In quantum free electron theory of metals the electrons were assumed to be moving in a region of constant potential and hence it moves freely about the crystal
ELECTRON
IN PERIODIC POTENTIAL
In
quantum free electron theory of metals the electrons were assumed to be moving
in a region of constant potential and hence it moves freely about the crystal.
But it fails to explain why some solids behaves as conductors, some as
insulators and some an semiconductors etc.
Therefore
instead of considering an electron to move in a constant potential, In Zone
theory of solids the electrons are assumed to move in a field of periodic
potential.
In
a metal piece, the positive ions are arranged in a regular and proper order,
therefore a periodic potential (i.e) the potential field which varies
periodically with the same period as the lattice, exists in the metal. Also the
potential is minimum near the centre of positive ions and is maximum between
the centres of ions as shown in Fig. 1.13.
Therefore
the potential energy of the electron near by the centre of positive ion is
maximum and will not be able to move freely, but the electrons which are above
these potential peaks are free to move inside the metal and hence they are
termed as free electrons.
Physics for Information Science: Unit I: Electrical Properties of Materials : Tag: : - Electron in Periodic Potential
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