A New Efficient Quantum Method: The Bohm Quantum Potential Model
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 ATLAS, a Schrödinger-Poisson solver and Density-Gradient model. The Schrödinger-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, ATLAS provides 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 ATLAS, 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 ATLAS. The table below summarizes the different models available in ATLAS related to the dimensionality and the transport models.
Historically, the definition of an effective quantum potential is Bohm’s 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.
The definition of the effective quantum potential Qeff is derived from a weighted average of the Bohm quantum potentials seen by all single particle wavefunctions
