{"id":29086,"date":"2010-01-01T14:58:56","date_gmt":"2010-01-01T14:58:56","guid":{"rendered":"https:\/\/silvaco.com\/uncategorized\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\/"},"modified":"2026-10-16T09:03:39","modified_gmt":"2026-10-16T16:03:39","slug":"a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field","status":"publish","type":"post","link":"https:\/\/silvaco.com\/ja\/simulation-standard\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\/","title":{"rendered":"A Box Method Discretisation for the Drift-Diffusion Equations in a Magnetic Field"},"content":{"rendered":"

Box Method Discretisation for the Drift-Diffusion Equations in a Magnetic Field<\/h1>\n

Introduction<\/strong><\/p>\n

The problem of discretising the semiconductor drift-diffusion equations in the presence of a uniform magnetic field using the Box Method has previously been addressed in the literature. For the case of a rectangular non-uniform grid in 2D see[1], and for a general triangular mesh see[2]. These methods have also been extended to 3D [3],[4]. We have implemented and analysed these methods and found them all to be flawed in some way. In this paper we describe the established discretisations and elaborate on their flaws. We then briefly describe the new discretisation developed by Silvaco, and give some examples of its use.<\/p>\n

\"\"<\/p>\n

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

The problem of discretising the semiconductor drift-diffusion equations in the presence of a uniform magnetic field using the Box Method has previously been addressed in the literature. For the case of a rectangular non-uniform grid in 2D see[1], and for a general triangular mesh see[2]. These methods have also been extended to 3D [3],[4]. We have implemented and analysed these methods and found them all to be flawed in some way. In this paper we describe the established discretisations and elaborate on their flaws. We then briefly describe the new discretisation developed by Silvaco, and give some examples of its use.<\/p>\n","protected":false},"author":5,"featured_media":19889,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[7570],"tags":[],"class_list":["post-29086","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simulation-standard","entry","has-media"],"yoast_head":"\nA Box Method Discretisation for the Drift-Diffusion Equations in a Magnetic Field - Silvaco<\/title>\n<meta name=\"description\" content=\"The problem of discretising the semiconductor drift-diffusion equations in the presence of a uniform magnetic field using the Box Method has previously been addressed in the literature.\" \/>\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\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Box Method Discretisation for the Drift-Diffusion Equations in a Magnetic Field\" \/>\n<meta property=\"og:description\" content=\"The problem of discretising the semiconductor drift-diffusion equations in the presence of a uniform magnetic field using the Box Method has previously been addressed in the literature.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/silvaco.com\/ja\/simulation-standard\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\/\" \/>\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=\"2010-01-01T14:58:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-10-16T16:03:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/silvaco.com\/wp-content\/uploads\/2020\/03\/simstd_Q1_2010_a4.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"782\" \/>\n\t<meta property=\"og:image:height\" content=\"1012\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Ingrid Schwarz\" \/>\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=\"Ingrid Schwarz\" \/>\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\\\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\\\/\"},\"author\":{\"name\":\"Ingrid Schwarz\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/#\\\/schema\\\/person\\\/f85f880bc8a7ce823b36a9072e1f0a29\"},\"headline\":\"A Box Method Discretisation for the Drift-Diffusion Equations in a Magnetic Field\",\"datePublished\":\"2010-01-01T14:58:56+00:00\",\"dateModified\":\"2026-10-16T16:03:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\\\/\"},\"wordCount\":127,\"image\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/silvaco.com\\\/wp-content\\\/uploads\\\/2020\\\/03\\\/simstd_Q1_2010_a4.jpg\",\"articleSection\":[\"Simulation Standard\"],\"inLanguage\":\"ja\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\\\/\",\"url\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/a-box-method-discretisation-for-the-drift-diffusion-equations-in-a-magnetic-field\\\/\",\"name\":\"A Box Method Discretisation for the Drift-Diffusion Equations in a Magnetic Field - 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