Material systems
A transistor requires silicon with fewer than one foreign atom per billion. Reaching that purity is a problem of separating mixtures, and it is solved with a technique you can understand from what is covered in this unit.
01How what is there gets classified
Everything you can touch is a material system, and the first question is whether it has a single composition or several. The whole classification follows from that:
| System | Phases | Separated | Example from the workshop |
|---|---|---|---|
| Simple pure substance | One | Cannot be separated | Copper from a wire, tin |
| Compound pure substance | One | Only by chemical reaction | Silicon oxide, water |
| Solution | One, but several components | By physical methods | Solder alloy, bronze |
| Heterogeneous mixture | Two or more | By physical methods, by sight | Solder paste, rosin flux |
The distinction between phase and component is the one most often confused. A phase is a portion with uniform properties and a visible boundary; a component is each substance present. Molten tin–lead solder is a single phase with two components: the separation cannot be seen, and that is why it is a solution. When it cools badly, on the other hand, two phases appear, and that is one of the causes of cold solder joints.
Almost all the materials in a circuit are solid solutions: the bronze of a connector, the brass of a plug, the steel of a chassis, the alloy of a solder. Their properties —conductivity, melting point, hardness— depend on the proportion, not on the components taken separately. And the most important of all, doped silicon, is a solid solution with a concentration of parts per million.
02Separating: choosing the property that differs
Every separation method relies on a property in which the components do not coincide. Choosing the method is choosing that property:
| Method | Relies on | Used for |
|---|---|---|
| Filtration | Particle size | Solid in liquid |
| Decantation | Density | Immiscible liquids, solids that settle |
| Distillation | Boiling point | Liquid solutions |
| Crystallization | Solubility | Dissolved solid |
| Chromatography | Affinity for two phases | Complex mixtures, analysis |
| Zone refining | Different solubility in solid and in liquid | Purifying metals and semiconductors |
The last row is the one that produces the silicon for transistors, and it deserves a section of its own because it is the method that makes it possible to reach purities that no other method achieves.
03Zone refining, which is how silicon is purified
The idea is remarkably simple. When a mixture melts and solidifies again, the impurities are not distributed equally between the solid and the liquid: they almost always prefer to stay in the liquid. That preference is measured with the distribution coefficient:
The method takes advantage of this: a narrow zone of a bar is melted and made to travel from one end to the other. At each position, the solid that crystallizes behind leaves its impurities in the liquid, and the molten zone carries them away. After several passes, the impurities end up concentrated at one end, which is cut off and discarded.
A bar with impurities spread evenly. Each pass melts a zone that travels along the bar from left to right, carrying the impurities along. Watch how the left end gets cleaned and the right end gets dirtier.
04Purity grades, and what they mean
In industry, purity is stated in “nines”: 4N is 99.99 %, and 9N is 99.9999999 %. Each nine is a factor of ten fewer impurities.
| Grade | Purity | Impurities | What it is good enough for |
|---|---|---|---|
| Metallurgical | 98 % | 2 in every 100 | Steel alloys, silicones |
| Solar, 6N | 99.9999 % | 1 ppm | Photovoltaic panels |
| Electronic, 9N to 11N | 99.9999999 % | 1 part in a billion | Wafers for integrated circuits |
The last row is hard to put in perspective. One part in a billion, in silicon, is about \( 5\times10^{13} \) foreign atoms per cubic centimeter. And that is still too much for some applications: the silicon used as a substrate is made with fewer than \( 10^{12} \) electrically active impurities, because the deliberate doping that comes afterward is \( 10^{15} \) to \( 10^{19} \), and the impurity left over has to be negligible compared with that.
All that purification ends in a material that is useless as it stands: pure silicon is a poor conductor and a poor insulator. What is done afterward is to add impurities to it in a controlled way —doping— in the exact amount and in the exact place. Purifying to the extreme makes sense precisely because the next step is to contaminate with precision: you cannot control what you add if you do not know what was there before.
05In the lab
Take ten materials from the workshop —tin, solder, flux, isopropyl alcohol, the plastic of a connector, copper, ferrite, thermal paste— and classify each one as a pure substance or a mixture, indicating phases and components. Justify the doubtful ones.
Separate a mixture of water and alcohol by simple distillation, measuring the vapor temperature every minute. Plot temperature against time and identify the plateaus that correspond to each component.
With \( k = 0.1 \) and a zone of 10 % of the bar, estimate how many passes are needed for the first tenth of the bar to drop its concentration a hundredfold. Compare with the lab above and explain why, beyond a certain number, additional passes stop improving the result.
06Common mistakes
- Confusing phase with component. A solution has several components and a single phase.
- Believing that a homogeneous mixture always looks homogeneous. What defines the phase is the properties, not the appearance to the naked eye.
- Thinking that a separation method is universal. Each one exploits a different property; if the components coincide in it, it does not work.
- Assuming that \( k \) is always less than 1. There are impurities with \( k \gt 1 \), which concentrate the other way around and have to be swept in the opposite direction.
- Believing that more passes always purify more. A limiting distribution is reached and it goes no further.
07Self-assessment
Is tin–lead solder a pure substance?
No: it is a solid solution, with two components and a single phase when it is properly cooled.
What does distillation rely on?
On the difference between the boiling points of the components.
What does \( k = 0.35 \) mean?
That the solid that crystallizes has 35 % of the impurity concentration that the liquid had: it comes out purer.
Why does zone refining need several passes?
Because each pass carries away only part of the impurity. The successive ones keep moving what is left toward the far end.
How many impurities does 9N silicon have?
One part in a billion, on the order of \( 5\times10^{13} \) atoms per cubic centimeter.
Why purify so much if it is going to be doped afterward?
Because the doping has to be controlled. If impurities of the same order were left, you would not know what electrical concentration you are introducing.
08Further reading
- Raymond Chang and Kenneth A. Goldsby. Chemistry. 12th ed. (Spanish edition, “Química”), McGraw-Hill, 2017. Chapter 1, with the classification of matter and the separation methods.
- 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. Solid solutions, phase diagrams and why an alloy does not behave like its components.
- Ben G. Streetman and Sanjay Banerjee. Solid State Electronic Devices. 7th ed., Pearson, 2015. Chapter 1 describes the growth and purification of silicon as it is done in industry.