This course aims to introduce the fundamental physical concepts and basic numerical analysis techniques required for a precise understanding of semiconductor device operation. Starting from the derivation and interpretation of the core semiconductor equations—such as Poisson’s equation, the continuity equations, and carrier transport equations—students will learn how to calculate the operational characteristics of practical devices using numerical solution methods based on finite-difference and finite-element frameworks.

By acquiring a balanced understanding of theoretical modeling as well as classical and modern simulation approaches, students will develop the practical capability to analyze and optimize not only conventional semiconductor devices but also novel and creative device structures of their own design.

1. Fundamental concepts of semiconductor physics
2. Fundamental concepts of Differential equations and vector calculus
3. basic proficiency in MATLAB or Python is recommended

1. Siegfried Selberherr, Analysis and Simulation of Semiconductor Devices, Springer, 1984.
2. S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2006.
3. Ben G. Streetman and Sanjay Kumar Banerjee, Solid State Electronic Devices, 7th ed., Pearson, 2015.

Week 1 — Concepts and Overall Framework of Semiconductor Device Simulation

Learning Objectives:
Understand why device simulation is necessary.
Understand the simulation framework: Physics → Equations → Numerical Methods.

Topics:
Roles of device modeling, analysis, and simulation
Purpose and basic components of TCAD
Overview of the Selberherr framework

Main Text Alignment: Chapter 1 — Introduction


Week 2 — Fundamental Equations for Electric Field, Potential, and Space Charge

Learning Objectives:
Understand the physical meaning of Poisson’s equation.
Explain how doping profiles determine electrostatic potential.

Topics:
Derivation of Poisson’s equation from Maxwell’s equations
Space charge and potential distribution
Concept of boundary conditions

Main Text Alignment: Chapter 2.1 — Poisson’s Equation


Week 3 — Continuity Equations Based on Charge Conservation

Learning Objectives:
Explain that continuity equations represent charge conservation.
Understand the role of generation and recombination terms.

Topics:
Current components and continuity equations
Steady-state vs. transient operation
Introduction to generation–recombination (G–R) terms

Main Text Alignment: Chapter 2.2 — Continuity Equations


Week 4 — Carrier Transport I: Fundamentals of Drift and Diffusion

Learning Objectives:
Distinguish and explain two carrier transport mechanisms.
Understand the basics of the drift–diffusion model.

Topics:
Drift current and mobility
Diffusion current and concentration gradients
Einstein relation

Main Text Alignment: Chapter 2.3 — Carrier Transport


Week 5 — Carrier Transport II: Advanced Transport and Model Limitations

Learning Objectives:
Understand assumptions and applicability of the drift–diffusion model.
Explain the concept of the Boltzmann Transport Equation (BTE).

Topics:
High-field transport and velocity saturation
Limitations of the drift–diffusion model
Conceptual structure of BTE and relaxation-time approach

Main Text Alignment: Chapter 2.3.1–2.3.2


Week 6 — Carrier Concentrations and Material Properties

Learning Objectives:
Understand carrier concentration models and dependence on doping and temperature.
Explain how material parameters affect simulation results.

Topics:
Electron and hole concentrations, intrinsic concentration
Effective density of states
Summary of basic semiconductor constants

Main Text Alignment: Chapter 2.4 — Carrier Concentrations


Week 7 — Mobility and Recombination Models / Midterm Exam (Weeks 1–7)

Learning Objectives:
Explain components and physical meaning of mobility models.
Understand operating principles of recombination models (SRH, Auger).

Topics:
Physical origins of mobility models
SRH and Auger recombination
Overview of thermal generation and temperature effects

Main Text Alignment: Chapters 4.1–4.2


Week 8 — Making Continuity Equations Computationally Solvable

Learning Objectives:
Understand the concept and necessity of discretization.
Explain conversion from PDEs to algebraic equations.

Topics:
Grid-based approximations
Discretized form of continuity equations
Basic mesh concepts

Main Text Alignment: Chapter 6 — Introduction to Discretization


Week 9 — Basic Numerical Methods: Simple Grid-Based Approaches

Learning Objectives:
Understand structures of Finite Difference Method (FDM) and Box Method.
Discretize Poisson’s equation in simplified form.

Topics:
FDM fundamentals in 1D and 2D
Finite Box Method and conservation-based approach
Grid spacing and accuracy

Main Text Alignment: Chapter 6.1–6.2


Week 10 — Numerical Methods for Complex Geometries

Learning Objectives:
Understand why FEM is used for complex structures.
Explain the concept of weighting functions intuitively.

Topics:
Basic idea of FEM
Element subdivision
Conceptual construction of FEM matrices

Main Text Alignment: Chapter 6.3


Week 11 — Iterative Solution of Nonlinear Systems

Learning Objectives:
Understand why Newton’s method is used for nonlinear problems.
Explain convergence and stability.

Topics:
Linearization of nonlinear PDEs
Newton iteration scheme
Convergence conditions

Main Text Alignment: Chapter 7


Week 12 — Efficient Solution Techniques

Learning Objectives:
Understand why device matrices are sparse.
Distinguish direct and iterative solvers.

Topics:
Sparse matrix structures
Matrix ordering
Comparison of solver types

Main Text Alignment: Chapter 8


Week 13 — Interpreting Simulation Results

Learning Objectives:
Interpret potential distributions and current flow.
Explain links between PDEs, numerical methods, and results.

Topics:
PN junction potential example
Basic MOSFET examples
Conceptual interpretation of breakdown
Plotting and result analysis

Main Text Alignment: Chapter 9


Week 14 — Overview of Modern TCAD Simulation Flow

Learning Objectives:
Relate modern simulation software flow to the Selberherr framework.
Understand the pipeline: Mesh → Model → Solver → Result.

Topics:
Typical TCAD computation flow
Model selection and mesh strategies
Modern significance of Selberherr PDE framework
Applications to FinFET, GAA, 2D devices, and vacuum devices

Main Text Alignment: Chapters 1, 6–8


Week 15 — Final Project Presentations and Course Summary

Learning Objectives:
Perform a simple analysis or simulation project based on learned theory.
Explain the unified structure of PDE–Mesh–Solver–Result.

Example Projects:
Implementation of a simple 1D Poisson solver
Comparison of results with different mobility or recombination models
Mesh refinement and numerical error analysis

1. Theory-based lectures combined with small-scale practical assignments
2. Simple example codes provided using MATLAB or Python

GSST 전공선택 분야: 반도체 소자/소재