no-more cut-off at E c . In this case, the effective energy of the inter-subband transition is defined by E 2 . However, despite a higher S oc , the power is just a little larger than in the boundto-continuum case. The current is indeed limited since the excited electrons hardly tunnel through the contact. The best trade-off between absorption, extraction and recombination, is obtained for the intermediate case shown Fig. 2c where L = 5 nm. The consequence of the corresponding moderate broadening is a much larger current and an intermediate S oc . Compared to the usually assumed bound-to-bound case, the current and the power are increased by ratio of 3 and 5, respectively.

These results show that it is essential to control the broadening of the state |2 via σ T to have a good balance between all transport processes. For that, as we had already suggested in Ref. [4], a well-designed tunnel barrier is a relevant solution. While the bound-tocontinuum case is generally considered in IBSC [32][33][34][35], some studies assume the quantum dot embedded in a high bandgap material [36][37][38][39][40]. This last solution is proposed to reduce the strain and the corresponding structural defects, but it could also make it possible to control the tunnel transit and hence the broadening of the excited state. It is also possible to design a dot directly in the host-material, without shell, if both the band-offset and the dot size are sufficient to have a localized excited state. In this case, the tunnel barrier between the dot and the contact has to be controlled by an electric field generated by doping and/or build-in charge [41].

FIG. 3: Maximum power P max versus the tunnel barrier thickness L extracted form the J -V characteristic calculated with Eq. ( 4) for B = 0.2 eV, m * = 0.07m 0 (m 0 the free electron mass), n = 3.5, E t = 0.6 eV, E r = 20 meV, C = 500 and various n r . We also report the estimation of the optimal thickness L opt obtain with Eq. (6). In order to estimate the precision of this equation, these values can be compared to the top position of the corresponding curves.

The optimal barrier thickness depends on all parameters and the precedent value of 5 nm cannot be generalized. In order to offer an extended study, it would be interesting to have an expression estimating such an optimal barrier thickness. For that, we remember that the current J(0, E 2 ) is maximum when σ T (E 2 ) = σ I (E 2 ) + σ S (E 2 )(1 -f 1 ), and checking that σ I σ S , we propose an expression allowing to approximately estimate the best trade-off:

σ T (E 2 ) = α(n r )σ S (E c ) with α(n r ) = 60 × exp(log10(n r ) -1)
. Considering this condition in Eq. ( 4), we extract an expression which estimates the value of the optimal thickness of the tunnel barrier, L opt , according to all the other parameters:

L opt = 1 ρ ln   8Et 3krW + 8Et 3krW -M (E c )πn r α(n r )(1 -f 1 ) M (E c )πn r α(n r )(1 -f 1 )   . (6)
This expression shows that, for example, in case of large non-radiative coefficient n r and/or low f 1 , the retrapping is naturally large and L should be chosen small in order to preserve a large σ T . At the opposite, close to the radiative limit, L should be large. We note also that all parameters modifying σ T also play a role, which includes k r related to the ratchet energy, E t and W both related to the dot design. Figure 3 illustrates the impact of the recombination by representing the maximum power versus L (calculated with the Eq. ( 4))

for various n r . These curves, in addition to illustrating the advantage of considering a tunnel barrier, confirm the good estimation of L opt given by Eq. ( 6). Finally, we can estimate thanks to our model, the minimum of the transition energy allowing the generation of a power with the considered inter-subband transition. Indeed, reducing E t and consequently E c involves an increase of the injection from the contact. If, at V = 0V, the retrapping current is of the same order of magnitude than the absorption current, application of any quasi-Fermi level splitting is impossible. For example, for n r = 10 2 and C = 1 we find that E t has to be larger than 0.28 eV. We calculate this limit, called E quant , for several concentrations and non-radiative factors as shown in Table I.

Regardless of the present study, the optical transitions in IBSCs must be large enough for such cells to offer higher efficiency than the optimal single bandgap cell. This limit can be estimated with a classical detailed-balance model (described in SM) considering the three optical transitions of the IBSC [24]. In Table I, we compare this classical limit E classic with the quantum limit E quant . These two limits are, in any case, very close.

This means that the inter-subband character of the transition, if it is well designed, does not increase the limitation to obtain an efficient IBSC. This validates the use of quantum dots as a judicious choice for the IBSC.

IV. CONCLUSION

In conclusion, we have presented a theoretical study on the inter-subband transition in quantum dot IBSCs. For this, we have developed a rigorous model, but nevertheless easy to implement. Using this model, we can give recommendations for designing an efficient inter-subband transition. Considering a realistic recombination rate, the transition energy E t between the intermediate-band and the excited state must be higher than 0.28 eV without concentration and 0.13 eV under 500 suns. Under this limit, the intermediate-band is at the thermodynamic equilibrium with the contact. Above this limit, the tunnel rate has to be controlled by a tunnel barrier. In the radiative limit, this barrier should be thick, while it should be all the thinner when the non-radiative processes increase. In case where the optimal design suggests a thick barrier, an energy ratchet may be considered without any damage because tunneling from E c to the dot is reduced. Such a ratchet could represent an advantage, since as we saw in another study [22,23], degrees-of-freedom on E r make it possible to match the different transitions of the IBSC. On the other hand, in case of thin barrier, both S oc and J sc are controlled by such a ratchet energy. This parameter has then to be carefully chosen using the Eq. ( 4) of this letter.

This study confirms that obtaining an efficient IBSC involves significant technological challenges, particularly for the band offsets in order to achieve a sufficiently large E t . On the other hand, we show that the inter-subband character of the transition does not worsen these conditions and we confirm that the quasi-Fermi level splitting can be achieved, even if the non-radiative processes are huge.

Finally, it is important to note that the analytical model presented in this work is not only dedicated to the IBSC. It may also be useful for other devices assuming an inter-subband transition such as photodetector or laser.

FIG. 1 :

 1 FIG. 1: Band diagram of the dot with the tunnel shell embedded in a 3D material. We assume flat bands and a perfect selected contact (infinite barrier on the left part). The input parameters are the energy E 1 of the ground-state |1 (the intermediate-band), the energy E 2 of the excited state |2 , the height and the thickness of the barrier B and L respectively and E c the energy of the band-edge of the contact. Concerning transport, the states |1 , |2 and the contact are coupled by tunneling (σ T ), induced and spontaneous optical couplings (σ I and σ S ). In all the present study, the origin of energy is E 1 = 0.

FIG. 2 :

 2 FIG. 2: Current spectrum, calculated at S oc , for B = 0.2 eV, m * = 0.07m 0 (m 0 the free electron mass), n = 3.5, n r = 10 2 , E t = 0.6 eV, E r = 0.2 eV, E m = 1.4 eV, a) L = 0 nm, b) L = 10 nm and c) L = 5 nm. The absorption current J A (S oc , E) is represented by the green line and the retrapping current J R (S oc , E) by the red line. For each value of L we also show J sc , S oc and P max .

TABLE I :

 I The minima of energy for the intermediate-band / conduction band transition calculated for several concentration C and non-radiative coefficient n r . E quant , calculated with our model, corresponds to the limit under which the inter-subband transition cannot produce power. E classic calculated with a detailed-balance model assuming sharp absorption, corresponds to the limit under which the IBSC is less efficient that the optimal single bandgap cell.

	C	n r	1 10 2 5 × 10 4
		E quant 0.15 0.27 0.43
	1
		E classic 0.14 0.30 0.49
		E quant	0.11 0.27
	500
		E classic	0.08 0.30
	10 4	E quant	0.03 0.19
		E classic	0.02 0.20

Acknowledgement

The authors thank ICEMAN (ANR-19-CE05-000) for financial support.