Читать книгу Semiconductor Basics - George Domingo - Страница 22

Four quantum numbers uniquely define an electron:

 The principal quantum number, n, defines the orbits and, therefore, the energy of the electrons. The energy released or absorbed as the electrons change orbits is determined exclusively by the value of n. The allowed values of n are any positive integers: 1, 2, 3, 4, etc.

 Electrons have two spins: up and down.

 Electrons also have angular momentum. The angular quantum number, ℓ, is associated with the shape of the orbits. The value of ℓ is also an integer number between 0 and n.

 The magnetic quantum number, ml, is associated with the orientation of the orbits. It is also an integer number between –ℓ and +ℓ.

Electrons follow these rules:

 The electrons in the first orbit, n = 1, can have two spins, but both ℓ and ml are 0. Thus the first orbit can hold only two electrons.

 The electrons in the second orbit, n = 2, can have two spins and two angular quantum numbers (ℓ equal to 0 or 1). Associated with ℓ = 0, only one ml value is possible, ml = 0. But for ℓ = 1, there are three possible values of ml: −1, 0, and +1. So, the total number of electrons in the second orbit is eight: that is, four ml times two spins each.

 You can do the calculations and prove that the third orbit can hold up to 18 electrons, and so on.

Figure 1.16 shows one way of visualizing these levels, including the relative energy of the orbits of the Bohr atom and the order in which the orbits are filled. At 0 K absolute temperature, the electrons first fill up the 1s band (two electrons), the next two electrons reside in the 2s band, and the next six are in the 2p band, etc., climbing up the energy level stairs. Note that level 4s fills up before 3d. (By the way, the letters mean s for sharp, p for principle, d for diffuse, and f for fundamental.)

Another point you may wonder about is why we write the 3d level at higher energy than the 4s level. There is quite a debate about explaining this. It has to do with the attraction and repulsion of electrons and protons, and I will leave it at that.

Figure 1.16 Subshell electron capacity. Notice that the number of sites in each level increases as the energy level, n, increases. Also notice that the 3d level has lower energy than the 4s level.