{"id":36574,"date":"2004-08-01T00:05:08","date_gmt":"2004-08-01T00:05:08","guid":{"rendered":"https:\/\/silvaco.com\/%e6%9c%aa%e5%88%86%e7%b1%bb\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\/"},"modified":"2026-10-15T14:21:34","modified_gmt":"2026-10-15T21:21:34","slug":"a-new-efficient-quantum-method-the-bohm-quantum-potential-model","status":"publish","type":"post","link":"https:\/\/silvaco.com\/zh-hans\/simulation-standard-zh-hans\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\/","title":{"rendered":"A New Efficient Quantum Method: The Bohm Quantum Potential Model"},"content":{"rendered":"<h1>A New Efficient Quantum Method: The Bohm Quantum Potential Model<\/h1>\n<p>This article presents a new approach to model the quantum confinement of carriers in MOSFET or heterostructure. SILVACO has already included in its device simulator\u00a0<strong><em>ATLAS<\/em><\/strong>, a Schr\u00f6dinger-Poisson solver and Density-Gradient model. The Schr\u00f6dinger-Poisson (SP) solver is the most accurate approach to calculate the quantum confinement in semiconductor but it cannot predict the currents flowing in the device. To overcome this limitation,\u00a0<strong><em>ATLAS<\/em><\/strong>\u00a0provides a Density Gradient (DG) model [1]. It allows the user to predict both the quantum confinement and the drift-diffusion currents along with the Fermi-Dirac statistics for a 2D structure. However this model exhibits poor convergence in 3D and with the hydrodynamic transport. Therefore, in collaboration with the University of Pisa, SILVACO has introduced in\u00a0<strong><em>ATLAS<\/em><\/strong>, a new approach called Effective Bohm Quantum Potential (BQP) model. This model presented at SISPAD 2004 conference [2] exhibits many advantages. It includes two fitting parameters which ensure a good calibration for silicon or non-silicon materials, planar or non-planar devices. It is numerically stable and robust, and independent of the transport models used. Therefore it has been successfully implemented and tested in\u00a0<strong><em>ATLAS<\/em><\/strong>. The table below summarizes the different models available in\u00a0<strong><em>ATLAS<\/em><\/strong>\u00a0related to the dimensionality and the transport models.<\/p>\n<p><span class=\"regular\">Historically, the definition of an effective quantum potential is Bohm\u2019s interpretation of quantum mechanics [3], and has generated other more recent derivations based on a first order expansion of the Wigner equation [4], or on the so-called density gradient approach [5]. The BQP model has a few advantages: it does not depend on the transport model (drift-diffusion or hydrodynamic); Fermi-Dirac statistics can be straightforwardly included; it provides two parameters for calibration, whereas the Density Gradient has only one fitting parameter; finally, it exhibits very stable convergence properties.<\/span><\/p>\n<p>The definition of the effective quantum potential\u00a0<em>Q<sub>eff<\/sub><\/em>\u00a0is derived from a weighted average of the Bohm quantum potentials seen by all single particle wavefunctions<\/p>\n<p><img loading=\"lazy\" width=\"644\" height=\"800\" src=\"https:\/\/silvaco.com\/wp-content\/uploads\/simulationstandard\/simstd_aug_2004_a2-e1611193566317.jpg\" class=\"cleaned-enfold-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/p>\n<p><a href=\"https:\/\/silvaco.com\/dynamicweb\/jsp\/downloads\/DownloadDocStepsAction.do?req=download&#038;nm=simstd_aug_2004_a2.pdf\" class=\"BGT-btn\" target=\"_blank\" rel=\"noopener noreferrer\">Download Simulation Standard<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This article presents a new approach to model the quantum confinement of carriers in MOSFET or heterostructure. SILVACO has already included in its device simulator\u00a0ATLAS, a Schr\u00f6dinger-Poisson solver and Density-Gradient model<\/p>\n","protected":false},"author":12,"featured_media":21640,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[7723],"tags":[],"class_list":["post-36574","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simulation-standard-zh-hans","entry","has-media"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.7 (Yoast SEO v28.7) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>A New Efficient Quantum Method: The Bohm Quantum Potential Model - Silvaco<\/title>\n<meta name=\"description\" content=\"This article presents a new approach to model the quantum confinement of carriers in MOSFET or heterostructure. 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SILVACO has already included\" \/>\n<meta property=\"og:url\" content=\"https:\/\/silvaco.com\/zh-hans\/simulation-standard-zh-hans\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\/\" \/>\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=\"2004-08-01T00:05:08+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-10-15T21:21:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/silvaco.com\/wp-content\/uploads\/simulationstandard\/simstd_aug_2004_a2-e1611193566317.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"644\" \/>\n\t<meta property=\"og:image:height\" content=\"800\" \/>\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=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"Casey Molver\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/\"},\"author\":{\"name\":\"Casey Molver\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/#\\\/schema\\\/person\\\/2763eb741ca5ac04477fdff50ed84c80\"},\"headline\":\"A New Efficient Quantum Method: The Bohm Quantum Potential Model\",\"datePublished\":\"2004-08-01T00:05:08+00:00\",\"dateModified\":\"2026-10-15T21:21:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/\"},\"wordCount\":332,\"image\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/silvaco.com\\\/wp-content\\\/uploads\\\/simulationstandard\\\/simstd_aug_2004_a2-e1611193566317.jpg\",\"articleSection\":[\"Simulation Standard\"],\"inLanguage\":\"zh-CN\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/\",\"url\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/\",\"name\":\"A New Efficient Quantum Method: The Bohm Quantum Potential Model - Silvaco\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/zh-hans\\\/simulation-standard-zh-hans\\\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/silvaco.com\\\/wp-content\\\/uploads\\\/simulationstandard\\\/simstd_aug_2004_a2-e1611193566317.jpg\",\"datePublished\":\"2004-08-01T00:05:08+00:00\",\"dateModified\":\"2026-10-15T21:21:34+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/#\\\/schema\\\/person\\\/2763eb741ca5ac04477fdff50ed84c80\"},\"description\":\"This article presents a new approach to model the quantum confinement of carriers in MOSFET or heterostructure. 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