Lec 06 Energy band theory - 1

Introduction

This tutorial provides an overview of energy band theory as discussed in the NPTEL lecture "Energy Band Theory - 1." Understanding energy bands is crucial for grasping the electrical properties of materials, particularly semiconductors and insulators. This guide will cover fundamental concepts such as energy bands, Peierls’ transition, Peierls’ instability, and the dispersion of s and p bands.

Step 1: Understand Energy Bands

Energy bands are ranges of energy levels that electrons can occupy in a solid. Key points to consider are:

• Valence Band: The highest range of energy levels occupied by electrons at absolute zero temperature.
• Conduction Band: The range of energy levels where electrons can move freely, contributing to electrical conductivity.

Band Gap: The energy difference between the valence band and conduction band. This gap determines a material's electrical properties

• Insulators have a large band gap.
• Conductors have overlapping bands.
• Semiconductors have a narrow band gap.

Step 2: Explore Peierls' Transition

Peierls’ transition describes the phenomenon where a material undergoes a structural distortion that opens up a band gap. This transition occurs in one-dimensional systems and has the following implications:

• Instability in the Structure: The original structure becomes unstable, leading to a new equilibrium position.
• Temperature Dependency: Peierls’ transition typically occurs at lower temperatures, where thermal vibrations are minimized.
• Significance: This concept is crucial in understanding certain materials that exhibit metal-insulator transitions.

Step 3: Examine Peierls' Instability

Peierls’ instability refers to the tendency of a material to distort to lower its energy state. Important aspects include:

• Formation of Charge Density Waves: The distortion leads to a periodic modulation of the charge density.
• Effects on Electronic Properties: The instability can affect conductivity and other electronic properties of materials.
• Examples: Transition metal oxides and certain organic conductors often exhibit Peierls’ instability.

Step 4: Analyze Dispersion of s and p Bands

The dispersion relation describes how the energy of electrons varies with their momentum. To analyze s and p bands:

• s Bands: Typically isotropic and have a parabolic shape in the dispersion relation, indicating that the energy increases smoothly with momentum.
• p Bands: More complex due to their directional nature, leading to anisotropic dispersion.
• Implications for Band Structure: The shape of these bands influences the electronic properties and behavior of materials under various conditions.

Conclusion

In this tutorial, we explored the essential concepts of energy band theory, including the significance of energy bands, Peierls’ transition and instability, and the dispersion of s and p bands. Understanding these concepts is foundational for studying semiconductor physics and materials science. For further exploration, consider delving into specific materials that exhibit these phenomena or investigating how temperature influences band structure.