Drift Currents and Conductivity: Poisson's Equation in Semiconductors

This lecture discusses the concepts of drift currents and conductivity in semiconductors, focusing on the physical effects that limit the time between collisions. The instructor explains how conductivity is related to the density of current and the electric field, introducing the concept of scattering due to impurities and phonons. The impact of temperature and doping on scattering is analyzed, highlighting that impurity scattering increases with doping while phonon scattering is influenced by temperature. The lecture also covers the saturation velocity at high electric fields, illustrating how drift velocity behaves under varying conditions. The relationship between charge distribution and electric fields is explored through Maxwell's equations and Poisson's equation, leading to an understanding of potential energy in semiconductor structures. The instructor provides examples of band structures, emphasizing the significance of charge density and electric fields in determining the behavior of semiconductors. Overall, the lecture integrates theoretical concepts with practical implications for semiconductor devices.