Electrons and holes, Electrical Engineering

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 Vj , there is a corresponding electron j moving with a velocity - Vj .
  • In a unit volume, the current density J can be given by

1147_Electrons and Holes 1.png (filled band)   (2)

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

1055_Electrons and Holes 2.png

  • 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 Vj.
  • 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 Vj.
  • Its current contribution (-q) (-Vj) is equivalent to that of a positively charged particle with velocity + Vj.
  • 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.
Posted Date: 1/11/2013 4:30:30 AM | Location : United States







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