Inside the crystal each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges. Because of this, each electron will have a different energy level
If the lowest level in the conduction band happens to be lower than the highest level of the valence band, the electrons from the valence band can easily move into the conduction band
If there is some gap between the conduction band and the valence band, electrons in the valence band all remain bound and no free electrons are available in the conduction band
For Si, the outermost orbit is the third orbit (n = 3), while for Ge it is the fourth orbit (n = 4). The number of electrons in the outermost orbit is 4 (2s and 2p electrons). Hence, the total number of outer electrons in the crystal is 4N. The maximum possible number of electrons in the outer orbit is 8 (2s + 6p electrons). So, for the 4N valence electrons there are 8N available energy states
At the distance between the atoms in the crystal lattices of Si and Ge, the energy band of these 8N states is split apart into two which are separated by an energy gap Eg
When a finite but small band gap (Eg <3 eV) exists, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band
Si and Ge have four valence electrons. In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbor atoms, and also to take share of one electron from each such neighbor. These shared electron pairs are referred to as forming a covalent bond/valence bond
At low temperatures, all bonds are intact and no bond is broken. As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break-away (becoming free electrons contributing to conduction)
In semiconductors, apart from the electrons, the holes also move. Holes move in the direction opposite from that of motion of electrons. But, the motion of hole is independent of the motion of free electrons and is a way of describing the motion of bound electrons
Apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination occurs in which the electrons recombine with the holes. At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers
An intrinsic semiconductor will behave like an insulator at T = 0 K. It is the thermal energy at higher temperatures (T > OK), which excites some electrons from the valence band to the conduction band
When a few parts per million (ppm) of a suitable impurity is added to the pure semiconductor, the conductivity of the semiconductor is increased manifold
When an atom of +5 valency element occupies the position of an atom in the crystal lattice of Si, four of its electrons bond with the four silicon neighbors while the fifth remains very weakly bound to its parent atom. This fifth electron is available for conduction
When Si or Ge is doped with a trivalent impurity like Al, B, In, etc. the dopant has one valence electron less than Si or Ge and, therefore, this atom can form covalent bonds with neighboring three Si atoms but does not have any electron to offer to the fourth Si atom, creating a hole available for conduction