{"id":29155,"date":"2006-11-01T00:02:03","date_gmt":"2006-11-01T00:02:03","guid":{"rendered":"https:\/\/silvaco.com\/uncategorized\/advanced-quantum-effects-simulation-in-atlas\/"},"modified":"2026-10-15T14:16:36","modified_gmt":"2026-10-15T21:16:36","slug":"advanced-quantum-effects-simulation-in-atlas","status":"publish","type":"post","link":"https:\/\/silvaco.com\/ja\/simulation-standard\/advanced-quantum-effects-simulation-in-atlas\/","title":{"rendered":"Advanced Quantum Effects Simulation in Atlas"},"content":{"rendered":"

Advanced Quantum Effects Simulation in ATLAS<\/h1>\n

Introduction<\/h3>\n

The trend toward smaller MOSFET devices with thinner gate oxide and greater doping is resulting in the increased importance of quantum mechanical effects, which are observed as shifts in threshold voltage and gate capacitance. Predicting these quantum effects requires solving the Schrodinger equation. This article presents the Poisson-Schrodinger solver and recent enhancements implemented in ATLAS from Silvaco.<\/p>\n

Schrodinger-Poisson<\/h3>\n

To model the effects of quantum confinement,\u00a0Quantum<\/em><\/strong>\u00a0allows the self-consistent solution of the Schrodinger equation with Poisson\u2019s equation. Poisson\u2019s equation is solved in two dimensions over the entire device while Schrodinger\u2019s equation is solved in one dimensional slices across the device.<\/p>\n

These solutions provide calculations of the bound sate energies (Eigen energies), the carrier wave functions (Eigen functions), and carrier concentrations in the presence of quantum mechanical confining potential variations.<\/p>\n

Considering ml, mt1 and mt2 the electron longitudinal effective mass and the electron transverse effective masses respectively, the electron density is written as:<\/p>\n

\"\"<\/p>\n

Download Simulation Standard<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Introduction<\/p>\n

The trend toward smaller MOSFET devices with thinner gate oxide and greater doping is resulting in the increased importance of quantum mechanical effects, which are observed as shifts in threshold voltage and gate capacitance. Predicting these quantum effects requires solving the Schrodinger equation. This article presents the Poisson-Schrodinger solver and recent enhancements implemented in ATLAS from Silvaco.<\/p>\n","protected":false},"author":12,"featured_media":22355,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[7570],"tags":[],"class_list":["post-29155","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simulation-standard","entry","has-media"],"yoast_head":"\nAdvanced Quantum Effects Simulation in Atlas - Silvaco<\/title>\n<meta name=\"description\" content=\"The trend toward smaller MOSFET devices with thinner gate oxide and greater doping is resulting in the increased importance of quantum mechanical effects\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/silvaco.com\/ja\/simulation-standard\/advanced-quantum-effects-simulation-in-atlas\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Advanced Quantum Effects Simulation in Atlas\" \/>\n<meta property=\"og:description\" content=\"The trend toward smaller MOSFET devices with thinner gate oxide and greater doping is resulting in the increased importance of quantum mechanical effects\" \/>\n<meta property=\"og:url\" content=\"https:\/\/silvaco.com\/ja\/simulation-standard\/advanced-quantum-effects-simulation-in-atlas\/\" \/>\n<meta property=\"og:site_name\" content=\"Silvaco\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/SilvacoSoftware\/\" \/>\n<meta property=\"article:published_time\" content=\"2006-11-01T00:02:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-10-15T21:16:36+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/silvaco.com\/wp-content\/uploads\/simulationstandard\/simstd_nov_2006_a2.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1344\" \/>\n\t<meta property=\"og:image:height\" content=\"1669\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Casey Molver\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@SilvacoSoftware\" \/>\n<meta name=\"twitter:site\" content=\"@SilvacoSoftware\" \/>\n<meta name=\"twitter:label1\" content=\"\u57f7\u7b46\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"Casey Molver\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u63a8\u5b9a\u8aad\u307f\u53d6\u308a\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-quantum-effects-simulation-in-atlas\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-quantum-effects-simulation-in-atlas\\\/\"},\"author\":{\"name\":\"Casey Molver\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/#\\\/schema\\\/person\\\/2763eb741ca5ac04477fdff50ed84c80\"},\"headline\":\"Advanced Quantum Effects Simulation in Atlas\",\"datePublished\":\"2006-11-01T00:02:03+00:00\",\"dateModified\":\"2026-10-15T21:16:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-quantum-effects-simulation-in-atlas\\\/\"},\"wordCount\":171,\"image\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-quantum-effects-simulation-in-atlas\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/silvaco.com\\\/wp-content\\\/uploads\\\/simulationstandard\\\/simstd_nov_2006_a2.jpg\",\"articleSection\":[\"Simulation Standard\"],\"inLanguage\":\"ja\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-quantum-effects-simulation-in-atlas\\\/\",\"url\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-quantum-effects-simulation-in-atlas\\\/\",\"name\":\"Advanced Quantum Effects Simulation in Atlas - 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