Electrons and Holes

• For T> 0 K, there would be some electrons in the otherwise empty conduction band, and some empty states in the otherwise filled valence band.
• The empty states in the valence band are referred to as holes.
• If the conduction band electron and the valence band hole are created by thermal excitation of a valence band electron to the conduction band, then they are called electron-hole pair (EHP).
• After excitation to the conduction band, an electron is surrounded via a large number of empty states, for example the equilibrium number of EHPs at 300 K in Si is ∼10¹⁰/cm³, whereas the Si atom density is ∼10²²/cm³ .
• Thus, the electrons in the conduction band are free to move about via the many available empty states.
• Corresponding problem of charge transport in the valence band is slightly more complex.
• Current transport in the valence band can be accounted for by keeping track of the holes themselves.
• 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 somewhere else in the band.
• Under an applied electric field, the net current is zero, since for every electron j moving with a velocity V_j , there is a corresponding electron j moving with a velocity - V_j .
• In a unit volume, the current density J can be given by

(filled band)   (2)

• where N is the number of electrons/cm³ in the band, and q is the electronic charge.
• Now, if the j^th electron is removed and a hole is created in the valence band, after that the net current density

• Thus, the current contribution of the empty state (hole), obtained by removing the jth electron, is equivalent to that of a positively charged particle with velocity V_j.
• Note that actually this transport is accounted for by the motion of the uncompensated electron j having a charge of q and moving with a velocity V_j.
• Its current contribution (-q) (-V_j) is equivalent to that of a positively charged particle with velocity + V_j.
• For simplicity, therefore, the empty states in the valence band are called holes, and they are assigned positive charge and positive mass.
• The electron energy increases as one move up the conduction band, and electrons gravitate downward towards the bottom of the conduction band.
• On the other hand, hole energy increases as one moves down the valence band (since holes have positive charges), and holes gravitate upwards towards the top of the valence band.