My question relates to semiconductor physics. The relationship between energy E and wavenumber k for the Kronig-Penny model looks like this, where a is the period of the potential function:
I am referring to a statement made in the book Advanced Semiconductor Fundamentals, 2nd Edition by Robert F. Pierret, page 61. In reference to the E-k diagram of the Kronig-Penney model it says:
...the energy band slope dE/dk is zero at the k-zone boundaries.
and referring to the gradient:
This is a feature common to all E-k plots, even those characterizing real materials.
Why is the gradient zero at the k-zone boundaries (i.e. edges of Brillouin zones)? What does it signify?