{"id":31135,"date":"2004-08-01T00:05:08","date_gmt":"2004-08-01T00:05:08","guid":{"rendered":"https:\/\/silvaco-stage.betagentechnologies.com\/%eb%b6%84%eb%a5%98%eb%90%98%ec%a7%80-%ec%95%8a%ec%9d%8c\/a-new-efficient-quantum-method-the-bohm-quantum-potential-model\/"},"modified":"2021-07-16T21:52:00","modified_gmt":"2021-07-17T04:52:00","slug":"a-new-efficient-quantum-method-the-bohm-quantum-potential-model","status":"publish","type":"post","link":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/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-stage.betagentechnologies.com\/wp-content\/uploads\/simulationstandard\/simstd_aug_2004_a2-e1611193566317.jpg\" class=\"cleaned-enfold-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/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":3,"featured_media":21642,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7486],"tags":[],"class_list":["post-31135","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simulation-standard-ko","entry","has-media"],"_links":{"self":[{"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/posts\/31135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/comments?post=31135"}],"version-history":[{"count":1,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/posts\/31135\/revisions"}],"predecessor-version":[{"id":31140,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/posts\/31135\/revisions\/31140"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/media\/21642"}],"wp:attachment":[{"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/media?parent=31135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/categories?post=31135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/silvaco-stage.betagentechnologies.com\/ko\/wp-json\/wp\/v2\/tags?post=31135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}