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I was reading text about n-type doping and it said:

'Such impurities are called donors for they donate electrons. Notice that in this case, no hole is created in conjunction with the creation of a conduction electron.'

I am not sure how they don't leave a hole? A Phosphorus atom would bond with the silicone and have one electron left over, when they loose this electron to the conduction band, they would be ionised, then will have a positive charge, would this not attract further electrons? Is it not a hole?

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  • $\begingroup$ or is it that the holes are on the donors level and not in the valence band so do not affect p? $\endgroup$ – birdleaf Feb 22 '18 at 16:45
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    $\begingroup$ The positive charge on the donor atom is not mobile, and is not part of the band structure since it is a localized state. So, no, it is not a hole. $\endgroup$ – Jon Custer Feb 22 '18 at 16:59
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The phosphorus atom has 5 valence electrons. When put into a lattice site of the silicon crystal it bonds with four electrons in covalent bonding pairs to the neighboring Si atoms which leaves one electron not in a covalent bond. At room temperature, this electron (charge -e) can easily leave the phosphorus atom leaving the immobile positively charged (+e) atom in the lattice behind. At low temperatures, the positively charged P center can catch an electron from the conduction band so that it is bound to the center like in an hydrogen atom. The phosphorus is called a donor, because it donates an electron to the conduction band. No hole in the valence band is produced in this process.

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Yes, the phosphorous atom would become positively charged when it becomes ionized due to the ambient temperature and its electron wanders away, but that's not what is meant by a "hole". A "hole" is not simply a positively charged object in the lattice. You have to move beyond a classical picture and think in terms of quantum mechanics and electronic band theory, which is where the concept of "holes" really arises. "Holes" are empty states in nearly filled electronic bands. Due to their behavior under electric fields, these empty states can equivalently be thought of as mobile, positively charged quasi-particles (i.e., "holes") with characteristics dictated by the electronic bands. Your phosphorous ion is something completely different. True, it is positively charged, but it does not move according to the material's electronic band structure and in fact is not mobile at all. It's simply a static, immobile entity in the crystalline lattice.

Bottom line: "Holes" are mobile, positively charged quasi-particles whose behavior is determined by the electronic band structure of the material.

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It's not an answer is a comment. Phosphorous atom have 5 electrons at valence shell and when you put this atom in silicon lattice with 4 electrons at valence shell you will creating an one extra electron. I think that all depends at covalent bonds becuase 4 electrons are in pair with adjacent silicon electrons and the fifth electron can easly (need small amount of energy - room temperature enough) go away to conduction band. And it will be no hole in covalent bonds. Thats how I image this. But your question are very interesting and i will wating for answer.

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