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If I have a semiconductor with a lot of defects what happens to its conductivity at at mK type temperatures? I'm expecting that defects would give rise to greater conductivity than for a perfect crystalline semiconductor. Does anyone know details? I'm particularly interested in silicon deposited by physical vapor deposition. Thanks.

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Your idea is correct: at low temperatures, "dirty" or doped semiconductors conduct better than clean ones. In fact, doping has been very seriously studied not just to tune the conductivity of semiconductors but to obtain spatial control of conductivity by doping profiles, so you can really pattern a circuit made of doped silicon in silicon.

The way it works is that the impurities add states to the band structure. Be careful, these states are localized therefore they do not have a well defined momentum. As you add more dopants, the trapped states will grow closer to each other until conductivity becomes possible by hopping. You then say that you added an "impurity band" to the semiconductor.

Things are of course more complicated because the dopants may be either electron donors (n type) or acceptors (p type). To create n-type regions, arsenic (As), arsine (AsH3), phosphine (PH3) and antimony (Sb) are commonly used. For p-type regions, typical dopants are boron (B), Boron Difluoride (BF2) and Boron Trifluoride (BF3). The type of dopants affects the type of band you create - a band of holes or of electrons, and also affects the bandgap as the dopants are charged. The presence of charge will shift the bands, yet the added density of charge carriers will reduce the screening length.

If you are interested in specific physical properties, you will have to consult the infinite literature on semiconductor properties, although you will easily find values for the common dopants at vraious concentrations in high quality silicon.

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