An attempt:
as you know:
consider the bohr model of hydrogen:
an electron can orbit the nucleus only in specific quantum levels
the lowest level, n = 1, is at -13.6 eV
the next level, n = 2, is at -3.4 eV
the next level, n = 3, is at -1.5 eV
reference:
http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html
these hydrogen energy levels are potential energy
when the electron is at energy level 0 eV, it is no longer bound to the nucleus
when the electron is at an energy > 0 eV, it has some kinetic energy, hence some velocity and is therefore moving,
free from the nucleus
the electron can only change potential energy level by emitting or absorbing the exact energy requiared for the transition,
say 10.2 eV for the change between n = 1 and n = 2
the energy is absorbed when the electron moves from 1 to 2
the energy is emitted when the electron moves from 2 to 1.
also, as you know:
instead of discrete levels, as in hydrogen, bulk materials show the energy in bands
for materials, there is the valence band and the conduction band
with an energy gap between the top of the valence band and the bottom of the conduction band.
the spacing between the bands determines if the material is an insulator, semiconductor
or conductor
the energy diagram is a graph of the energy available to electrons in the material
the valence band represents the energy available to the outer shell of the atom of the material
this is the region where the electrons are bound to their individual atoms
as they do not have enough energy to be free of their nucleus.
the conduction band is where the electron have sufficient energy to move around essentially freely
like the electron with energy > 0 eV in hydrogen
the gap in between is the (so-called) forbidden region
what this really means is that we do not see electrons at that energy level
in insulators, the band gap is relatively large, hence electrons are NOT free to move about
in conductors, the band gap is does not really exist - the valence band and the conduction band overlap
therefore, at least some of the electrons are free to move about
good conductors (silver, gold, copper) have a larger overlap than poor conductors (lead).
in semiconductors, the band gap is relatively small
by adding dopants (contaminants) we control the band gap and the behavior of electrons between
the valence and conduction bands
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/band.html#c4
now KE and PE:
the energy levels in individual atoms (such as hydrogen) are KE levels
the lower limit of the conduction band Ec (as you called it) is like one of these atomic
energy levels - potential energy
when the electron is "higher" in the energy level diagram, i.e. higher in the conduction band,
that additional energy is kinetic energy.
i hope this helps a little
i am afraid i may have only re-stated what you already know.