Now I understand!
Empty bands do not contain electrons and therefore are not expected to contribute to the electrical conductivity of the material.
Completely filled bands do contain plenty of electrons but do not contribute to the conductivity of the material!
Tofik, you are on the right track. But do you understand why?
In crystals, electrons are no point objects but may bee seen als Bloch wave type objects. Bloch states are (among others) characterized by their momentum. For every state with given momentum there is an equivalent state with opposite momentum (except for topological surface states, but that is a very contemporary, special and nontrivial case!!). Without any field applied, electron states are filled (at zero temperature, say, which makes it easier to argue) up to the Fermi level. Since all equivalent states with opposite momenta are either all occupied or all unoccupied, there is no net momentum and therefore no net flow of charges. Applying an electric field accelerates electrons in one specific direction and the electron gain extra momentum in that direction: hitherfore unoccupied states now get occupied at the expense of others.
In terms of the original distribution of occupied states this new arrangement of occupied and unoccupied states represents an excitation (it would cost energy to produce this reshuffling of electrons).
In a semiconductor you have a band gap between occupied and unoccupied states (in contrast to metals, where bands crossing the Fermi level are partially filled). in metals, the reshuffling of electrons "in momentum space" (= reciprocal space) can be started at quasi zero energy. In semiconductors you have to pay the band gap energy. A normal electric field (=voltage, applied to the solid) cannot promote the electrons that high. Therefore the reshuffling of states, required to build a current carrying state, is suppressed and there is no conduction.
Empty conduction band means there are no electrons with sufficient energy for conduction.
Similarly, full valence band means, all the electrons have energy lower than the required to be in CB.
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