Charge Carriers In Semiconductors: Electrons and Holes
Since the semiconductor has a filled valence band and an empty conduction band at 0 K, we must consider the increase in conduction band electrons by thermal excitations across the band gap as the temperature is raised. In addition, after electrons are excited to the conduction band, the empty states left in the valence band can contribute to the conduction process.
Electrons & holes:
As the temperature of a semiconductor is raised from 0 K, some electrons in the valence band receive enough thermal energy to be excited across the
band gap to the conduction band.
- The result is a material with some electrons in an otherwise empty conduction band and some unoccupied states in an otherwise filled valence band that is shown in fig given below.
- For convenience, an empty state in the valence band is referred to as a hole.
- If the conduction band electron and the hole are created by the excitation of a valence band electron to the conduction band, they are called an electron-hole pair (abbreviated EHP).
- After excitation to the conduction band, an electron is surrounded by a large number of unoccupied energy states.
- For example, the equilibrium number of electron-hole pairs in pure Si at room temperature is only about 1010 EHP/cm3, compared to the Si atom density of 5 X 1022 atoms/cm3.
- Thus the few electrons in the conduction band are free to move about via the many available empty states.
In a filled band, all available energy states are occupied. For every electron moving with a given velocity, there is an equal and opposite electron motion
elsewhere in the band.
- If we apply an electric field, the net current is zero because for every electron j moving with velocity vj there is a corresponding electron j' with velocity -vj
Figure given below illustrates this effect in terms of the electron energy vs wave vector plot for the valence band. Since k is proportional to electron momentum, it is clear the two electrons have oppositely directed velocities. With N electrons/cm3 in the band we express the current density using a sum over all of the electron velocities, and including the charge — q on each electron. In a unit volume,
Now if we create a hole by removing the jth electron, the net current density in the valence band involves the sum over all velocities, minus the contribution
of the electron we have removed:
But the first term is zero, from Eq. 1.Thus the net current is qVj. In other words, the current contribution of the hole is equivalent to that of a positively charged particle with velocity vj that of the missing electron. Of course, the charge transport is actually due to the motion of the new uncompensated electron (j'). Its current contribution ( - q) (-vj) is equivalent to that of a positively charged particle with velocity vj.For simplicity, it is customary to treat empty states in the valence band as charge carriers with positive charge and positive mass.