Energy bands

Semiconductors are defined by their unique electric conductive behavior. Metals are good conductors because at their Fermi level, there is a large density of energetically available states that each electron can occupy. Electrons can move quite freely between energy levels without a high energy cost. Metal conductivity decreases with temperature increase because thermal vibrations of crystal lattice disrupt the free motion of electrons. Insulators, by contrast, are very poor conductors of electricity because there is a large difference in energies (called a band gap) between electron-occupied energy levels and empty energy levels that allow for electron motion. Insulator conductivity increases with temperature because heat provides energy to promote electrons across the band gap to the higher electron conduction energy levels (called the conduction band). Semiconductors, on the other hand, have an intermediate level of electric conductivity when compared to metals and insulators. Their band gap is small enough that small increase in temperature promotes sufficient number of electrons (to result in measurable currents) from the lowest energy levels (in the valence band) to the conduction band. This creates electron holes, or unoccupied levels, in the valence band, and very loosely held electrons in the conduction band.[4][5] A simplified diagram illustrating the energy band levels of an insulator, a semiconductor, and a conductor. Electrons can only exist in certain energy levels. In the classic crystalline semiconductors, electrons can have energies only within certain bands (ranges). The range of energy runs from the ground state, in which electrons are tightly bound to the atom, up to a level where the electron can escape entirely from the material. Each energy band corresponds to a large number of discrete quantum states of the electrons. Most of the states with low energy (closer to the nucleus) are occupied, up to a particular band called the valence band. Semiconductors and insulators are distinguished from metals by the population of electrons in each band. The valence band in any given meta

is nearly filled with electrons under usual conditions, and metals have many free electrons with energies in the conduction band. In semiconductors, only a few electrons exist in the conduction band just above the valence band, and an insulator has almost no free electrons. The ease with which electrons in the semiconductor can be excited from the valence band to the conduction band depends on the band gap. The size of this energy gap (bandgap) determines whether a material is semiconductor or an insulator (nominally this dividing line is roughly 4 eV). With covalent bonds, an electron moves by hopping to a neighboring bond. The Pauli exclusion principle requires the electron to be lifted into the higher anti-bonding state of that bond. For delocalized states, for example in one dimension – that is in a nanowire, for every energy there is a state with electrons flowing in one direction and another state with the electrons flowing in the other. For a net current to flow, more states for one direction than for the other direction must be occupied. For this to occur, energy is required, as in the semiconductor the next higher states lie above the band gap. Often this is stated as: full bands do not contribute to the electrical conductivity. However, as the temperature of a semiconductor rises above absolute zero, there is more energy in the semiconductor to spend on lattice vibration and on exciting electrons into the conduction band. Electrons excited to the conduction band also leave behind electron holes, i.e. unoccupied states in the valence band. Both the conduction band electrons and the valence band holes contribute to electrical conductivity. The holes themselves don't move, but a neighboring electron can move to fill the hole, leaving a hole at the place it has just come from, and in this way the holes appear to move, and the holes behave as if they were actual positively charged particles. One covalent bond between neighboring atoms in the solid is ten times stronger than the binding of the single electron to the atom, so freeing the electron does not imply destruction of the crystal structure.