it should be around 0.5 A

https://arxiv.org/vc/cond-mat/papers/0405/0405378v1.pdf

I am not aware of any dependence on particle size. Hafnia is a wide-bandgap dielectric, the range of quantum confinement for such materials is practically not reachable.

Here, Roman, you are quite right. My guess is it should be around 10A (1nm). At least.

I've just found a good paper explaining the difference between the Bohr radius (a_0) and the excitonic Bohr radius (a_ex). Unfortunately not for HfO2 but still it gives you a clue. For Si, a_0=0.5A and a_ex=4.2nm. Big difference!

Bohr radius a0 is a constant that does not depend on specific material. Seems like we don't know how large the excitonic Bohr radius for hafnia should be, but I guess it is much smaller than that of silicon.

According to Eq.(4) from the attached paper, the Bohr radius a_H=0.5A and the excitonic Bohr radius a_ex are related to each other as follows:

a_ex=a_H*epsilon_r*(m_0/m_eff)

where epsilon_r is the dielectric constant and m_eff is an effective mass.

For Si, epsilon_r=12 and m_eff=0.15m_0 which gives a_ex=80a_H=4nm in good agreement with the previously mentioned value for Si.

For HfO2, epsilon_r=25 and m_eff=0.1m_0 which gives a_ex=250a_H=12.5nm for the excitonic Bohr radius.

And just in case, regarding the experimental determination of an effective mass for HfO2, check this paper.

http://www.sciencedirect.com/science/article/pii/S0038110108004048

The topic starter, are you happy with the provided answer or not? I just don't get it.

Dear  Sir, Thank you very much for your discussion ,

in one publication effective mass of electron and hole masses are given m*e=0.22m0 and m*h=0.15m0. i hahe calculated according to eq (4) as mentioned you. bohr exciton radius is 14.8 nm. your calculation is closely matching with this.

 but in some other publication for m-HfO2 m*e/m0=1.1 and m*h/m0=1.6, from this bohr exciton radius is 0.8 nm.     (i am attaching both the publications)

i am little bit confusing that which value we have to consider. please give your valuable suggestions. 

we have synthesised HfO2 NPs by using RF M sputtering method, NPs (size of the NPs around 2.5 to 4 nm) after SHI irradiation with 100 MeV Ag ion, NPs are showing monoclinic phase (from TEM and XRD measurements). 

Dr. Roman Kubrin, Thanks for your discussion.

i am sorry, in my earlier discussion second one is 2 nm (not 0.8 nm).

and also...

they have given different effective masses  for different brillouin zone directions. which brillouin zone direction we have to consider ? 

Thank you Sir,

you are correct, because we are not getting the exact stoichiometry  of HfO2,  we found that some O defects in HfO2 NPs  (from the PL measurement), so  dielectric constant may not be equal to 25, we are also planing to do dielectric measurements. i am happy that you suggested to do the same. 

Thank you sir, once again for your suggestions. 

I am glad you corrected your earlier estimate to 2nm. If you remember, my first guess was  (at least!)  1nm for HfO2 and I still stick to this value. Regarding  the value of an effective mass. This is actually quite a common feature called "anisotropy" which means that you may have a rather significant variation of m_eff (and other parameters) in your sample depending on the direction  (parallel or perpendicular). For example, in high-Tc superconductors, the effective mass anisotropy (along c-axis and within ab-plane)  can reach a hefty 200%. So, I do believe that something like this may take place in HfO2. It means that in this material you can have both "light"  and "heavy" carriers at the same time which will result in co-existence of both "big" and "small" excitons. The only problem is that to experimentally view "small-sized" (at least 1nm!) excitons, you need a really good (defect-free) single crystal. Otherwise, these two carriers will mix up in your sample giving something "in-between" for an effective mass and corresponding excitonic Bohr radius. Usually, the defects come from oxygen (due to even a slight deviation from stoichiometry).

But in addition to this "sample-dependent" complication, you have to deal with the dielectric properties of your samples because according to Eq.(4), the excitonic Bohr radius (apart from the effective mass) also depends on the dielectric constant. Usually, for HfO2 it is around 25. But, like I said, it is quite possible to have very different values for this parameter depending on the direction (same anisotropy!). That is why, I would strongly suggest you to measure the dielectric properties of your samples in order to estimate the value of the epsilon_r.

Of course, there is another possibility related to the validity of Eq.(4). Apparently, this expression is approximate and it is not sensitive (at least explicitly) to any size effects. It is quite possible that for particles sizes of the order of just a few nanometers, a simple Eq.(4) will break down and should be replaced by a more accurate expression (explicitly depending on the particle size). Unfortunately, I can not suggest any form of such a modified equation. Perhaps somebody could help us with this problem.

And finally, since you are interested in excitonic radius, I assume that you are after the confinement effect in HfO2. If this is indeed the case, you need to perform transport measurements (including Hall effect). This will also give you a clue about the value of the excitonic Bohr radius in your samples.