Dear all,
Recently i've been challenged by a question.
In a paper i'm writing i'm reporting the synthesis of a-Ge quantum dots, in which i observe a small blue shift along with particle shrinking. I explained this observation with standard solid state quantum theory.
The general theory of quantum confinement, molecular orbital and infinite number approximation in the build up of the band structure are all generally clear to me.
Now a reviewer is telling me that that all of the mentioned theories above apply to crystalline structure but not to amorphous nanoparticles.
I keep missing the point made from this reviewer, according to my knowledge the general theory should apply also to amorphous materials. I've done a small literature research, which didn't quite solve my doubts.
Do any of you have a better knowledge than mine on the topic, does any of you know also some references which i can use to back up my statement?
Hi, Bruno,
I basically agree with your idea. It is hard work to convince reviewers...
I remember that amorphous Si has wider band gap than that of crystalline Si. The electron orbits in a crystal spread to the whole crystal. Whereas a orbit in a amorphous has a limited size. The electrons in a amorphous are already confined, and this is why amorphous has wider band gap. So, if the size of the particle was bigger than the size of the orbit, the confinement does not affect to the energy level---the band gap... I think the reviewer may think as above.
However, if the particle size was smaller, the confinement surely work! If you could explain the sizes of the electron orbits are bigger than the size of your particle, you may convince the reviewer. You may need to add a few articles concerning electron orbit in amorphous.
I hope this helps you.
Dear Yoshiki Fukada,
Thanks a lot for the answer!
yeah the particle are about 4 nm while the Bohr radius for germanium is close to 24 nm, so waaaaaaay inside the quantum confinement regime. I will talk to him more and see what is his point.
But for curiosity and the sake of discussion.
the development of the band structure is in the theory strongly linked with the periodicity of the crystal lattice, and is clear that a well ordered structured spatial disposition will interact in a peculiar way, "easily" describable with periodical function such as the Bloch´s one.
But as a thought experiment, if we considered a random disposition of very closely packed atoms, their interaction will be of course random but different from 0. The orbitals overlapping might be smaller, the development of the molecular orbital would be not trivial to calculate, and dependent from the topological disposition of atoms. Still the presence of conduction and valence band is a fact, and eventually comes almost only because of the great number of atoms and orbitals involved, so decreasing the number of atoms, from simple MO-LCAO, should in any case result in the widening of the band gap... that's my point, i see why crystalline structure and periodicity are needed for the mathematical description of the band structure, but is not a necessity for the band structure to develop. As extension of this concept, decreasing the number of orbitals participating to this band structure , might as well result in the development of some localized quantized states, but the band gap (defined as homo-lumo "distance") should increase no matter what.
I'd like to know your (as much as everybody) opinion about it.
HI Bruno,
I also experienced a 'wrong' comment from a reviewer. Reviewers are not always experienced authorities. In sometimes, even a student also do a reviewer. However, we need careful explanation to them. Usually, there are two or more reviewers and they can see their review comments each other. So there is a possibility that other reviewers find the errors in other review comments and help you.
4nm is quite small, I think it is small enough for confinement effects. I believe your explanation works.
Do you know that your nanoparticles are actually amorphous? I think that for such small NP it is very easy that they actually have very good structure, being actually monocrystalline. I have work with organic NPs, and one of the ideas is that they can have good order because of the small size. I have also seen HRTEM of metallic NPs where good order is also seen
dear Raul Rangel-Rojo,
The amorphousness have been confirmed via Raman, Powder XRD, TEM, SAED (and SAXS maybe, not sure since i didn't do the last one myself).
Sorry i can't show you the data yet...
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