Empty band

In many crystals there is sufficient overlap of atomic orbitals of adjacent atoms so that each group of a given quantum state can be treated as a crystal orbital or band. Such crystals will be electrically conducting if they have a partly filled band but if the bands are all either full or empty, the conductivity will be small. Metal oxides constitute an example of this type of crystal if exactly stoichiometric, all bands are either full or empty, and there is little electrical conductivity. If, however, some excess metal is present in an oxide, it will furnish electrons to an empty band formed of the 3s or 3p orbitals of the oxygen ions, thus giving electrical conductivity. An example is ZnO, which ordinarily has excess zinc in it. 

The occupied bands are called valence bands the empty bands are called conduction bands. The top of tire valence band is usually taken as energy zero. The lowest conduction band has a minimum along the A direction the highest occupied valence band has a maximum at F. Semiconductors which have the highest occupied k -state and lowest empty state at different points are called indirect gap semiconductors. If k = k, the semiconductor is call direct gap semiconductor. Gennanium is also an indirect gap semiconductor whereas GaAs has a direct gap. It is not easy to predict whether a given semiconductor will have a direct gap or not. 

Ordinarily, the energy gap (Eg) between the filled and empty bands is appreciably greater than kT. The concentration of conduction electrons n in the pure stoichiometric material is equal to the concentration of holes p and is given by... 

The electronic band structure of a neutral polyacetylene is characterized by an empty band gap, like in other intrinsic semiconductors. Defect sites (solitons, polarons, bipolarons) can be regarded as electronic states within the band gap. The conduction in low-doped poly acetylene is attributed mainly to the transport of solitons within and between chains, as described by the intersoliton-hopping model (IHM) . Polarons and bipolarons are important charge carriers at higher doping levels and with polymers other than polyacetylene. 

Semimetals show metallic conductivity due to the overlap of a filled and an empty band. In this case electrons spill over from the filled band into the bottom of the empty band until the Fermi surface intersects both sets of bands. In semimetals holes and electrons coexist even at 0 K. 

With conductors either the valence band is only partially filled (as with metals) or it overlaps with the next higher allowable empty band. Hence only small amounts of energy are required to raise a valence electron into a higher-level empty band where it is free to move from atom to atom. 

Within Koopmans theorem approximation, therefore, photoemission probes the occupied bands of a solid, establishing their relative position in energy BIS in the same approximation probes its empty bands. The combination of the two methods is therefore a very powerful tool for the elucidation of the band structure. 

The effect of an external electric field is to produce an acceleration of the electrons in the direction of the field, and this causes a shift of the Fermi surface. It is a necessary condition for the movement of electrons in the fc-space that there are allowed empty states at the Fermi surface hence electrical conductivity is dependent on partially filled bands. An insulating crystal is one in which the electron bands are either completely full or completely empty. If the energy gap between a completely filled band and an empty band is small, it is possible that thermal excitation of electrons from the filled to the empty band will result in a conducting crystal. Such substances are usually referred to as intrinsic semiconductors. A much larger class of semiconductors arises from impurities... 

Extrinsic Semiconductors. Impurity levels can be either donor levels near the empty zone (normal or n-type), or acceptor levels near the filled band (abnormal or p-type). Conductivity in n-type conductors will be due to electrons in the empty band donated by the impurity levels, and in p-type conductors, to positive holes in the previously filled band, arising from the transition of electrons to the impurity acceptor levels. 

---