半导体物理基础理论.ppt

Appendix II. Probability of a State at E being Occupied Modern Semiconductor Devices for Integrated Circuits (C. Hu) Slide 1-* 1.5.2 How to Measure the Effective Mass Cyclotron Resonance Technique Centripetal force = Lorentzian force B - - - Microwave fcr is the Cyclotron resonance frequency. It is independent of v and r. Electrons strongly absorb microwaves of that frequency. By measuring fcr, mn can be found. Modern Semiconductor Devices for Integrated Circuits (C. Hu) Slide 1-* 1.6 Density of States E D c D v E c E v D E c E v DE Derived in Appendix I Modern Semiconductor Devices for Integrated Circuits (C. Hu) Slide 1-* 1.7 Thermal Equilibrium and the Fermi Function 1.7.1 An Analogy for Thermal Equilibrium · There is a certain probability for the electrons in the conduction band to occupy high-energy states under the agitation of thermal energy. Dish Vibrating Table Sand particles There are g1 states at E1, g2 states at E2… There are N electrons, which constantly shift among all the states but the average electron energy is fixed at 3kT/2. The equilibrium distribution is the distribution that maximizes the number of combinations of placing n1 in g1 slots, n2 in g2 slots…. : There are many ways to distribute N among n1, n2, n3….and satisfy the 3kT/2 condition. ni/gi = EF is a constant determined by the condition Modern Semiconductor Devices for Integrated Circuits (C. Hu) Modern Semiconductor Devices for Integrated Circuits (C. Hu) Slide 1-* 1.7.2 Fermi Function–The Probability of an Energy State Being Occupied by an Electron Ef is called the Fermi energy or the Fermi level. Boltzmann approximation: f(E) 0.5 1 Ef Ef – kT Ef – 2kT Ef – 3kT Ef + kT E f Ef + 2kT Ef + 3kT E Modern Semiconductor Devices for Integrated Circuits (C. Hu) Slide 1-* 1.8 Electron and Hole Concentrations 1.8.1 Derivation of n and p from D(E) and f(E) Modern Semiconductor Devices for Integrated Circuits (C. Hu) Slide 1-* Electron a