[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657667-105":59,"doc-detail-657667-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","slopetemperature-faceting-diagram-for-macrosteps-at-equilibrium","Slope–temperature faceting diagram for macrosteps at equilibrium","","Slope–temperature faceting diagrams for macrosteps at equilibrium are computed numerically using statistical mechanics for inclined surfaces between (001) and (111). A lattice model incorporates point-contact-type step–step attractions derived from quantum-mechanical couplings of neighboring steps. Effective step–step attraction for Si(113) is estimated by comparison with an existing phase diagram for step bunching. Monte Carlo calculations provide slope-dependent mean heights for macrosteps with (111) and (001) side surfaces. The resulting diagrams guide controlling assembly and disassembly for designing new surface arrangements.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/slopetemperature-faceting-diagram-for-macrosteps-at-equilibrium/657667/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/slopetemperature-faceting-diagram-for-macrosteps-at-equilibrium/657667.png","ImageObject",300,407,{"name":92,"@type":93},"Helloiii","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What method is used to calculate the slope–temperature faceting diagrams for macrosteps at equilibrium?","Question",{"text":112,"@type":113},"A numerical approach based on statistical mechanics is used, employing a lattice model and Monte Carlo calculations for slope-dependent properties.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the effective step–step attraction energy for Si(113) determined?",{"text":117,"@type":113},"It is estimated by comparing the obtained faceting diagrams with a phase diagram for step bunching proposed for Si(113).",{"name":119,"@type":110,"acceptedAnswer":120},"What practical use do the faceting diagrams provide?",{"text":121,"@type":113},"They serve as a guide for controlling the assembling and disassembling of faceted macrosteps, supporting the design of new surface arrangements.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657667,1792986042,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},5909897196768,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","[www. nature.com/scientificreports](www. nature.com/scientificreports)  \nOPEN  \nSlope–temperature faceting diagram for macrosteps at equilibrium  \nNoriko Akutsu1* & Yasuhiro Akutsu2  \nFaceting diagrams between surface slope and temperature are calculated numerically based on statistical mechanics for inclined surfaces between (001) and (111) surfaces at equilibrium. A lattice model is employed that includes point-contact-type step–step attractions from the quantum mechanical couplings between neighbouring steps. Comparing the obtained faceting diagrams with the phase diagram for step bunching proposed by Song and Mochrie for Si(113), the effective step– step attraction energy for Si(113) is approximately estimated to be 123 meV. The slope dependencesof the mean height of the faceted macrosteps with a (111) side surface and that with a (001) side surface are calculated using the Monte Carlo method. The faceting diagrams can be used as a guide for controlling the assembling/disassembling of faceted macrosteps for designing new surface arrangements.  \nTo meet the urgent need for energy efficiency to address global warming, it has become important to develop methods to reliably produce semiconductor materials with low energy consumption. In particular, III–V and II–VI compound semiconductors such as SiC and GaN are expected to be appropriate materials to meet this purpose1,2. However, macrostep formation or step bunching on crystal surfaces degrades the quality of crystals of these materials in the melt or during solution growth 1. Extensive experimental studies have investigated methods to prevent macrostep formation, but achieving macrostep-free crystal growth is still difficult. Therefore, fundamental theoretical studies are required to control step assembling/disassembling on inclined surfaces.  \nExtensive studies have been made on macrostep instabilities for vapour growth or for molecular beam epitaxy (MBE)3–5. However, there have been few theoretical studies on macrostep instabilities at equilibrium. Cabrera and Coleman6 and Cabrera7 studied the relationship between the anisotropy of the surface free-energy density (surface tension) and the morphology of an inclined surface. They showed that the “type II” anisotropic shape of surface tension causes a macrostep on an inclined surface. However, they did not develop a microscopic model for macrostep instabilities.  \nRottman and Wortis8 studied faceting transitions of the equilibrium crystal shape (ECS), i.e. the crystal droplet shape with the lowest total surface free energy8–12. The faceting transition is a phenomenon where a shrinking facet vanishes at a certain temperature on the ECS as the temperature increases. They adopted a threedimensional (3D) Ising model with nearest neighbour (nn) and next nearest neighbour (nnn) couplings with anti-boundary conditions to form a 2D interface. They established that the faceting transition temperature is the same as the roughening transition temperature for the facet surface8, 13, 14. They also studied the case where the nnn coupling constant is anti-ferromagnetic, and showed that the ECS has a first-order shape transition ata facet edge (sharp facet edge) at low temperature (Fig. 1a,b,e). That is, the Wulff figure, the polar graph of the surface tension (surface free energy per normal area), becomes discontinuous at low temperature. As illustrated in Fig. 1e, the slope p of the tangential surface on the ECS is zero for the (001) surface, and the slope then increases continuously to as the surface point moves to the right. As this point moves further to the right, the slope of the surface jumps from to that for a (111) surface. Though they considered the shape transition, they did not provide details on the morphology of the inclined surface (Fig. 1c,d) .  \nWilliams and Bartelt15 observed a faceted macrostep on a Si(111) vicinal surface tilted towards [11-2] . The (111) terrace has a ( × ) structure, and the side surface of the macrost","cbCaisR0SuZA2bJj","https://ap.wps.com/l/cbCaisR0SuZA2bJj","pdf",1791651,11,"English","# Introduction\n## Energy efficiency and need for reliable semiconductor crystal growth\n## Background: macrostep instabilities at equilibrium\n## Related models and prior observations\n# Methods and results\n## Numerical faceting diagrams using a lattice model\n## Comparison for Si(113) and estimated attraction energy\n## Monte Carlo slope dependences of macrostep heights\n# Applications","[{\"question\":\"What method is used to calculate the slope–temperature faceting diagrams for macrosteps at equilibrium?\",\"answer\":\"A numerical approach based on statistical mechanics is used, employing a lattice model and Monte Carlo calculations for slope-dependent properties.\"},{\"question\":\"How is the effective step–step attraction energy for Si(113) determined?\",\"answer\":\"It is estimated by comparing the obtained faceting diagrams with a phase diagram for step bunching proposed for Si(113).\"},{\"question\":\"What practical use do the faceting diagrams provide?\",\"answer\":\"They serve as a guide for controlling the assembling and disassembling of faceted macrosteps, supporting the design of new surface arrangements.\"}]","Slope–temperature faceting diagram for macrosteps at equilibrium | PDF",28]