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SchroedingersLion
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- TL;DR Summary
- How are acceptor levels formed? Doped semiconductors.
Greetings,
I have troubles at getting a good intuition on how acceptor energy levels are formed above the valence band in p-doped semiconductors.
Ashcroft describes the following scenario:
With n-type doping, the added impurity can be modeled as a positive ion with an additional electron. The ion has enough valence electrons to perfectly form the typical covalent bonds with neighboring atoms, as if it was part of the intrinsic semiconductor. Now, due to the attraction of the electron and the ion, the energy state of the electron is not part of the conduction band but slightly below that level: It would take a bit of energy to break the attraction to the ion.
With p-type doping it is the same, only now the impurity can be modeled as a negatively charged ion that forms the covalent bonds with neighboring atoms, coupled to a weakly bound positively charged particle (hole).
Now, I have troubles understanding the p-type model. How can the impurity form covalent bonds if one electron is missing? This should be impossible. The very naive picture is that electrons from other covalent bonds can 'jump in', but this would already correspond to the state where the hole entered the valence band, which is initially not true as it should still be bound to the impurity.
I have taken a look into a more advanced book by Jenö Sólyum who writes:
"On the other hand, the outermost shell of elements of group IIIA is one electron short compared to silicon. With spatially well localized covalent bonds in mind this implies that in samples doped with such impurities the number of electrons per impurity atom is one less than what would be necessary to form valence bonds. The formation of the chemical bond requires an additional electron, creating an electron deficiency, an apparently positively charged hole. Such impurities are called acceptors.
One would expect that the electron deficiencies brought about by the covalent bonds in the presence of acceptors give rise to empty states, holes, in the valence band [the naive picture I described above and which many undergraduate courses introduce]. This is not the case, as the states in the valence band are reorganized by the impurity potential. When the bonds are formed, the acceptor can be considered as a negatively charged ion, which therefore repels other electrons. The repulsive potential pushes a state outside the continuum, above the band. Since the impurity does not change the total number of possible electron states, there remain one less state in the band as without the impurity. Thus,in spite of the electron deficiency, the valence band is completely filled in the ground state, and there is one electron per impurity atom in the bound state above the band. Since this level could accommodate two electrons, one may say that acceptors add weakly bound holes to the system."
So how exactly can the acceptor impurity form covalent bonds if there is an electron missing? I need four electrons, but I only have three.
Sure, I can act as if I had 4 electrons (=negatively charged ion) and an additional hole and then do the maths, but in reality, there are still only 3 electrons, so it is impossible to form the covalent bonds.
He said "the states in the valence band are reorganized by the impurity potential". What exactly does this mean? Does this mean the typical covalent bond structure does not apply to the impurity and it can 'somehow' form bonds with one electron less? Or that one of the three electrons or neighboring electrons does twice the 'work' and thus the impurity can be considered as negatively charged since the number of electrons that reside in its proximity to form the bonds is greater than the actual number of impurity valence electrons and, to compensate for this, we have to introduce the positively charged hole?
And even if I accept the model of negatively charged impurity + attached hole:
One electron is pushed out of the continuum into the acceptor state. Which electron is it? Is it one of the valence electrons that are part of the bonds of the impurity?
Please help me understand this conceptually.
SL
I have troubles at getting a good intuition on how acceptor energy levels are formed above the valence band in p-doped semiconductors.
Ashcroft describes the following scenario:
With n-type doping, the added impurity can be modeled as a positive ion with an additional electron. The ion has enough valence electrons to perfectly form the typical covalent bonds with neighboring atoms, as if it was part of the intrinsic semiconductor. Now, due to the attraction of the electron and the ion, the energy state of the electron is not part of the conduction band but slightly below that level: It would take a bit of energy to break the attraction to the ion.
With p-type doping it is the same, only now the impurity can be modeled as a negatively charged ion that forms the covalent bonds with neighboring atoms, coupled to a weakly bound positively charged particle (hole).
Now, I have troubles understanding the p-type model. How can the impurity form covalent bonds if one electron is missing? This should be impossible. The very naive picture is that electrons from other covalent bonds can 'jump in', but this would already correspond to the state where the hole entered the valence band, which is initially not true as it should still be bound to the impurity.
I have taken a look into a more advanced book by Jenö Sólyum who writes:
"On the other hand, the outermost shell of elements of group IIIA is one electron short compared to silicon. With spatially well localized covalent bonds in mind this implies that in samples doped with such impurities the number of electrons per impurity atom is one less than what would be necessary to form valence bonds. The formation of the chemical bond requires an additional electron, creating an electron deficiency, an apparently positively charged hole. Such impurities are called acceptors.
One would expect that the electron deficiencies brought about by the covalent bonds in the presence of acceptors give rise to empty states, holes, in the valence band [the naive picture I described above and which many undergraduate courses introduce]. This is not the case, as the states in the valence band are reorganized by the impurity potential. When the bonds are formed, the acceptor can be considered as a negatively charged ion, which therefore repels other electrons. The repulsive potential pushes a state outside the continuum, above the band. Since the impurity does not change the total number of possible electron states, there remain one less state in the band as without the impurity. Thus,in spite of the electron deficiency, the valence band is completely filled in the ground state, and there is one electron per impurity atom in the bound state above the band. Since this level could accommodate two electrons, one may say that acceptors add weakly bound holes to the system."
So how exactly can the acceptor impurity form covalent bonds if there is an electron missing? I need four electrons, but I only have three.
Sure, I can act as if I had 4 electrons (=negatively charged ion) and an additional hole and then do the maths, but in reality, there are still only 3 electrons, so it is impossible to form the covalent bonds.
He said "the states in the valence band are reorganized by the impurity potential". What exactly does this mean? Does this mean the typical covalent bond structure does not apply to the impurity and it can 'somehow' form bonds with one electron less? Or that one of the three electrons or neighboring electrons does twice the 'work' and thus the impurity can be considered as negatively charged since the number of electrons that reside in its proximity to form the bonds is greater than the actual number of impurity valence electrons and, to compensate for this, we have to introduce the positively charged hole?
And even if I accept the model of negatively charged impurity + attached hole:
One electron is pushed out of the continuum into the acceptor state. Which electron is it? Is it one of the valence electrons that are part of the bonds of the impurity?
Please help me understand this conceptually.
SL