Two-dimensional fully numerical solutions of molecular Schrödinger equations. I. One-electron molecules

1983 ◽  
Vol 23 (1) ◽  
pp. 309-317 ◽  
Author(s):  
Leif Laaksonen ◽  
Pekka Pyykkö ◽  
Dage Sundholm
Keyword(s):  
Numerical Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Two Dimensional

ANALYTICAL MODELING OF DRAIN CURRENT, CAPACITANCE AND TRANSCONDUCTANCE IN SYMMETRIC DOUBLE-GATE MOSFETs CONSIDERING QUANTUM EFFECTS

2013 ◽  
Vol 12 (01) ◽  
pp. 1350005 ◽  
Author(s):  
VIMALA PALANICHAMY ◽  
N. B. BALAMURUGAN
Keyword(s):  
Numerical Solutions ◽  
Inversion Layer ◽  
Drain Current ◽  
Quantum Effects ◽  
Schrodinger Equations ◽  
Double Gate ◽  
Schrödinger Equations ◽  
Inversion Charge ◽  
Physical Insight ◽  
Quantum Mechanical Effects

An analytical model for double-gate (DG) MOSFETs considering quantum mechanical effects is proposed in this paper. Schrödinger and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum effects (QME) that influence the performance of DG MOSFETs. This model is developed to provide an analytical expression for inversion charge distribution function for all regions of device operation. This expression is used to calculate the other important parameters like inversion layer centroid, inversion charge, gate capacitance, drain current and transconductance. We systematically evaluate and analyze the parameters of DG MOSFETs considering QME. The analytical solutions are simple, accurate and provide good physical insight into the quantization caused by quantum confinement under various gate biases. The analytical results of this model are verified by comparing the data obtained with one-dimensional self-consistent numerical solutions of Poisson and Schrödinger equations known as SCHRED.

The Conservative Splitting High-Order Compact Finite Difference Scheme for Two-Dimensional Schrödinger Equations

2017 ◽  
Vol 15 (01) ◽  
pp. 1750079
Author(s):  
Bo Wang ◽  
Dong Liang ◽  
Tongjun Sun
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Two Dimensions ◽  
High Order ◽  
Optimal Error Estimate ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Time Step ◽  
Order Accuracy

In this paper, a new conservative and splitting fourth-order compact difference scheme is proposed and analyzed for solving two-dimensional linear Schrödinger equations. The proposed splitting high-order compact scheme in two dimensions has the excellent property that it preserves the conservations of charge and energy. We strictly prove that the scheme satisfies the charge and energy conservations and it is unconditionally stable. We also prove the optimal error estimate of fourth-order accuracy in spatial step and second-order accuracy in time step. The scheme can be easily implemented and extended to higher dimensional problems. Numerical examples are presented to confirm our theoretical results.

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