Chemical bonding
Whether a material conducts, insulates or lies in between depends not on its atoms but on how they bond. Energy bands come from that, and from the bands comes every solid-state device.
01Three ways of sharing electrons
Atoms bond because doing so lowers their energy, and they do it in three ways depending on how hard they contest the electrons. What decides it is electronegativity: the tendency of each atom to pull the bond's electrons toward itself.
| Bond | Difference \( \Delta\chi \) | What happens | Example |
|---|---|---|---|
| Ionic | \( \gt 1.7 \) | One tears them away from the other: ions are left | NaCl, metal oxides |
| Polar covalent | \( 0.4 \) to \( 1.7 \) | They share them, but unevenly | H₂O, SiO₂ |
| Nonpolar covalent | \( \lt 0.4 \) | They share them equally | Si—Si, diamond |
| Metallic | Between metals | The electrons come loose and belong to all | Cu, Al, Au |
The third row is the bond of silicon with itself: four electrons shared with four neighbors, all committed, none free. And the fourth explains why metals conduct: their valence electrons do not belong to any particular atom, but form a cloud that moves under any applied field.
Between molecules act much weaker forces —dipole–dipole, hydrogen bonding, London— that do not form compounds but do determine the melting point, the viscosity and the adhesion. On them depend flux wetting the surface, an epoxy resin sticking, and isopropyl alcohol carrying away dirt and then evaporating by itself.
02From bonds to bands
In an isolated atom the electrons have discrete levels. When two atoms are brought together, each level splits in two; with \( N \) atoms, into \( N \) levels so close together that they form a continuous band. That is what happens in a crystal, where \( N \) is on the order of \( 10^{23} \).
Between two bands there may be a gap of forbidden energies, the band gap or gap. And all electrical conduction is explained by two questions: whether the valence band is full, and how wide the gap is that separates it from the next one.
| Material | Bands | It conducts because… |
|---|---|---|
| Metal | The last band is half full | There are empty states right next to it: a minimal field moves the electrons |
| Insulator | Full valence band, gap of more than 4 eV | It does not conduct: no electron gathers enough energy to jump |
| Semiconductor | Full valence band, gap of 0.5 to 3 eV | At room temperature a few jump, and doping controls how many |
How many electrons jump through thermal agitation comes from an exponential, and that is the formula that governs the behavior of every solid-state device:
The band gap drawn to scale and the carriers that temperature manages to promote. Change the material and the temperature, and watch the orders of magnitude.
03What doping does to the bands
A phosphorus atom in the lattice contributes an electron that finds no bond to fit into. That electron sits in a level of its own, only 0.045 eV below the conduction band, and with such a small distance thermal agitation promotes it effortlessly: at room temperature, practically all the dopants are ionized.
| Level | Distance to its band | Compare with |
|---|---|---|
| Phosphorus in silicon, donor | 0.045 eV below the conduction band | \( kT = 0.026 \) eV |
| Boron in silicon, acceptor | 0.045 eV above the valence band | It ionizes just as easily |
| Gold in silicon, trap | 0.54 eV, in the middle | It does not contribute carriers: it captures them |
The third row shows the other side. An impurity with a level in the middle of the gap does not dope: it acts as a recombination center, trapping electron–hole pairs. That is a misfortune in an ordinary transistor, and it is used on purpose in fast diodes, where it matters that the carriers disappear as soon as possible so that switching can be faster.
04In the lab
Look up the electronegativities of Si, O, Na, Cl, Cu and Ga, calculate \( \Delta\chi \) for SiO₂, NaCl, GaAs and a Cu–Zn alloy, and classify each bond. Compare with the known properties of each material.
Measure the reverse current of a germanium diode and a silicon diode while heating them with a hot-air gun from 25 to 90 °C. Plot on a logarithmic scale and compare the slopes with what \( e^{-E_g/2kT} \) predicts.
Measure the resistance of an NTC thermistor between 0 and 80 °C, linearize with \( \ln R \) against \( 1/T \) and obtain its constant \( \beta \). Relate that constant to the band gap of the thermistor material.
05Common mistakes
- Believing that a bond is either ionic or covalent. It is a continuum; almost all bonds have something of both.
- Thinking that an insulator never conducts. It conducts with sufficient fields: that is dielectric breakdown.
- Confusing the band gap with a potential barrier. One belongs to the material; the other, to the junction.
- Forgetting that \( n_i \) depends exponentially on temperature. Doubling the degrees does not double the carriers: it multiplies them.
- Assuming that every impurity dopes. Deep-level ones capture carriers instead of contributing them.
06Self-assessment
What type of bond does SiO₂ have?
Polar covalent: \( \Delta\chi \approx 1.5 \), close to the boundary with the ionic.
Why does a metal conduct?
Because its last band is half full: there are empty states right next to the occupied ones and any field moves the electrons.
What is the value of \( kT \) at room temperature?
0.026 eV, about 26 mV. It is the number that appears in the diode equation.
Why does germanium fail at 70 °C and silicon does not?
Because its band gap is almost half as wide, and \( n_i \) grows exponentially: at that temperature it already conducts by itself and the doping stops being in charge.
What does gold do in silicon?
It creates a deep level that captures electron–hole pairs. It is used deliberately to make fast diodes.
Why are SiC and GaN suitable for power applications?
Their wide band gap lets them work at temperatures and voltages where silicon already conducts on its own.
07Further reading
- Raymond Chang and Kenneth A. Goldsby. Chemistry. 12th ed. (Spanish edition, “Química”), McGraw-Hill, 2017. Chapters 9 and 10: ionic, covalent and metallic bonding, with the electronegativity scale.
- William D. Callister and David G. Rethwisch. Materials Science and Engineering: An Introduction. 9th ed. (Spanish edition, “Introducción a la ciencia e ingeniería de los materiales”), Reverté, 2019. The step from bonds to bands, with the comparison between metals, ceramics and polymers.
- Ben G. Streetman and Sanjay Banerjee. Solid State Electronic Devices. 7th ed., Pearson, 2015. Bands, intrinsic concentration and impurity levels, with the numerical values for silicon.