Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
Kronig and Penney treated a simplest example for one dimensional periodic potential. In this model it is assumed that the potential energy of an electron has the form of a periodic array of square wells as shown in Fig
Definition, Explanation, Proof, Equation | Electrical Properties of Materials
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
Bloch theorem is a mathematical statement of an electron wave function moving in a perfectly periodic potential. These functions are called bloch functions.
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
To picture the energy spectra in atoms, molecules and solids let us consider a metal say sodium, which consists of 11 electrons with electronic configuration of 1s2 2s2 2p6 3s1.
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
In quantum free electron theory of metals the electrons were assumed to be moving in a region of constant potential and hence it moves freely about the crystal
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
The Fermi function F (E) gives only the probability of filling up of electrons in a given energy state, it does not gives the information about the number of electrons that can be filled in a given energy state.
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
The effect of temperature on Fermi function F (E) can be discussed with respect to equation (1)
Definition, Formula | Electrical Properties of Materials
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
Definition: Fermi function F (E) represents the probability of an electron occupying a given energy state.
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
We know according to Quantum free electron theory the energy levels are discrete (microscopically). But since the spacing between any two energy levels is very less (10-6 eV), the distribution of energy levels seems to be continuous. (macroscopically).
Electrical Properties of Materials
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
In the case of Fermi-dirac statistics the following points are considered.The particles (electrons) are indistinguishable.
Definition, Example | Electrical Properties of Materials
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
Degeneracy: It is seen from equation (28) and equation (29), for several combination of quantum numbers we have same energy eigen value but different eigen functions.
Electrical Properties of Materials
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
The solution of one-dimensional potential box can be extended for a three dimensional potential box. In a three dimensional potential box, the particle (electron) can move in any direction in space.
Subject and UNIT: Physics for Information Science: Unit I: Electrical Properties of Materials
The drawbacks of classical theory can be rectified using quantum theory.In classical theory the properties of metals such as electrical and thermal conductivities are well explained on the assumption that the electrons in the metal freely moves like the particles of a gas and hence called "free-electron gas."