Structure of matter
That silicon has four valence electrons and phosphorus has five is not an isolated fact: it is the reason one forms crystals and the other serves to dope them. All of solid-state electronics starts here.
01Where the electrons are
The Bohr model —electrons circling in orbits— is enough to draw a picture, but not to explain. The current model says that an electron has no trajectory but a probability distribution, and that its state is described by four numbers:
| Number | What it says | Values |
|---|---|---|
| \( n \), principal | The energy level, the “size” | 1, 2, 3, … |
| \( \ell \), azimuthal | The shape of the orbital | 0 to \( n-1 \): s, p, d, f |
| \( m_\ell \), magnetic | The orientation in space | \( -\ell \) to \( +\ell \) |
| \( m_s \), spin | The electron's own spin | \( +\tfrac12 \) or \( -\tfrac12 \) |
And acting on those four numbers is the Pauli exclusion principle: two electrons of the same atom cannot have all four equal. That prohibition is what forces electrons to fill ever higher levels instead of all piling up in the lowest one, and the whole periodic table follows from it.
02The filling order, and the table that results
Electrons first occupy the sublevels of lowest energy —the Aufbau rule— following the order \( 1s\,2s\,2p\,3s\,3p\,4s\,3d\,4p\ldots \), which does not coincide with the order of \( n \). In sublevels with several orbitals, Hund's rule says that electrons are distributed one at a time before pairing up.
The periodic table is that filling order, drawn out. The columns group elements with the same valence configuration, and that is why they are chemically similar.
Tap an element and its configuration, its valence electrons and the role it plays in electronics appear. Groups 13, 14 and 15 are highlighted: they are the groups of the semiconductors and their dopants.
03Why silicon and not something else
Group 14 —carbon, silicon, germanium— has four valence electrons, which is exactly half of the eight that fit. That allows them to form four covalent bonds in a perfect three-dimensional lattice, in which all the electrons are committed.
| Group | Valence | In silicon it acts as | Examples |
|---|---|---|---|
| 13 | 3 | Acceptor: one electron is missing, leaving a hole | Boron, aluminum, gallium, indium |
| 14 | 4 | The crystal itself | Carbon, silicon, germanium |
| 15 | 5 | Donor: one electron is left over, and it becomes free | Phosphorus, arsenic, antimony |
That is all of solid-state electronics in three lines. Pure silicon does not conduct well because it has no free electrons; by adding one group 15 atom per million, one out of every million positions has an extra electron, and that electron can move. With group 13 the opposite happens: an electron is missing, and the hole moves as if it were a positive charge.
The first transistors were made of germanium, from the same group 14. It lost to silicon for two chemical reasons: its band gap is narrower —0.67 eV against 1.12— so at 70 °C it already conducts on its own, and above all its oxide is soluble in water. SiO₂, on the other hand, is stable, insulating and grows on the material itself: that is what made planar technology possible and, with it, the integrated circuit. Silicon won because of its oxide, not because of the semiconductor.
04Periodic properties
As you move across the table, several properties vary regularly because they depend on the configuration:
| Property | Moving to the right | Moving down a group |
|---|---|---|
| Atomic radius | Decreases | Increases |
| Ionization energy | Increases | Decreases |
| Electronegativity | Increases | Decreases |
| Metallic character | Decreases | Increases |
The fourth row explains a band that runs diagonally across the table: the metalloids, between the metals on the left and the nonmetals on the right. Boron, silicon, germanium, arsenic, antimony and tellurium are there, and it is no coincidence that solid-state electronics was built almost entirely from that diagonal: they are the ones that neither fully conduct nor fully insulate.
And electronegativity is what anticipates the type of bond, which is the subject of the next unit: when two atoms have very different electronegativities, the bond is ionic; when they have similar ones, covalent.
05In the lab
Write the complete electron configuration of Si, P, B, Ga, As and Cu, and mark the valence electrons in each one. Predict which ones can act as a donor or an acceptor in silicon and justify your answer.
Use a diffraction-grating spectroscope to observe the light from a sodium lamp, a mercury lamp and a white LED. Explain why the first two show lines and the third a continuous band.
Locate the six metalloids in the table and look up the resistivity of each one. Plot it on a logarithmic scale next to that of a metal and that of an insulator, and mark where doped silicon falls.
06Common mistakes
- Filling in order of \( n \). The 4s fills before the 3d; you have to follow the order of energy.
- Pairing electrons too soon. Hund's rule requires distributing them one per orbital.
- Counting all the electrons of the outermost level as valence in the transition metals. The d electrons are also involved there.
- Believing that the Bohr model describes the atom. It works as a picture, not as a model.
- Confusing electronegativity with ionization energy. One is the tendency to attract electrons in a bond; the other, the energy needed to pull one off an isolated atom.
07Self-assessment
What is the configuration of silicon?
\( 1s^2\,2s^2\,2p^6\,3s^2\,3p^2 \), with four valence electrons in the third level.
Why is phosphorus a donor in silicon?
Because it has five valence electrons: four form the bonds of the crystal and the fifth is left free to conduct.
How many electrons fit in a d sublevel?
Ten: there are five orbitals with two electrons each.
What does the Pauli principle say?
That two electrons of the same atom cannot have all four quantum numbers equal. Filling by levels follows from that.
Why did silicon win out over germanium?
Above all because of its oxide: SiO₂ is stable, insulating and grows on the material itself. Germanium's is soluble in water.
What are the metalloids?
The diagonal between metals and nonmetals: boron, silicon, germanium, arsenic, antimony and tellurium. They neither fully conduct nor fully insulate.
08Further reading
- Raymond Chang and Kenneth A. Goldsby. Chemistry. 12th ed. (Spanish edition, “Química”), McGraw-Hill, 2017. Chapters 7 and 8: atomic structure, electron configuration and periodic properties.
- Peter Atkins and Julio de Paula. Physical Chemistry. 10th ed. (Spanish edition, “Química física”), Editorial Médica Panamericana, 2018. The quantum treatment of orbitals, for those who want to see where the numbers come from.
- Ben G. Streetman and Sanjay Banerjee. Solid State Electronic Devices. 7th ed., Pearson, 2015. The step from the isolated atom to the bands of the crystal, which is the natural continuation of this unit.