Nanostructure Physics of non-isolated Quantum Well of symmetric double barrier

Inhaltsverzeichnis (Table of Contents)

• Chapter I
  • Background on Quantum Mechanics
• Chapter II
  • Background on Microelectronics
• Chapter III
  • Background on Nanostructure Physics
• Chapter IV
  • Analytical calculation of transcendental equation obeyed by quasi-bound energy levels of the non-isolated Quantum Well of symmetric rectangular double barrier
• Chapter V
  • Taking effective mass inequality into account: analytical calculation of transcendental equation obeyed by quasi-bound energy levels of the non-isolated Quantum Well of symmetric rectangular double barrier
• Chapter VI
  • Derivation of WKB solution of Schroedinger equation and introduction to WKB connection formulae
• Chapter VII
  • Analytical calculation of transfer matrix and transmission coefficient of single tunnel barrier of general shape using WKB method
• Chapter VIII
  • Symmetric double barrier of general shape: analytical calculation of condition or equation obeyed by quasi-bound energy levels of non-isolated Quantum Well using WKB method

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This work aims to provide an in-depth analysis of the physics of non-isolated quantum wells, specifically focusing on symmetric double barriers. The study utilizes analytical methods, including the calculation of transfer matrices and transcendental equations, to determine the quasi-bound energy levels of the quantum well. Key themes explored in the text include:

• Quantum mechanics principles and their application to semiconductor systems
• Analytical derivation of transcendental equations governing quasi-bound energy levels
• The impact of effective mass inequality on the energy levels
• Application of the WKB method to solve the Schroedinger equation and calculate transmission coefficients
• The role of resonant transmission peaks in determining quasi-bound energy levels

Zusammenfassung der Kapitel (Chapter Summaries)

Chapter I: Background on Quantum Mechanics

This chapter serves as an introduction to the fundamental principles of quantum mechanics, essential for understanding the behavior of electrons in semiconductor structures. It covers topics such as the Schrödinger equation, probability current density, time-independent Schrödinger equation, and the characteristics of wavefunctions.

Chapter II: Background on Microelectronics

Chapter II provides an overview of key concepts in microelectronics, laying the foundation for understanding the semiconductor devices discussed in later chapters. It explores the properties of intrinsic and extrinsic semiconductors, bandgap engineering, and heterojunctions.

Chapter III: Background on Nanostructure Physics

This chapter focuses on the physics of nanostructure systems, specifically addressing the behavior of electrons in single and double barrier structures. It introduces quantum wells and examines the transmission coefficients of different barrier configurations.

Chapter IV: Analytical calculation of transcendental equation obeyed by quasi-bound energy levels of the non-isolated Quantum Well of symmetric rectangular double barrier

Chapter IV delves into the central problem of the study: deriving the analytical equation for quasi-bound energy levels in a non-isolated quantum well with a symmetric rectangular double barrier. It presents the methodology and physics behind the calculation, focusing on the transfer matrices of each barrier and the final transcendental equation.

Chapter V: Taking effective mass inequality into account: analytical calculation of transcendental equation obeyed by quasi-bound energy levels of the non-isolated Quantum Well of symmetric rectangular double barrier

This chapter expands on the analysis in Chapter IV by considering the effect of different effective masses in the quantum well. It recalculates the transfer matrices and transcendental equation, incorporating the effective mass inequality.

Chapter VI: Derivation of WKB solution of Schroedinger equation and introduction to WKB connection formulae

Chapter VI introduces the Wentzel-Kramers-Brillouin (WKB) approximation, a powerful method for solving the Schrödinger equation. It explains the derivation of the WKB solution and explores the concept of classical turning points and connection formulas.

Chapter VII: Analytical calculation of transfer matrix and transmission coefficient of single tunnel barrier of general shape using WKB method

This chapter demonstrates the application of the WKB method to calculate the transfer matrix and transmission coefficient of a single tunnel barrier with a general shape.

Chapter VIII: Symmetric double barrier of general shape: analytical calculation of condition or equation obeyed by quasi-bound energy levels of non-isolated Quantum Well using WKB method

Chapter VIII extends the WKB analysis to the case of a symmetric double barrier with general shapes. It derives the condition or equation obeyed by the quasi-bound energy levels using the WKB method.

Schlüsselwörter (Keywords)

The central focus of this work lies in the study of non-isolated quantum wells with symmetric double barriers. The key areas of research include analytical methods, transfer matrices, transcendental equations, quasi-bound energy levels, effective mass inequality, WKB approximation, and resonant transmission peaks.