Group 14 are semiconducting elements. Your question regarding s-p promotion energy has to do with the MO band theory of solids. This deals with the electronic structures of metals and materials tat behave as semiconductors.
Semiconductor: Conductivity increases w/ T low
Conductor: Conductivity decreases w/ T high
Superconductor: Conductivuty decreases w/ T infinite at low T
An insulator is simply a semiconductor with a very low conductivity. We can rationalize these conductivity behaviors using MO theory.
A semiconductor is a solid with a full band and a small band gap. There is a small thermal population of the conduction band at normal temperature, hence a small conductivity.
Element = C Band Gap = 5.47
Element = Si Band Gap = 1.12
Element = Ge Band Gap = 0.66
Element = Si Band Gap = 0
So Si and Ge are semiconductors at room T, and Sn is a conductor. Pure compounds which are electronically analogous to the group 14 elements are also semiconductors. These include the compounds boron nitride, BN, and gallium arsenide, GaAs. Note that these compounds contain one element from group 13 and one element from group 15, in a 1:1 stoichiometric ratio.
They have exactly the same number of valence electrons as a group 14 element, and will arrange these electrons in a group-14 type band structure. They are often called 3-5 compounds, to indicate that they consist of elements taken from groups 13 and 15. Similarly, 2-6 compounds such as ZnS and CdS (both of which have the zincblende structure, which is analogous to the diamond structure) function as semiconductors.
Generally, band gaps vary with position in the periodic table, but tend to decrease with increasing MW of the semiconductor.
The temperature dependence of conductivity is readily understood within the framework of band theory. For a conductor, promotion of electrons is facile within a band at any T.
However, As T increases, vibrational motions of the metal atoms in the lattice increases and interferes with the motion of the conducting electrons. The result is a decrease in conductivity as T increases.
For a semiconductor, an increase in T causes an exponential increase in the population of the conduction band, because of the Boltzmann distribution.
Therefore the conductivity of semiconductors increases dramatically with T. Because an insulator is actually a semiconductor with a large band gap, the conductivity of an insulator should also increase markedly if the temperature is made high enough.
REF: Introduction to MO Theory