Small RNAs involved in plant response to abiotic stresses
\r\n\tThe study of populations and plant communities in their different aspects; ecological, structural, functional and dynamic, it is essential to establish a posteriori models of forest and agricultural management.
\r\n\r\n\tFor this, the methodological approaches on the type of sampling are considered essential, since there are differences between the purely ecological and the phytosociological methods, despite the fact that both pursue the same objective.
\r\n\tAlthough the ecological method for the knowledge of the vegetation is widely extended, the phytosociological one is no less so, since in the European Union it has been developed as a consequence of policies on sustainability, through which regulations have been issued, such as the habitats directive.
\r\n\tOn the other hand, research on plant dynamics and knowledge of the landscape in an integral way, have multiplied in the last 30 years, which has favored a deep knowledge of the floristic and phytocenotic wealth, which is fundamental for agricultural management, livestock and forestry.
",isbn:"978-1-83969-386-1",printIsbn:"978-1-83969-385-4",pdfIsbn:"978-1-83969-387-8",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"0abf2a59ee63fc1ba4fb64d77c9b1be7",bookSignature:"Dr. Eusebio Cano Carmona, Dr. Ricardo Quinto Canas, Dr. Ana Cano Ortiz and Dr. Carmelo Maria Musarella",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9662.jpg",keywords:"Climatic Factors, Bioclimate, Thermotype, Flora, Conservation, Phytocenosis, Plant Dynamics, Landscape, Cartography, Vegetation Series, Crops, Reforestation",numberOfDownloads:55,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 23rd 2020",dateEndSecondStepPublish:"January 25th 2021",dateEndThirdStepPublish:"March 26th 2021",dateEndFourthStepPublish:"June 14th 2021",dateEndFifthStepPublish:"August 13th 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Dr. Cano Carmona and colleagues have directed 12 doctoral theses and more than 200 publications among articles, books, and book chapters. He has participated in national and international congresses with about 250 papers. He has held a number of different academic positions, including Dean of the Faculty of Experimental Sciences at the University of Jaen, Spain, and founder and director of the International Seminar on Management and Conservation of Biodiversity.",coeditorOneBiosketch:"Ricardo Jorge Quinto Canas is currently an Invited Assistant Professor in the Faculty of Sciences and Technology at the University of Algarve – Portugal, and a member of the Centre of Marine Sciences (CCMAR), University of Algarve. His current research projects focus on Botany, Vegetation Science (Geobotany), Biogeography, Plant Ecology, and Biology Conservation, aiming to support Nature Conservation.",coeditorTwoBiosketch:"Ana Cano Ortiz's fundamental line of research is related to botanical bioindicators. She has worked in Spain, Italy, Portugal, and Central America. It presents more than one hundred works published in various national and international journals, as well as books and book chapters; and has presented a hundred papers to national and international congresses.",coeditorThreeBiosketch:"Carmelo Maria Musarella is a biologist, specialized in Plant Biology. He is a member of the permanent scientific committee of the International Seminar on “Biodiversity Conservation and Management” guested by several European universities. He has participated in several international and national congresses, seminars, and workshops and presented oral communications and posters.",coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"87846",title:"Dr.",name:"Eusebio",middleName:null,surname:"Cano Carmona",slug:"eusebio-cano-carmona",fullName:"Eusebio Cano Carmona",profilePictureURL:"https://mts.intechopen.com/storage/users/87846/images/system/87846.png",biography:"Eusebio Cano Carmona obtained a PhD in Sciences from the\nUniversity of Granada, Spain. He is Professor of Botany at the\nUniversity of Jaén, Spain. His focus is flora and vegetation and he\nhas conducted research in Spain, Italy, Portugal, Palestine, the\nCaribbean islands and Mexico. As a result of these investigations,\nDr. Cano Carmona and colleagues have directed 12 doctoral theses\nand more than 200 publications among articles, books and book\nchapters. He has participated in national and international congresses with about\n250 papers/communications. He has held a number of different academic positions,\nincluding Dean of the Faculty of Experimental Sciences at the University of Jaen,\nSpain and founder and director of the International Seminar on Management and\nConservation of Biodiversity, a position he has held for 13 years. He is also a member of the Spanish, Portuguese and Italian societies of Geobotany.",institutionString:"University of Jaén",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"5",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"University of Jaén",institutionURL:null,country:{name:"Spain"}}}],coeditorOne:{id:"216982",title:"Dr.",name:"Ricardo Quinto",middleName:null,surname:"Canas",slug:"ricardo-quinto-canas",fullName:"Ricardo Quinto Canas",profilePictureURL:"https://mts.intechopen.com/storage/users/216982/images/system/216982.JPG",biography:"Ricardo Quinto Canas, Phd in Analysis and Management of Ecosystems, is currently an Invited Assistant Professor in the Faculty\nof Sciences and Technology at the University of Algarve, Portugal, and member of the Centre of Marine Sciences (CCMAR),\nUniversity of Algarve. He is also the Head of Division of Environmental Impact Assessment - Algarve Regional Coordination\nand Development Commission (CCDR - Algarve). His current\nresearch projects focus on Botany, Vegetation Science (Geobotany), Biogeography,\nPlant Ecology and Biology Conservation, aiming to support Nature Conservation.\nDr. Quinto Canas has co-authored many cited journal publication, conference articles and book chapters in above-mentioned topics.",institutionString:"University of Algarve",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"0",institution:null},coeditorTwo:{id:"203697",title:"Dr.",name:"Ana",middleName:null,surname:"Cano Ortiz",slug:"ana-cano-ortiz",fullName:"Ana Cano Ortiz",profilePictureURL:"https://mts.intechopen.com/storage/users/203697/images/system/203697.png",biography:"Ana Cano Ortiz holds a PhD in Botany from the University of\nJaén, Spain. She has worked in private enterprise, in university\nand in secondary education. She is co-director of four doctoral\ntheses. Her research focus is related to botanical bioindicators.\nDr. Ortiz has worked in Spain, Italy, Portugal and Central America. She has published more than 100 works in various national\nand international journals, as well as books and book chapters.\nShe has also presented a great number of papers/communications to national and\ninternational congresses.",institutionString:"University of Jaén",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"6",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"University of Jaén",institutionURL:null,country:{name:"Spain"}}},coeditorThree:{id:"276295",title:"Dr.",name:"Carmelo Maria",middleName:null,surname:"Musarella",slug:"carmelo-maria-musarella",fullName:"Carmelo Maria Musarella",profilePictureURL:"https://mts.intechopen.com/storage/users/276295/images/system/276295.jpg",biography:"Carmelo Maria Musarella, PhD (Reggio Calabria, Italy –\n23/01/1975) is a biologist, specializing in plant biology. He\nstudied and worked in several European Universities: Messina,\nCatania, Reggio Calabria, Rome (Italy), Valencia, Jaén, Almeria\n(Spain), and Evora (Portugal). He was the Adjunct Professor\nof Plant Biology at the “Mediterranea” University of Reggio\nCalabria (Italy). His research topics are: floristic, vegetation,\nhabitat, biogeography, taxonomy, ethnobotany, endemisms, alien species, and\nbiodiversity conservation. He has authored many research articles published in\nindexed journals and books. He has been the guest editor for Plant Biosystems and a\nreferee for this same journal and others. He is a member of the permanent scientific\ncommittee of International Seminar on “Biodiversity Conservation and Management”, which includes several European universities. 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From chapter submission and review to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"6893",title:"Endemic Species",subtitle:null,isOpenForSubmission:!1,hash:"3290be83fff5bc015f5bd3d78ae9c6c7",slug:"endemic-species",bookSignature:"Eusebio Cano Carmona, Carmelo Maria Musarella and Ana Cano Ortiz",coverURL:"https://cdn.intechopen.com/books/images_new/6893.jpg",editedByType:"Edited by",editors:[{id:"87846",title:"Dr.",name:"Eusebio",surname:"Cano Carmona",slug:"eusebio-cano-carmona",fullName:"Eusebio Cano Carmona"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"6418",title:"Hyperspectral Imaging in Agriculture, Food and Environment",subtitle:null,isOpenForSubmission:!1,hash:"9005c36534a5dc065577a011aea13d4d",slug:"hyperspectral-imaging-in-agriculture-food-and-environment",bookSignature:"Alejandro Isabel Luna Maldonado, Humberto Rodríguez Fuentes and Juan Antonio Vidales Contreras",coverURL:"https://cdn.intechopen.com/books/images_new/6418.jpg",editedByType:"Edited by",editors:[{id:"105774",title:"Prof.",name:"Alejandro Isabel",surname:"Luna Maldonado",slug:"alejandro-isabel-luna-maldonado",fullName:"Alejandro Isabel Luna Maldonado"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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In recent years, much progress has been made in unraveling the complex and sophisticated molecular mechanisms by which plants have evolved during periods of environmental stresses, and a great deal of attention has been paid to identifying these stress-responsive proteins and their relevant gene networks. Plant-stress responses depend on the precise expression of the genes and their accurate regulation, which is attained by multiple mechanisms at different levels such as transcriptional, posttranscriptional, and posttranslational regulations. Although studies have been mostly focused on the transcriptional level of regulatory mechanisms so far, recent results lead us to the point that posttranscriptional events also play a very important role in gene expression regulation in major scenarios of a plant life, from developmental processes to stress responses. Small noncoding RNAs (sRNAs) are the important posttranscriptional regulatory factors in gene regulatory networks. They are involved in many important processes of plant development and stress responses.
sRNAs are roughly divided into different categories based on the genomic origins of their precursors: microRNAs (miRNAs), trans-acting small interfering RNAs (ta-siRNAs), and natural antisense small interfering RNAs (nat-siRNAs). These sRNAs are loaded into RNA-induced silencing complexes (RISC) and regulate the expression of their relative target genes negatively by affecting the mRNA levels, chromatin remodeling, and DNA methylation. Understanding of sRNA-guided stress regulatory networks should provide us with new tools and vision for the genetic improvement of plant stress tolerance and eventually developing more stress-resistant plants in future.
This chapter highlights the recent advances in understanding the crucial roles of sRNAs in plant responses to heat, drought, salinity, nutrient deficiency and low-temperature stresses, and proposes potential technologies and strategies used to identify abiotic stress-regulated sRNAs in addition to the recent advances and methods for validation and analysis of their target genes.
The discovery of RNA interference (RNAi) in the late 1990s has been a tornado for the past decade in terms of surprising geneticists for it changed the earlier understanding of the RNA field and the complexity of posttranscriptional control and epigenetic regulation caused by small RNAs. In 1995, Guo and Kemphues used antisense RNA sequence to block the par-1 mRNA in
Posttranscriptional gene silencing (PTGS) by RNAs was first reported in plants in 1996. The lin-4 gene, which is known to be essential for the timing of larval development in
One of the main reasons that small RNAs called so much attention was that soon after their discovery, the target genes for these small RNAs were reported to be crucial in leaf or flower development, which was consistent with the previous reports [9-13]. They have been found to have an impact on almost all the biological processes in eukaryotic cells as they have a wide range of target genes, which are corresponded to some of the previously identified regulatory genes and transcription factors that proved to play key roles such as in controlling cellular metabolism, growth and differentiation, phase transition timing and leaf patterning, and defense mechanisms against biotic and abiotic stresses in case of plants. These 18–25-nucleotide (nt) RNAs are categorized into many different classes based on their size, their biogenesis pathway, and their mode of action.
sRNAs are short nucleic acid sequences that give rise to the assembly of protein–RNA complexes, which later are able to repress the expression of their identified target genes by sequence-specific base pairing. This silencing of the target sequence can occur through several ways by (1) reducing their rates of transcription, (2) reducing the stability of their mRNAs in the cell, or (3) reducing the translation of their mRNAs into protein.
Although much of the work on ncRNAs field has been focused on small RNAs of under 40 nucleotides long, there are larger ncRNAs called mRNA-like ncRNAs (or mlncRNAs)that have received much less attention and have been reported to play some roles in some of the plant functions such as phosphate starvation response and nodulation. The article by Rymarquis et al. explains about them [14].
The generation of sRNAs involves a set of evolutionary conserved proteins, such as Dicer (DCR) or Dicer-like (DCL), Argonaute (AGO), and RNA-dependent RNA polymerase (RDR), which all together form the RNA silencing machinery in plants. The DCLs have been the most studied enzyme so far, which, in
The sRNAs are categorized into different classes based on their size, their biogenesis pathway, and their mode of action to at least six groups, including microRNAs (miRNAs), heterochromatic small interfering RNAs (hc-siRNAs), trans-acting small interfering RNAs (ta-siRNAs), natural antisense small interfering RNAs (nat-siRNAs), repeat-associated small interfering RNAs (ra-siRNAs), and the piwi-interacting RNAs (piRNAs), which are found in metazoans.
Typically, miRNAs are derived from single-stranded RNA precursors that are transcribed by RNA polymerase II from MiRNA genes called primary microRNA transcript (pri-miRNA), which are capable of forming a self-complementary fold-back structure named hairpin or stem loop in which the mature miRNA could reside on the 3’ or 5’ end (Table 1). This imperfect double-stranded structure is further recognized and processed by DCL1 in association with other protein factors [15]. This gives birth to the miRNA/miRNA* duplex which based on the thermodynamic features will have a different fate but usually the pre-miRNA strand is loaded onto an AGO1-containing, RNA-induced silencing complex (RISC) and the miRNA* strand lives for a short time in the cell. Mature microRNAs (miRNAs), which are the so-called hairpin-derived RNAs, are 20–24 nt long and single stranded while miRNA genes are 70–300 nt long. Mature miRNAs help the target recognition and cleavage in cooperation with AGO1 and miRISC. The first cleavage by DCL1 generates a stem-loop intermediate, called the precursor miRNA (pre-miRNA), and the second cleavage by DCL1 releases the miRNA duplex, one strand of which is known as mature miRNA and the other strand is known as miRNA* (miRNA star).
\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t
miRNA | \n\t\t\tmicroRNA | \n\t\t\t\n\t\t\t\t | \n\t\t\tRepress target gene expression through mRNA cleavage and translational repression | \n\t\t\tThe fold-back structures of long ssRNA transcripts are cleaved by Dicers | \n\t\t
siRNA | \n\t\t\tshort-interfering RNA | \n\t\t\tRepeats, transposons, and retroelements (endogenous). Transgenes and viral RNAs (exogenous) | \n\t\t\tSilence repeats and transposons through RNA-dependent DNA methylation and chromatin modification | \n\t\t\tRDR-generated dsRNAs are cleaved by Dicers | \n\t\t
ta-siRNA | \n\t\t\ttrans-acting siRNA | \n\t\t\tTAS loci | \n\t\t\tRepress target gene expression through mRNA cleavage | \n\t\t\tTAS transcripts are cleaved by miRNAs, transcribed by RDR into dsRNA, and then processed by Dicers | \n\t\t
nat-siRNA | \n\t\t\tnatural antisense transcript- derived siRNA | \n\t\t\tLoci producing pairs of sense-antisense transcripts | \n\t\t\tStressed-induced nat-siRNA to repress target gene expression through mRNA cleavage | \n\t\t\tThe dsRNA derived from overlapping transcripts is cleaved by Dicers | \n\t\t
piRNA | \n\t\t\tpiwi-interacting RNA | \n\t\t\tRepeats, transposons, and retroelements | \n\t\t\tGerm-line-specific piRNA to suppress repeats and transposons in flies and mammals | \n\t\t\tssRNA derived from transposons is cleaved by PIWI protein | \n\t\t
Small RNAs involved in plant response to abiotic stresses
Mammals use only one class of RNAse III enzyme, Dicer, to generate both miRNAs and siRNAs. In plants, there are a variety of specialized DCL endonucleases, which are classified into 10 categories. DCL1 is involved in miRNA biogenesis pathway while other DCLs participate in various aspects of sRNA-mediated generation or gene silencing pathway (Figure 1) [16].
All the information about the reported miRNAs and their sequences and annotations are stored in a database called miRBase (www.mirbase.org), which is updated on a regular basis with the new published data in the literature [17]. So far, there are 205 precursors and 384 mature miRNAs reported in the model plant
siRNAs were first identified in 1999 in plants [18], and later there were many reports about diverse sets of endogenous siRNAs in plants as well as in animals (Table 1) [6] [8][19][20-22]. Most of the plant siRNAs are around 24 nt in length that are excised from the long double-stranded RNA duplexes or transcripts generated from inverted repeat regions [23-24]. The sources of these double-stranded sequences that eventually trigger biogenesis of siRNAs could be endogenous or exogenous. Endogenous plant siRNAs can be classified into several categories, including miRNA-induced trans-acting siRNAs (tasiRNAs), natural antisense siRNAs (nat-siRNAs), cis-acting siRNAs (casiRNAs), heterochromatic siRNAs, and many other unclassified small RNAs [25]. In plants, ta-siRNAs are generated from the genomic loci named TAS genes, which are transcribed by RNA-pol II. The generation of ta-siRNAs is triggered by an miRNA, which cleaves a nonprotein-coding transcript of a tasiRNA gene [26-29]. In plants, there are eight TAS loci reported so far, which belong to four families (TAS1–4). TAS1 and TAS2 families are cleaved by miR173 with the association of AGO1. TAS3 family transcripts are cleaved by the guidance of miR390 and AGO7 and usually target the auxin response factor (ARF) transcripts. TAS4 transcript is cleaved by miR828 guided together with AGO1 and they usually target myeloblastosis (MYB) transcription factors [30]. These cleaved RNAs are then processed by the suppressor of gene silencing 3 (SGS3) and copied into double-stranded RNAs by RNA-dependent RNA polymerase 6 (RDR6). DCL4 cleaves them in multiple rounds so that it finally gives rise to the 21-nt ta-siRNAs. ta-siRNAs are loaded onto AGO1 complex to degrade the target mRNAs [31].
The other class of siRNAs called nat-siRNAs are separated into two groups: cis-nat-siRNAs that are generated from two RNAs, which were transcribed from the same loci but opposite strands, and trans-nat-siRNAs, which were transcripts from different loci [32]. RDR6 and DCL2 are involved in generating 24-nt nat-siRNAs, and RDR6 and DCL1 are involved in generating 21-nt nat-siRNAs. trans-nat-siRNAs are transcripts from different loci but processed by the same proteins (RDR6 and DCL2). ta-siRNAs cleave the target mRNAs by being partially or fully complementary with them.
Heterochromatic siRNAs mostly originate from transposable elements or repeats and their mode of action is slightly different from miRNAs and ta-siRNAs, as they modulate the histone modification at their homologous regions in the genome and inhibit the gene expression at the transcriptional level.
Natural antisense transcripts (NATs) are small RNA molecules, which are endogenous and show partial or entire complementarity to other transcripts (Table 1). cis-NATs are categorized in the nat-siRNAs group and are transcribed from the same genomic loci but in the opposite strand of DNA as their sense transcripts. This class of NATs is very common in eukaryotes (l7–30% of the genes encode complementary cis-NATs in animals and plants) [33-37]. In animals, NATs are involved in alternative splicing, DNA methylation, RNA editing, and genomic imprinting [38-41]. In plants, several cis-NATs are involved in gene regulatory mechanisms [42-43]. There are already some reports about the identified cis-NATs in
ta-siRNAs are 21 nt in length and are reported to be found only in plants so far (Table 1). ta-siRNAs originate from a noncoding RNA precursor, which is initially targeted to be cleaved by an miRNA molecule. RNA-dependent RNA polymerase converts the cleaved products into double-stranded RNA molecules, which are later cleaved again into 21-nt ta-siRNAs. Hence, the formation of these RNAs is determined by the presence of both miRNA (Dicer-Like1, Argonaute1, HYPONASTIC LEAVES1, and HUA ENHANCER 1) and siRNA (RNA-dependent RNA polymerase 6 and DCL4) biosynthesis pathways components. ta-siRNAs can guide cleavage of target mRNAs and regulate gene expression at the posttranscriptional level like plant miRNAs.
Abiotic stress is known to be one of the attention-calling factors globally, which causes a considerable yield loss each year. Hence, much effort has been made in understanding the complex stress-response mechanisms, especially in the identification of stress-responsive protein-coding genes. But, in recent years, after the discovery of small noncoding RNAs, they have been found to be involved in plant stress responses and indeed very functional players in these pathways. These small RNAs regulate the gene expression in different levels and hence are entangled within all the vital pathways in the plant development, metabolism, and stress response.
As sessile organisms, plants have evolved their specific adaptation and acclimation mechanisms in order to survive during the hard spell. To do the morphological and physiological adaptations to abiotic stresses, the plant needs to manage the complicated rearrangement of gene expression networks, which are controlled at transcriptional and post-transcriptional levels. The concern about future food shortages makes it imperative to better understand the genetic control of stress tolerance networks and pathways and to use this knowledge to increase the total tolerance of important crop species. As the first step, we have to understand the complex responses of the plants to stress, from changes in molecular level to physiological level.
With the help of high-throughput gene expression analysis, there have been many reports about the modulated genes and different small RNAs under abiotic stresses. The difference in the expression level of these genes could indicate that it might be responsive to stress condition and, as a result, it can help the plant to survive the hard condition. Many studies have been published in this regard in various plant species, some of which having an economic importance, like rice, wheat, legumes, barley, sugarcane, potato, and tomato as well as many other species. Some of the genes are induced after facing the stress conditions in these studies while some are downregulated, which is connected with the roles these genes play during the stress condition. Also, the respective miRNAs or other sRNAs that target these mRNAs show a different expression pattern during the stress condition. sRNAs, which are accumulated by stress, might downregulate their target genes and act as a negative regulator of stress tolerance; for instance, the genes involved in cell expansion and division should be downregulated as the plant needs to save energy in order to pass through the hard environmental condition. On the other hand, reduction of sRNA level might lead to upregulation of their target genes, mRNAs, which positively regulates the stress tolerance.
The molecular basis of plant tolerance to abiotic stresses and stress regulation of small RNAs has been studied using different methods to observe the altered expression of these molecules and their related target genes; for instance, the sequence analysis of small RNA libraries before and after the stress condition, microarray data analysis, mutagenesis, and RNAi. Their reports have identified numerous genes and sRNAs that are induced by applying different stress conditions, which is the material for the next step: making transgenic plants and check if these overexpressed transgenics could exhibit an improvement in stress tolerance. But the fact is that even though some of the genes and small RNAs show altered expression under stress, they do not play any role to make the plant more tolerant to the stress. And the reason is largely because of the complex genetic interactions underlying the plant tolerance toward stress, which are still to be understood.
From transcriptomic studies, we know that the stress conditions such as heat, drought, cold, and salt evoke the expression of an overlapping set of genes, suggesting that their signaling transduction pathways share common control points. Most of the genes, which are detected to be responsive to abiotic stresses, are usually the genes that regulate plant development and reproduction (as the plant faces the urge to save more energy for producing viable seeds rather than a high biomass), also senescence-related genes (as to recycle the nutrients from the old leaves to younger leaves and reproductive parts and wasting less water and energy for them), as well as the genes that are involved in the abscisic acid (ABA) pathway, which play a crucial role in plant growth and development pathway and redox pathway.
RNA interference technology is one of the potential reverse genetics tools for understanding the functional significance of these genes and their respective regulatory sRNAs. The information about stress-induced genes and sRNAs including the sequence and annotation could be found in the genome databases like National Centre for Biotechnology Information (NCBI) or stress complementary DNA (cDNA) databases. In addition to these stress-induced genes, the regulatory elements for these genes are also altered during stress condition including small regulatory RNAs. A number of these sRNAs, which are induced in different plant species and under different stress conditions, can be found in some recent review papers [47]. A vast amount of data has been published about the expression profiling of different sRNAs in various stress conditions. Although these expression-profiling experiments can provide us with some clues about the involvement of these sRNAs in gene regulation under those specific circumstances, to find the relevance of each of these sRNAs in imparting stress tolerance in plants can only be studied by functional genomic approaches like gene overexpression or downregulation. RNA interference technology using constructs transcribing self-complementary hairpin RNA is one of the reverse genetics approaches to downregulate genes in plants.
Another powerful technique to learn about gene functions in a developmental or physiological context in plants is by mutagenesis and to isolate the corresponding mutants with altered phenotypes. Various mutagenic agents, including chemical and biological, have been widely used in this regard, each of them with its own advantages and inconveniences.
For
Drought stress is known as the most significant stress especially with regard to the climate change and global warming. It restricts plant growth and development severely, while tolerant plants are able to survive by several mechanisms such as consuming small amounts of water or keeping their stomata closed at a high rate under drought conditions.
Approximately two-thirds of the potential yield of major crops are lost every year due to the adverse growing environments [48]. A worldwide increase in arid areas, including the Mediterranean basin, has been predicted by the International Plant Protection Convention (IPPC) in 2001 and 2007. Water deficit also leads to salinity stress in many cases, which makes the growth situation even harder for the plants. Therefore, it is regarded as the most important abiotic stress and it is necessary to develop strategies toward sustainable use of water and improve plant-drought resistance [49]. Many genes have already been studied and reported to be involved in the drought-resistance response network in the plants. But in recent years, it has become clear that sRNAs play pivotal roles in stress responses as well in regulating the expression of resistance genes.
MiRNA-expression profiling under drought stress has now been performed in
Another group has worked on miRNA expression patterns of drought-resistant
Crops worldwide are threatened by excessive soil salinity due to the accumulation of salt delivered along with irrigation water and by coastal flooding and the high evapotranspiration rates caused by climate change. About 6% of the total arable land in the world is affected by excess salt [55] and it has been predicted to increase to about 30% of the world’s arable land by 2025 and 50% by the year 2050 [56]. Several genes and pathways in plants are affected by salt stress [57]. Hence, the promising approach to address the problem of soil salinity is to increase the understanding of response of plants to salinity-related stress. These genes are mostly involved in signal transduction, activation of ion channels, and growth-factor-regulated modification of plant architecture, and, in particular, root morphology.
Besides the genes, numerous differentially regulated miRNAs have also been identified in salt-stressed plants. For instance, miR156, miR158, miR159, miR165, miR167, miR168, miR169, miR171, miR319, miR393, miR394, miR396, and miR397 were all reported to be overexpressed in response to salt stress in
miR169 was also reported to be induced by high salinity stress [46]. The authors found a cis-acting ABA-responsive element (ABRE) in the upstream region of miR169n, which suggested that miR169n might be regulated by ABA. Another group used microarray experiments as a method to explore the miRNA profile of maize in different lines (salt-tolerant and salt-sensitive); finally, it was reported that the expression levels of miR156, miR164, miR167, and miR396 family members were downregulated considerably, while it was increased in miR162, miR168, miR395, and miR474 families after salt-shock in root tissue [58].
Some plants increase their tolerance to cold in order to deal with the low temperatures. This phenomenon is known as cold acclimation. In recent years, many cold-regulated genes have been identified in plants under cold stress. The C-repeat binding factor (CBF) cold-responsive pathway was considered as the most known cold tolerance pathway in plants [59]. There are three CBF/DREB1 family members, including CBF1, CBF2, and CBF3 (DREB1b, DREB1c, and DREB1a, respectively), encoding the DNA-binding proteins of Apetala2/ethylene responsive factor (AP2/ERF) family [60]. Also, the expression of many miRNAs in cold stress has been examined in different plants including
The average temperature of our planet is rising year by year because of the climate change. As a result, changes in the patterns of rainfall, droughts, and submergence stress are induced to the natural environments. Heat stress even alters the distribution and productivity of important crops negatively throughout the earth. A temperature rise of −5°C above the plant’s optimum temperature is considered as a heat stress. It disrupts normal functions of cellular processes, may lead to delay in plant growth and development, and it might even result in death of the plant, but, usually, high temperatures result in water deficiency, which eventually leads to increase in salt concentration. Recent studies indicate that the projected global warming in the upcoming years will negatively affect the yield of important crops; hence, the necessity of focusing on gene networks and their regulatory components becomes obvious.
A major component with regard to responding to heat stress is the induction of heat shock proteins (HSPs), which get activated by heat shock transcription factors (HSFs). There are five classes of HSPs based on their molecular weights: HSP100, HSP90, HSP70, HSP60, and small heat shock proteins (sHSPs, 15–30 kDa). On the other hand, HSFs recognize heat stress elements on the promoter of heat stress-responsive genes (HSE: 5′-GAAnnTTC-3′). Plant HSFs are categorized into three classes based on their oligomerization domains (A, B, and C) [61].
However, the more upstream regulators of HSFs remain to be identified. Guan et al. have reported that miR398 is rapidly induced by being subjected to heat stress while its target genes (CSD1, CDS2, and CCS) are downregulated. They further reported that the expression levels of HSF and HSP genes in
Based on deep sequencing experiments, Wang et al. suggest that there is a new class of small RNAs that originate from the chloroplast genome, which are responsive to heat stress [63]. They performed RNA sequencing (RNA-seq) and found 1031 cis-NATs in
Wheat miRNAs showed differential expression in response to heat stress; by using Solexa high-throughput sequencing, Xin et al. cloned the small RNAs from wheat leaves treated by heat-stress gene [66]. Stief et al. also reported that miR156 is responsible for heat stress memory in
Biogenesis of miRNAs and ta-siRNAs
Physiological responses to stress are controlled by expression of a large number of genes, many of which are regulated by microRNAs. At the molecular level, identification of stress-responsive genes is an initial step toward understanding plant stress response as pyramiding of different genes in the same plant is an option for achieving better stress tolerance. Although finding genes and sRNAs, which show induction by stress, is an important step toward stress tolerance improvement, most of the studies in which they use transgenics only show the importance of the introduced transgene and not the overall metabolic effects that the trans-host gets exposed to. On the other hand, the new stress-tolerant transgenic lines should have no or few undesired phenotypic changes plus a minimal yield penalty. In stress-tolerant transgenics, which are introduced so far, a constitutive promoter has been used for expressing the transgene in most of the cases. These transgenes must be utilized to overcome the problem of yield penalty and growth retardation in these experiments. Admittedly, most reports published on stress-tolerant transgenic plants are based on the limited characterization of the stress condition as well as the tolerant phenotypes. Adequate assays for phenotyping of the stress-tolerance trait must be undertaken under natural stress conditions. Overall, there is a lack of uniformity in the stress induction regimes applied by various research groups, which makes the comparisons of the responses among different reports difficult and this fact must be taken into consideration.
In statistical physics only a few problems can be solved exactly. For complex problems, numerical methods can give exact results for problems that could only be solved in an approximate way. Numerical simulation can be a way to test the theory. The numerical results can be compared to the experimental results. The numerical simulation is placed between the fundamental and the experimental treatment; it has a quasi-experimental character (numerical experience). For problems of statistical physics, the most widely used simulation methods are the Monte Carlo method and the molecular dynamics method.
The first Monte Carlo simulation (MCS) was proposed by Metropolis et al. in 1953 [1]. The second Monte Carlo simulation was proposed by Wood and Parker in 1957 [2]. The obtained results were in good agreement with the experimental results of Bridgman [3] and those of Michels et al. [4]. In this method we attribute a series of initial positions chosen randomly to a system of N particles interacting through a defined potential. A sequence of particle configurations is generated by giving successive displacements to particles; we only retain configurations to ensure that the probability density is that of the chosen.
Molecular dynamics simulation (MDS) has been first introduced to simulate the behavior of fluids and solids at the molecular or atomic level. MDS was used for the first time by Alder and Wainwright in the late 1950s [5, 6] to study the interactions of hard spheres. The principle is the resolution of equations of motion for a hard sphere system in a simulation cell. The basic algorithm is Verlet’s algorithm [7].
In this chapter, we will present techniques of numerical simulations using the Monte Carlo method. We will present an application on the gas phase during plasma-enhanced chemical vapor deposition (PECVD) of thin films. The application concerns collisions between particles. Particles are in Brownian motion. Collisions, elastic or inelastic, are considered to be binary. Non-elastic collisions result in effective chemical reactions.
In Section 2, we cite some MCS and MDS works on PECVD processes. Section 3 presents general rules on numerical simulation methods. Section 4 presents how to simulate a physical problem using MCS? We present the Metropolis algorithm as a scheme to trait random configurations and different modules related to elaborate an MCS code. In Section 5, we apply the MCS on SiH4/H2 gas mixture during a PECVD process. Finally the conclusion summarizes the contents of the chapter.
The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.
Gorbachev et al. [10, 11, 12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].
Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].
For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17, 18, 19].
In our previous works [20, 21, 22, 23, 24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].
The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:
The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model.
Mathematical model requires a mathematical formulation of the problem. It may be a problem of elements or discrete object or a problem of a continuous medium; it may be a spatiotemporal problem or frequency problem and may be a deterministic or probabilistic problem.
It would be interesting to know the mathematical equations that govern the phenomenon:
The forces between particles and elements
The potential interaction
The determination of a time scale
The determination of a length scale
Definition of constant magnitudes of motion and equilibrium magnitudes
Continuity equations, balance equations, transfer equations, etc.
The MCS technique has been chosen for this work; knowing its basic algorithm is necessary for elaborating the simulation. This step requires some actions:
Validation of the model on simple cases
Simulation calculation on complex phenomena
The MCS is based on a probabilistic process with a random choice of configurations and samples of the situation of the physical system. The two pedagogical examples most cited in the literature are the integration of a single variable function and Ising’s model of spin. In the following subsection, we define the integration of a single variable function. We introduce the Ising model at the end of Section 4.2.2.
Calculation of the definite integral for a function f(x) of a single variable x on domain {a, b} has been proposed (Figure 1):
The integral of a function f(x).
Let:
Let xi and yi be real random numbers (i = 1, 2,…, N), and let H be a real number greater than the f(x) for x belonging to the domain {a, b} (or x ∈ {a, b}).
Let r1 and r2 be two random numbers belonging to the domain {0, 1} according to a uniform distribution law. Generators (e.g., Ran, RANDOM, RANDUM, or other IMSL mathematical libraries) of random numbers can be used:
where xi and yi are random numbers (xi ∈ {a, b} and yi ∈ {0, H}).
The Monte Carlo (MC) method is based on a probabilistic process. Let N be the total number of cases chosen (possible cases). It is necessary to count the number of favorable cases (or the number of points below the curve y = f(x)); let yi ≤ f(xi)). The number of favorable cases is Nfav. When N➔∞, the value
An example [26] is the calculation of the value π by calculating the integral
We take a = 0.0, b = 1.0, and H = 1.0.
For different values of N, we show that the numerical solution tends to π = 4
Although this integral is simple, it shows the strength and simplicity of the method. The technique can be generalized for the integration of multivariate functions.
We note that integration by the MC method is based on:
The choice of
Each configuration chosen is either
For statistical physics problems, the probabilistic choice of configurations is not always deterministic; the favorable and unfavorable cases are not exclusive. According to the Metropolis algorithm [26, 27], the steps of the simulation are:
Choice of a simulation cell of adequate shape to the studied phenomena. The size of the simulation cell is related to a scale of length characteristic of the forces and interaction potential of the studied phenomenon. This cell may contain Npc particles (and/or elements).
Choice of an initial configuration that responds to some physical and thermodynamic properties. The total or internal energy of the system is Ei.
Infinitesimal random displacement of a particle (or element of the system) and calculation of the new internal energy of the system Ef. This displacement is related to the physical magnitudes: time scale and length scale.
If
If
If
Figure 2 shows how to choose between the selected configurations. Let
Configuration choice according to Metropolis scheme.
Numerical simulation using the MC method is a very important tool for the study of static properties. The basic algorithm is based on probability notions. Understanding of the distribution function and/or interaction potentials is the heart of the calculation.
In equilibrium statistical physics, the system has a certain probability that can be in any states. The probability of being in a state
where T is the absolute temperature and kB is called Boltzmann’s constant. It is conventional to denote the quantity (kBT)−1 by the symbol β. The normalizing factor Z, or partition function, is given by:
The average of a quantity Q fora system in equilibrium is:
The internal energy U, is given by:
which can be written in terms of a derivative of the partition function:
From thermodynamics we have expressions for the specific heat C, the entropy S, and the Helmholtz free energy F:
or
and
and
We can calculate other parameters affecting the system.
The Monte Carlo method is an excellent technique for estimating probabilities, and we can take advantage of this property in evaluating the results. The simplest and most popular model of a system of interacting variables in statistical physics is the Ising model. It consists of spins
The Ising model has been studied in one and two dimensions to obtain results of thermal properties, phase transition, and magnetic properties [26, 27, 28]. For chosen values of J and/or B, different steps may be taken for the calculations (simulation cell, initialization, configurations, boundary conditions, calculation algorithms). For any configuration, each spin takes the two possible directions. The detail of the calculation procedure is not the purpose of this chapter.
We give a system of N particles (atoms, molecules, ions or particles) placed in a cell of fixed volume, generally of cubic form. The initial positions may, depending on the case, be distributed randomly according to a certain law (uniform or otherwise) or have a given symmetry. In a fluid, a gas, or a plasma, the particles may have random positions in general; in a solid or surface, with a crystal structure, the particles take ordered positions. The choice of random initial positions allows great freedom on the choice of the number of particles in the cell.
At the first step, the particles are given velocities that are generally selected to have a zero total momentum. If the system is in thermodynamic equilibrium, the initial velocities will be randomly chosen according to a Maxwell-Boltzmann law. In the general case, the velocity distribution is according to the problem dealt with. All other phase properties can be initialized to the particles; the main thing is the conservation of the total quantities of the system.
The particles interact with each other according to chosen interaction potentials. Since the interaction potentials are specific for each “numerical experiment,” the main part of the work consists in calculating the interaction energies for each proposed configuration.
The choice of interaction potentials is directly related to the mathematical formulation of the problem according to the state of the medium: fluid, gas, plasma, or solid. It can be Lennard-Jones potential, Coulomb potential, Debye potential, Morse potential, Stillinger-Weber potential, Born-Mayer potential, Moliere potential, or others.
In general, two main boundary conditions are used: periodic boundary conditions (PBC) and minimum image convention (MIC) [29].
To minimize the surface effect, periodic boundary conditions (PBC) [30] are invariably imposed. The simulation cell is reproduced throughout the space to form an infinite mesh. We can simulate the properties of an infinite system. The particles that we follow are in the central cell; if a particle crosses a wall with a certain velocity, its image returns with the same velocity by the opposite wall. Under these conditions, the number of particles in the central cell, and consequently the density, is constant. These conditions also allow the conservation of the energy and the momentum of the system and do not introduce periodic effects (because of the interaction between particles).
According to the hypotheses and according to the geometry of the problem, other boundary conditions are proposed [26]. For example, in order to model thin films, the simulation cells are longitudinal and parallel to the film; one uses PBC in the directions parallel to the film. In the direction normal to the film, free edge boundary conditions can be used. In such cases, it may be appropriate to also include surface fields and surface interactions. In this way, one can study phenomena such as wetting, interface localization-delocalization transitions, surface-induced ordering and disordering, etc.
The core of the program includes calculating the potential energies of particle configuration and particle collisions. The interactions and collisions between particles can be elastic or inelastic; they can be binary or collective. For computation, the interaction energy of a particle with its neighbors is carried out by refocusing a base cell on the particle. This particle only interacts with particles in this region. This is called the “minimal image convention” (MIC) [1].
Generally, a RANDOM generator of real random numbers ri belonging to the domain {0, 1} (or ri ∈ {0, 1} is available. This distribution law is uniform.
To have a real random number xi belonging to the domain {a, b} (or
To have a real random number xi belonging to the domain {a, b} (or xi ∈ {a,b}) according to a formula (or law) of nonuniform distribution f(x), a histogram technique is used. Let Nm be the number of intervals. If the mesh is regular (Figure 3):
Random number selection according to f (x) distribution.
We define:
We define the sequence:
and the sequence:
Hence each real random number ri belongs to the domain {0, 1} (where ri ∈ {0, 1}) (according to the uniform law); this number belongs to the domain {rxj-1, rxj}. It corresponds to a random value xran of the domain {xj-1, xj}; this number satisfies the formula (or the law) of nonuniform distribution f(x).
This technique can be generalized for a nonuniform distribution law f(x) with an irregular mesh Δxi, or with tabular data f(xi) with
The technique can be generalized, too, for a discrete distribution law f(i) with
In the literature, the reader can find simple algorithms for the choice of random numbers of some simple functions (Gaussian, etc.).
It is necessary to find some parameters allowing the control of the smooth course of the evolution of the system. We must look for the constants of movement. For example for an isolated system, we have the conservation of the total energy and the quantity of matter.
By using the numerical simulation, it is possible to calculate many spatiotemporal quantities F(r,t). These quantities can be positions, speeds, kinetic moments, particle energies, concentrations, transport coefficients, etc. It would then be possible to calculate all other quantities related to F(r,t).
For the calculation of the averages, one can note the quantities on the space, on the time or on both. The histogram methods can be used. Static or dynamic distribution functions and spatial or temporal correlation functions can be calculated. It should be noted that the SMC is much more adequate for static properties because of the probabilistic choice of configurations.
Any calculated function or parameter F(r,t) can be used for another application in another calculation program.
In the MCS model discussed extensively in this chapter, it’s more about collisions between particles. It’s
Other MCS models, named
For statistical physics problem solving (such as thin film deposition problems), MCS models use experimental, numerical, or theoretical data from other methods and models. Models can be improved to
Schematic of a hybrid model of three modules used to study gas mixtures in the PECVD [
To solve statistical physics problems with evolutions as a function of time,
Other CVD and PECVD works on MCS are presented in Ref.s [15, 34, 35, 36, 37, 38]. They show how MCS methods can study properties of gas mixtures and properties of the growth of thin films.
In this section, we present an example of PP-MCS of collisions and reactions in gas phase of SiH4/H2 mixture used in PECVD process. Some paragraphs have been treated in previous works [21, 24].
We use a MCS to study collisions and chemical reactions in gas phase of SiH4/H2 mixture used in the PECVD process. In this phase, important reactions have been identified that contribute to the production and the consumption of hydrogen (H), silylene (SiH2), and silyl (SiH3). The hydrogen consumption reactions SiH4 + H → SiH3 + H2 and SiH3 + H → SiH2 + H2 are found to play a central role in deciding the distribution of hydrogen [39].The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [40]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si film growth from SiH4 plasmas in the PECVD; it is the key precursor of a-Si:H deposition [41]. The proposed MCS allowed to get the ratio SiH2/SiH3 and mean value of densities of species. It provides information on SiH4 dissociation and on the production of SiH3, H, SiH2, and Si2H6 and other important parameters.
The plasma in the PECVD reactor is weakly ionized. For our study, the mixture gas contains 22% of SiH4 and 78% of H2; the pressure is 100 mtorr, the temperature of the gas ranges from 373 to 723 K, the electron temperature is about 2.5 eV, and the electron density is 3. 108 cm−3. The process is considered to be stationary. We take into account electrons and eight neutral species (SiH4, SiH3, SiH2, H, H2, Si2H6, Si2H5, SiH).
Symbol | Reactions | Kreac (cm3/s) |
---|---|---|
R1 | SiH4 + e→SiH3 + H+e | k1 = 3 × 10−11 [42] |
R2 | SiH4 + e→SiH2 + 2H + e | K2 = 1.5 × 10−10 [42] |
R3 | SiH4 + e→SiH + H + H2 + e | K3 = 9.34 × 10−12 [42] |
R4 | SiH4 + e→SiH2 + H2 + e | K4 = 7.19 × 10−12 [42] |
R5 | H2 + e→2H + e | K5 = 4.49 × 10−12 [42] |
R6 | Si2H6 + e→SiH3 + SiH2 + H + e | K6 = 3.72 × 10−10 [42] |
R7 | Si2H6 + e→SiH4 + SiH2 +e | K7 = 1.1 × 1010× (1.(1./(1. + (0.63 × P)))) [43] |
R8 | SiH4 + H→SiH3 + H2 | K8 = 2.8 × 10−11 × exp.(−1250/T) [44] |
R9 | SiH4 + SiH2→Si2H6 | K9 = 1.1 × 1010 × (1.−(1./(1. + (0.63 × P)))) [43] |
R10 | SiH3 + SiH3→SiH4 + SiH2 | K10 = 0.45 × 1.5 × 10−10 [44] |
R11 | SiH4 + Si2H5→SiH3 + Si2H6 | K11 = 5 × 10−13 [42] |
R12 | SiH3 + H→SiH2 + H2 | K12 = 2 × 10−11 [44] |
R13 | SiH3 + Si2H6→SiH4 + Si2H5 | K13 = 4 × 10−10 × exp. (−2500/T) [44] |
R14 | SiH2 + H→SiH + H2 | k14 = 2 × 10−11 [44] |
R15 | Si2H6 + H→Si2H5 + H2 | K15 = 0.66 × 2.4 × 10−10 × exp. (−1250/T) [43] |
R16 | Si2H6 + H→SiH4 + SiH3 | K16 = 0.34 × 2.4 × 10−10 × exp. (−1250/T) [44] |
R17 | SiH + H2→SiH3 | K17 = 2 × 10−12 [43] |
R18 | SiH2 + SiH3→Si2H5 | K18 = 3.77 × 10−13 [43] |
R19 | SiH2 + H2→SiH4 | K19 = 3 × 10−12 × (1. + (1./1. + (0.03 × P))) [43] |
R20 | 2SiH3→Si2H6 | K20 = 0.1 × 1.5 × 10−10 [43] |
R21 | SiH4 + SiH→Si2H5 | K21 = (1.−(1./(1. + (0.33 × P)))) × (6.9 × 10−10) [43] |
List of gas phase reactions and corresponding rate constants [24].
Let
And chemical reaction for the production of A is as:
Rate production and consumption for any species A are taken as:
The MCS is based on binary collisions at the microscopic level. Elastic collisions are between all particles, and inelastic collisions (or effective collisions) are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons, or molecules). According to kinetic theory, gases consist of particles in random motion. These particles are
Form of the simulation cell.
Let ni be the density of neutral spice
The chosen particle takes randomly three components of space in cell
Let ni and nj be the densities of species
According to the kinetic theory of gases, we have for an incident particle
where <sij> is the cross section of the particle
The mean free path
The time between two collisions τij is then:
For chemical effective reactions (inelastic collisions) between two reactive species
General rules of collision theory are applied:
The new velocities of the colliding particles are calculated using conservation of energy and momentum for elastic collisions.
Conservation of total energy as isolated system.
Movement of the center of mass and relative motion around the center of mass.
The reader can refer to some fundamental physics books that deal with general notions of collisions and corresponding parameters [45, 46, 47, 48].
The plasma in the PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each other and move under the effect of thermal agitation. In reality, only a small fraction of collisions are effective (result in a chemical reaction) [21].
In our MCS, after traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical, or electron). The last particle
where
The activation energy is given by:
where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction.
The two colliding particles (e.g., the electron and SiH4 molecule) can interact by several reactions (R1, R2, R3, and R4 in Table 1); we choose randomly one of gas phase reactions occurring according to a,
where
All chemical systems go naturally toward states of minimum Gibbs free energy [21, 24]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kreac and the equilibrium constant with reactants and product concentrations. Each set of binary collisions can be related or converted into time. As cited in section (a), Table 1 gives gas phase reactions and corresponding rate constants used in this MCS.
To continue the simulation, after the elastic collision, particle
From Metropolis algorithm, the scheme of this MCS is as follows:
Choices of particle of spice
Choices of random collision with a spice j.
Study of collision type (elastic, inelastic). If the collision is elastic the particle i move with a new velocity and mean free path, and we return to step (b). If the collision is inelastic particles i and j give new particles i’ and j’, according to Metropolis scheme, and we return to step (a) or (b). Periodic boundary conditions are used to keep particles in the elementary cell.
At each step, we can note the different statistics.
Once the species are selected for the simulation model, an estimate of species densities should be made. Following the model of interaction and collisions between particles (binary, collective, etc.), a first choice of the minimum number Ni of particles of each species is made. A first estimate of the sizes (Lx, Ly, Lz) of the elementary cell is made.
The study of the types of interaction potentials and the calculation of the approximate values of the force ranges, the kinetic energies, the internal energies, and the energies of activation make it possible to correct the minimal numbers Ni of particles and the sizes (Lx, Ly, Lz) of the elementary cell.
Let kp be the number of a species, kp = 1,…, 9. The minimal numbers Qnp(kp) and the sizes (Lx, Ly, Lz) have to be discussed for statistical calculations.
For numerical programming, according to the programming language used and according to the size (or the computational capacity) of the computer, it is necessary to find a judicious choice of the tables of integer or real values and which values would be useful to save all during simulation. Let Ncol,m be the maximum number of elastic collisions per particle, and let Ncycle be the number of cycles to average the simulation calculations.
For this MCS, the numerical chosen values are in Table 2.
Cell dimensions and steps for collisions | Number of species Kp | Initial number of particles in cell | ||
---|---|---|---|---|
Lx (m) | 4.68 10−6 | 1 | Qnp(SiH4) | Qnp1 |
Ly (m) | 4.68 10−6 | 2 | Qnp(SiH3) | 10 |
Lz (m) | 20.0 10−3 | 3 | Qnp(SiH2) | 10 |
4 | Qnp(H) | 10 | ||
Ncol,m | 500 | 5 | Qnp(H2) | Qnp5 |
Ncycle internal cycle | 2000 | 6 | Qnp(Si2H6) | 10 |
Ncycle external cycle | 200,000 | 7 | Qnp(SiH) | 10 |
8 | Qnp(Si2H5) | 10 | ||
9 | Qnp(e) | Qnp9 |
Used quantities and parameters in calculations for the gas temperature Tg = 520 K.
For radicals (e.g., SiH3), particle numbers Qnp(k) are very small; we take Qnp(k) = 10. These numbers cannot take value 1 or 0, even if a species k is in trace form in the gas. The value 0 for a species k means that any other species k’ does not make a collision with the species k; and the value 1 means that we have no collisions between particles of the same species in the cell.
Qnp1, Qnp5, and Qnp9 are calculated from the volume of cell, the pressure, the temperature, and the total number of particles in the cell (Qnp1 = 0.81187824 * 109; Qnp5 = 0.20296956 * 109; Qnp9 = 131).
As we have chosen a stationary regime, we must reach the values and properties at equilibrium. The results of the simulation show this trend. In MCS, averaged values, distribution functions, autocorrelation functions, and correlation functions can be calculated. To ensure rapid convergence of calculations, it would be useful to look for statistically symmetric (or stationary or unsteady) parameters [26, 50].
As an example for our MCS calculation, we have:
The number of Si2H6, SiH, and Si2H5 particles reaching the surface is negligible.
Let Ns,i and Ns, H2 be the densities of a species
Let Ns,i be the density of a species
The reactions begin with the dissociation (consumption) of H2 and SiH4 by R5, R1, and R2 reactions.
The production of SiH3 is done by R8, and then there is production of SiH2 by R12.
The reaction R2: SiH4 + e → SiH2 + 2H + e plays the central role in SiH4 dissociation by electron impact [24]. This result is compatible with [39].
The second important chemical reaction in the SiH4 dissociation is R1: SiH4 + e → SiH3 + H + e [24]. This result is compatible with that of Perkins et al. [51] and that of Doyle et al. [52].
Type | H2 | SiH4 | H | SiH3 | SiH2 |
---|---|---|---|---|---|
Ns,i/Ns, H2 | 1 | 0.23 | 1.67 10−4 | 8.60 10−5 | 9.86 10−6 |
Ratios Ns,i/Ns, H2 of particles reaching the surface compared to H2.
Type | SiH4 | SiH3 | SiH2 |
---|---|---|---|
6.695 10−6 | 7.965 10−6 | 775 10−6 |
Ratios Ns,i/Nv,i of particles reaching the surface compared to volume.
MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.
We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.
A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].
Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.
The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.
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I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. 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