To test exciton binding energy

[Bauer Yee]

Hi,
I want to test exciton binding energy of some particles, what should i do ?

 

[Bauer Yee]

Hi,
I want to test exciton binding energy of some particles, what should i do ?

supplement to the problem:
it's semiconductor powders, what dictate the exciton binding energy ? how could it be caculated ? how could it be tested ?

 

[Kholdstare]

I know how exciton binding energy can be calculated. Though I know only for Mott-Warnier excitons. I also have an idea of how it could be tested.

 

[Bauer Yee]

I know how exciton binding energy can be calculated. Though I know only for Mott-Warnier excitons. I also have an idea of how it could be tested.

So what is binding energy equation for the Mott-Warnier excitons ? Would you please give further reference ? thanks

 

[Kholdstare]

Mott-Warnier exciton binding energy is given by,

E_ex = \frac{-m^{*}_{r}e^{4}}{2(4\pi\epsilon)^2\hbar^{2}}\cdot\frac{1}{n^{2}}

Where m^{*}_{r} is effective mass of the particles in the material (for eg GaAs).

m^{*}_{r} = \frac{m^{*}_{e}m^{*}_{hh}}{m^{*}_{e}+m^{*}_{hh}}

m^{*}_{e} and m^{*}_{hh} are effective mass for electrons and heavy holes in the material. \epsilon is the permittivity of the material. n signifies nth excitonic orbital, which corresponds to nth excitonic binding energy. nth excitonic energy level is obtained by subtracting the nth binding energy from the conduction band.

For GaAs considering heavy holes we get E_ex \approx -\frac{4.6}{n^{2}} meV

BTW i was talking about 3D materials. In 2D materials it is a little different. To measure the excitonic binding energy experimentally you have to get the absorption spectra of the sample. It will show fine absorption values below the cut-off light frequency. those are caused by absorption of photon by an electron to jump from valance band to an excitonic energy level (where it forms an exciton with the hole left by it). The difference between the forbidden energy gap and excitonic energy gap (i. e. exciton absorption peak frequency multiplied by Plank's constant) will be the binding energy for that exciton.

Sorry for the late reply. Hope this helps.

 

[Bauer Yee]

Mott-Warnier exciton binding energy is given by,

E_ex = \frac{-m^{*}_{r}e^{4}}{2(4\pi\epsilon)^2\hbar^{2}}\cdot\frac{1}{n^{2}}

Where m^{*}_{r} is effective mass of the particles in the material (for eg GaAs).

m^{*}_{r} = \frac{m^{*}_{e}m^{*}_{hh}}{m^{*}_{e}+m^{*}_{hh}}

m^{*}_{e} and m^{*}_{hh} are effective mass for electrons and heavy holes in the material. \epsilon is the permittivity of the material. n signifies nth excitonic orbital, which corresponds to nth excitonic binding energy. nth excitonic energy level is obtained by subtracting the nth binding energy from the conduction band.

For GaAs considering heavy holes we get E_ex \approx -\frac{4.6}{n^{2}} meV

BTW i was talking about 3D materials. In 2D materials it is a little different. To measure the excitonic binding energy experimentally you have to get the absorption spectra of the sample. It will show fine absorption values below the cut-off light frequency. those are caused by absorption of photon by an electron to jump from valance band to an excitonic energy level (where it forms an exciton with the hole left by it). The difference between the forbidden energy gap and excitonic energy gap (i. e. exciton absorption peak frequency multiplied by Plank's constant) will be the binding energy for that exciton.

Sorry for the late reply. Hope this helps.

Thank you very much!

 

[Bauer Yee]

To measure the exciton binding energy, whether is it not enough to get absorption spectra ? for example, in an absorption spectra of UV-vis spectra under room temperature, there is no fine absorption values. Does the fine absorption values appear at low temperature, or other conditions ?

 

[Kholdstare]

In fact I don't know how practically you will get the spectra, but I think you should get some absorption in the visual spectra. However the intensity of absorption may be very small. In that case you have to look for the way to intensify it.

Theoritically I can guide you to follow some derivation and calculation from the idea that electromagnetic radiations are created by accelerating electric charge (Here oscillating electric dipole). Thus consider the two states : ground state wavefunction of the electron in the valance band and excited state wavefunction of the electron in the excitonic state. During the photon absorption process the electronic wavefunction will start from ground state, oscillate between these two states with frequency corresponding to the photon energy, and settle down to the excited state. The Rate of absorption of energy can be calculated from the amplitude and frequency of the oscillation. This rate will be immediately translated as the intensity of absorption.

I guess I've given a very vague idea of electronic transition. For a detailed analysis you can consider reading book (Quantum Physics by Resnick & Eisberg, Chapter 8.7 and Appdx B).

 

[Cthugha]

To measure the exciton binding energy, whether is it not enough to get absorption spectra ?

That depends. Do you know the "pure" band gap without any excitonic effects your material has? While the band gap is well known for GaAs and many other materials, it is less well known for some materials commonly used for colloidal QDs. Have a look at R. W. Meulenberg et al., "Determination of the Exciton Binding Energy in CdSe Quantum Dots", ACS Nano, 2009, 3 (2), pp 325–330 http://pubs.acs.org/doi/abs/10.1021/nn8006916" to check how exciton binding energies are measured in detail.

for example, in an absorption spectra of UV-vis spectra under room temperature, there is no fine absorption values. Does the fine absorption values appear at low temperature, or other conditions ?

Well, low temperatures always make it easier to see the excitonic absorption. What kind of material do you have? For most II-VI materials you would expect excitonic absorption in the blue, green or yellow range, while for many III-V materials, it is in the red or infrared. Of course this is strictly valid only for self-assembled QDs, for colloidal ones there is also a huge size dependence.

 

[Bauer Yee]

That depends. Do you know the "pure" band gap without any excitonic effects your material has? While the band gap is well known for GaAs and many other materials, it is less well known for some materials commonly used for colloidal QDs. Have a look at R. W. Meulenberg et al., "Determination of the Exciton Binding Energy in CdSe Quantum Dots", ACS Nano, 2009, 3 (2), pp 325–330 http://pubs.acs.org/doi/abs/10.1021/nn8006916" to check how exciton binding energies are measured in detail.



Well, low temperatures always make it easier to see the excitonic absorption. What kind of material do you have? For most II-VI materials you would expect excitonic absorption in the blue, green or yellow range, while for many III-V materials, it is in the red or infrared. Of course this is strictly valid only for self-assembled QDs, for colloidal ones there is also a huge size dependence.

Greatly appreciate your information !
my materials is ZnO, modified by other elements, or doped. Intuitively, the exciton binding energy will change, nevertheless, I don't know whether it reduces or increases.

 

[Bauer Yee]

In fact I don't know how practically you will get the spectra, but I think you should get some absorption in the visual spectra. However the intensity of absorption may be very small. In that case you have to look for the way to intensify it.

Theoritically I can guide you to follow some derivation and calculation from the idea that electromagnetic radiations are created by accelerating electric charge (Here oscillating electric dipole). Thus consider the two states : ground state wavefunction of the electron in the valance band and excited state wavefunction of the electron in the excitonic state. During the photon absorption process the electronic wavefunction will start from ground state, oscillate between these two states with frequency corresponding to the photon energy, and settle down to the excited state. The Rate of absorption of energy can be calculated from the amplitude and frequency of the oscillation. This rate will be immediately translated as the intensity of absorption.

I guess I've given a very vague idea of electronic transition. For a detailed analysis you can consider reading book (Quantum Physics by Resnick & Eisberg, Chapter 8.7 and Appdx B).

Acknowledge your support! I've learned much from what you provided.