Angles between <110> and [11w] directions (°)
\\n\\n
Dr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\\n\\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\\n\\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\\n\\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\\n\\nThank you all for being part of the journey. 5,000 times thank you!
\\n\\nNow with 5,000 titles available Open Access, which one will you read next?
\\n\\nRead, share and download for free: https://www.intechopen.com/books
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Preparation of Space Experiments edited by international leading expert Dr. Vladimir Pletser, Director of Space Training Operations at Blue Abyss is the 5,000th Open Access book published by IntechOpen and our milestone publication!
\n\n"This book presents some of the current trends in space microgravity research. The eleven chapters introduce various facets of space research in physical sciences, human physiology and technology developed using the microgravity environment not only to improve our fundamental understanding in these domains but also to adapt this new knowledge for application on earth." says the editor. Listen what else Dr. Pletser has to say...
\n\n\n\nDr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\n\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\n\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\n\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\n\nThank you all for being part of the journey. 5,000 times thank you!
\n\nNow with 5,000 titles available Open Access, which one will you read next?
\n\nRead, share and download for free: https://www.intechopen.com/books
\n\n\n\n
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Solutions",subtitle:null,fullTitle:"Applied Electromechanical Devices and Machines for Electric Mobility Solutions",slug:"applied-electromechanical-devices-and-machines-for-electric-mobility-solutions",publishedDate:"March 25th 2020",bookSignature:"Adel El-Shahat and Mircea Ruba",coverURL:"https://cdn.intechopen.com/books/images_new/9290.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"193331",title:"Dr.",name:"Adel",middleName:null,surname:"El-Shahat",slug:"adel-el-shahat",fullName:"Adel El-Shahat"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}}},ofsBook:{item:{type:"book",id:"5119",leadTitle:null,title:"Smart Metering Technology and Services",subtitle:"Inspirations for Energy Utilities",reviewType:"peer-reviewed",abstract:"Global energy context has become more and more complex in the last decades; the raising prices of fuels together with economic crisis, new international environmental and energy policies that are forcing companies. Nowadays, as we approach the problem of global warming and climate changes, smart metering technology has an effective use and is crucial for reaching the 2020 energy efficiency and renewable energy targets as a future for smart grids. The environmental targets are modifying the shape of the electricity sectors in the next century. The smart technologies and demand side management are the key features of the future of the electricity sectors. The target challenges are coupling the innovative smart metering services with the smart meters technologies, and the consumers' behaviour should interact with new technologies and polices. The book looks for the future of the electricity demand and the challenges posed by climate changes by using the smart meters technologies and smart meters services. The book is written by leaders from academia and industry experts who are handling the smart meters technologies, infrastructure, protocols, economics, policies and regulations. It provides a promising aspect of the future of the electricity demand. This book is intended for academics and engineers who are working in universities, research institutes, utilities and industry sectors wishing to enhance their idea and get new information about the smart meters.",isbn:"978-953-51-2452-8",printIsbn:"978-953-51-2451-1",pdfIsbn:"978-953-51-6661-0",doi:"10.5772/61356",price:119,priceEur:129,priceUsd:155,slug:"smart-metering-technology-and-services-inspirations-for-energy-utilities",numberOfPages:170,isOpenForSubmission:!1,hash:"9068fb3ae88f309a33ac632bae27da1d",bookSignature:"Moustafa Eissa",publishedDate:"June 29th 2016",coverURL:"https://cdn.intechopen.com/books/images_new/5119.jpg",keywords:null,numberOfDownloads:11960,numberOfWosCitations:4,numberOfCrossrefCitations:12,numberOfDimensionsCitations:16,numberOfTotalCitations:32,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 3rd 2015",dateEndSecondStepPublish:"November 24th 2015",dateEndThirdStepPublish:"January 21st 2016",dateEndFourthStepPublish:"January 20th 2016",dateEndFifthStepPublish:"July 6th 2016",remainingDaysToSecondStep:"5 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:"Edited by",kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"35245",title:"Prof.",name:"Moustafa",middleName:null,surname:"Eissa",slug:"moustafa-eissa",fullName:"Moustafa Eissa",profilePictureURL:"https://mts.intechopen.com/storage/users/35245/images/3312_n.png",biography:"Prof. Moustafa Mohammed Eissa\n(Digital Protection, Smart Grid, Wide Area Monitoring and Application, Grid Modeling and assessment, Smart Grid based on GIS), Smart Meters (AMI)\nProf. at Faculty of Engineering-Helwan University-Cairo-EGYPT\n(www.helwan-ntra.com)\nRECENT AWARDS ETRERA_2020 PRIZE (European Member States and the Mediterranean countries) For the Category Smart Grids: Faculty of Engineering, Helwan University, Egypt for the project on “Frequency Monitoring Network Architecture and Applications”. http://www.etrera2020.eu/link-9/135-and-the-winners-of-the-etrera-2020-prize-are.html\nSCOPUS CITATION\n• M.M. Eissa’s publications have 349 total citation cited by 291 documents in Scopus and he has H-index= 10 from 1995 at (1st of January, 2015)\n• http://www.scopus.com/authid/detail.url?authorId=35581693900\nGOOGLE SCHOLAR CITATIONS\n• M.M. Eissa’s publications on Google Scholar Citation is 520 and H-index=12\nCitation Indices = 520 h-index = 12\nhttp://scholar.google.com/citations?hl=en&user=5useqg4AAAAJ\nProf. Moustafa Mohammed Eissa (Digital Protection, Smart Grid, Wide Area Monitoring and Application, Grid Modeling and assessment, Smart Grid based on GIS) (www.helwan-ntra.com)\nProf. at Faculty of Engineering-Helwan University-Cairo-EGYPT\n\nM. M. Eissa (M’96–SM’01) was born in Helwan, Cairo, Egypt, on May 17, 1963. He received the B.Sc. and M.Sc. degrees in electrical engineering from Helwan University, Cairo, in 1986 and 1992, respectively, and the Ph.D. degree from the Research Institute for Measurements and Computing Techniques. Hungarian Academy of Science Budapest, Hungary, in 1997 (PhD Study is cooperated with Duisburg University-Institute of Electrical Engineering-GERMANY). Currently, he is a Professor with Helwan University. In 1999, he was invited to be a Visiting Research Fellow at the University of Calgary, Calgary, AB, Canada. He was a chair Prof. at King Abdul-Aziz University-KSA for sponsored project \\Demand Side Management and Energy Efficiency\\ from Saudi Electricity Company during period 2008-2010. From 2012, he is the PI for the large scale project \\SMART GRID FREQUENCY MONITORING NETWORK (FNET) ARCHITECTURE AND APPLICATIONS-220kV/500kV\\ NTRA-Egypt (www.helwan-ntra.com)-2012, END-USER Egyptian Electricity Company. From 2013, he is the PI for \\NOVEL OPTIMAL WIDE AREA COORDINATING PROTECTION AND CONTROL SYSTEM BASED ON WIDE-AREA SYNCHRONIZED MEASUREMENTS IN SYSTEMS WITH RENEWABLE ENERGY RESOURCES AND MULTIPLE FACTS EFFECT\\.\n\nDr. Eissa initiated the first application in 2010 at the Middle East by applying the smart grid and the wide area monitoring and application on the Egyptian 220kV/500kV Cairo Zone Grid.\n\nDr. Eissa is the author of more than 120 publications (40/120 IEEE, IET and Elsevier journal papers), including books, book chapters, and papers in the area of digital protection, demand side management and smart grid.\n\nHe is invited as speaker in several Universities and international events, and involved in many Technical Program Committees for international conferences. \n\n150 citations are listed in Web of Science (as of 4th of April 2012)\n\nDr. Eissa received \\State country prize in the advanced technology science from Academy of Scientific Research and Technology (Egypt), 2002, (http://www.asrt.sci.eg)\\, \\Distinguished Researcher Award, October 2005, University of Helwan, and \\Incentive Researcher Award, 2011, University of Helwan (www.helwn.edu.eg). Incentive Researcher Award, 2012- Awarded from \\Program for Continuous Improvement and Qualifying for Accreditation\\ - Ministry of Higher Education-Egypt. (high Citation according to ISI and Scopus)- http://www.qaap.edu.eg/\n\nHe has 7 major scientific reports and more than 150 collected materials in different topics related to industry. \n\nHe has many novel techniques in the digital protections. He has many consultations with the industrial sectors. He has many international and local projects. He has numerous honors for his research, leadership, supervision and teaching. His research interests include topics related to Digital Protection, Smart Grids, Wireless application on power system, Wide area Protection, Demand Side Management, Energy Efficiency, Control Schemes for Renewable Energy Resources using Harmony Search Algorithms, Power Quality and Automation system, Smart Grid based on GIS.",institutionString:null,position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"4",totalChapterViews:"0",totalEditedBooks:"3",institution:{name:"Helwan University",institutionURL:null,country:{name:"Egypt"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"756",title:"Power Electronics",slug:"power-electronics"}],chapters:[{id:"51231",title:"Introductory Chapter: Demand Response Incentive Program (DRIP) with Advanced Metering and ECHONET",slug:"introductory-chapter-demand-response-incentive-program-drip-with-advanced-metering-and-echonet",totalDownloads:2274,totalCrossrefCites:1,authors:[{id:"35245",title:"Prof.",name:"Moustafa",surname:"Eissa",slug:"moustafa-eissa",fullName:"Moustafa Eissa"}]},{id:"50284",title:"Smart Grid Implementation in Brazil Must Focus on Consumer Behavior and Markets, Regulation, and Energetic Mix Availability",slug:"smart-grid-implementation-in-brazil-must-focus-on-consumer-behavior-and-markets-regulation-and-energ",totalDownloads:1068,totalCrossrefCites:0,authors:[{id:"177889",title:"Dr.",name:"Carlos Alberto",surname:"Fróes Lima",slug:"carlos-alberto-froes-lima",fullName:"Carlos Alberto Fróes Lima"}]},{id:"50727",title:"Advanced Metering Infrastructure Based on Smart Meters in Smart Grid",slug:"advanced-metering-infrastructure-based-on-smart-meters-in-smart-grid",totalDownloads:3421,totalCrossrefCites:8,authors:[{id:"178015",title:"Dr.",name:"Trong Nghia",surname:"Le",slug:"trong-nghia-le",fullName:"Trong Nghia Le"},{id:"178169",title:"Prof.",name:"Wen-Long",surname:"Chin",slug:"wen-long-chin",fullName:"Wen-Long Chin"}]},{id:"51232",title:"The Post Carbon City and Smart Metering",slug:"the-post-carbon-city-and-smart-metering",totalDownloads:1199,totalCrossrefCites:0,authors:[{id:"178083",title:"Dr.",name:"Martin",surname:"Anda",slug:"martin-anda",fullName:"Martin Anda"}]},{id:"50257",title:"MAC Protocol Design for Smart Meter Network",slug:"mac-protocol-design-for-smart-meter-network",totalDownloads:1158,totalCrossrefCites:0,authors:[{id:"177820",title:"Dr.",name:"Yue",surname:"Yang",slug:"yue-yang",fullName:"Yue Yang"}]},{id:"50712",title:"Power Electronics Platforms for Grid-Tied Smart Buildings",slug:"power-electronics-platforms-for-grid-tied-smart-buildings",totalDownloads:1613,totalCrossrefCites:0,authors:[{id:"177821",title:"Dr.",name:"Mahmoud",surname:"Amin",slug:"mahmoud-amin",fullName:"Mahmoud Amin"}]},{id:"50356",title:"Estimating the Photovoltaic Hosting Capacity of a Low Voltage Feeder Using Smart Meters’ Measurements",slug:"estimating-the-photovoltaic-hosting-capacity-of-a-low-voltage-feeder-using-smart-meters-measurements",totalDownloads:1233,totalCrossrefCites:3,authors:[{id:"31945",title:"Prof.",name:"Jacques",surname:"Lobry",slug:"jacques-lobry",fullName:"Jacques Lobry"},{id:"174062",title:"Mr.",name:"Jean-François",surname:"Toubeau",slug:"jean-francois-toubeau",fullName:"Jean-François Toubeau"},{id:"174063",title:"Dr.",name:"François",surname:"Vallée",slug:"francois-vallee",fullName:"François Vallée"},{id:"174064",title:"Ph.D. Student",name:"Vasiliki",surname:"Klonari",slug:"vasiliki-klonari",fullName:"Vasiliki Klonari"}]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"177730",firstName:"Edi",lastName:"Lipovic",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/177730/images/4741_n.jpg",email:"edi@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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. 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Recrystallization (Rex) takes place through nucleation and growth. Nucleation during Rex can be defined as the formation of strain-free crystals, in a high energy matrix, that are able to grow under energy release by a movement of high-angle grain boundaries. The nucleus is in a thermodynamic equilibrium between energy released by the growth of the nucleus (given by the energy difference between deformed and recrystallized volume) and energy consumed by the increase in high angle grain boundary area. This means that a critical nucleus size or a critical grain boundary curvature exists, from which the newly formed crystal grows under energy release. This definition is so broad and obscure that crystallization of amorphous materials is called Rex by some people, and Rex can be confused with the abnormal grain growth when grains with minor texture components can grow at the expense of neighboring grains with main texture components because the minor-component grains can be taken as nuclei. Here we will present a theory which can determine whether grains survived during deformation act as nuclei and which orientation the deformed matrix is destined to assume after Rex. A lot of Rex textures will be explained by the theory.
Rex occurs by nucleation and growth. Therefore, the evolution of the Rex texture must be controlled by nucleation and growth. In the oriented nucleation theory (ON), the preferred activation of a special nucleus determines the final Rex texture [1]. In the oriented growth theory (OG), the only grains having a special relationship to the deformed matrix can preferably grow [2]. Recent computer simulation studies tend to advocate ON theory [3]. This comes from the presumption that the growth of nuclei is predominated by a difference in energy between the nucleus and the matrix, or the driving force. In addition to this, the weakness of the conventional OG theory is in much reliance on the grain boundary mobility.
One of the present authors (Lee) advanced a theory for the evolution of Rex textures [4] and elaborated later [5,6]. In the theory, the Rex texture is determined such that the absolute maximum stress direction (AMSD) due to dislocation array formed during fabrication and subsequent recovery is parallel to the minimum Young’s modulus direction (MYMD) in recrystallized (Rexed) grains and other conditions are met, whereby the strain energy release can be maximized. In the strain-energy-release-maximization theory (SERM), elastic anisotropy is importantly taken into account.
In what follows, SERM is briefly described. Rex occurs to reduce the energy stored during fabrication by a nucleation and growth process. The stored energy may include energies due to vacancies, dislocations, grain boundaries, surface, etc. The energy is not directional, but the texture is directional. No matter how high the energy may be, the defects cannot directly be related to the Rex texture, unless they give rise to some anisotropic characteristics. An effect of anisotropy of free surface energy due to differences in lattice surface energies can be neglected except in the case where the grain size is larger than the specimen thickness in vacuum or an inert atmosphere. Differences in the mobility and/or energy of grain boundaries must be important factors to consider in the texture change during grain growth. Vacancies do not seem to have an important effect on the Rex texture due to their relatively isotropic characteristics. The most important driving force for Rex (nucleation and growth) is known to be the stored energy due to dislocations. The dislocation density may be different from grain to grain. Even in a grain the dislocation density is not homogeneous. Grains with low dislocation densities can grow at the expanse of grains with high dislocation densities. This may be true for slightly deformed metals as in case of strain annealing. However, the differences in dislocation density and orientation between grains decrease with increasing deformation. Considering the fact that strong deformation textures give rise to strong Rex textures, the dislocation density difference cannot be a dominant factor for the evolution of Rex textures. Dislocations cannot be related to the Rex texture, unless they give rise to anisotropic characteristics.
The dislocation array in fabricated materials looks very complicated. Dislocations generated during plastic deformation, deposition, etc., can be of edge, screw, and mixed types. Their Burgers vectors can be determined by deformation mode and texture, and their array can be approximated by a stable or low energy arrangement of edge dislocations after recovery. Figure 1 shows a schematic dislocation array after recovery and principal stress distributions around stable and low energy configurations of edge dislocations, which were calculated using superposition of the stress fields around isolated dislocations, or, more specifically, were obtained by a summation of the components of stress field of the individual dislocations sited in the array. It can be seen that AMSD is along the Burgers vector of dislocations that are responsible for the long-range stress field. The volume of crystal changes little after heavy deformation because contraction in the compressive field and expansion in the tensile fields around dislocations generated during deformation compensate each other. That is, this process takes place in a displacement controlled system. The uniaxial specimen in Figure 2 makes an example of the displacement controlled system. When a stress-free specimen
(a) Schematic dislocation array after recovery, where horizontal arrays give rise to long-range stress field, and vertical arrays give rise to short-range stress field [
Displacement controlled uniaxial specimen for explaining strain-energy-release being maximized when AMSD in high dislocation density matrix is along MYMD in recrystallized grain.
AMSD for active slip systems
Schematic of two slip planes S1 and S2 that share common slip direction along
We first calculate AMSD in an fcc crystal deformed by a duplex slip of (111)[-101] and (111)[-110] that are equally active. The duplex slip can be taken as a single slip of (111)[-211], which is obtained by the sum of the two slip directions. In this case, the maximum stress direction is [-211]. However, some complication can occur. One slip system has two opposite directions. The maximum stress direction for the (111)[-101] slip system represents the [-101] direction and its opposite direction, [1 0-1]. The maximum stress direction for the (111)[-110] slip system represents the [-110] and [1-1 0] directions. Therefore, there are four possible combinations to calculate the maximum stress direction, [-101] + [-110] = [-211], [-101] + [1-1 0] = [0-1 1], [1 0-1] + [-110] = [0 1-1], and [1 0-1] + [1-1 0] = [2-1-1], among which [-211]//[2-1-1] and [0-1 1]//[0 1-1]. The correct combinations are such that two directions make an acute angle. If the two slip systems are not equally active, the activity of each slip system should be taken into account. If the (111)[-101] slip system is two times more active than the (111)[-110] system, the maximum stress direction becomes 2[-101] + [-110] = [-312]. This can be generalized to multiple slip. For multiple slip, AMSD is calculated by the sum of active slip directions of the same sense and their activities, as shown in Figure 3. It is convenient to choose slip directions so that they can be at acute angles with the highest strain direction of the specimen, e.g., RD in rolled sheets, the axial direction in drawn wires, etc.
When two slip systems share the same slip direction, their contributions to AMSD are reduced by 0.5 for bcc metals and 0.577 for fcc metals as follows. Figure 4 shows two slip planes, S1 and S2, intersecting along the common slip direction, the
where PN1 and PN2 are normal to the planes S1 and S2, respectively. Therefore,
where OP,
Because
The apparent shear strains
For bcc metals, sin
For fcc metals, sin
The activity of each slip direction is linearly proportional to the dislocation density
If a crystal is plastically deformed by
The above equation is illustrated in Figure 5. If a deformation texture is stable, the shear strain rates on the slip systems are independent of deformation.
So far methods of obtaining AMSD have been discussed. This is good enough for prediction of fiber textures. However, the stress states around dislocation arrays are not uniaxial but triaxial. Unfortunately we do not know the stress fields of individual dislocations in real crystals, but know Burgers vectors. Therefore, AMSD obtained above applies to real crystals. Any stress state has three principal stresses and hence three principal stress directions which are perpendicular to each other. Once we know the three principal stress directions, the Rex textures are determined such that the three directions in the deformed matrix are parallel to three <100> directions in the Rexed grain, when MYMDs are <100>. In figure 6, let the unit vectors of
Calculation of
Relationship between three principal stress directions
If the unit vectors
It should be mentioned that
The 1st priority: When AMSD is cristallographically the same as MYMD, No texture changes after Rex [10].
The 2nd priority: When AMSD crystallographically differs from MYMD, the Rex texture is determined such that AMSD in the matrix is parallel to MYMD in the Rexed grain, with one common axis of rotation between the deformed and Rexed states. The common axis can be ND, TD, or other direction (e.g. <110> for bcc metals). This may be related to minimum atomic movement at the AMSD//MYMD constraints. However, we do not know the exact physical picture of this.
The 3rd priority: When the first two conditions are not met, the method explained to obtain Eq. 9 is used.
When the density of dislocations in electrodeposits and vapor deposits is high, the deposits undergo Rex when annealed. AMSD in the deposits can be determined by their textures. The density of dislocations whose Burgers vectors are directed away from the growth direction (GD)of deposits was supposed to be higher than when the Burgers vector is nearly parallel to GD because dislocations whose Burgers vector is close to GD are easy to glide out from the deposits by the image force during their growth [11]. This was experimentally proved in a Cu electrodeposit with the <111> orientation [12]. Therefore, AMSDs are along the Burgers vectors nearly normal to GD.
Lee et al. found that the <100>, <111>, and <110> textures (inverse pole figures: IPFs) of Cu electrodeposits which were obtained from Cu sulfate and Cu fluoborate baths [13,14], and a cyanide bath [15] changed to the <100>, <100>, and <√310> textures, respectively, after Rex as shown in Figure 7. The texture fraction (TF) of the (
where I(
Deposition and Rex textures of Cu electrodeposits. <
where
For fcc Cu, S11=0.018908, S44 =0.016051, S12 = -0.008119 GPa-1 at 800 K [17], which in turn gives rise to [
For the <100> oriented Cu (simply <100> Cu) deposit, two of the six <110> directions are at 90° and the remaining four are at 45o with GD, as shown in Figure 8. The two <110> directions, which is AMSD, change to the <100> directions after Rex, resulting in the <100> Rex texture (Figure 8b) in agreement with the experimental result.
For the <111> Cu deposit, three of the six <110> directions are at right angles with the [111] GD; the remaining three <110> directions are at 35.26o with GD, as shown in Figure 9 a. The former three <110> directions, AMSD, can change to <100> after Rex, but angles between the <110> directions are 60o and the angle between the <100> directions is 90°. Correspondence between the <110> directions in as-deposited grains and the <100> directions in Rexed grains is therefore impossible in a grain. Two of the <110> directions in neighboring grains, which are at right angles with each other, can change to the <100> directions to form the <100> nuclei in grain boundaries, which grow at the expense of high energy region, as shown in Figure 9b. Thus, the <111> deposition texture change to the <100> Rex texture, in agreement with the measured result.
Drawings explaining that <100> deposition texture (a) remains unchanged after Rex (b).
(a) <110> directions in <111> oriented fcc crystal in which arrow indicates [111] growth direction. (b) Drawings for explanation of <111> deposition to <100> Rex texture transformation.
directions in [110] oriented fcc crystal.
For the <110> Cu deposit, one <110> direction is normal to the <110> GD and the remaining four <110> directions are at 60o with the <110> GD, as shown in Figure 10. The first one of the <110> directions and the last four <110> directions are likely to determine the Rex texture because the last four directions are closer to the deposit surface than to GD. Recalling that the <110> directions change to <100> directions after Rex, GD of Rexed grains should be at 60o and 90o with the <100> directions, MYMD, at the same time. GD satisfying the condition is <√310>, in agreement with the experimental results.
So far we have discussed the evolution of the Rex textures from simple deposition textures. A Cu deposit whose texture can be be approximated by a weak duplex texture consisting of the <111> and <110> orientations developed the Rex texture which is approximated by a weak <√310> orientation rather than <100> + <√310> [18]. For the duplex deposition texture, the Rex texture may not consist of the Rex orientation components from the deposition orientation components because differently oriented grains can have different energies. The tensile strengths of copper electrodeposits showed that the tensile strength of the specimens with the <110> texture was higher than those with the <111> texture obtained from the similar electrodeposition condition. This implies that the <110> specimen has the higher defect densities than the <111> specimen [18,19]. Therefore, the <110> grains are likely to have higher driving force for Rex than the <111> grains, resulting in the <√310> texture after Rex, in agreement with experimental result [18].
For Ni, S11= 0.009327, S44 = 0.009452, S12 = -0.003694 GPa-1 at 760 K [20], which in turn gives rise to [
For Ag, S11= 0.03018, S44 = 0.02639, S12 = -0.0133 GPa-1 at 750 K [17], which in turn gives [
Deposition (top) and Rex (bottom) textures (IPFs) of Ag electrodeposits [
The deposition texture of Sample d was well described by 0.32<112> + 0.14<127>T + 0.25<113> + 0.23<557>T + 0.06<19 19 13>TT with each of individual orientations being superimposed with a Gaussian peak of 8°. Here <127>T indicates the twin orientation of its preceeding <112> orientation, and TT indicates secondary twin. Thus, the main components in deposition texture of Sample d are <112>, <113>, and <557>. The <110> directions that are nearly normal to GD will be AMSD and in turn determine the Rex texture. Table 1 gives angles between <110> and [11w]. Table 1 shows that the probability of <110> directions being normal to GD is the highest. The <110> directions normal to GD will become parallel to the <100> directions (MYMS) after Rex. Therefore, the Rex texture will be the <100> orientation for the same reason as in the <111> orientation of the deposit [22].
Table 2 shows TFs (Eq. 10) of Cr electrodeposits obtained under three electrodeposition conditions. Specimen Cr-A has a strong <111> fiber texture. The texture of Cr-B is characterized by weak <111>, and that of Cr-C is by weak <100>. The optical microstructure and hardness test results and others indicated that all the specimens were fully Rexed at 1173 K. TFs as functions of annealing temperature and time in Figure 12 indicate that the deposition texture of Cr-A little change after Rex. The pole figures in Figures 13 and 14 indicate the deposition textures of Cr-B and Cr-C little change after Rex. In conclusion, the <100> and <111> deposition textures of Cr electrodeposits little change after Rex. These results are compatible with SERM as discussed in what follows. There are four equivalent <111> directions in bcc Cr crystal, with opposite directions being taken as the same. For the <111> Cr deposit, one of four <111> directions is along GD and the remaining three <111> directions are at an angle of 70.5o with GD (Figure 15). The remaining three <111> directions can be AMSDs. They will become parallel to MYMDs of Rexed grains. The compliances of Cr are
\n\t\t\t | ||||||
557 | \n\t\t\t44.7 | \n\t\t\t90 | \n\t\t\t31.5 | \n\t\t\t81.8 | \n\t\t\t31.5 | \n\t\t\t81.8 | \n\t\t
112 | \n\t\t\t54.7 | \n\t\t\t90 | \n\t\t\t30 | \n\t\t\t73.2 | \n\t\t\t30 | \n\t\t\t73.2 | \n\t\t
113 | \n\t\t\t64.8 | \n\t\t\t90 | \n\t\t\t31.5 | \n\t\t\t64.8 | \n\t\t\t31.5 | \n\t\t\t64.8 | \n\t\t
Angles between <110> and [11w] directions (°)
\n\t\t\t | |||||||
Cr-A | \n\t\t\t0.02 | \n\t\t\t0.05 | \n\t\t\t0 | \n\t\t\t0 | \n\t\t\t0 | \n\t\t\t\n\t\t\t\t | \n\t\t\tStrong <111> | \n
Cr-B | \n\t0.03 | \n\t0.15 | \n\t0.28 | \n\t0 | \n\t0.01 | \n\t\n\t\t | \n\t<111> | \n
Cr-C | \n\t0.19 | \n\t\n\t\t | \n\t0.13 | \n\t0.05 | \n\t0.13 | \n\t0.03 | \n\t<100> | \n
Texture fractions (TF) of reflection planes of Cr electrodeposits A, B, and C [14]. Bold-faced numbers indicate highest TFs in corresponding deposits.
TFs of Cr-A as functions of annealing (a) temperature for 1 h and (b) time at 903 K [
(200) pole figures of Cr-B (left) before and (right) after annealing at 1173 K for 1 h [
(200) pole figures of Cr-C (left) before and (right) after annealing at 1173 K for 1 h [
Patten et al. [24] formed deposits of Cu up to 1mm in thickness at room temperature in a triode sputtering apparatus using a krypton discharge under various conditions of sputtering rate, gas purity, and substrate bias. The 3.81 cm diameter target was made from commercial grade OFHC forged Cu-bar stock containing approximately 100 ppm oxygen by weight with only traces of other elements. The substrates were 2.54 cm diameter by 6.2 mm thick disks made of OFHC Cu. These disks were electron beam welded to a stainless-steel tube to provide direct water-cooling for temperature control during sputtering. As-deposited grains were approximately 100 nm in diameter. Room-temperature Rex and grain growth displaying no twins were observed approximately 9 h after removal from the sputtering apparatus. Nucleation sites were almost randomly distributed. Hardness of the unrecrystallized matrix remained at ~230 DPH from the time it was sputtered until Rex, when it abruptly dropped to approximately 60 DPH in the Rexed grains. Rex resulted in a texture transformation from the <111> deposition texture to the <100> Rex texture. Since the substrate is also Cu, the orientation transition from <111> to <100> cannot be attributed to thermal strains. The driving force for Rex must be the internal stress due to defects such as vacancies and dislocations. Therefore, the texture transition is consistent with the prediction of SERM.
Thin arrows (AMSDs) and thick arrows (GD) in [111] and [001] Cr crystals.
Greiser et al. [25] measured the microstructure and texture of Ag thin films deposited on different substrates using DC magnetron sputtering under high vacuum conditions (base pressure: 10-8 mbar, partial Ar pressure during deposition: 10-3 mbar). A weak <111> texture in a 0.6 μm thick Ag film deposited on a (001) Si wafer with a 50 nm thermal SiO2 layer at room temperature becomes stronger with increasing thickness. It is generally accepted that a random polycrystalline structure is obtained up to a critical film thickness unless an epitaxial growth condition is satisfied. Therefore, the <111> texture developed in the 0.6 μm film was weak and became stronger with increasing thickness. This is consistent with the preferred growth model [26]. They also found that the texture of the film deposited at room temperature was "high <111>", whereas the texture of the film deposited at 200 °C was characterized by a low amount of the <111> component and a high amount of the random component. This is also consistent with the preferred growth model.
Post-deposition annealing was carried out in a vacuum furnace at 400 °C with a base pressure of 10-6 mbar, a partial H2 pressure of 10 mbar, and under environmental conditions. The post-deposition grain growth was the same for annealing in high vacuum and in environmental conditions. A dramatic difference in the extent of growth was recognized in the micrographs of the 0.6 and 2.4 μm thick films. The 0.6 μm thick film showed normally grown grains with the <111> orientation; the average grain size was about 1 to 2 μm. This can be understood in light of the surface energy minimization. In contrast, in 2.4 μm thick films, abnormally large grains with the <001> orientation were found. These grains grew into the matrix of <111> grains. The grain boundaries between the abnormally grown grains have a meander-like shape unlike the usual polygonal shape. They could not explain the results by the model of Carel, Thomson, and Frost [27]. According to the model, the strain energy minimization favors the growth of <100> grains. The growth mode should be affected by strain and should not be sensitive to the initial texture. These predictions are at variance with the experimental results in which freestanding, stress-free films also showed abnormal growth of giant grains with <001> texture. The 2.4 μm thick films deposited at 100 °C or below could have dislocations whose density was high enough to cause Rex, which in turn gave rise to the texture change from <111> to <001> regardless of the existence of substrate when annealed, as explained in the previous section. Thus, the <111> to <100> texture change in the 2.4 μm thick films is compatible with SERM [28].
It is known that the texture of axisymmetrically drawn fcc metals is characterized by major <111> + minor <100> components, and the drawing texture changes to the <100> texture after Rex [29,30]. Figure 16 shows calculated textures in the center region of 90% drawn copper wire taking work hardening per pass into account. The drawing to Rex texture transition was explained by SERM [4]. Since the drawing texture is stable, we consider the [111] and [100] fcc crystals representing the <111> and <100> fiber orientations constituting the texture. Figure 17 shows tetrahedron and octahedron consisting of slip planes (triangles) and slip directions (edges) for the [111] and [100] fcc crystals. The slip planes are not indexed to avoid complication. The slip-plane index can be calculated by the vector product of two of three slip directions (edges) of a triangle constituting the slip-plane triangle. It follows from Figure 17a that three active slip directions that are skew to the [111] axial direction are [101], [110], and [011]. It should be noted that these directions are chosen to be at acute angles with the [111] direction (Section 2). Therefore, AMSD // ([101] + [110] + [011]) = [222] // [111]. That is, AMSD is along the axial direction. According to SERM, AMSD in the deformed matrix is along MYMD in the Rexed grain. MYMDs of most of fcc metals are <100>. Therefore, the <111> drawing texture changes to the <100> Rex texture. Now, the evolution of <100> Rex texture in the <100> deformed matrix is explained. Eight active slip systems in fcc crystal elongated along the [100] direction are calculated to be (111)[1 0-1], (-111)[101], (1-1 1)[110], (1 1-1)[1-1 0], (111)[1-1 0], (-111)[110], (1-1 1)[10-1], and (1 1-1)[101], if the slip systems are {111}<110> [32]. It is noted that the slip directions are chosen to be at acute angles with the [100] axial direction. These slip systems are shown in Figure 17 b. AMSD is obtained, from the vector sum of the active slip directions, to be parallel to [100], which is also MYMD of fcc metals. Therefore, the <100> drawing texture remains unchanged after Rex (1st priority in Section 2), and the <111> + <100> orientation changes to <100> after Rex, regardless of relative intensity of <111> to <100> in the deformation texture. The <100> grains in deformed fcc wires are likely to act as nuclei for Rex. The texture change during annealing might take place by the following process. The <100> grains retain their deformation texture during annealing by continuous Rex, or by recovery-controlled processes, without long-range high-angle boundary migration. The <100> grains grow at the expense of their neighboring <111> grains that are destined to assume the <100> orientation during annealing.
Calculated IPFs in centeral axis zone of Cu wire drawn by 90% in 14 passes (~15% per pass) through conical-dies of 9° in half-die angle, taking strain-hardening per pass into count [
Tetrahedron and octahedron representing slip planes (triangles) and directions (edges) in [111] and [100] fiber oriented fcc crystals. Thick arrows show (a) [111] and (b) [100] axial directions.
Cold drawn Ag wires develop major <111> + minor <100> at low reductions (less than about 90%) as do other fcc metals, whereas they exhibit major <100> + minor <111> at high reductions (99%) as shown in Figure 18 [32]. This result is in qualitative agreement with that of Ahlborn and Wassermann [33], which shows that the ratio of <100> to <111> of Ag wires was higher at 100 and -196oC than at room temperature. They attributed the higher <100> orientation to Rex and mechanical twinning, because Ag has low stacking fault energy. They suggested that the <111> orientation transformed to the <115> orientation by twinning, which rotated to the <100> orientation by further deformation.
The hardness of deformed Ag wires as a function of annealing time at 250 and 300 oC indicated that Rex was completed after a few min. This was also confirmed by microstructure studies [32]. Figure 18 shows the annealing textures of drawn Ag wires of 99.95% in purity, which shows that drawing by 61 and 84% and subsequent annealing at 250 oC for 1 h gives rise to nearly random orientation. Ag wires with the <111> + <100> deformation texture develop Rex textures of major <100> and minor <111>, or major <100> + its twin component <122> and minor <111>. The almost random orientation can be seen in Figures 19 d. Figure 20 shows the IPFs of 99% drawn 99.99% Ag wire annealed at 600 ℃ for 1 min to 200 h. Their microstructures showed that the specimen annealed at 600 oC for 1min is almost completely Rexed. The specimen has major <100> + minor <111> as the specimens annealed at 300 oC. After annealing at 600 oC for 3min, some grains showed abnormal grain growth (AGG), indicating complete Rex, and the intensity of <100> component increased. However, as the annealing time incresed, the orientation density ratio (ODR) of <111> to <100> increased, accompanied by grain growth. It is noted that the annealing texture is diffuse at the transient stage from <100> to <111> (5 min in Figure 20 and Figure 19d). The <100> to <111> transition is associated with AGG in low dislocation-density fcc metals, which has been discussed in [31,32]. The Rex results before AGG lead to the conclusion that the Rex texture of the heavily drawn Ag wires is <100> regardless of relative intensity of <111> and <100>, as expected from SERM.
IPFs of (a) 61, (b) 84, (c) 91, and (d) 99% drawn Ag wires (initial texture: random) of 99.95% in purity (top) before and (bottom) after annealing at 250 °C for 1 h [
IPFs of 99.99% pure Ag wires (a) drawn by 90% and (b) annealed at 300 °C for 1 h; (c) drawn by 99% and (d) annealed at 300 °C for 1 h [
IPFs of 99.99% Ag wire drawn by 99% and annealed at 600 °C for 1-12000 min [
Axisymmetrically extruded Al alloy rod [34], drawn Al wire [30] and Cu and some Cu alloy wires [29] generally have major <111> + minor <001> double fiber textures in the deformed state. Park and Lee [35] studied drawing and annealing textures of a commercial electrolytic tough-pitch Cu of 99.97% in purity. A rod of 8mm in diameter, whose microstructure was characterized by equiaxed grains having a homogeneous size distribution, was cold drawn by 90% reduction in area in 14 passes through conical dies of 9° in half-die-angle with about 15% reduction per pass. The drawing speed was 10 m/min. The drawn wire was annealed in a salt bath at 300 or 600 °C and in air, argon, hydrogen or vacuum (< 1x10-4 torr) at 700 °C for various periods of time. Figure 21 shows orientation distribution functions (ODFs) for the 90% drawn Cu wire. The drawing texture can be approximated by a major <111> + minor <100> duplex fiber texture. The orientation density ratio of the <111> to <100> components is about 2.6. The orientation densities were obtained by averaging the f(g) values on the [
ODFs of 90% drawn Cu wire (a) before and after annealing at (b) 300, (c) 600, (d) 700 °C for 3 h, measured by X-ray [
IPFs for center regions of 90% drawn Cu wires after annealing at 300 and 700oC [
ODR of <100> to <111> of 90% drawn Cu wire vs. annealing time at 700oC [
Grain size and volume fraction of ● ○ <111> and ▲△ <100> grains in Au wire vs. annealing time at 300 °C (solid symbols) and 400 °C (open symbols) [
Figure 23 shows ODR of <100> to <111> of the 90% drawn Cu wire as a function of annealing time at 700 °C. The ratio increases very rapidly up to about 1.8 after annealing for 180 s, wherefrom it decreases and reaches to about 0.3 after 6 h. The increase in the ratio indicates the occurrence of Rex and the decrease indicates the texture change during subsequent grain growth, that is, AGG. A similar phenomenon is observed in drawn Ag wire during annealing (Figure 20).
Cho et al. [36] measured the drawing and Rex textures of 25 and 30 μm diameter Au wires of over 99.99% in purity, which had dopants such as Ca and Be that total less than 50 ppm by weight. The Au wires were made by drawing through a series of diamond dies to an effective strain of 11.4.
Figure 24 shows the grain size and the volume fraction of the <111> and <100> grains as a function of annealing time at 300 and 400 oC. These values are based on EBSD measurements. The aspect ratio of grain shape was in the range of 1.5 - 2, which is little influenced by annealing time and temperature [36]. The grain growth occurs in whole area of the wire and is more rapid at 400 oC than at 300 oC as expected for thermally activated motion of grain boundaries. The volume fraction of the <111> grains decreases and that of the <100> grains increases with annealing time when Rex takes place, as expected from SERM.
The annealing texture of single-phase crystals of Al-0.05% Si of the Goss orientation {110}<001> deformed in channel-die compression was studied by Ferry et al. [37]. In the channel-die compression, the compression and extension directions were <110> and <001> directions, respectively. Their experimental results showed that, even after deformation to a true strain of 3.0 which is equivalent to a compressive reduction of 95%, the original orientation was maintained as shown in Figure 25a. Figure 25b shows one (110) pole figure typical of a deformed crystal after annealing at 300 °C for 4 h. The comparison of Figures 25a and 25b suggests that the annealing texture is essentially the same as the deformation texture. They also reported that even after 90% reduction and annealing for up to 235 h, the orientation was the same as that of the as-deformed crystal. For deformed specimens electropolished and annealed for various temperatures between 250 and 350 °C, no texture change took place before and after annealing, although grains which had different orientations were sometimes found to grow from the crystal surface after very long annealing treatments. For samples deformed over the true strain range of 0.5 to 3.0 in their work, annealing at a given temperature resulted in similar microstructural evolution. They called the phenomenon discontinuous subgrain growth during recovery. They stated that crystals of an orientation which was stable during deformation were generally resistant to Rex. This statement cannot be justified in light of single crystal examples in Sections 5.2 to 5.4.
pole figures for 95% channel-die compressed Al single crystal (a) before and (b) after annealing at 300 ˚C for 4 h. (Contour levels: 2, 5, 11, 20, 35, 70 x random) [
The result was discussed based on SERM [38]. The (110)[001] orientation is calculated by the full constraints Taylor-Bishop-Hill model to be stable when subjected to plane strain compression. The active slip systems for the (110)[001] crystal are calculated to be (111)[0-1 1], (111)[-101], (-1-1 1)[011], and (-1-1 1)[101], whose activities are the same. It is noted that all the slip directions are chosen so that they can be at acute angle with the maximum strain direction [001]. AMSD is [0-1 1] + [-101] + [011] + [101] = [004]//[001], which is MYMD because [
Blicharski et al. [40] studied the microstructural and texture changes during recovery and Rex in high purity Al bicrystals with S orientations, e.g. (123)[4 1-2]/(123)[-4-1 2] and (123)[4 1-2]/(-1-2-3)[4 1-2], which had been channel-die compressed by 90 to 97.5% reduction in thickness. The geometry of deformation for these bicrystals was such that the bicrystal boundary, which separates the top and bottom crystals at the midthickness of the specimen, lies parallel to the plane of compression, i.e. {123} and the <412> directions are aligned with the channel, and the die constrains deformation in the <121> directions. The annealing of the deformed bicrystals was conducted for 5 min in a fused quartz tube furnace with He + 5%H2 atmosphere. The textures of the fully Rexed specimens were examined by determining the {111} and {200} pole figures from sectioned planes at 1/4, 1/2 and 3/4 specimen thickness. This roughly corresponds to the positions at the midthickness of the top crystal, the bicrystal boundary, and the midthickness of the bottom crystal, respectively. The deformation textures of the two bicrystals, (123)[4 1-2]/(123)[-4-1 2] and (123)[4 1-2]/(-1-2-3)[4 1-2], channel-die compressed by 90%, are reproduced in Figure 26. The initial orientation of the component crystals is also indicated in these pole figures. The annealing textures are shown in Figure 27. As Bricharski
where the factor 0.577 originates from the fact that the slip systems of (1-1 1)[110] and (-111)[110] share the same slip direction [110] (Eq. 7). Two other principal stress directions are obtained as explained in Figure 6. Possible candidates for the direction equivalent to
pole figures for 90% channel-die compressed Al crystals of {123}<412> orientations [
pole figures of 90 and 95% channel-die compressed Al bicrystals after annealing at 125 and 185 °C for 5 min [
Orientation rotations of {123}<412> crystals during plain strain compression by 90% [
Calculated shear strain rate with respect to thickness reduction of 0.01,
Orientation relations in deformed and Rexed states. Subscripts d and r indicate deformed state and Rexed state, respectively.
The calculated result means that the (0.1534 0.5101 0.8463)[0.8111 0.4242 -0.4027] crystal, which is obtained by the channel die compression by 90% reduction, transforms to the Rex texture (-0.0062 0.2781 0.9606)[0.9907 0.1322 -0.0319]. Similarly, crystals deformed by channel die compression from (123)[-4-1 2] and (-1-2-3)[4 1-2] orientations transform to (-0.0062 0.2781 0.9606)[-0.9907 -0.1322 0.0319] and (0.0062 -0.2781 -0.9606)[0.9907 0.1322 -0.0319], respectively, after Rex. The results are plotted in Figure 27 superimposed on the experimental data. It can be seen that the calculated Rex textures are in good agreement with the measured data.
Butler et al. [42] obtained a {112}<111> Al crystal by channel-die compression of the (001)[110] single crystal. The (001)[110]orientation is unstable with respect to plane strain compression, to form the (112)[1 1-1] and (112)[-1-1 1] orientations as shown in Figure 31a. The Rex texture produced after annealing at 200 °C was a rotated cube texture (Figure 31b). Lee [43] analyzed the result based on SERM. Figure 32 shows shear strains/extension strain on slip systems of 1 to 6 as a function of rotation angle about TD [-110] of the (001)[110] fcc crystal obtained from the Taylor-Bishop-Hill theory. The contribution of the slip systems to the deformation is approximated to be proportional to the area under the shear strains
All the slips may not occur on the related slip systems uniformly in a large single crystal. Some regions of the crystal may be deformed by 1, 3, and 5 slip systems, while some other regions by 2, 4, and 6 slip systems.
(a) (111) pole figure of Al single crystal with initial orientation (001)[110] after 70% reduction by channel-die compression; (b) (111) pole figure of measured Rex texture (contours), (100)[0-4 1], and (100)[041] [
Shear strains on slip systems of 1 to 6 as a function of rotation angle about TD [-110] of (001)[110] crystal [
Vector sum of slip directions ① [1 0-1], ③ [0-1-1], and ⑤ [110] assuming that their activities are proportional to 30:3:20.6 (Eq. 15).
For the contribution of the former three slip systems to the crystal deformation, AMSD is obtained by the vector sum of the [1 0-1], [0-1-1], and [110] directions whose contributions are assumed to be proportional to the area ratio obtained earlier (30 : 3 : 20.6). The vector sum is shown in Figure 33. The resultant direction passes through point E, which divides line BC by a ratio of 1 to 2. Thus, AMSD // AE // [3 1-2]. Another high stress direction equivalent to
If the directions [3 1-2], [2-4 1], and [112], whose unit vectors are [3/√14 1/√14 -2/√14], [2/√21 -4/√21 1/√21], and [1/√6 1/√6 2/√6], respectively, are set to be parallel to [100], [010] and [001] directions in the Rexed crystal, components of the unit vectors are direction cosines relating the deformed and Rexed crystal coordinate axes (Eq. 9). Therefore, ND, [112], and RD, [1 1-1], in the deformed crystal coordinate system can be transformed to the expressions in the Rexed crystal coordinate system using the following calculation:
Therefore, the (112)[11-1] deformation texture transforms to the (001)[ √6-1 0] Rex texture. Similarly, from the (111)[0 1-1], (-1-1 1)[-1 0-1], and (-1 1-1) [110] slip systems, another AMSD AF, or the [1 3-2] direction, can be obtained. In this case, the (112)[1 1-1] deformation texture transforms into the (001)[-√6 -1 0] Rex texture. The {001}<√6 1 0> orientation has a rotational relation with the {001}<100> orientation through 22° about the plane normal. The calculated Rex texture is superimposed on the measured data in Figure 31b. The calculated results are in relatively good agreement with the measured data. It is noted that Figure 32 does not represent the correct strain path during deformation. Therefore, there is a room to improve the calculated Rex texture. The Rex texture is at variance with the {001}<100> Rex texture in polycrystalline Al and Cu.
Kamijo et al. [44] rolled a (123)[-6-3 4] Cu single crystal reversibly by 99.5% under oil lubrication. The (123)[-6-3 4] orientation was relatively well preserved up to 95%, even though the orientation spread occurred as shown in Figure 34a. However, the crystal rotation proceeded with increasing reduction. A new (321)[-4 3 6] component, which is symmetrically oriented to the initial (123)[-6-3 4] with respect to TD, developed after 99.5% rolling as shown in Figure 34b. It is noted that other two equivalent components are not observed. The rolled specimens were annealed at 538 K for 100 s to obtain Rex textures. In the Rex textures of the crystals rolled less than 90%, any fairly developed texture could not be observed, except for the retained rolling texture component. They could observe a cube texture with large scatter in the 95% rolled crystal and the fairly well developed cube orientation in the 99.5% rolled crystal after Rex as shown in Figure 34c. They concluded that the development of cube texture in the single crystal of the (123)[-6-3 4] orientation was mainly attributed to the preferential nucleation from the (001)[100] deformation structure. The cube deformation structure was proposed to form due to the inhomogeneity of deformation. Lee and Shin [45] explained the textures in Figure 34 based on SERM. Figure 35 shows
pole figures for (123)[-6-3 4] Cu single crystal after rolling by (a) 95%, (b) 99.5%, and (c) 99.5% and subsequent annealing at 538 K for 100 s [
(a) Shear strain rates
a) Orientation relationship between deformed (d) and Rexed (r) states and (b) (111) pole figures of ○ (0 3-1)[100] and □ (001)[100] orientations. Contours were calculated assuming Gaussian scattering (10°) of (0 3-1)[100] and (001)[100] components with their density ratio being 2:1 [
The calculated Rex orientation is (0.049 3.543–1.192)[7.801-0.017-0.275] ≈ (0 3-1)[100]. Similarly the (321)[-436] crystal is calculated to have slip systems of (111)[-101], (111)[-110], (-1-1 1)[011], and (-1 1-1)[011], on which the shear strain rates at
According to the discussion in Section 6.1, if the cube oriented regions are generated during rolling, they are likely to survive and act as nuclei and grow at the expense of neighboring {112}<111> region during annealing because the region tend to transform to the {001}<100> orientation to reduce energy. The grown-up cube grains will grow at the expense of grains having other orientations such as the {123}<634> orientation, resulting in the {001}<100> texture after Rex, even though the Cu orientation is a minor component in the deformation texture. Meanwhile, the main S component in the deformation texture can form its own Rex texture, the near (0 3-1)[100] orientation. In this case, the Rex texture may be approximated by main (001)[100] and minor (0 3-1)[001] components. Figure 36b shows the texture calculated assuming Gaussian scattering (half angle=10°) of these components with the intensity ratio of (001)[100]: (0 3-1)[001] = 2 : 1. It is interesting to note that the cube peaks diffuse rightward under the influence of the minor (0 3-1)[100] component in agreement with experimental result in Figure 34c.
The rolling texture of fcc sheet metals with medium to high stacking fault energies is known to consist of the brass orientation {011}<211>, the Cu orientation {112}<111>, the Goss orientation {011}<100>, the S orientation {123}<634>, and the cube orientation {100}<001>. The fiber connecting the brass, Cu, and S orientations in the Euler space is called the β fiber. Major components of the plane-strain rolling texture of polycrystalline Al and Cu are known to be the Cu and S orientations. The Rex texture of rolled Al and Cu sheets is well known to be the cube texture. The 40°<111> orientation relationship between the S texture and the cube texture has been taken as a proof of OG, and has made one believe that the S orientation is more responsible for the cube Rex texture. OG is claimed to be associated with grain boundary mobility anisotropy. However, experimental data indicate that the Cu texture is responsible for the cube texture. For an experimental result of Table 3, the deformation texture is not strongly developed below a reduction of 73% and its Rex texture is approximately random. At a reduction of 90%, a strong Cu texture is obtained and its Rex texture is a strong cube texture. For 95% cold rolled Al-0 to 9%Mg alloy after annealing at 598K for 0.5 to 96 h, the highest density in the Cu component in the deformation texture and the highest density in the cube component in Rex textures were observed at about 3% Mg (Figure 37). This implies that the Cu component is responsible for the cube component. However, these cannot prove that the Cu texture is responsible for the cube texture because deformation components with the highest density are not always linked with highest Rex components [47].
Changes in orientation densities of 95% rolled Cu during annealing at 400 to 500 °C (Figure 38), 95% rolled AA8011 Al alloy during annealing at 350 °C (Figure 39a), and 95% rolled Fe-50%Ni alloy during annealing at 600℃ (Figure 39b), and 95% rolled Cu after heating to 150 to 300℃ at a rate of 2.5 K/s followed by quenching showing that the Cu component disappears most rapidly when the cube orientation started to increase [52]. These results imply that the Cu component is responsible for the cube Rex texture. Rex is likely to occur first in high strain energy regions. It is known that the energy stored in highly deformed crystals is proportional to the Taylor factor (Σ
\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\t\n\t\t\t\t | \n\t\t\t\n\t\t\t\t | \n\t\t
Rolling texture | \n\t\t\t58% | \n\t\t\t3.6 | \n\t\t\t2.6 | \n\t\t\t1.1 | \n\t\t\t1.4 | \n\t\t\t0.6 | \n\t\t
73% | \n\t\t\t2.8 | \n\t\t\t3.0 | \n\t\t\t0.9 | \n\t\t\t1.1 | \n\t\t\t1.1 | \n\t\t|
90% | \n\t\t\t0.7 | \n\t\t\t5.7 | \n\t\t\t0.1 | \n\t\t\t0.7 | \n\t\t\t1.3 | \n\t\t|
Rex texture | \n\t\t\t58% | \n\t\t\t2.1 | \n\t\t\t1.4 | \n\t\t\t1.0 | \n\t\t\t1.3 | \n\t\t\t1.2 | \n\t\t
73% | \n\t\t\t1.8 | \n\t\t\t1.5 | \n\t\t\t1.3 | \n\t\t\t1.4 | \n\t\t\t2.1 | \n\t\t|
90% | \n\t\t\t0.2 | \n\t\t\t0.8 | \n\t\t\t0.2 | \n\t\t\t0.4 | \n\t\t\t20.0 | \n\t\t
Texture component strength of high purity OFE copper [46]
Effect of Mg content on (a) densities of {112}<111>, {123}<634>, and {110}<112> orientations in Al-Mg alloys cold rolled by 95% and on (b) density of {001}<100> orientation in specimens annealed at 598 K for 0.5, 4, and 96 h [
Changes in densities of copper Cu, S, brass Bs, and cube orientations in 95% cold rolled copper during annealing at (a) 400, (b) 450, and (c) 500 °C [
a) Changes in densities of cube, brass, copper and S orientations in 95% cold-rolled AA8011 Al alloy during annealing at 350 oC [
The copper to cube texture transition was first explained by SERM [4], and elaborated later [54]. The orientations of the (112)[1 1-1] and (123)[6 3-4] Cu single crystals remain stable in the center layer for all degree of rolling [55]. The Cu orientation (112)[1 1-1] is calculated to be stable by the
The above calculation indicates that the Cu orientation tends to turn into the cube orientation during annealing. In order for the transformation to occur, the cube oriented nuclei are needed, whether they may be generated from the deformed matrix or already existing cube bands. In order for the cube bands to be nuclei, they must be stable during annealing. The cube orientation (001)[100] is calculated by the full constrains method to be metastable with respect to plane strain compression, with active slip systems being (111)[1 0-1], (1 1-1)[101], (1-1-1)[101], and (1-1 1)[1 0-1] on which the shear strain rates are the same. If cube oriented grains survive after rolling, they must have undergone the plane strain compression with the slip systems. Therefore, AMSD is [1 0-1] + [101] + [101] + [1 0-1] = [400] // [100]. This is MYMD of Cu. Since AMSD is the same as the MYMD, the cube texture is expected to remain unchanged whether Rex or recovery (1st priority in Section 2).
SERM does not tell us how the cube oriented nuclei form. If the cube oriented grains survived during rolling, they are likely to survive and act as nuclei and grow at the expense of neighboring Cu oriented grains during annealing, because the Cu oriented grains tend to transform to the cube orientation. The grown up cube grains will grow at the expense of grains having other orientations such as the S and brass orientations, resulting in the cube texture after Rex. This discussion applies to other fcc metals with high stacking fault energy (SFE).
The evolution of rolling textures in copper alloys depends strongly on their SFEs. A continuous transition from the copper orientation to the brass orientation tends to occur with increasing content of alloying elements or decreasing SFE. However, Mn can be dissolved in copper up to 12 at.% without significantly changing SFE unlike various Cu alloys [58]. Engler [59,60] studied the influence of Mn on the deformation and Rex behavior of Cu-4 to 16%Mn alloys, as this should yield a clear separation of the effects caused by the changes in SFE from those due to other factors. It is particularly interesting that the alloys develop a deformation texture in which the density of the brass orientation can be higher than the densities of the copper orientation and the S orientation despite the fact that SFEs of the alloys are almost the same as that of pure Cu. The brass orientation is obtained in many Cu alloys with low SFEs, which is well known to transforms to the {236}<385> orientation. However, the Cu-Mn alloys do not develop the {236}<385> orientation after Rex. The texture transformation cannot be well explained by 40° <111> relation between the deformation and Rex textures.
β-fiber intensity lines of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions from 50 to 97.5% [
pole figures of (a) Cu-4%Mn, (b) Cu-8%Mn, and (c) Cu-16%Mn alloys after complete Rex (97.5% rolling, annealing for 1000 s at 450 °C) [
Orientation density ratios (ODR) among brass B, S, and copper C components in rolling texture (Figure 40) as a function of Mn concentration in Cu-Mn alloy [
Figure 40 shows the orientation densities f(g) along the β-fiber of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions of 50 to 97.5%. The figure indicates that with increasing Mn content and rolling reduction the brass orientation tends to dominate the rolling texture. The brass orientation in the Cu-Mn alloys is particularly interesting because the transformation of the orientation to the Rex texture will not be complicated by twinning as in low SFE alloys. Figure 41 shows {111} pole figures of the three Cu-Mn alloys rolled by 97.5% after complete Rex by annealing for 1000 s at 450 °C. In Cu-4%Mn the texture maximum lies in the cube-orientation. In Cu-8%Mn the texture maximum has shifted from the cube orientation to an orientation which can be approximated by the {013}<100> orientation. In Cu-16%Mn the texture maximum is in the Goss orientation. The orientation density ratios among the copper, S, and brass components in the rolling texture are shown in Figure 42. The density ratio of the brass to S component increases from about 1 to 2, the density ratio of the S to copper component increases from about 5 to 8, and the density ratio of the brass to copper component increases from about 5 to 18 with increasing Mn content from 4 to 16% in the Cu- Mn alloy. The density ratio of the S to copper and that of the brass to copper component are lowest in 4%Mn and highest in 16%Mn.
{110}<112> rolling and {110}<001> Rex textures of Cu-1% P alloy [
Comparison of the Rex textures with the corresponding deformation textures indicates that the brass component in the deformation texture seems to be responsible for the Goss components in the Rex texture. In what follows, the Rex textures are discussed based on SERM [61]. In order to find which component in the rolling texture is responsible for the Goss Rex texture, the brass rolling texture is first examined because it is the highest component in the deformation texture of Cu-16% Mn alloy, which changed to the Goss texture when annealed. When fcc crystals with the (110)[1-1 2] orientation are plane strain compressed along the [110] direction and elongated along the [1-1 2] direction, the relation between the strain
According to SERM, AMSD is parallel to MYMD of Rexed grain, the <100> directions in fcc metals. Therefore, the Rexed grains will have the (hk0)[001] orientation. The 2nd priority in Section 2 gives rise to the (110)[001] orientation because the (110) plane is shared by the deformed and Rexed grains. That is, the (110)[1-1 2] rolling texture transforms to the (110)[001] Rex texture. Similarly, for the (011)[2-1 1] crystal, equally active slip systems of (111)[1-1 0] and (1-1-1)[101] are obtained. Therefore, the (011)[2-1 1] rolling texture is calculated to transform to the (011)[100] Rex texture. It is concluded that the Goss Rex texture is linked with the brass rolling texture. The Goss orientation is stable with respect to plane strain compression and thermally stable (Section 5.1). Therefore, the Goss grains that survived during rolling are likely to act as nuclei during subsequent Rex and will grow at the expense of surrounding brass grains which are destined to change to assume the Goss orientation.
Figure 44 shows the rolling and Rex textures of Cu-1% P alloy sheet. The {110}<112> rolling texture changes to the (110)[001] texture after Rex. This is another example of the transition from the {110}<112> rolling texture to the {110}<001> Rex texture as explained in the Cu-16% Mn alloy.
In Section 5.4 the (123)[-6-3 4] rolling to (031)[100] Rex orientation transformation was discussed. Here we discuss the {123}<634> rolling to {031}<100> Rex orientation transformation. Figure 43b shows the shear strain rates as a function of strain for the (123)[6 3-4] crystal, which was calculated by the
The calculated result means that rolled fcc metal with the (123)[6 3-4] orientation transforms to (-0.1156 3.5441 1.1947)[7.8 0.1455 0.3263] ≈ (-1 31 10)[54 1 2] after Rex. For polycrystalline metals, the {123}<634> deformation texture transforms to the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> ≈ {1 31 10}<54 1 2> Rex texture. The Rex texture is shown in Figure 46a. If the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> orientations are expressed as Gaussian peaks with scattering angle of 10°, the Rex texture is very well approximated by the {310}<001> texture as shown in Figure 46b. This texture is similar to Figure 27 which shows the Rex texture of the plane strain compressed {123}<412> crystal.
Orientation relationship between deformed and Rexed states [
(a) (111) pole figure of {0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> ≈ {1 31 10}<54 1 2>. (b) Sum of {0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> expressed as Gaussian peaks with scattering angle of 10°. Calculated orientation can be approximated by {310}<001> [
It is noted that the highest density component in the deformation texture does not always dominate the Rex texture. All the components in the deformation texture are not in equal position to nucleate and grow the corresponding components in the Rex texture. The brass component has the highest density, but has lowest stored energy or the Taylor factor, while the copper component has the lowest density, but has the highest stored energy or the Taylor factor. If grains with the Goss or cube orientation survived during rolling, they must have undergone plane strain compression. They could undergo recovery and act as nuclei for Rex during annealing. This is the reason why the cube Rex texture could be obtained even though the copper component is the least in the deformation texture. When other conditions are the same, the higher relative density component in the deformation texture will give rise to the higher density in the corresponding component in the Rex texture, as shown in the highest relative copper component in the deformation texture yielding the highest cube component in the Rex texture in the Cu-4%Mn alloy among the three Cu-Mn alloys.
The Goss orientation {110}<001> in about 3% Si steel has been the subject of speculation due to its scientific and technological points of view. The grain oriented Si steel is made by hot rolling, cold rolling, followed by annealing. The Goss texture is formed near the sheet surface layer rolled in the α phase region at elevated temperatures. The friction between the sheet and rolls tends to increase with increasing temperature, and in turn increases the shear deformation and the Goss texture (Figure 47).
During hot rolling, Rex can take place, thereby the Goss orientation may change to a different orientation. Lee and Lee [64] obtained an IF steel specimen with only the shear texture by a multi- layer warm rolling and discussed the evolution of its Rex texture. The material used was a hot rolled 3.2 mm thick IF steel sheet. The hot-rolled sheet was cold-rolled to 1.1 mm in thickness in several passes. Four of the 1.1mm thick sheet were stacked, heated at 700 oC for 30 min and rolled by 70% in the ferrite region without lubrication. The rolled specimen was quenched into 25 oC water. Each layer was separated from the warm rolled sheet. In order to obtain a uniform shear texture, the surface layer was thinned from the inner surface to a half thickness by chemical polishing. The thinned surface and center layers were annealed at 750 oC for 1 h in Ar atmosphere.
The measured (110) pole figures and ODFs of the outer and inner surfaces of the 75% warm-rolled surface layer were similar. The similarity indicates that the texture of the layer is uniform. The texture was approximated by the Goss orientation plus minor {112}<111>. The center layer was similar to the typical texture of cold rolled steel sheet, RD//<110> and ND//{111}(Section 8). The surface texture could also be described as that which is obtained when the center layer texture is rotated through 35o about TD. The measured textures were similar to the calculated textures in Figure 47. The textures of the chemically thinned rolled surface layer and the center layer after annealing at 750 oC for 1 h showed that the texture of the surface layer was almost the same before and after annealing while the center layer underwent a texture change after annealing. Microstructures and hardness tests of the surface layer before and after annealing indicated Rex occurring after annealing [64].
Deformed FEM meshes in rolling and calculated (110) pole figures of layers A and E. In FEM calculation, flow characteristics of IF steel
Rotation rate
\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t
0.5 1.0 1.2 √2 1.5 | \n\t\t1.225 1.225 1.225 1.225 1.225 | \n\t\t1.225 1.225 1.225 1.225 1.225 | \n\t\t0.245 1.120 1.466 1.837 1.986 | \n\t\t0.245 1.120 1.466 1.837 1.986 | \n\t
Shear strain on each slip system as a function of
The unchanged texture in the surface layer after annealing can be explained based on SERM. AMSD is obtained from the slip systems activated during deformation. On the basis of the Taylor-Bishop-Hill theory, the (110)[001] orientation is calculated to be stable at
The (110)[001] orientation of bcc metals is calculated to be metastable with respect to plane strain compression (Figure 48), with active slip systems being (-1 0-1)[-1-1 1], (1 0-1)[111], (0-1-1)[-1-1 1], and (0 1-1)[111], on which the shear strain rates are the same. It is noted that the slip directions are chosen to be at acute angles with the [001] direction (Section 2). The two slip directions, [-1-1 1] and [111], are on the (-110) plane, which can be a slip plane in bcc crystals. Therefore, AMSD is [-1-1 1] + [111] = [002] // [001]. This is also MYMD of iron. Since the AMSD is the same as MYMD, if the Goss oriented crystal survives the plane-strain compression, the Goss texture is likely to remain unchanged during annealing according to SERM (1st priority in Section 2).
The Goss orientation, which is not stable with respect to plane strain deformation, rotates toward the {111}<112> orientation forming a strong maximum [66]. The relaxed constraints Tayor model, in which shear strains parallel to RD may occur, causes the formation of the {111}<112> orientation [67]. The {111}<112> rolling component is known to lead to the Goss orientation after Rex [66, 68]. Dorner et al. [68] attributed the transition from the {111}<112> deformation texture to the Goss Rex texture to the fact that the Taylor factor (2.4) of the Goss grains is lower than that (3.7) of the {111}<112> matrix. Dorner et al. [69], in their study with 3.2% Si-steel single crystals, also found two types of Goss crystal volumes in 89 % cold-rolled specimen. Most of the Goss crystal regions are situated inside of shear bands. The Goss crystal volumes are also observed inside of microbands. These Goss crystals may act as nuclei because they are thermally stable (Section 7.2).
The evolution of the Goss orientation in the (111)[1 1-2] component, a {111}<112>, has been explained by SERM [70]. Slip systems of (-1-1 0)[-1 1-1], (-1-1 0)[1-1-1], (101)[1 1-1], and (011)[1 1-1] are calculated, by the relaxed constraints Taylor model, to be equally active in the (111)[1 1-2] crystal undergoing the plane strain compression. It is noted that the three slip directions are chosen to be at acute angles with RD [1 1-2] of the crystal. Taking the (101)[1 1-1] and (011)[1 1-1] slip systems sharing the same slip direction [1 1-1] into account, AMSD is [-1 1-1] + [1-1-1] + [1 1-1] = [1 1-3]. According to SERM, this AMSD [1 1-3] becomes parallel to MYMD, the <100> directions in bcc iron, in Rexed crystals. Other directional relationships between the matrix and Rexed crystal can be obtained from the 2nd priority in Section 2. Let one of the <100> directions be the [001] direction, then it must be on the (100), (010) or (110) plane, taking the symmetry condition into account. TD of the (111)[1 1-2] crystal is the [1-1 0] direction. These facts give rise to orientation relationship between the deformed and Rexed states (Figure 49). It is noted that the [1-1 0] direction is TD of both the deformed and Rexed states. It follows that the (111)[1 1-2] orientation becomes the (441)[1 1-8] orientation after Rex. The symmetry yields another equivalent orientation, (441)[-1-1 8]. The (110) pole figure of the {441}<118> orientation is shown in Figure 50a along with the Goss orientation {110}<001>. The {441}<118> orientation is deviated from the Goss orientation by 10°. If each {441}<118> orientation is represented by the Gauss type scattering with a half width angle of 12°, the calculated result is as shown in Figure 50b, which is in very good agreement with the measured data in Figure 50c, where the highest intensity poles are the same as those of the Goss orientation, even though it is not real Goss orientation. It is also interesting to note that the rotation angle between (111)[1 1-2] and (441)[1 1-8] about a common pole of [110] is calculated to be 25°and the rotation angle between (111)[1 1-2] and (110)[001] about a common pole of [110] is 35°. Thus the {111}<112> matrix can favor the growth of Goss-oriented crystals or nuclei, which are stable during annealing, if any, or may generate Goss-oriented nuclei, especially in polycrystalline materials.
Orientation relationship between deformed (
pole figures for (a) {110}<001> and {441}<118> orientations (●(110)[0 0-1], ■(441)[1 1-8], ▲(4 4-1)[-1-1-8]) [
It is well known that the rolling texture of bcc Fe is characterized by the α fiber (<110>//RD) plus the γ-fiber (<111>//ND) and the rolling texture is replaced by the γ-fiber after Rex (Figure 51). This texture transformation will be discussed based on SERM. Figure 52 shows ODFs of 50, 80, and 95% cold-rolled IF steel sheets and their Rex textures, which indicate that the deformation textures are approximated by the α and γ fibers and the Rex texture by the γ fiber, as well known. As the deformation increases, peak type orientations tend to form. For the 80 and 95% cold rolled specimens, the {665}<110>, {558}<110>, and {001}<110> orientations develop as the main components. The {665}<110> and {558}<110> orientations may be approximated by the {111}<110> and {112}<110> orientations, respectively. The {001}<110> component is the principal component inherited from the hot band. It is stable and its intensity increases with deformation [72,73]. The Rex texture is approximated by the γ fiber whose main component is approximated by {111}<112>. The density of this orientation increased with increasing cold rolling reduction.
Figure 53 shows the orientation densities along the α and γ fibers for IF steel rolled by 80% and annealed at 695 °C. Up to 100 s, little change in the orientation density occurs, although appearance of the {111}<112> component in the γ fiber is apparent. For the specimen annealed for 200 s, the orientation density along the γ fiber is almost as high as that of the fully annealed one, while the density along α fiber decreases with increasing annealing time.
We want to know if the {111}<112> Rex texture results from the {111}<110> deformation texture. The (111)[1-1 0] orientation is taken as an orientation representing the {111}<110> deformation texture. The (111)[1-1 0] orientation is calculated to be stable using the rate sensitive model with pancake relaxations (
Section of
ODFs (
Orientation densities along α and γ fibers for IF steel sheets cold-rolled by 80% and subsequently annealed at 695°C for 10 to 1000 s [
These two slip systems are depicted as locating in the opposite sides of the rolling plane as shown in Figure 54a, and they are physically equivalent. They may not be activated homogeneously, even though they are equally activated macroscopically. In this case, AMSD is [1-1-1] or [1-1 1]. It should be mentioned that all active slip directions are not summed unlike fcc metals in which all slip directions are related to each other through associated slip planes. Figure 54b shows angular relationships among MYMD [100], ND [111], and RD [2-1-1] in the (111)[2-1-1] grains, whose orientation has been supposed to be the Rex texture of the (111)[1-1 0] rolling texture. It can be seen that [1-1 1] in Figure 54a is not parallel to [100] in Figure 54b. According to SERM, the {111}<110> rolling texture is not likely to link with the {111}<112> Rex texture.
Examining the experimental results more closely, the evolution of the {665}<1 1 2.4> Rex texture [(
Angular relationships (a) among AMSD, ND, and RD in rolled (111)[1-1 0] crystal and. (b) among MYMD, ND, and RD in (111)[2-1-1] crystal.
Slip direction | \n\t\t\t1-1-1 | \n\t\t\t1-1 1 | \n\t\t\t1 1-1 | \n\t\t||||||
Slip plane | \n\t\t\t101 | \n\t\t\t211 | \n\t\t\t312 | \n\t\t\t0-1-1 | \n\t\t\t-1-2-1 | \n\t\t\t-1-3-2 | \n\t\t\t112 | \n\t\t\t123 | \n\t\t\t213 | \n\t\t
| | \n\t\t\t0.0536 | \n\t\t\t0.0086 | \n\t\t\t0.0843 | \n\t\t\t0.0536 | \n\t\t\t0.0086 | \n\t\t\t0.0843 | \n\t\t\t0.0368 | \n\t\t\t0.0148 | \n\t\t\t0.0148 | \n\t\t
Shear strain rates on slip systems in plane strain compressed (665)[1-1 0] crystal calculated based on rate sensitive pancake model [71]
For the (665)[-1-1 2.4] orientation as an orientation representing the {665}<1 1 2.4> Rex texture, the angles among ND, TD, RD, and [001] are shown in Figure 55b. Comparison of Figures 55a and 55b shows that AMSD in the deformed specimen is almost parallel to [001], MYMD of iron, in the Rexed specimen. This is compatible with SERM. In other words, the transformation from the (665)[1-1 0] deformation orientation to the (665)[1-1 2.4] Rex orientation is compatible with SERM. The deformed matrix and Rexed grains share the [665] ND (2nd priority in Section 2). Taking symmetry into account, the {665}<110> rolling texture is calculated to transform to the {665}<1 1 2.4> Rex texture, in agreement with the experimental result. This transformation relationship may be approximated by the transformation from the {111}<110> deformation texture to the {111}<112> Rex texture.
The {111}<112> orientation is not stable with respect to plane-strain compression. However, if the orientation survived during rolling, grains with the orientation must have been plane-strain compressed. The plane-strain compressed (111)[1 1-2] crystal is calculated, by the full constrains model, to have slip systems of (110)[1-1-1] and (110) [-1 1-1], whose activities are the same, if we consider slip systems on one side of the rolling plane. It is noted that the slip directions are at acute angles to RD and on the same slip plane. AMSD is calculated to be [1-1-1] + [-1 1-1] = [0 0-2], which is parallel to a MYMD (Figure 56a). Therefore, the {111}<112> deformation texture is likely to remain unchanged during annealing (1st priority in Section 2). The {111}<112> grains may act as nuclei.
Yoshinaga et al. [74] observed that a {111}<112> nucleation texture was strongly formed in 65% rolled iron electrodeposit with a weak {111}<112> texture, resulting in the {111}<112> Rex texture, whereas a {111}<110> nucleation texture was formed in 80% rolled electrodeposit having a strong{111}<112> texture, resulting in the {111}<110> Rex texture. They noted the importance of the nucleation texture in the Rex texture formation and attributed to the {111}<110> Rex texturing in the 80% rolled sheet to higher mobility of grain boundaries between the {111}<110> grains and the{111}<112> deformed matrix. They did not account for the differences in nucleation texture between the 65% and 80% rolled sheets.
(a) AMSD in (665)[1-1 0] rolled crystal; (b) MYMD in (665)[-1-1 2.4] Rexed crystal [
Explanation of {111}<112> rolling texture changing to {111}<112> or {111}<110> after Rex. F’B’ and F’D’ are MYMDs in Rexed state and are almost parallel to AMSDs, FB and FD, in deformed state, respectively [
According to SERM, the {111}<112> deformation texture is likely to remain unchanged after Rex because AMSD in the deformed state is parallel to MYMD, as mentioned above. If the activities of the slip systems of (110)[-1 1-1] and (110)[1-1-1] in Figure 56a are well balanced, MYMD becomes [0 0-1]. This may be the case in the 65% rolled sheet. As the rolling reduction increases, the balance can be broken. When the (110)[1-1-1] slip system is two times more active than the (110)[-1 1-1] system, AMSD is parallel to the [1-1-3] direction (2[1-1-1] + [-1 1-1] = [1-1 -3]). Similarly if the (110)[-1 1-1] system is two times more active than the (110)[1-1-1] slip system, AMSD is parallel to the [-1 1-3] direction. These directions are shown in Figure 56a. If one of the two slips takes place in one layer and another one does in another layer and so on, as in
As the Rexed {665}<1 1 2.4> and {111}<112> grains grow, they are likely to meet the α fiber grains. If the Rexed grains are not in a favorable orientation relationship with the α fiber grains, they may not grow at the expense of the α fiber grains. This is discussed in the next section.
Park et al. [75,76] discussed orientation relationships between the rolling and Rex textures in rolled IF steel sheets based on both SERM and the conventional OG, in which the α-fiber rolling texture was assumed to transform to the γ-fiber Rex texture. The {001}<110> and {112} <110>rolling orientations, which are main components in the α-fiber texture, are calculated to be stable using the full constraints Taylor model. For the (001)[110] orientation as an orientation representing the {001}<110> orientation, active slip systems are calculated to be (1 1-2)[111] and (112)[1 1-1] from the full constraints Taylor model. Therefore, AMSD can be [111] or [1 1-1]. Figure 57a shows the angular relation between the [111] direction and the (001)[110] specimen axes. Figure 57b shows the angular relation between the [001] direction, which is a MYMD, and the axes of the specimen with the (111)[-1-1 2] Rex texture. It can be seen from Figure 57 that AMSD in the deformed state is parallel to MYMD in the Rexed state and TD is shared by the deformed and Rexed states (2nd priority in Section 2). Taking the symmetry into account, the {001}<110> deformation texture is calculated to transform into the {111}<112> Rex texture. This transformation was observed in the experimental results (Figures 52 and 53, [75], [77]). It is often addressed that the {001}<110> orientation is difficult to be Rexed. It may be attributed to the fact that the orientation has a low Taylor factor [66].
For the (558)[1-1 0] orientation as an orientation representing the {558}<110> orientation, active slip systems are calculated to be 2.283(101)[1-1-1], (101)[-1-1 1], 2.283(0-1-1)[1-1 1], and (0-1-1)[1 1-1] from the full constraints Taylor model, where the factor 2.283 in front of slip systems indicates that their activities are 2.283 times higher than other slip systems [66]. The slip systems reduce effectively to (101)[1-2.56-1] and (0-1-1)[2.56-1 1]. Therefore, AMSD becomes [1-2.56-1] or [2.56 -1 1]. Figure 58 shows that the [1-2.56-1] direction in the (558)[1-10] crystal is nearly parallel to MYMD in the Rexed state, and the [101] direction is shared by the deformed and Rexed states (2nd priority in Section 2). Taking the symmetry into account, the {558}<110> deformation texture is calculated to transform into the {334}<483> Rex texture. This transformation relation was observed in the experimental result. The {334}<483> orientation is away from the {111}<112> orientation. An exact correspondence between the (112)[-110] deformation and (-2.45 2 –2.45)[1 2.45 1] Rex orientations can be seen in Figure 59.
AMSD in (001)[110] rolled crystal and MYMD in (111)[-1-1 2] Rexed crystal [
AMSD in (558)[1-1 0] rolled crystal and MYMD in (334)[4-8 3] Rexed crystal [
AMSD in (112)[-110] rolled crystal and MYMD in (-2.45 2 -2.45)[1 2.45 1] Rexed crystal [
Park et al. [75] studied relationships between rolling and Rex textures of IF steel. When the {112}<110>, {225}<110>, and {112}<110> components had the highest density in cold rolling texture, the {567}<943>, {223}<472>, and {554}<225> components had the highest density in Rex texture, respectively. Rolling and Rex textures of low carbon steel (C in solution), and Fe-16%Cr and Fe-3%Si steels indicate that the strong rolling texture components {001}<110> and {112}<110> have an effect on the evolution of a very strong Rex texture {111}<112> [77].
Park et al. [76] investigated the macrotexture changes in 75% cold-rolled IF steel with annealing time at 650ºC along the α-fiber. The cold rolling texture showed the development of the α fiber as typical in bcc steels. The orientation densities of the α-fiber increased slightly after annealing for 300 s. This is a well-known recovery phenomenon. A part of the α-fiber, near {114}<110>, substantially decreased after annealing for 1000 s. EBSD analysis indicated that the {556}<175> Rex component was formed at the expense of the {114}<110> deformation component. This texture transformation could be explained by SERM. Relationships between various rolling and Rex textures are summarized in Table 6.
These results can be explained based on SERM [4,75,76]. Figure 60 shows drawings relating the rolling texture components to the Rex texture components. AMSDs can be easily obtained by choosing the <111> directions, the slip directions in bcc metals, closest to 45o to the compression axis without calculation of rolling deformation. For the cold rolling texture (001)[110], TD is calculated by the vector product of [110] and [001] to be [-110]. The <111> directions closest to 45o with the [001] compression axis are [-111], [-1-1 1], and [111]. The [-111] direction is likely to contribute to spread of the width of sheets. Therefore, slip along the [-111] direction is unlikely. The effective slip planes are likely to be parallel to TD and contain the [111] and [-1-1 1] slip directions. The planes are those normal to the vector product of the [-110] TD and the [-1-1 1] and/or [111] directions. They are calculated to be the (112) and/or (1 1-2) planes. The related slip systems are therefore (112)[-1-1 1] and (1 1-2)[111]. These systems are physically equivalent. Therefore, it is sufficient to choose one of them. Let us choose the [111] direction. The [111] direction and other related directions and planes are shown in Figure 60a. The [111] direction is on ND-RD plane. Therefore, it is likely to be AMSD.
Correspondence between AMSD in rolled state (top), MYMD in Rexed state (bottom) in orientation relationships between (a) (001)[110] roll ↔ (111)[-1-1 2] Rex, (b) (112)[-110] roll ↔ (545)[-2 5-2] Rex, (c) (114)[-110] roll ↔ (556)[-1 7-5] Rex.
If the [111] direction in the deformed state is set to be parallel to MYMD [001] in the Rexed state, the (111) plane becomes parallel to the rolling plane and the [-1-1 2] direction becomes parallel to RD in the Rexed state, giving rise to the (111)[-1-1 2] Rex texture as shown in Figure 60a. This result is the same as that obtained based on the full-constraints Taylor model (Figure 57). Therefore, the {001}<110> may be responsible for the measured {111}<112> Rex texture. It is noted that the [-110] TD is shared by both the deformed and Rexed states (2nd priority in Section 2). It is also noted that the angle between AMSD and RD is about 30o which is the usually observed angle between the shear band and RD.
Other examples in Figure 60 are self-explainable. In all the examples except Figure 60d, the <110> directions are shared by the deformed and Rexed states. In fact, the Rex textures in Figure 60b and 60c are very similar. This is the reason why there exists an angular relation between the deformed and Rexed states about the <110> axes (Table 6). This has often been interpreted to be associated with CSL boundaries. However, there is no consistency in the CSL boundaries. Anyhow the high density orientations along the α fiber change to near {111}<112> orientations on Rex.
As the Rexed γ fiber grains grow, they are likely to meet the α fiber grains. Main components in α fiber including the {112}<110> orientation are predicted to tend to change to near {111}<112> orientations according to SERM. Therefore, the {111}<112> Rexed grains will grow at the expense of the α fiber grains with little disturbance of orientation. It is interesting to note that SERM can satisfy the relation between the deformation and Rex textures in the nucleation and growth stages. The two prominent components, (334)[4-8 3] and (554)[-2-2 5], in the Rex texture are related to the (558)[1-1 0] and (112)[1-1 0] components in the rolling texture, respectively.
{112}<110> | \n{567}<943> | \n30 | \n29 | \n30°<110> | \nΣ19a(26.5°<110>) | \n
{225}<110> | \n{223}<472> | \n35.3 | \n32.6 | \n25°<110> | \nΣ19a(26.5°<110>) | \n
{112}<110> | \n{554}<225> | \n30 | \n29.5 | \n35°<110> | \nΣ9(38.9°<110>) | \n
{001}<110> | \n{111}<112> | \n35.3 | \n35.3 | \n55°<110> | \nΣ11(50.5°<110>) | \n
{114}<110> | \n{556}<175> | \n35 | \n36 | \n\n | \n |
{558}<110> | \n{334}<483> | \n30.6 | \n32 | \n29°<110> | \nΣ19a (26.5°<110> | \n
Orientation relationships (OR) between major components which dominate rolling and Rex textures.
Orientation densities along α- and β- fibers for 70% rolled and annealed Ta [
The texture evolution in Ta after 70% rolling and subsequent annealing at various temperatures is shown in Figure 61 [78]. The rolling texture of Ta is characterized by a partial α-fiber extending from {001}<110> to {111}<110> and a complete γ-fiber {111}<uvw>. The major deformation texture components are {112}<110> and {001}<110> as in steel. MYMD of Ta is <100> (A>0 in Table 6), the development of the Rex texture is expected to be similar to that in steel. It can be seen that an enhancement of {001}<110> due to recovery and a strong decrease in {001}<110> to {112}<110> accompanied by a strong increase in γ-fiber {111}<112> and/or {554}<225> due to Rex. The Rex behavior is readily understood from Figure 60 [4, 75].
(a)
The deformation texture of rolled Mo sheets was characterized by a weak γ-fiber and α-fiber with a strong {100}<110> component [79]. Full Rex does not change the rolling texture but reduces its intensity (Figure 62). This result is compatible with SERM considering that the <111> directions are not only slip directions, which is approximately AMSD (Figure 60a, top), but also MYMD of Mo (
Since the slip systems of W are {112}<111> [80], it is predicted that the {001}<110> component dominates the rolling texture as shown in Figure 60a. Figure 63a shows the rolling texture which is dominated by the {100}<011> component as predicted. The deformation texture is approximately randomized after Rex (Figure 63b). This is compatible with SERM because W is almost isotropic in its elastic properties (
\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t\t\n\t\t\t | \n\t
Ta | \n\t\t1300 1400 1500 1600 | \n\t\t8.137 8.297 8.408 8.576 | \n\t\t13.966 14.025 14.184 14.409 | \n\t\t-3.150 -3.224 -3.274 -3.357 | \n\t\t1.6164 1.6429 1.6472 1.6563 | \n\t\t82 | \n\t
Mo | \n\t\t273 373 973 | \n\t\t2.607 2.655 3.010 | \n\t\t9.158 9.242 9.823 | \n\t\t-0.622 -0.682 -0.833 | \n\t\t0.7052 0.7092 0.7824 | \n\t\t83 | \n\t
W | \n\t\t100 297 973 2073 | \n\t\t2.398 2.454 2.711 3.509 | \n\t\t6.158 6.218 6.553 7.375 | \n\t\t-0.665 -0.690 -0.798 -1.160 | \n\t\t0.9948 1.0113 1.0710 1.2662 | \n\t\t84 85 85 85 | \n\t
Pole figure of W sheet (a) after cold rolling by 96% and (b) subsequent annealing at 2000 °C for 30 min [
The Rex textures of freestanding electro- and vapor-deposits of metals and heavily deformed metals and alloys whose stored energies due to dislocations constitute the main driving forces for Rex can be determined such that AMSDs in the fabricated matrix can be along MYMDs in Rexed grains or nuclei, and by other conditions which can maximize the strain-energy release in the system. The strain-energy-release-maximization theory can explain the following results.
The <100>, <111> and <110> electro- and vapor-deposition textures of Cu, Ni, and Ag transform to the <100>, <100>, and <√3 1 0> textures, respectively, after Rex.
The <100> and <111> deposition textures of Cr remain unchanged after Rex.
The <111>+<100> drawing textures of uniaxially drawn Ag, Al, Cu, and Au wires change to the <100>textures after Rex.
Channel-die compressed {110}<001> Al single crystal keeps its {110}<001>deformation texture after Rex.
The {135}<2 1-1> Al sheet obtained by channel-die compression of Al crystals of {123}<412> orientations by 90% develops {-0.0062 0.2781 0.9606}<0.9907 0.1322 -0.0319> ≈ {0 1 3.5}<31 4 -1> after Rex.
An Al crystal of {112}<111> obtained by channel-die compression of a (001)[110] Al single crystal develops {001}<√610> after Rex.
The (123)[-6-3 4] + (321)[-436] + {112}<111> Cu sheet obtained after reversible rolling of a (123)[-6-3 4] Cu single crystal by 99.5% under oil lubrication develops the Rex texture of major {001} <100> + minor (0 3-1)[100] orientations. The {001}<100> and (0 3-1)[100] components are calculated to result from the {112}<111> and (123)[-6-3 4] components in the deformation textures, respectively.
The {011}<211>, {112}<111>, and {123}<634> components in the rolling texture of cold-rolled polycrystalline fcc metals and alloys with medium to high stacking fault energy are respectively linked with the {011}<100>, {100}<001>, and {031}<100> component in the Rex texture.
The {111}<112> bcc crystal undergoing plane strain rolling can develop three different Rex textures of {441}<118>≈ {110}<001>, {111}<112>, and ~{111}<110> depending on local slip systems and their activities in the same gloval deformation.
The {665}<110>, {001}<110>, {558}<110>, {112}<110>, {114}<110> components in the rolling texture of steel are respectively linked with the {665}<1 1 2.4>, {111}<112>, {334}<483>, {545}<252>, {556}<175> components in the Rex texture.
The rolling and Rex textures of Ta are similar to those of steel.
Full Rex of Mo does not change the rolling texture but reduces its intensity.
The rolling texture of W transforms to a texure which can be approximated by random orientation distribution after Rex.
The growth of polar zinc-blende GaAs on a non-polar Si(001) substrate can lead to planar defects named antiphase boundary (APB). The APB planes are made of III-III or/and V-V bonds that can propagate in the layer through the {110}, {111} or higher index planes (Figure 1) [2, 3].
Ball-and-stick model of III-V-on-Si with {110} and {111}-APBs. The single-layer step edges initiate the formation of the APBs while the surface with double-layer steps allows a single-domain III-V cristal. From reference [
The elastic strain field due to APB changes atomic distances and hence electronic states, acts as a carrier diffusion and/or non-radiative recombination centers. APBs nucleate at the edges of the single-layer steps present at nominal (001) silicon surfaces. Until now, the APBs formation was mainly inhibited by using (i) off-axis Si(001) substrates tilted by 4–6° towards [110] direction [4, 5] or (ii) Si(211) substrates [6] where Si double-layer steps could be formed easily. However, these wafers are not compatible with industrial Si CMOS standards which uses nominal Si(001) wafers, i.e. with a miscut angle equal or lower than 0.5°. The best option to prevent the APBs nucleation is to promote double layer step formation on nominal Si(001) substrate as it is the case for off-axis wafers.
Considering the thermodynamical models, the double-layer steps formation on nominal Si(001) is predicted as highly unfavorable in ultra-high Vacuum (UHV) or in inert gas ambient. The stress relaxation induced by dimerization of the (2 × 1)-Si(001) reconstruction promotes single step formation until a miscut angle lying in a range between 1 and 3° [7, 8, 9, 10]. Thus, the (001) surface of nominal wafers is made of alternating (2 × 1) and (1 × 2)-reconstructed terraces (named A-type and B-type terraces respectively) separated by SA and SB single steps according to the Chadi’s nomenclature (Figure 2) [8]. For A-type terraces the Si-dimer rows are parallel to the step edges while they are perpendicular for B-type terraces.
Dimerization of the Si(001) surface with alternating (2 × 1) and (1 × 2)-reconstructed terraces (named A-type and B-type terraces respectively) separated by SA and SB single steps.
However, computational modeling highlights a possible mechanism to get a nearly single-domain Si(001) surface by selective etching of SB steps (i.e. by removing the B-type terraces)
The removal of two neighboring silicon atoms from the considered Si(001) surface (Figure 2) creates the so-called single-dimer vacancy (SDV) [12]. Line defects on the surface can appear by aligning SDV together, either in lines, creating dimer-vacancy lines (DVL) or in rows creating dimer-vacancy rows (DVR) [13] as shown respectively in green and pink areas of Figure 3a.
(a) Schematic view of the DVR and DVL line defects on the 2 × 2 reconstructed silicon surface. Only two silicon bulk layers are represented (black and dark grey) in addition to the surface layer which is reconstructed. The distance from the surface is coded in gray-scale. Silicon atoms marked with a small white disk are hydrogenated in the case of hydrogenated DVR and DVL. (b) The variation of the formation energy of both DVR and DVL defects, bare or hydrogenated with respect to the chemical potential of the hydrogen. From [
The formation energy of the bare line defects DVR and DVL (i.e. with dangling bonds, labelled DVR and DVL no hydrogen), are represented on the Figure 3b. In order to take into account the hydrogen of the chamber in CVD ambient, the bare line defects are modified by placing a single hydrogen atom on each silicon of the first bulk layer with a dangling bond (Figure 3a), changing their geometry and their formation energies. Indeed, the DFT calculations show that for both defects and whatever the surface states, the geometry distortions of the bare defects are considerably reduced when the defect is hydrogenated. In the DVR case, for instance, the dimers in the line adopt a flat position instead of a tilted one. This reduction in elastic stress is key in the formation energy lowering of the line defects. As shown on Figure 3b, for hydrogen rich conditions (right handside of the graph Figure 3b), the formation energies of both hydrogenated DVR (H-DVR) and DVL (H-DVL) are lower than for the bare defects. Moreover, two regimes can be observed whatever the surface state is. One range for superhigh H chemical potentials where the H-DVL is favored, and a medium range of H chemical potentials where the H-DVR takes prominence. It is worth to note that the gain in energy per dimer can be quite important (several eVs) when comparing the different ranges, showing that the selectivity with respect to H chemical potential is quite strong.
The role of hydrogen is thus twofold. It first induces a large increase of dimer-vacancy concentration due to the lowering of their formation energy. The second effect of hydrogen is to select DVR with respect to DVL when using suitable hydrogen annealing conditions. This latter point is the key to obtain a single domain Si(001) surface. Indeed, the DVRs cross the B-type terraces in a direction perpendicular to the step edges. This can generates a nearly complete etching of the SB steps if the terraces are not too large. This assumption was tested with a 600 Torr/900°C/10 min H2 annealing of different on-axis Si(001) wafers. Prior to the H2 annealing, the native oxide is removed by SICONI™ process [14]. Atomic force microscopy (AFM) images of Figure 4a. shows the result obtained from a wafer with a very slight 0.05° misorientation near the [110] direction. The DVRs that run across the B-type terraces can be clearly distinguished. They lead to comb-like shaped B-type terraces. Nevertheless, the terrace width is too large (the miscut angle too small) to obtain a complete removal of B-type terraces. On the contrary, when using a wafer with an higher misorientation (0.15°) in the [110] direction, the B-type terraces can be selectively etched as shown in Figure 4b. The AFM line profile confirms the formation of double steps (∼2.7 Å in height)). However, there is still a few small islands remaining at the step edges (not clearly visible from the AFM image). This behavior was also observed by other authors working on GaP-on-Si growth [15, 16]. H2 annealing of a Si(001) substrate with a 0.12° miscut near the [100] direction was also tested. When the miscut direction slightly differs from the <110> azimuthal directions, each terrace boundary is made of two types of step edge (with both SA and SB steps). The selective etching of the SB-segments leads to a dendritic shape of the terraces (Figure 4c). Thus, it is not possible to achieve double-layer steps formation on wafers having a miscut direction different from <110>. It should also be noted that the SB step etching only occurs for hydrogen conditions near the atmospheric pressure and for a temperature > 850°C [11]. Otherwise, the generation of dimer-vacancies agglomeration is energetically not favorable for such hydrogen chemical potential (Figure 3b).
2 × 2 μm2 AFM image of nominal Si(001) surfaces after 600 Torr/900°C/10 min H2 annealing (a) substrate 0.05° misoriented near [
The effectiveness of the Si surface preparation for APBs removal was proven from GaAs growth on different types of nominal wafers. MOCVD growth of GaAs-on-Si can be achieved using a two-step process [4, 5]: few nanometers of a high-density nucleation layer is first deposited at low temperature (350–450°C) followed by the coalescence of the nuclei during temperature ramp up to 550–700°C. Then at this temperature, a thicker GaAs layer is epitaxially grown to improve the material quality. Classical group-III precursors are TMGa or TEGa while group-V precursors are often TBAs or AsH3 for the high temperature step. The precursors are injected in the MOCVD chamber using purified H2 as carrier gas. Figure 5a shows the morphology of the GaAs surface grown on Si wafer with miscut angle <0,1° (the type of Si surface presented in Figure 4a). Thanks to their V groove shapes, randomly oriented APBs can be observed by AFM with a linear density of several μm−1. This APB density is equivalent to the one obtain for a GaAs growth on a silicon substrate without any surface preparation. It results in a large surface roughness with a root mean square (RMS) value of about 1.5–2 nm. As mentioned before, the APBs originate at the single-step edges between the very large (2 × 1)/(1 × 2)-Si(001) terraces of Figure 4a. Thus, the self-annihilation of the APBs is not possible in the GaAs layer (with a typical thickness around 400 nm) due to the large inter-APB distance.
5 × 5 μm2 AFM images of (a) 400 nm-thick GaAs epitaxially grown on 0.05°-miscut angle Si(001) wafer: High density of randomly oriented APBs. RMS roughness = 1.7 nm. (b) 150 nm-thick epitaxially grown APBs-free GaAs on Si(001) wafer with a 0.15°-miscut angle toward the [
As the Si wafer miscut angle is increased above 0.1° exactly in the [110] direction, the APBs can be easily removed. The AFM image of a 150 nm thick GaAs layer is shown in Figure 5b. The surface roughness is improved and the RMS value drop to 0.8 nm. This roughness is similar to the one reported for 1 μm thick GaAs grown on 4°-6° offcut Si(001) substrate [18, 19, 20], despite the fact that only 150 nm of GaAs were grown. No V-groove feature is observed indicating that a APBs-free surface is formed. The absence of APBs on top of the GaAs layer is confirmed by the STEM cross section image (inset of Figure 5b.). The (110)-STEM cross-section shows a dark zone at the bottom of the GaAs layer due to the highly defective Si/GaAs heterointerface. The defective area is a combination of multiple crystalline defects such as dislocations, stacking faults and APBs due to the remaining small monoatomic silicon islands mentioned before. However, for a thickness beyond about 70 nm, no more APB planes propagate toward the surface. Indeed, the APB planes that nucleate at these monoatomic step edges have intersected pairwise during the high temperature growth and thus self-annihilated. The kinking of APBs in the III-V layers followed by their self-annihilation is often explained by kinetic phenomena [21, 22]. In such mechanisms, the adatoms incorporation rate is anisotropic along the two azimuthal <110> directions. In GaAs, several groups have indeed already shown a diffusion constant of Ga atoms 4 times larger along the As dimer lines regarding to the one along the dimer rows [23, 24, 25]. It results in a bias between the growth rate of the domains in antiphase responsible for the kinking of the APBs.
Interestingly, a GaAs film grown on Si wafer with a misorientation above 0.1° and toward a random direction (different from the <110>) is also APBs-free beyond a thickness of about 300-400 nm (Figure 5c). This can be achieved even though the Si surface is only made of single-layer steps. Actually, this silicon surface, described in the previous section and in Figure 4c, is made of very narrow dendritic terraces. Thus, the (2 × 1)/(1 × 2)-Si domains size are small enough to enable the self-annihilation of the APBs. However, when the misorientation is not in the <110>, a 100 nm-thick GaAs layer is not sufficient to get rid of the APBs and a thicker buffer layer is required.
In an industrial point of view, this is particularly important to relax the constraint on the wafer miscut specifications. Any substrate with a miscut-angle >0.1° can be used whatever the in-plane direction of the wafer slicing. Therefore, contrary to the GaP-on-Si system, the double-layer steps on nominal silicon wafers is not mandatory to achieve a APBs-free GaAs layer.
In the same fashion, the GaAs layer can be epitaxially grown by using a lattice-matched Germanium buffer layer [26]. Beyond the APBs issue, using a relaxed Ge buffer layer is also an interesting strategy to decrease the threading dislocation density in the GaAs layer, as we will see in the next paragraph. Due to the fact that GaAs will be quasi-lattice matched to the Ge strain relaxed buffer and thanks to a reuse of the existing threading dislocations to create new misfit sements if needed, the GaAs/Ge interface should exhibit no such high density of defects as when growing directly GaAs on Si. This will permit a clearer view of the GaAs/Ge interface to precisely observe the defects present when growing polar material on Ge, which is not possible when growing GaAs directly on Si.
5 × 5 μm2 AFM images (Figure 6) show the surface of 300 nm thick GaAs layers grown on 1 μm-thick Ge/Si(001) substrates with three different offcut angles in the <110> direction: (a) 0.1°, (b) 0.3°, and(c) 0.5°. The APBs density decrease as function of the miscut angle. With a silicon wafer having a miscut angle of 0.5° the 300 nm-thick GaAs layer is completely free of APBs.
5 × 5 μm2 AFM images of the surface of GaAs layers grown on Ge-buffered silicon(001) substrates with three different offcut angles: (a) 0.1°-offcut angle, (b) 0.3°-offcut angle, and (c) 0.5°- offcut angle. All the offcut angles are in the <110> direction. The scale on the right hand side of each image is labeled in nm. The table (d) presents the APB density measured for each sample. AFM image sides are along the <100> directions. From [
Contrary to the direct growth of GaAs on Si, we still observe APBs with a 0.3° offcut Si substrate.
In order to have insight on the defects at the interface in this case, cross-sectional TEM images of a GaAs layer grown on Ge-buffered Si substrate with a 0.5° offcut in the <110> direction are shown in Figure 7. The left hand image shows the overall stack, with (from bottom to top) the 0.5° offcut silicon substrate, the 800 nm thick Ge strain relaxed buffer and the 280 nm thick GaAs layer. The interface between GaAs and Ge is highlighted by a thin white line superimposed in the left hand part of the image. No APBs nucleating at this interface are observed, but some dark dots are nevertheless present. The image in the right hand part of Figure 5 is a magnified view of this interface, showing randomly distributed, different size dark dots which are small (<50 nm), and not at the origin of any extended defects.
Cross-sectional TEM images of a GaAs layer on a Ge-buffered Si substrate. The left hand image is an overview of the overall stack, with the 0.5° offcut Si substrate at the bottom. The right hand image is a zoom of the GaAs/Ge interface.
Higher resolution images of two of these interface defects have shown that dark spots at the interface are voids, not APBs. Therefore, we observe no APB when using a 0.5° offcut Si substrate for growing GaAs with an intermediate Ge strain relaxed buffer. This hints that bi-atomic steps are achieved at the surface of the Ge strain relaxed buffer using the appropriate hydrogen bake (T > 750°C at 80 Torr H2), and we observe no APB annihilation such a seen previously when growing GaAs directly on Si.
The progressive improvement of the GaAs layer quality as function of the Si-miscut angle can also be observed from the FWHM of the (004) diffraction line in XRD
High resolution, X-ray diffraction profiles around the (004) order (in the triple axis configuration) for a GaAs layer grown on a Ge-buffered silicon substrate with a 0.1° (solid line), 0.3° (dashed line), and 0.5° (dotted line) offcut. From [
Detrimental influence of APBs on the optical properties is highlighted from photoluminescence (PL) measurements at 300 K [17]. PL spectra of Figure 9 compares the near band edge luminescence (1,42 eV) of GaAs-on-Si layers with and without APBs. Both layers are n-doped at 7.1017 cm−3. The PL intensity of the APBs-free GaAs film is three times higher than the one of the GaAs layer with APBs. Furthermore, the PL peak of the APBs-free is 40% narrower. These results are directly correlated to the role of APBs acting as non-radiative recombination centers.
PL spectra at 300 K for GaAs-on-Si layers with and without APBs. The PL intensity is 3 times higher for the layer without APBs. The FWHM of the peak is 40% lower [
In the same way, the influence of APBs on the electrical properties is highlighted from the Hall effect measurements on a 250 nm-thick GaAs active layer n-doped at 7.1017 cm−3. This n-doped active layer is grown on intrinsic GaAs-on-Si buffer layers with/without APBs. Hall effect measurements, in the Van der Pauw configuration, are performed by taking 5 points across the whole 300 mm wafer. The mean electron mobilities are reported in Table 1. The electron mobility (μe) of the GaAs active layer grown on the APBs-free buffer layer is one decade higher than the one obtained on the buffer with APBs. The μe = 2000 cm2V−1 s−1 value of the APBs-free layer is nearly equivalent to the mobility measured from an homoepitaxy n:GaAs-on-GaAs in the same reactor.
250 nm GaAs:Si (7 × 1012 cm−3) Active layer without APBs | VS | 250 nm GaAs:Si(7 × 1012 cm−3) Active layer without APBs | |
---|---|---|---|
400 nm GaAs buffer With APBs | 400 nm GaAs buffer Without APBs | ||
Si(001) | Si(001) | ||
Sample | Doping level (cm−3) | Electron mobility (cm2/V.s) | Resistivity (W/cm) |
GaAs-on-Si with APB | 7 × 1017 | 200 | 2 × 10−2 |
GaAs-on-Si without APB | 7 × 1017 | 2000 | 4 × 10−3 |
GaAs-on-GaAs | 7 × 1017 | 2500 | 3 × 10−3 |
Hall effect measurements at 300 K for GaAs-on-Si layers with/without APBs. The electron mobility is 10 times higher for the layer without APBs [17].
The strategies to reduce the threading dislocation density (TDD) in the III-V layer can be classified according to two major tendencies: 1) engineering of thick buffer layer (strained layer superlattices, germanium buffer layer,…) to annihilate the defects before growth of the III-V active layer. 2) Selective area epitaxy in dielectric cavities (SiO2,SiN,…) formed by standard technological steps (deposition, lithography, etching,…). In this last approach, the threading dislocation (TD)propagation is geometrically limited in one direction by the sidewalls of the patterns. These two majors will be described more deeply in the following paragraphs.
The technology of monolithic integration of III-V on Si is of great interest due to combining the superior optical properties of III-V materials and the advantages of Si substrates such as low cost and high scalability [27]. However, as most III-V semiconductor materials have a relative large difference in lattice constant to Si, high density of crystal defects are generated during the epitaxial growth. This leads to the failure of the technique of direct deposition of III/V on Si become commercially viable in 1980s, despite intensive studies have been demonstrated in that era [28]. The lattice mismatch property creates a substantial stress accumulation in the first few pseudomorphic layers of deposited material, as shown in Figure 10a. As the stress is accumulated above a critical value of growth thickness, the strain-relaxation process leads the generation of misfit dislocations (MDs). The MDs are associated with missing or dangling bonds along the mismatched interface which are shown in Figure 10b [30], thus MDs lie entirely on the growth plane. Since the dislocations cannot be eliminated within a crystal due to energetic reasons, the MDs must either reach the edge of crystal or turn upward through the deposited layers to form TDs. As a result, from the transmission electron microscopy (TEM) shown in Figure 10c, TDs seem to extend from the interface of III-V and Si, and go through the epilayer. TDs are likely to be transferred from MDs when the distance to the sample edge is much longer than the distance to the epi-layer surface. Meanwhile, TDs could also transfer to MDs either through dislocation glides, extending the misfit segment beneath it, or in active region during the electron–hole recombination through the phenomenon known as recombination-enhanced dislocations motion [31]. Typically, in the growth of GaAs on Si, the TDD is around 1010 cm−2 at the growth interface [32]. Unfortunately, the viable TDD in active region for practical optoelectronic devices should be below 106 cm−2 [32], which held back the development of many III-V on Si material systems for some time. Those dislocations have associated trap states serving as nonradiative recombination centers to reduce the photon emission efficiency and/or minority carrier lifetime [32], resulting in a degradation of devices performance. In addition, those states in the band could also increase the leakage current of the devices [3].
Schematic change in lattices of thin film on substrates and bright field scanning TEM image of TDs. (a) denoting the initial pseudomorphic layers of deposited materials. (b) denoting MD as spinning “T”. (c) a bright-field STEM image showing the TDs. (adapted from Ref. [
Efforts have been made to control the TDD in GaAs grown on Si substrates. As the thickness of deposited layer increases, TDs will glide, move and react with other TDs depending on their Burger vectors, resulting in a repulsion or annihilation as Figure 11 shows. As TDs keep propagating in the overlayers, they are likely to meet other dislocations to be self-annihilated as shown in Figure 11. If there is a strain induced by the lattice mismatched between the underlayer and overlayer, generated TDs are expected to experience lateral forces which drive TDs into edge as Figure 11 deflection to edge shows.
Mechanisms of dislocation motion in GaAs/Si. (Reproduced from Ref. [
The deflection process relives the strain induced by lattice mismatch and makes TDs to react with other TDs more likely and/or convert TDs into MDs to decrease the TDD. As demonstrated by Masami and Masafumi in 1990, the dislocation density n in a thick GaAs layer grown on Si can be estimated through the following Equation [34]:
where x is the thickness of the GaAs layer, D0 is the dislocation density at the interface, a and b are two constants related to the density of etch pit defects (EPD) and coalescence of dislocations respectively. According to their characterization, D0 = 1012 cm−2, a = 2 × 10 cm−1, and b = 1.8 × 10−5 cm. For the dislocation density in a thin GaAs film on Si, it can be estimated through n(x) = D0hm, where D0 is the dislocation density at the interface and m is the empirical value with minus symbol [28, 35, 36]. In order to reduce the TDD to the level of 106 cm−2, the thickness of GaAs is estimated to be as thick as 100 μm [34].
However, due to the difference in thermal expansion coefficients of GaAs and Si, a GaAs layer which is thicker than 7 μm will induce micro cracks on GaAs thin films [37]. In addition, a thick GaAs buffer on Si will bend the wafer [34]. Thus, a more effective method known as dislocation filtering has been put forward to induce designed strain to bend the TDs and to encourage TDs to move, interact and annihilate [28]. The most common dislocation filter layer (DFL) system includes strained layer superlattice (SLSs) and quantum-dot (QD) DFL, while different SLS structure including InGaN/GaN [38], InGaAs/GaAs, InAlAs/GaAs [32] and GaAsP/GaAs [39], have been studied. A typical cross-sectional TEM measurement for InGaAs/GaAs SLSs DFLs is shown in Figure 12(a), indicating how the TDs are eliminated within DFLs. Taking InGaAs/GaAs DFL for example, a layer structure of InGaAs/GaAs is shown in Figure 12(b). The strain direction, induced by the lattice mismatch, inside the DFL is shown in Figure 12(c).
An InGaAs/GaAs DFL schematic structure in different views. (a) The DFL sample structure in the cross-section TEM. (Reproduced from Ref. [
The appropriate choice of composition and thickness for SLS is dependent on the material and the prior dislocation density. Since the purpose of DFL structure is to introduce strain to promote the TD motions, forming dislocations should be avoided within DFL, which means the thickness for each layer should below the critical thickness. For most SLSs, the thickness of each layer should below 20 nm [28, 29, 32]. By using SLS DFL technique, researchers from University College London have successfully reduced the TD density down to the 106 cm−2 [27].
Although SLSs have been proved to remove more than 90% of TDs [28], the induced strain which bends TDs is still within 2 dimensions. QD is a 0-dimensional nanostructure with much larger strain field compared to SLS. As a result, it is believed that QD can also sever as the DFL, which might be even superior than SLSs [40]. Researchers from University of Michigan have proved that InAs QDs were the most suitable QD. A fabricated laser structure with InAs QD DFL was demonstrated with a threshold current density of 900 Acm−2 [40].
InxGa1-xAs/GaAs SLSs have been recently studied on the GaAs/Si material platform due to its variable strain force. Since the bending efficiency to TDs depends on the strained induced by the lattice-mismatched, the indium composition, the thickness of strained layer, and the repetition of SLSs as well as the DFLs are of the greatest interest and need to be considered when optimizing the SLS.
We have investigated the InxGa1-xAs/GaAs SLSs DFLs [32, 41]. As shown in Figure 13a, a 1 μm two-step grown GaAs were grown on n-doped Si substrate (001) with 4° offcut towards <011> by using Molecular Beam Epitaxy (MBE) system, while the Si substrate was performed at 900°C for 30 minutes to deoxidize. Then three sets of DFLs were grown, while each DFL structure was composed of five periods of InxGa1-xAs/GaAs SLSs. On the top of DFL, an optimized InAs dot-in-a-well (DWELL) structure was embedded between two 100 nm GaAs layers and 50 nm Al0.4Ga0.6As layers [42, 43]. A final 300 nm GaAs was deposited on the whole structure.
Schematic diagram of InAs/GaAs DWELL structure monolithically grown on Si substrates with different DFL structures. (a) Schematic diagram of the whole structure. (b) Schematic diagram of the InGaAs/GaAs SLSs as DFL.
PL measurement was applied through a 635-nm solid-state laser excitation at room temperature. The PL results of InAs QDs with different InxGa1-xAs/GaAs DFL parameters are summarized in Table 2 and shown in Figure 14. In view of the PL intensity and the full width at half maximum (FWHM), it can be known that sample 1 (18% In composition) exhibits a higher PL intensity than sample 2(16% In composition) and sample 3(20% In composition). The PL intensity is highly related to the crystal quality, which corresponds to the TDD. Thus, 18% In composition is proved to contribute to the best crystal quality compared with the other indium compositions. When the thickness of GaAs layer was changed, sample 4 is similar to sample 1 in view of the PL intensity, while sample 5 has a significant reduce. In addition, the FWHM of sample 5 is much wider than other 2. This phenomenon is explained through an 8 nm thin GaAs layer cannot release the strain completely so that the accumulated strain degrades the material quality [32].
Sample | InxGa1-xAs | GaAs Thickness (nm) | PL intensity (a.u) | FWHM (nm) |
---|---|---|---|---|
1 | 10 | 4 | 40.3 | |
2 | 10 | 2.6 | 39.8 | |
3 | 10 | 2.2 | 42 | |
4 | 9 | 3.9 | 40.4 | |
5 | 8 | 2 | 46.1 |
Details parameters for InxGa1-xAs/GaAs SLSs in each sample.
PL spectra of different samples at room temperature. (a) Sample 1, 2, and 3 with indium composition of 18%, 16%, 20% respectively. (b) Sample 1, 4, and 5 with GaAs spacer layer thickness of 10 nm, 9 nm and 8 nm respectively. (Reproduced from Ref. [
To further investigate the effectiveness of DFL, Cross-sectional TEM measurements were applied to examine the crystal quality and the effectiveness of DFL. The dark-field TEM image and the bright-field TEM image are shown in Figure 15. As shown in Figure 15a, high number of TDs appear at the GaAs/Si interface propagating towards the epilayers, as most of them annihilate with others in the first 200 nm. However, there are still a great number of TDs propagating towards the upper layer. After the DFL, only a few TDs puncture the DFL and keep propagating upwards, while most TDs are blocked by the DFL.
The cross-sectional TEM image for TDs around DFL structure. (a) Dark-field TEM image (b) Bright-field TEM image (Reproduced from Ref. [
In order to further investigate the DFL performance, DFL efficiency (η) is defined as the fraction of TDs it removes, which can be described as [28, 44].
Where n(experiment) denotes the number of dislocations just above the DFL, and n(predict) denotes the dislocations predicted by the equation n(x) = D0hm, where m = −0.5. The efficiencies of different types of DFL are shown in Figure 16. From the figure, it can be known that almost half of TDs propagate through the first set of DFL regardless of indium composition of InxGa1-xAs layer. However, the sample with In0.18Ga0.82As/GaAs SLSs shows a superior ability in filtering efficiency compared to others, which achieves over 80%. The demonstrated highest efficiency presents a good balance between TD generation and strain induced to annihilate TDs.
Summary of the efficiency of dislocation filter for Sample 1, 2 and 3 respectively (Reproduced from Ref. [
Apart from the InGaAs/GaAs SLSs, InAlAs/GaAs SLSs is also another great option severing as DFL [45, 46, 47]. Due to the larger shear modulus of InAlAs, it is expected that the critical misfit for generating new TDs is much larger than that of InGaAs. We compared In0.15Ga0.85As/GaAs DFL and In0.15Al0.85As/GaAs DFL by growing InAs/GaAs QD samples on Si (100) substrates [41]. The In0.15Ga0.85As/GaAs DFL composed three repeats of 5 period of 10-nm In0.15Al0.85As and 10-nm GaAs SLS separated by 400 nm GaAs spacer layer, while the In0.15Al0.85As/GaAs DFL had almost same structure except replacing the In0.15Ga0.85As to In0.15Al0.85As. EPD were counted for both samples. After three sets of SLSs, the defects density of the sample with InAlAs/GaAs DFL was around 2 × 106 cm−2, while the other one with InGaAs/GaAs DFL was round 5 × 106 cm−2 [41]. In addition, the sample with InAlAs/GaAs DFL had a higher PL peak intensity as well as thermal activation energy compared to the sample with InGaAs/GaAs [41].
Since it is the Peach-Koehler force in strained layer to bend the TDs to encourage annihilation, self-organized QDs possess an even stronger Peach-Koehler forces, which means QDs are expected to bent TDs more efficiently [48]. Meanwhile, the strain field surrounding QD is 3 dimensions which is superior than 2 dimensions in SLSs.
Several parameters need to be considered when using self-organized QDs as DFLs including QD composition, size, areal density, and the number of dots. The theoretical simulation of the effectiveness of dislocation bending is developed by J. Yang et al. [48], which assuming QD islands are coherently strained with pyramidal in shape. The energy ∆Erel releases when the MD formed to bend the TDs can be calculated through
While the dislocation self-energy ∆Edis can be described as
The bending will occur when the ∆Erel ≥ ∆Edis. Here, L is the length of the MD, Gdot (Gbuff) is the shear module of dot (buffer layer), ν is the Poisson ration,b is the Burger’s vector, beff is the project of Burger’s vector on the buffer layer, feff is the effective lattice mismatch between the QD and the underlying buffer layer, h is the height of QD, β is the angle between the Burger’s vector and the dislocation line, r denotes an outer cutoff radius of the dislocation strain field.
According to the simulations, the bending area ratio, which denotes the bending area divided by the area of QD bases, is shown in Table 3. InAs QDs are proved to be the most suitable self-organized QD serving as dislocation filters with the largest bending area and largest critical layer numbers for QD multilayers [48].
Quantum Dots | Dot Density | QD base area | Bending area ratio of a single QD | Bending area ratio of a single layer |
---|---|---|---|---|
Unit | (cm−2) | (nm2) | ||
In0.6Al0.4As | 27–56 | ∼0 | ∼0 | |
In0.5Ga0.5As | 80–132 | ∼0 | ||
InAs | 120–210 |
Bending area ratios for different QDs (Reproduced from Ref. [48]).
Considering the theory and results above, InAs QDs DFL has the highest efficiency compared with other QD DFLs for GaAs monolithically grown on Si. In order to investigate the TD behavior in QD DFL region, a buffer structure shown in Figure 17 is grown with N-type doped InAs QD dislocation filter on Si (001) substrate with 4° misorientation towards [111]. A thin (<2 μm) GaAs layer is first grown by MOVPE with free of antiphase domain. The TDD at its surface is estimated to be (2–5) × 107 cm−2. The dislocation filter consists of 10 layers of InAs QD separated by 50 nm GaAs layers. On the top of QD dislocation filter, a 800 nm GaAs is grown.
GaAs grown on Si with 10 InAs QD layer as dislocation filter. (reproduced from Ref. [
Cross-sectional TEM measurements were applied to investigate the propagation of dislocations in the QD DFLs. Images were obtained with various g, including [2,
Cross-section TEM images of dislocation propagation in the ten-layers InAs QD with various diffraction conditions: (a) g = [2,
In the past 30 years, efforts have been made to decrease the TDs induced by the lattice mismatch between GaAs and Si. Many researchers have successfully adopted DFL method to decrease the density of TD to 2 × 106 cm−2 [45, 50]. However, a 9-μm thick GaAs buffer is indispensable if no other technique applied to achieve that density. Thus, the DFL technique is much more effective in reducing TDs comparing to grow GaAs buffer, which is summarized in Table 4.
Technique | Thickness |
---|---|
Thick GaAs buffer layer | 9 μm |
InAlAs/GaAs SLSs as DFL | 2.35 μm |
InAs QD as DFL | 2.205 μm |
Summary of the requisite thickness with different methods to reduce the density of TD to 2 × 106 cm−2.
With the DFL technique, researchers make it possible to reduce the vast number of TDs to a level which is commercially viable in a thin film around 2.5 μm. This technique has promoted the implement of III-V materials directly grown on Si such as growth of III-V lasers on Si substrates [27, 50].
As germanium material has lattice parameter and thermal expansion coefficient close to those of the GaAs, a common strategy is to benefit from all the Ge heteroepitaxy on silicon developments to reduce the structural defects in the GaAs layer [31, 41, 51, 52, 53]. This way, we avoid additional threading dislocation nucleation. Currently, the TDD in a 1.5 μm thick Ge-buffer on Si(100) is in the 107 cm−2 range by using [54, 55] a thermal cycle annealing (TCA). The Figure 19a, extract from the works of Bogumilowicz et al. [56], shows the TDD evolution in function of the Ge buffer and GaAs total thickness, with a GaAs layer fixed at 270 nm thick. The GaAs layer is smooth (<1 nm RMS) and free of APBs thanks to the process described in the previous section. The TDD was estimated by using three methods: (i) from the XRD rocking curve width, the value is extracted with the Ayer’s model [57] (ii) by counting the dark spots on the cathodoluminescence (CL) image of the GaAs surface, (iii) by counting the pits on the AFM image of the GaAs surface. Whatever the method, the authors show that the TDD tends to reach a plateau at a value around 3
(a) Plot of the TDD in the GaAs overlayers as a function of the total Ge + GaAs thickness. The light gray area corresponds to the expected TDD values in Ge or GaAs single layers as a function of thickness. Estimated error bars are shown for the TDD extracted from AFM and CL. The TDD error bar for the XRD data is
Selective growth method is often used in heteroepitaxy of semiconductors where cavities are used to block geometrically the propagation of structural defects that generate at the interface of lattice mismatch semiconductors. Different techniques could be implemented such as Epitaxial Lateral Overgrowth (ELOG) and Aspect Ratio Trapping (ART). We will describe more in details the last one.
ART allows to block inside the cavities some of the threading dislocations and planar defects propagating perpendicularly to the trench direction. Still, a few structural defects propagate through the film. Figure 20a summarizes the principle of the method. In fact, the TDs propagating through the dense {111}-planes can be blocked by the geometry of the patterns. In this case the aspect ratio (height on width
(a) Principle of ART. (b) GaAs growth in V-groove shaped Si/SiO2 trenches. (c) SFs and microtwins at Si/GaAs interface. (d) STEM cross-section along the trench. The TDs are indicated by the red arrows. The Moiré fringes are formed by the interferences between the Si et GaAs crystal at the V-groove level. From [
In the example of ART from the works of Lau et al. [58], they use about 100 nm-width oxide trenches on Si(001) etched by a wet solution of KOH to form a “V-groove” (Figure 20b and c). Indeed, with this type of wet etching the {111}-Si planes are revealed at the bottom of the trenches. This approach has the advantage to free the III-V layer from the APBs which doesn’t form on Si(111) surface. The GaAs is then epitaxialy grown to obtain a nanoribbons array in the trenches. The growth process is achieved in a classical way with two steps: one low temperature nucleation (365°C) step followed by a fast growth at high temperature (570°C). The STEM images highlight some microtwins, at the Si/GaAs interface, which are trapped by the V-groove structure (Figure 20c). However, outside that thin area the GaAs layer is single-domain with a good crystalline quality. The XRD rocking curve from the (004) peak was measured in both configuration parallel and perpendicular to the line. For a 200 nm-thick GaAs the FWHM of each peaks are measured at 400 arcsec and 550 arcsec for the perpendicular and parallel configuration respectively. That difference is attributed to the defects not trapped by the trenches in the parallel direction. Some of these defects can be seen on the STEM cross-section, parallel to the trench, of Figure 20d. The Moiré fringes are formed by the interferences between the Si et GaAs crystal at the V-groove level. Besides the defects trapping by the cavity, the low defectivity is ascribed to the stress relaxation by the partial dislocations associated to the stacking faults and microtwins at the interface. This phenomenon has already been reported with the InP growth in other works [60, 61].
More recently, Kunert et al. [62] used a SAE approach to achieve some GaAs and GaSb nano-ridges (NRs) which come out from the cavities with tunable shapes and facets as function of the process conditions (Figure 21a). These type of NRs can serve as laser diodes structure as well as planar photodetectors. The nano-ridges growth is achieved in trenches where the silicon has been etched in wet solution to form a v-groove of Si-{111} planes. The defect density on the top surface of NRs was assessed in the direct space from electron channeling contrast imaging (ECCI). This latter method can be implemented more easily and with a better statistic than TEM. The graph of Figure 21b summarizes the TDD and planar defect density (PDD) in surface of the GaAs as function of the trenches width. A remarkable achievement is the low TDD which decrease below 4.5
(a) GaAs nano-ridges in SAE. (b) TDD and PDD as function of the trench-width. From [
Furthermore, Baron et al. [63] highlighted the efficiency of the ART method for the optical emission of AlAs/InGaAs/AlAs QWs. The QWs are grown on top of a 150 nm-thick GaAs buffer layer in SiO2 trenches with differents aspect ratio ranging from 0.2 to 1.3 (Figure 22a). In this work a 1.3 AR is necessary to free the GaAs buffer layer from APBs and to obtain a PL at 300 K. This way the Figure 22b shows the normalized μPL spectra for InGaAs QWs with different Indium content. The PL peak position measurement combined with the InGaAs layer thickness measurement by STEM (Figure 22c) allows for the calculation of an Indium content of 7%, 16%, 35%, 42% in the 4 samples. These values are very close to the targeted concentrations. Besides, to observe the influence of defects at the local scale, CL measurements at 15 K were performed on top of the nanoribbon arrays (Figure 22d). Since the layer is free of APBs, the dark zone, corresponding to non-luminescent areas, are attributed to the dislocations that are not trapped by the structure and propagating through the QWs.
(a) low magnification cross-sectional STEM image of a GaAs layer grown in 140 nm wide SiO2 trenches on (001)-oriented Si substrate showing a good uniformity of the selective growth. The trenches are oriented along the [
This explanation of the TDs acting as luminescence quenchers was pushed further in another work [64] combining FIB-STEM, CL and strain measurement of the III-V nanoribbons by precession electron diffraction (PED) [65, 66]. The Figure 23a. shows a STEM cross-section of the nanoribbons with their AlAs/InGaAs QWs. The structural defects crossing the QWs are labeled from d1 to d5. Prior to the STEM lamella preparation CL intensity imaging (Figure 23b) was performed at the same location of the nanoribbon (the area is located thanks to platinum marker deposited on top of the NRs array). The authors highlighted that the luminescence is not homogenous along the NRs and the dark and bright area are bounded by two TDs indexed as d3 and d4 on the image. In addition, the CL peak position of the brighter area shift of about 10 nm toward the higher wavelength (Figure 23c). Both the intensity and the peak shifting can be spatially correlated to the 0.5%
Spatial correlation between mappings: (a) cross section STEM, (b) top-view CL intensity, (c) CL peak positions, and (d) cross section ε [
The SAE approach entails a large number of variants, including epitaxial lateral overgrowth ELO [67] and confined epitaxial lateral overgrowth (CELO) [68]. These alternatives often use a “3D” confinement of defects. However, if they are in certain cases, very efficient, they generally require a complex and cost consuming patterning of the substrates. For an overview of the latter methods one can refer to the references [59, 69].
The advantages of high data rate, broad bandwidth, mature fabrication processes and low power consumption make Si photonics become a desirable approach, meeting the future demands of optical interconnections. To date, significant achievements have been made in Si photonics and most of key components have been well demonstrated, including low-loss waveguides, high-speed modulators and high-performance photodetectors [70, 71, 72, 73, 74]. However, the realization of high-performance Si-based on-chip light sources still remains challenging for the full integration of optoelectronics integrated circuits [75]. Among various of approaches, monolithically integrating high-performance III-V QD lasers on Si substrate has been considered as a promising method to develop an on-chip optical source for Si photonics [76, 77, 78]. The advanced properties of low threshold, high defects tolerance and high temperature stability contribute largely to the development of QD lasers [27, 79, 80, 81].
Before illustrating the recent progress of QD lasers grown on Si (001) substrates, it is worth to discuss briefly about some key milestones in the development of monolithic integration of III-V lasers on Si. Although some optimized heteroepitaxy techniques have reduced the TDD of III-V on Si from originally ∼109 cm−2 to ∼106 cm−2, QW lasers directly grown on Si still suffered on their high threshold and limited lifetime due to the enhanced TD generation [82, 83, 84, 85]. An early result presented a QW laser with InP buffer as thick as 15 μm with decent performance and lifetime [86]. However, due to the difference of thermal expansion coefficient between III-V epi-layer and Si substrate, the thick buffer is also vulnerable to the formation of micro-cracks, which destroys the yield of Si-based devices [87]. The research of III-V QD lasers on Si (001) comes out since early 2000s. After the early attempt by using droplet epitaxy to grow QD lasers, the successful address of Stranski-Krastanov growth mode on the growth of QDs presents significant advantages on emitting light with the presence of high TDD caused by mismatch in lattice constants and thermal expansion coefficients [88, 89]. By taking the benefits of ultra-high vacuum and precise control, MBE system has been widely considered as a suitable technique for the growth of high-performance QDs.
Recently, numerous achievements that pursuing high performance III-V QD lasers on Si have been demonstrated. The offcut Si substrate was addressed initially to prevent the formation of APB. In 2001, the first QD laser on Si emitting at 855 nm at room temperature under continuous-wave operation was presented by growing InGaAs QDs on Si substrate with MOCVD [90]. More importantly, the aging test illustrated the advantage of reliability for QD lasers on Si compared with QW counterparts. By further optimizing the active region and III-V buffer, such as utilizing DFLs and P-type modulation doped QD region, the performance of QD lasers on Si was highly improved, realizing a characteristic temperature (T0) of 244 K between operation temperature of 25–95°C and a reduced threshold current density of 900A/cm2 at that time [48, 91]. These results suggest the possibility of QD lasers directly grown on Si substrate as an efficient and reliable light source for Si photonics.
The aforementioned works of QD lasers were all operated under emission of 1.1 μm. However, the recent ever-growing demands on telecommunication and data-communication system, led to significant achievements on 1.3 μm InAs/GaAs QD lasers on Si substrate. The first room temperature 1.3 μm emission of QDs on Si grown by MOCVD was achieved by Li et al. at 2008, with the help of Sb [92]. However, due to the high TDD in the GaAs buffer, its PL intensity was eight times weaker than QDs grown on the native GaAs substrate, even with a high QD density obtained of 7 × 1010 cm−2. This also suggested the importance of developing improved GaAs buffer on Si substrate associated with well-performed DFLs. The first electrically pumped 1.3 μm InAs/GaAs QD laser directly grown on Si substrate by MBE was successfully demonstrated by Wang et al. in 2011 [93]. The laser structure was grown on an offcut Si substrate with 4° miscut angle to [110] orientation. An improvement initialized from the growth of AlAs nucleation layer instead of GaAs nucleation layer, realizing a reduction of defects observed at the interface of AlAs/Si [94]. The threshold current density was reduced to 725A/cm2 at room temperature under pulsed operation, with a single facet output power of ∼26 mW achieved at room temperature. The highest operation temperature was 42°C with a T0 of 44 K.
Extensive studies were devoted following the first demonstration of electrically pumped 1.3 μm QD laser on Si. In 2012, by utilizing Ge-on-Si virtual substrate, the first room-temperature continuous-wave electrically pumped InAs/GaAs QD laser monolithically grown on Si substrate with a Ge buffer layer was demonstrated by MBE [95]. A low threshold current density of 162 A/cm2 was achieved at continuous-wave mode with a room temperature lasing emission of 1.28 μm. The operation temperature was as high as 84°C under pulsed mode. Although these results were outstanding, a 1.3 μm InAs/GaAs QD laser directly grown on Si substrate was still far from practice, until the successful demonstration by us in 2016. By applying unique epitaxial method and improved fabrication process, the first high-performance and long-lifetime 1.3 μm QD laser directly grown on Si was achieved [29]. As shown in Figure 24a,1 μm GaAs buffer was grown by three steps on a deoxidized Si substrate to improve the material quality, followed by four sets of DFLs consisted of five sets of InGaAs/GaAs SLSs and high temperature annealed 300 nm GaAs spacer layer. The TDD after DFLs was successfully reduced to the level of 105 cm−2. High-performance laser structure with five stacks of InAs/GaAs DWELL active region was developed upon this platform. A TEM image of active region was shown in Figure 24b where QDs were coherently grown, without any visible defects. The two inset images presented a 1 × 1 μm2 AFM image which show a good uniformity with 3 × 1010 cm−2 dot density and the typical shape of a single QD. Broad-area lasers were fabricated as shown schematically by a scanning electron microscope (SEM) image in Figure 24c. The light-current–voltage curve of the device was shown in Figure 24d. An ultra-low threshold current density of 62.5 A/cm2 under continuous wave at room temperature was obtained, which was the lowest threshold current density value achieved for any kind of lasers on Si substrate at that time. The single facet output power measured under injection current density of 650 A/cm2 was exceeded 105 mW. The highest operation can be achieved up to 75°C under continuous-wave mode and 120°C under pulsed mode. Moreover, negligible degradation was observed after 3100 h aging test, realizing an extraordinaire mean time to failure lifetime more than 100,158 h. After that, Si-based monolithically integrated narrow-ridge Fabry-Perot and distributed feedback QDs laser are fabricated based on these outstanding outcome [96, 97].
(a) TEM image of GaAs buffer on Si including dislocation filter layers. (b) TEM image of active region, upper inset: 1 × 1 μm2 AFM image of uncapped QDs, and bottom inset: TEM image of a single QD. (c) SEM image of fabricated broad-area laser. (d) Light-current–voltage curve of lasing characteristics under continuous-wave condition at room temperature. Reproduce from [
These previous discussions on QD lasers were all fabricated on offcut Si substrate, which are not fully compatible to the CMOS technique. The commercialized on-axis Si (001) platform demands an miscut angle less than 0.5°. As discussed in the first section of this chapter, the heteroepitaxy technique on on-axis Si (001) was satisfied by forming APB-free GaAs buffer. Beyond the successful demonstration of QD lasers on offcut Si platform, QD lasers grown on CMOS-compatible Si (001) substrate were successfully developed in recent years [98, 99, 100, 101, 102, 103, 104, 105], owing to the demonstration of the APB-free GaAs and GaP templates on Si.
The first electrically pumped continuous-wave InAs/GaAs QD laser monolithically grown on-axis GaAs/Si (001) substrate was demonstrated in 2017 [98]. Following by a 400 nm APB-free on-axis GaAs/Si (001) platform grown by MOCVD, MBE system was employed to grow QD laser structure with four repeats of DFLs, which consist of five sets of InGaAs/GaAs SLSs. The five stacks of InAs/GaAs QD layers sandwiched by AlGaAs cladding layers were grown subsequently. A 1 × 1 μm2 AFM image of uncapped InAs QD on Si (001) substrate was shown in Figure 25a, realizing a good uniformity and a dot density of ∼3.5 × 1010 cm−2. The sample was fabricated to broad-area laser devices with as-cleaved facets for laser characteristic measurements. A comparison of room-temperature continuous-wave light-current–voltage characteristics between QD laser on on-axis GaAs/Si (001) platform and native GaAs substrate was shown in Figure 25b. The GaAs-based QD laser presented a threshold current density of 210 A/cm2, while that of on-axis Si-based QD laser was 425 A/cm2. The calculated slope-efficiency and differential quantum efficiency of GaAs-based QD laser were ∼ 0.12 W/A and 12.7%, respectively. The QD laser on on-axis Si (001) also show decent results on corresponding characteristics, which the calculated slope-efficiency was 0.068 W/A and differential quantum efficiency was 7.2%. Figure 25c presents a temperature dependent light-current curve of Si-based QD laser operated under continuous-wave mode. The maximum operating temperature achieved was 36°C. As shown in Figure 25d, the pulsed results of light-current characteristic at various heatsink temperature presented a highest operation temperature of 102°C, which was the first demonstration of QD laser directly grown on on-axis Si (001) substrate that observed lasing over 100°C. The inset image of Figure 25d shows the characteristic temperature T0 of 32 K between 16–102°C. This result is further improved by K. Li et al. with an optimized DFLs and QDs [99].
(a) 1 × 1 μm2 AFM image of uncapped InAs QDs grown on on-axis Si (001) substrate. (b) Light-current–voltage characteristic comparison of an InAs/GaAs QD laser grown on on-axis Si (001) and native GaAs substrate at room temperature under continuous-wave operation. (c) Single facet light-current curve for InAs/GaAs QD laser on on-axis Si (001) as a function of temperature under continuous-wave operation, inset: light-current curve at a heat sink temperature of 36°C. (d) Single facet light-current curve for InAs/GaAs QD laser grown on on-axis Si (001) substrate at different heat sink temperatures under pulsed condition, inset: natural logarithm of threshold current density against temperature in the ranges of 16–102°C. Reproduce from [
As shown in Figure 26a, four repeats of In0.18Ga0.82As/GaAs SLSs DFLs were well performed to annihilate TDs with total buffer thickness of ∼2 μm. The active region of laser was consisted of five repeats of InAs/GaAs DWELL structure, realizing a room temperature peak PL emission of ∼1308 nm with a linewidth of ∼32 meV. A comparison of room temperature PL results of InAs/GaAs QD on on-axis Si (001) and native GaAs substrates was shown in Figure 26b, the inset image shows an AFM image of uncapped InAs/GaAs QD layer with about ∼4 × 1010 cm−2 dot density. The laser samples were fabricated into 50 μm × 3 mm broad-area laser devices. The characterization of laser devices was all measured under continuous wave. As shown in the inset image of Figure 26c, the threshold current density as low as ∼160 A/cm2 has been achieved at room temperature, which was improved compare to previous result. A single facet output power of 48 mW was obtained at an injection current density of 500 A/cm2 without any thermal rollover. The threshold current density increased with the rising of operation temperature and laser operation was observed up to 52°C. The T0 obtained was ∼60.8 K between 16–36°C.
(a) Cross-sectional TEM image for whole buffer; (b) A comparison of room temperature PL results, inset: an AFM image of uncapped InAs/GaAs QD layer; (c) Light-current characteristics of InAs/GaAs QD laser grown on Si exact (001) at various operation temperature, inset: light-current–voltage characteristic at room temperature. Reproduce from [
In order to investigate the defect tolerance of QD and QW structure, an InAs/GaAs QD laser directly grown on on-axis GaAs/Si (001) platform and an InGaAs QW laser in the same structure except active region were grown for comparison [100]. By further analyzing the performance of QD and QW laser and their thermal activation energy (Ea), the great characteristics of QD laser on dislocation tolerance and thermal reliability have been proved.
Temperature dependent PL measurements were performed for both QD and QW samples. As shown in Figure 27a, PL intensity of the QD sample at room-temperature was about six times lower than the PL intensity at 20 K. In contrast, the difference for the QW sample shown in Figure 27b was ∼1000 times between 20 K and room temperature. Moreover, the integrated PL intensity for both samples was measured in order to estimate their Ea. The results were shown in Figure 27c, which were 240 meV and 35 meV for QD and QW lasers, respectively. The significantly higher Ea observed for the QD could contribute to its higher optical intensity at high temperatures. As shown in Figure 28a,25 μm × 3 mm broad-area lasers were fabricated for both QD and QW samples. The room-temperature characteristics of them under continuous-wave mode were illustrated in Figure 28b. The threshold current density of ∼173 A/cm2 for QD laser was achieved. In addition, over 100 mW single-facet output power was obtained under injection current density of 670 A/cm2. In contrast, there was no lasing observed for the QW device at room-temperature even at higher injection levels. After comparing with modelling results, this study indicated that QW laser cannot work properly above 107 cm−2 of TDD [100, 101]. Figure 28c presented a temperature dependent light-current curve of QD laser on Si (001). The highest continuous-wave operation was observed over 65°C. These results quantitively suggested that QD laser had its natural advantages on defect tolerance and temperature insensitivity. It also demonstrated that QD laser monolithically integrated on on-axis Si (001) substrate can be a promising on-chip optical source for Si photonics.
Comparison of PL spectra at room-temperature (300 K) and 20 K for (a) the QD laser, and (b) the QW laser. (c) Temperature-dependent integrated PL intensities of the InAs QD and InGaAs QW lasers from the temperature region of 20 K to 300 K, showing Ea of both samples. Reproduce from [
(a) SEM image of an example of broad area laser fabricated by QD and QW samples with 25 μm ridge width and 3 mm cavity length. (b) Comparison of room-temperature light-current–voltage characteristics for QD and QW lasers directly grown on on-axis Si (001) substrate. (c) Temperature-dependent light-current measurement of the QD laser under continuous-wave mode. Reproduce from [
Despite the outstanding progress has been made on edge-emitting QD lasers on on-axis GaAs/Si (001) substrate. For the dense integration with light source on Si that compatible to CMOS technique, microdisk lasers with small footprint has been considered as a promising approach for realizing nanophotonic integrated circuits. Additionally, compared with Fabry-Perot laser cavity, microdisk lasers also benefit from their advantages on low threshold and high quality factor which could bring less optical loss [106]. Recently, by applying the well-performed on-axis GaAs/Si (001) platform and optimized DFLs, a monolithically grown InAs/GaAs QD microdisk laser on on-axis Si (001) substrate with ultra-low threshold at room temperature was successfully demonstrated [107]. The device was optically pumped under continuous-wave mode. Figure 29a presented a schematic structure of this fabricated microdisk laser where the top of disk was the active region that consisted of three stacks of InAs/GaAs DWELL layers separated by 50 nm of GaAs space layer and 69 nm of AlGaAs cladding layer. A typical fabricated microdisk laser with disk diameter of 1.9 μm was shown in the SEM image of Figure 29b, which indicated a smooth etched surface with 73.5° sidewall tilt. The cross-sectional TEM image in Figure 29c shows the whole epilayer structure on on-axis GaAs/Si (001) substrate.
(a) Schematic diagram of a QD microdisk laser fabricated on on-axis Si (001) substrate. (b) SEM image of a QD microdisk laser with 1.9 μm diameter. (c) Cross section TEM image of the epitaxial structure of QD microdisk laser on on-axis Si (001) substrate. Reproduce from [
The collected lasing spectra for the microdisk laser with 1.9 μm diameter was illustrated in Figure 30a. The results presented a free spectral range of 76 nm – 89 nm between adjacent whispering gallery modes. Both ground state and excited state emission were observed. A main peak wavelength of 1263 nm was located at the first excited state. Figure 30b shows the collected intensity and linewidth as a function of input optical power for the corresponding peak emission at 1263 nm. An ultra-low threshold of 2.6 ± 0.4 μW and a clear narrowing trend of FWHM was obtained. The threshold of this result was even lower than the InAs QD microdisk lasers on native GaAs and InP substrates [109, 110, 111]. Additionally, the sample was fabricated into microdisk lasers with variable diameter from 1 μm to 2 μm. The corresponding threshold of main peak of microdisk lasers were presented as a function of diameter in Figure 30c. All the results of threshold were below 3.5 μW. The fluctuation of threshold versus the diameter of microdisk may result from the slight factor difference in fabrication process.
(a) Collected intensity as a function of wavelength with different pumped power below and above the threshold of QD microdisk laser on on-axis Si (001). (b) The corresponding collected intensity and linewidth versus pumped power for the first excited state emission at 1263 nm. (c) Threshold of main lasing peak of QD microdisk laser as a function of various diameter. Reproduce from
As a promising ultra-compact on-chip light source, III-V photonic crystal lasers on Si benefits on their ultralow power consumption and small footprint. Most recently, Zhou et al. demonstrated an optically pumped InAs QD photonic crystal laser on on-axis GaAs/Si (001) substrate, which was the first monolithic integration of photonic crystal laser emitting at 1.3 μm on CMOS-compatible Si (001) substrate [108]. A single mode operation with ultra-low threshold down to ∼0.6 μm and a large coupling efficiency for room temperature spontaneous emission under continuous-wave condition were achieved. 3D finite-difference time- domain (FDTD) simulation method was applied in order to obtain a high-quality factor for the resonance among QDs emission spectrum. Figure 31a shows a schematic structure of fabricated photonic crystal laser with 1 μm thickness of air slab underneath the cavity to enhance the vertical light confinement. The structure of active region that consists of four repeats of InAs/InGaAs/GaAs DWELL layers sandwiched by 50 nm GaAs space layers and 40 nm AlGaAs cladding layers was shown in Figure 31b. The collected intensity and linewidth of photonic crystal laser as a function of input power were shown in Figure 31c. The optically pumped QD photonic crystal lasers exhibited single-mode operation with an ultra-low threshold of ∼0.6 μW. The inset image shows a peak wavelength at ∼1306 nm with different pumped power. The Lorentzian fitting curve indicated a linewidth of ∼0.68 nm and a calculated cavity quality factor of 2177. The soft turn on process shown in Figure 31c also presented a typical behavior of laser with high spontaneous emission coupling efficiency (β). The logarithmic plot of light–light curve with fitting results of this QD photonic crystal laser were shown in Figure 31d. It indicated the best fitting data obtained at β = 0.18, realizing a large spontaneous emission coupling efficiency under continuous-wave condition at room temperature.
(a) Schematic structure of QD photonic crystal laser on on-axis Si (001). (b) A diagram of active region in our photonic crystal laser. (c) Collected light–light curve and linewidth of the lasing peak at 1306 nm, inset: Lorentzian fitting of data below the threshold. (d) Logarithmic light–light plot of fitted and collected data. Reproduce from Ref. [
QD laser on Si has attracted great research interests in recent years, which brings new approach for achieving efficient light source of Si-based photonics integration. These works discussed in this section with established epitaxy technique of APB-free on-axis GaAs/Si (001) platform, effective DFLs and optimized QD layers demonstrate that high-performance QD laser monolithically integrated on on-axis Si (001) substrate can be a promising on-chip optical source for Si photonics. Different approaches also provide new routes to form the basis of future monolithic light sources for the application of optical interconnects in large-scale silicon optoelectronics integrated circuits.
Heterogeneous integration of III–V compound semiconductors is promising to realize functionalities such as laser sources and photodetectors, and silicon based waveguides on Si platform. The direct heteroepitaxy of GaAs on nominal Si(100) wafers used by the microelectronics industry faces several issues to produce high quality material. In this chapter, we discussed the recent advances to tackle the formation of antiphase domains and to reduce the threading dislocation density. Currently, APB is no more an issue, as solutions have been proposed to obtain thin \t(<400 nm) GaAs film without APB, solutions based on dedicated cleaning and annealing processes of Si substrate before the GaAs epitaxy. The threading dislocations have hindered the development of GaAs devices on a Si CMOS platform and many solutions have been studied in th epast. We have reviewed the most efficient methods that used interchangeably the insertion of a Ge buffer between silicon and GaAs, the insertion of dislocation filter layers in the GaAs, or selective epitaxy in a cavity with a proper aspect ratio. All these progresses allowed reaching the range of 106–105 cm−2 TDD required to elaborate performant optoelectronics devices. Next we developed the fabrication of InAs QDs/GaAs laser emitters in the infrared region integrating GaAs buffer without APB grown on nominal Si(100) wafers and DFL to reduce the TDD. Different type of devices were fabricated such as broad area laser electrically pumped and operating at room temperature and up to 65°C, microdisk QDs lasers and continuous-wave QD photonic crystal lasers.
This paves the way towards the monolithic integration of optoelectronics and microelectronics functionalities on the same silicon CMOS platform, promising tremendous evolution in the data treatment and computing fields.
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