Modeling and simulation of electronic structure, material interface and random doping in nano electronic devices

Area of Science:

• Applied and computational mathematics
• Nano-electronics
• Quantum mechanics

Background:

• Miniaturization of nano-scale electronic devices like MOSFETs necessitates new theoretical frameworks for quantum mechanical effects.
• Accurate modeling of these effects is crucial for advancing integrated circuit design.

Purpose of the Study:

• To develop advanced mathematical models and computational algorithms for simulating nano-scale MOSFETs.
• To unify microscopic and macroscopic descriptions of electron behavior at the nano scale.
• To enhance the accuracy and efficiency of nano-device simulations.

Main Methods:

• A unified two-scale energy functional was introduced, leading to consistently-coupled Poisson-Kohn-Sham equations.
• Material interface and individual dopant models (using Dirac delta function) were proposed for improved electrostatics and doping effect analysis.
• The matched interface and boundary (MIB) method and Dirichlet-to-Neumann mapping (DNM) technique were employed for computational efficiency.
• Electronic structures were computed via subband decomposition and transport properties via non-equilibrium Green's functions (NEGF) formalism.

Main Results:

• The study successfully simulated double-gate and four-gate MOSFETs in 3D.
• Explored current fluctuations and voltage threshold lowering effects due to discrete dopant models.
• Investigated numerical convergence and model well-posedness for the proposed methods.

Conclusions:

• The developed models and algorithms provide a robust framework for simulating nano-scale MOSFETs.
• The unified approach effectively bridges microscopic and macroscopic descriptions.
• The proposed methods enhance the accuracy and efficiency of nano-electronic device simulations, aiding future designs.