{"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":"2021-10-13T10:36:39","modified_gmt":"2021-10-13T17:36:39","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":"
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A New Efficient Quantum Method: The Bohm Quantum Potential Model<\/h1>\n

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<\/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,\u00a0ATLAS<\/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\u00a0ATLAS<\/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\u00a0ATLAS<\/em><\/strong>. The table below summarizes the different models available in\u00a0ATLAS<\/em><\/strong>\u00a0related to the dimensionality and the transport models.<\/p>\n

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

The definition of the effective quantum potential\u00a0Qeff<\/sub><\/em>\u00a0is derived from a weighted average of the Bohm quantum potentials seen by all single particle wavefunctions<\/p>\n<\/div><\/section><\/div>

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