Dispersion Relationships: Band Structures and Density of States

This lecture covers the dispersion relationship in real crystals, focusing on the band structures of materials like silicon and gallium arsenide. The instructor begins by reviewing concepts from the previous class, including the periodicity in crystal lattices and the reciprocal space, which is essential for understanding the Brillouin zone. The discussion progresses to the effective mass of charge carriers, including electrons and holes, and how these relate to the energy gaps in semiconductors. The instructor illustrates the differences between direct and indirect band gaps, emphasizing their implications for material properties. The lecture also explores the density of states in three-dimensional systems and how it varies with dimensionality, particularly in low-dimensional structures like quantum wells and dots. The instructor engages students with exercises on calculating band gaps in ternary alloys, highlighting the importance of understanding how composition affects electronic properties. Overall, the lecture provides a comprehensive overview of the fundamental concepts in solid-state physics relevant to semiconductor materials.