Lecture Notes: Semiconductor Physics and Nanotechnology - Density of States and Nanoscience

Introduction to Density of States

• Definition: Describes the number of energy states available in a system.
• Essential for determining carrier concentrations and energy distributions in semiconductors.
• Free motion of carriers is limited to two, one, and zero spatial dimensions in semiconductors.

Density of States by Dimension

3D (Bulk Material)

• Defined as the number of allowed electronic energy states per unit energy range per unit volume.

Lower-Dimensional Systems

• Issues in 3D:
  • Strong disorder due to ionized impurities.
  • Quantum effects are more pronounced in lower dimensions.
• Benefits: Reduced dimensionality leads to new electronic and photonic devices operating under quantum mechanics rules.
• Applications: Double heterostructure lasers, high effective LEDs, bipolar transistors, HEMT, etc.

2D Density of States

• Arises when electrons are confined in one dimension (e.g., Quantum Well).
• DOS in 2D is independent of energy but depends on the number of quantized levels.

1D Density of States

• Created when electrons are free to move in one direction but confined in two (e.g., Quantum Wire).

0D Density of States

• Complete confinement in all dimensions (e.g., Quantum Dot).
• DOS represented as a delta function due to discrete energy levels.

Introduction to Nanoscience

• Definition: Involves the study of phenomena and manipulation of materials at atomic, molecular, and macromolecular scales.
• Scale: Ranges from 0.1nm to 100nm.
• Surface to Volume Ratio: Increases dramatically, leading to better catalysts.

Properties at the Nanoscale

• Nano-sized particles show different properties (e.g., Gold appears red at nanoscale due to restricted electron movement).

Interdisciplinary Nature

• Disciplines Involved: Physics, Chemistry, Biology, Computer Science, Engineering.
• Special Properties: High structure density, changes in physical and chemical properties.

Technological and Scientific Implications

• Richard Feynman: Advocated for the potential of nanoscale technology.
• Applications: Medicine, computing, military, transportation, solar energy, pollution reduction.

Novel Low Dimensional Systems

• Materials: PbS, GaAs, CdS can be synthesized at nanometer scale.
• Properties: Unique band gaps, luminescence, used in high efficiency solar cells, detectors, lasers.

Variation in Physical Properties with Size

• Electronic Properties: Change with size due to band narrowing.
• Magnetic and Mechanical Properties: Altered in nanoparticles.

Synthesis and Applications of Nanomaterials

• Synthesis Methods: Top-down and bottom-up.
• Applications: Making materials stronger, lighter, and more efficient.