Video Transcript
The following diagrams show a lattice of silicon atoms. Which of the diagrams shows the lattice at a higher temperature? Our answer options are this lattice here marked as (A), this lattice here marked as (B), or (C) that both diagrams show the lattice at the same temperature.
Considering the element that these lattices are made of, we can recall that a single neutral silicon atom has four electrons in its valence electron shell. When silicon atoms form a lattice, bonds form between adjacent atoms. These bonds allow for the sharing of valence electrons between adjacent atoms. The overall effect is that silicon atoms within the bulk of the lattice, that is, those in its interior, now have a full complement of eight valence electrons.
Because silicon is a semiconductor, the electrons in its valence shell are not very far away, energetically speaking, from becoming conducting electrons. That is, it only takes a small amount of energy to turn a valence electron in a silicon atom into a free electron. The energy that does this is typically from the thermal energy of the silicon lattice’s environment. A typical indicator of this energy is the temperature of the lattice. A lattice at higher temperature will have more thermal energy available to be transferred to valence electrons in the lattice. As we’ve seen, when that happens, a valence electron is likely to become a free electron, free to move about throughout the lattice.
If we look at diagram (A), we see here all of the valence electrons, indicated by small blue dots, as fixed in place around each atomic nucleus. If we pick one of the interior atomic nuclei, say this one right here, then we can see that this nucleus has one, two, three, four, five, six, seven, eight electrons in its valence shell. And indeed, as we look across all the interior atoms in our lattice in diagram (A), we see that each one of them also has eight valence electrons. This diagram then shows us a lattice where the temperature is so low that none of the valence electrons, as far as we can see, have been liberated to become free electrons. If a lattice has literally zero free electrons, that indicates a lattice at the lowest possible temperature, absolute zero.
In contrast, the lattice shown in diagram (B) does have free electrons. For example, there’s one here indicated by the fact that it’s in motion and one here and one here and so on. Notice that along with free electrons in this lattice, there are also holes or vacancies. Here’s a vacancy and here’s a vacancy and here’s a vacancy and so forth. The lattice in diagram (B) then indicates a lattice at a high-enough temperature that some of the valence electrons have been liberated to become free electrons, leaving holes behind them. This lattice, we can say, has had more thermal energy transferred to it and therefore exists at a higher temperature than the lattice shown in diagram (A).
It’s not true then that both diagrams show the lattice at the same temperature. For our answer, we choose option (B).
