{"id":26043,"date":"2018-10-12T14:28:42","date_gmt":"2018-10-12T12:28:42","guid":{"rendered":"https:\/\/www.iemn.fr\/?page_id=26043"},"modified":"2019-02-11T17:40:29","modified_gmt":"2019-02-11T15:40:29","slug":"monte-carlo-simulation","status":"publish","type":"page","link":"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/monte-carlo-simulation","title":{"rendered":"Monte Carlo simulation of 2D materials for electronic and spintronic applications"},"content":{"rendered":"<div id='layer_slider_1'  class='avia-layerslider main_color avia-shadow  avia-builder-el-0  el_before_av_submenu  avia-builder-el-first  container_wrap sidebar_right'  style='height: 261px;'  ><div id=\"layerslider_45_lmsfv5m1amf6\" data-ls-slug=\"homepageslider\" class=\"ls-wp-container fitvidsignore ls-selectable\" style=\"width:1140px;height:260px;margin:0 auto;margin-bottom: 0px;\"><div class=\"ls-slide\" data-ls=\"bgposition:50% 50%;duration:6000;transition2d:5;\"><img loading=\"lazy\" decoding=\"async\" width=\"2600\" height=\"270\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1.jpg\" class=\"ls-bg\" alt=\"\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1.jpg 2600w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1-300x31.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1-768x80.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1-1030x107.jpg 1030w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1-1500x156.jpg 1500w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde-1-705x73.jpg 705w\" sizes=\"auto, (max-width: 2600px) 100vw, 2600px\" \/><ls-layer style=\"font-size:14px;text-align:left;font-style:normal;text-decoration:none;text-transform:none;font-weight:700;letter-spacing:0px;background-position:0% 0%;background-repeat:no-repeat;mix-blend-mode:normal;top:231px;left:0px;height:30px;width:360px;line-height:32px;color:#ffffff;border-radius:6px 6px 6px 6px;padding-left:50px;background-color:rgba(0, 0, 0, 0.57);\" class=\"ls-l ls-ib-icon ls-text-layer\" data-ls=\"minfontsize:0;minmobilefontsize:0;\"><i class=\"fa fa-user-circle\" style=\"color:#f2f2f2;margin-right:0.8em;font-size:1em;transform:translateY( -0.125em );\"><\/i>GROUPE DE RECHERCHE : SILPHYDE<\/ls-layer><\/div><div class=\"ls-slide\" data-ls=\"bgposition:50% 50%;duration:6000;transition2d:5;\"><img loading=\"lazy\" decoding=\"async\" width=\"2600\" height=\"270\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1.jpg\" class=\"ls-bg\" alt=\"\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1.jpg 2600w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1-300x31.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1-768x80.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1-1030x107.jpg 1030w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1-1500x156.jpg 1500w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde1-705x73.jpg 705w\" sizes=\"auto, (max-width: 2600px) 100vw, 2600px\" \/><ls-layer style=\"font-size:14px;text-align:left;font-style:normal;text-decoration:none;text-transform:none;font-weight:700;letter-spacing:0px;background-position:0% 0%;background-repeat:no-repeat;mix-blend-mode:normal;top:231px;left:0px;height:30px;width:360px;line-height:32px;color:#ffffff;border-radius:6px 6px 6px 6px;padding-left:50px;background-color:rgba(0, 0, 0, 0.57);\" class=\"ls-l ls-ib-icon ls-text-layer\" data-ls=\"minfontsize:0;minmobilefontsize:0;\"><i class=\"fa fa-user-circle\" style=\"color:#f2f2f2;margin-right:0.8em;font-size:1em;transform:translateY( -0.125em );\"><\/i>GROUPE DE RECHERCHE : SILPHYDE<\/ls-layer><\/div><div class=\"ls-slide\" data-ls=\"bgposition:50% 50%;duration:6000;transition2d:5;\"><img loading=\"lazy\" decoding=\"async\" width=\"2600\" height=\"270\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2.jpg\" class=\"ls-bg\" alt=\"\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2.jpg 2600w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2-300x31.jpg 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2-768x80.jpg 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2-1030x107.jpg 1030w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2-1500x156.jpg 1500w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/sliders_groupe_silphyde2-705x73.jpg 705w\" sizes=\"auto, (max-width: 2600px) 100vw, 2600px\" \/><ls-layer style=\"font-size:14px;text-align:left;font-style:normal;text-decoration:none;text-transform:none;font-weight:700;letter-spacing:0px;background-position:0% 0%;background-repeat:no-repeat;mix-blend-mode:normal;top:231px;left:0px;height:30px;width:360px;line-height:32px;color:#ffffff;border-radius:6px 6px 6px 6px;padding-left:50px;background-color:rgba(0, 0, 0, 0.57);\" class=\"ls-l ls-ib-icon ls-text-layer\" data-ls=\"minfontsize:0;minmobilefontsize:0;\"><i class=\"fa fa-user-circle\" style=\"color:#f2f2f2;margin-right:0.8em;font-size:1em;transform:translateY( -0.125em );\"><\/i>GROUPE DE RECHERCHE : SILPHYDE<\/ls-layer><\/div><\/div><\/div>\n<div id='sub_menu1'  class='av-submenu-container av-jrqfadqy-807d5a51dd3616f0d00a06e9b2d077f0 footer_color  avia-builder-el-1  el_after_av_layerslider  el_before_av_heading  submenu-not-first container_wrap sidebar_right' style='z-index:301' ><div class='container av-menu-mobile-disabled av-submenu-pos-left'><ul id='av-custom-submenu-1' class='av-subnav-menu' role='menu'>\n<li class='menu-item av-av_submenu_item-8cfdaa9ad07fd6a0ccb509a50dffc6f6 menu-item-top-level menu-item-top-level-1' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/?page_id=25957'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Introduction<\/span><\/a><\/li>\n<li class='menu-item av-av_submenu_item-b4f170efd399a2be0e3448b0ed0e8486 menu-item-top-level menu-item-top-level-2' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/members'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Members<\/span><\/a><\/li>\n<li class='menu-item av-av_submenu_item-8e1a366b5289a4655e340360bb600c95 menu-item-top-level menu-item-top-level-3' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Research<\/span><\/a><\/li>\n<li class='menu-item av-kbk05k-5c5944fac313107f26dddee0ba9e2d5b menu-item-top-level menu-item-top-level-4' role='menuitem'><a href='https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes'  ><span class='avia-bullet'><\/span><span class='avia-menu-text'>Other groups<\/span><\/a><\/li>\n<\/ul><\/div><\/div><div id='after_submenu_1'  class='main_color av_default_container_wrap container_wrap sidebar_right'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-small alpha units'><div class='post-entry post-entry-type-page post-entry-26043'><div class='entry-content-wrapper clearfix'>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-js0hmnag-89046582c7788b1fc19dfe7ebf6e37ef\">\n#top .av-special-heading.av-js0hmnag-89046582c7788b1fc19dfe7ebf6e37ef{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-js0hmnag-89046582c7788b1fc19dfe7ebf6e37ef .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-js0hmnag-89046582c7788b1fc19dfe7ebf6e37ef .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-js0hmnag-89046582c7788b1fc19dfe7ebf6e37ef av-special-heading-h3  avia-builder-el-2  el_after_av_submenu  el_before_av_hr  avia-builder-el-first'><h3 class='av-special-heading-tag'  itemprop=\"headline\"  >SILPHYDE Group : Monte Carlo simulation of 2D materials for electronic and spintronic applications<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-js0hqeqy-d1ac741a88b365449792cab93465469d\">\n#top .hr.av-js0hqeqy-d1ac741a88b365449792cab93465469d{\nmargin-top:10px;\nmargin-bottom:10px;\n}\n.hr.av-js0hqeqy-d1ac741a88b365449792cab93465469d .hr-inner{\nwidth:100%;\n}\n<\/style>\n<div  class='hr av-js0hqeqy-d1ac741a88b365449792cab93465469d hr-custom  avia-builder-el-3  el_after_av_heading  el_before_av_textblock  hr-left hr-icon-no'><span class='hr-inner inner-border-av-border-thin'><span class=\"hr-inner-style\"><\/span><\/span><\/div>\n<section  class='av_textblock_section av-jn5zrw93-1bf84c42f0caae6860addbc44a7d097d'   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>In collaboration with our colleagues from Warsaw University of Technology, we have started an operation aimed at developing Monte Carlo simulation codes for systems based on 2D materials. These materials, whose prototypical example is graphene, exhibit many extraordinary properties which can find applications in many fields, including electronics and spintronics and the emerging field of \u2018valleytronics\u2019.<\/p>\n<p>The first step was to build models of electron transport in 2D materials, in particular graphene and silicene (its silicon counterpart), which are both gapless with linear dispersion near the K points minima. Piecewise analytic approximations of high energy dispersion relation, have been used, in order to make easier future implementation in device simulator. Velocity field characteristics, mobility and diffusion coefficients in the materials have been calculated. Special attention has been paid to the case of high carrier density, often overlooked in the literature, and special techniques have been developed to account for Pauli exclusion and Coulomb scattering.<\/p>\n<p>In view of spintronics applications, a Monte Carlo model has been developed which describes both electron transport and spin dynamics. The originality is that Pauli principle is treated in a special way to account for both random (scattering induced) and coherent spin evolution, enabling to consider high carrier densities. Our results are consistent with experimental findings and support the idea that spin polarization may be conserved for a long time (several ns), in graphene, which is attractive for spintronic applications.<\/p>\n<p>In spintronics, the spin of electrons is used to carry information. In systems such as graphene and \u2018graphene-like\u2019 2D materials, band structure presents two valleys, not equivalent but energetically degenerate, at points K and K\u2019. The valley index bears some similarity with the spin and this additional degree of freedom can also be used to carry information. This is the realm of an emerging discipline called valleytronics. In the next years, we plan to investigate \u2018valley properties\u2019 of graphene and other 2D materials.<\/p>\n<h4 style=\"text-align: center;\">Velocity-field characteristics in silicene<\/h4>\n<div id=\"attachment_26047\" style=\"width: 809px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde13_velocity.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26047\" class=\"wp-image-26047\" title=\"Velocity-field characteristics in silicene, calculated by Monte Carlo simulations for several temperatures. ( Analytical approximations of band structure and scattering rates have been used ). The Electron sheet density is equal to 1\u00d71012 cm-2. The impact of electron density on electron transport is two-fold : (i) Some regions of reciprocal space are significantly populated. Since Pauli exclusion principle forbids double occupation of states, it may strongly affect electron distribution function. (ii) Direct Coulomb scattering between electrons. To illustrate the influence of these phenomena, three cases are compared: (i) neglecting the effect of electron density, i.e. without two body coulomb scattering, without Pauli rejection. (ii) Pauli principle is accounted for but not two body coulomb scattering, (iii) full account of electron population, with Pauli and Coulomb scattering. P. Borowik, J.-L. Thobel, L. Adamowicz, Semicond. Sci. Technol. 31 115004 (2016) doi:10.1088\/0268-1242\/31\/11\/115004\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde13_velocity.png\" alt=\"Velocity-field characteristics in silicene, calculated by Monte Carlo simulations for several temperatures. ( Analytical approximations of band structure and scattering rates have been used ). The Electron sheet density is equal to 1\u00d71012 cm-2. The impact of electron density on electron transport is two-fold : (i) Some regions of reciprocal space are significantly populated. Since Pauli exclusion principle forbids double occupation of states, it may strongly affect electron distribution function. (ii) Direct Coulomb scattering between electrons. To illustrate the influence of these phenomena, three cases are compared: (i) neglecting the effect of electron density, i.e. without two body coulomb scattering, without Pauli rejection. (ii) Pauli principle is accounted for but not two body coulomb scattering, (iii) full account of electron population, with Pauli and Coulomb scattering. P. Borowik, J.-L. Thobel, L. Adamowicz, Semicond. Sci. Technol. 31 115004 (2016) doi:10.1088\/0268-1242\/31\/11\/115004\" width=\"799\" height=\"501\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde13_velocity.png 900w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde13_velocity-300x188.png 300w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde13_velocity-768x481.png 768w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde13_velocity-705x442.png 705w\" sizes=\"auto, (max-width: 799px) 100vw, 799px\" \/><\/a><p id=\"caption-attachment-26047\" class=\"wp-caption-text\">Velocity-field characteristics in silicene, calculated by Monte Carlo simulations for several temperatures. ( Analytical approximations of band structure and scattering rates have been used ). The Electron sheet density is equal to 1\u00d71012 cm-2. The impact of electron density on electron transport is two-fold : (i) Some regions of reciprocal space are significantly populated. Since Pauli exclusion principle forbids double occupation of states, it may strongly affect electron distribution function. (ii) Direct Coulomb scattering between electrons. To illustrate the influence of these phenomena, three cases are compared: (i) neglecting the effect of electron density, i.e. without two body coulomb scattering, without Pauli rejection. (ii) Pauli principle is accounted for but not two body coulomb scattering, (iii) full account of electron population, with Pauli and Coulomb scattering. P. Borowik, J.-L. Thobel, L. Adamowicz, Semicond. Sci. Technol. 31 115004 (2016) doi:10.1088\/0268-1242\/31\/11\/115004<\/p><\/div>\n<h4 style=\"text-align: center;\">Spin relaxation in graphene<\/h4>\n<div id=\"attachment_26050\" style=\"width: 491px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde14_spin_relaxation.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26050\" class=\"wp-image-26050 size-full\" title=\"Monte Carlo simulation of spin relaxation in graphene at high carrier density (Ns=1\u00d71012 cm-2). At initial time the population is fully spin polarized: all carriers have their spin aligned in the same direction (x, y, or z direction for top, center, and bottom panel respectively). Then spin evolves under the effect of effective magnetic field (precession motion) and random carrier scattering (Dyakonov-Perel and Elliott-Yafet mechanisms). , , and are the components of spin polarization measured along direction x,y,z. Owing to spin procession motion, and exhibit oscillations, damped by random scattering, while the total polarization exhibit only an exponential decay. The time constant, spin relaxation time, is here of the order of 2 ns. P. Borowik, J.-L. Thobel and L. Adamowicz, Journ. Appl. Phys. 122, 045704 (2017), doi: 10.1063\/1.4995821\" src=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde14_spin_relaxation.png\" alt=\"Monte Carlo simulation of spin relaxation in graphene at high carrier density (Ns=1\u00d71012 cm-2). At initial time the population is fully spin polarized: all carriers have their spin aligned in the same direction (x, y, or z direction for top, center, and bottom panel respectively). Then spin evolves under the effect of effective magnetic field (precession motion) and random carrier scattering (Dyakonov-Perel and Elliott-Yafet mechanisms). , , and are the components of spin polarization measured along direction x,y,z. Owing to spin procession motion, and exhibit oscillations, damped by random scattering, while the total polarization exhibit only an exponential decay. The time constant, spin relaxation time, is here of the order of 2 ns. P. Borowik, J.-L. Thobel and L. Adamowicz, Journ. Appl. Phys. 122, 045704 (2017), doi: 10.1063\/1.4995821\" width=\"481\" height=\"627\" srcset=\"https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde14_spin_relaxation.png 481w, https:\/\/www.iemn.fr\/wp-content\/uploads\/2018\/10\/silphyde14_spin_relaxation-230x300.png 230w\" sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/><\/a><p id=\"caption-attachment-26050\" class=\"wp-caption-text\">Monte Carlo simulation of spin relaxation in graphene at high carrier density (Ns=1\u00d71012 cm-2). At initial time the population is fully spin polarized: all carriers have their spin aligned in the same direction (x, y, or z direction for top, center, and bottom panel respectively). Then spin evolves under the effect of effective magnetic field (precession motion) and random carrier scattering (Dyakonov-Perel and Elliott-Yafet mechanisms). , , and are the components of spin polarization measured along direction x,y,z. Owing to spin procession motion, and exhibit oscillations, damped by random scattering, while the total polarization exhibit only an exponential decay. The time constant, spin relaxation time, is here of the order of 2 ns. P. Borowik, J.-L. Thobel and L. Adamowicz, Journ. Appl. Phys. 122, 045704 (2017), doi: 10.1063\/1.4995821<\/p><\/div>\n<\/div><\/section>\n<div  class='av_promobox av-js09a3uo-95c6a6ac9fb24e9e4d24e2dec1561c1b avia-button-no  avia-builder-el-5  el_after_av_textblock  avia-builder-el-last'><div class='avia-promocontent'><p>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-w73dns-418873852a2a8329b913b5be35537f92\">\n.av_font_icon.av-w73dns-418873852a2a8329b913b5be35537f92 .av-icon-char{\nfont-size:25px;\nline-height:25px;\n}\n<\/style>\n<span  class='av_font_icon av-w73dns-418873852a2a8329b913b5be35537f92 avia_animate_when_visible av-icon-style- avia-icon-pos-left av-no-color avia-icon-animate'><span class='av-icon-char' aria-hidden='true' data-av_icon='\ue87f' data-av_iconfont='entypo-fontello' ><\/span><\/span><\/p>\n<p><strong>SILPHYDE Group : OTHER ACTIVITIES<\/strong><\/p>\n<ul>\n<li class=\"page_item page-item-25984\"><a href=\"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/simulation-of-nitride-based-electronic-devices\/\">Simulation of nitride-based electronic devices<\/a><\/li>\n<li class=\"page_item page-item-25999\"><a href=\"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/modeling-of-thz-sources\/\">Modeling of THz sources based on Quantum Cascade Lasers<\/a><\/li>\n<li class=\"page_item page-item-26023\"><a href=\"https:\/\/www.iemn.fr\/en\/la-recherche\/les-groupes\/silphyde\/research\/study-nanostructures\/\">Study of ferroelectric nanostructures<\/a><\/li>\n<\/ul>\n<p>\n<\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":25981,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-26043","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages\/26043","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/comments?post=26043"}],"version-history":[{"count":0,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages\/26043\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/pages\/25981"}],"wp:attachment":[{"href":"https:\/\/www.iemn.fr\/en\/wp-json\/wp\/v2\/media?parent=26043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}