Configuration coordinate diagram

[mendes]

For a defect in a semiconductor. We plot the energy against some "configuration coordinate", noted in general as "Q".

What is this coordinate ?

In my understanding it is some position related to the defect in question.


Also, is the energy plotted in the diagram the energy of the whole crystal or just for one electron that the defect may capture or emit ?


Thanks.

 

[asheg]

When you have a periodic structure you will have clean energy bands but when there be defects you will have some energy states in middle of these band.

As far as I know, we always plot E-K (or name it E-Q) where k(/q) is wave vector.

Since defect is localized in space it would spread in k-space (Fourier transform: delta function Fourier transforms to a constant value)

All the energy states in crystal are consequence of spreading electron wavefunction all over the crystal and belong to whole crystal.

 

[mendes]

When you have a periodic structure you will have clean energy bands but when there be defects you will have some energy states in middle of these band.

As far as I know, we always plot E-K (or name it E-Q) where k(/q) is wave vector.

Since defect is localized in space it would spread in k-space (Fourier transform: delta function Fourier transforms to a constant value)

All the energy states in crystal are consequence of spreading electron wavefunction all over the crystal and belong to whole crystal.

When such a configuration diagram is plotted for a metastable defect for example I have seen quite a few graphs in articles where it is said that the configuration coordinate is taken for the distance between the defect in question and the neighboring atoms, and they show that this distance has to change due to the relaxation mechanism that accompanies the emission or capture of carriers on the defect !
Is there then a parallel that can be made between the "wavevector" and the distance between the defect and its neighboring atoms in this case ?

 

[asheg]

When such a configuration diagram is plotted for a metastable defect for example I have seen quite a few graphs in articles where it is said that the configuration coordinate is taken for the distance between the defect in question and the neighboring atoms, and they show that this distance has to change due to the relaxation mechanism that accompanies the emission or capture of carriers on the defect !
Is there then a parallel that can be made between the "wavevector" and the distance between the defect and its neighboring atoms in this case ?

Excuse me if I was wrong but I think q usually stands for momentum or wave vector. i.e. see following link (page 35/57):

http://docs.google.com/viewer?a=v&q...qCb1v6&sig=AHIEtbSjBinA2E6_wALEf-4DdVUprZ5ZWA

I'm not sure but from Fourier transform (between x and q) or uncertainty principle, I think
Q = 1/(Size of defect: distance between the defect and its neighboring atoms).

 

[mendes]

Excuse me if I was wrong but I think q usually stands for momentum or wave vector. i.e. see following link (page 35/57):

http://docs.google.com/viewer?a=v&q...qCb1v6&sig=AHIEtbSjBinA2E6_wALEf-4DdVUprZ5ZWA

I'm not sure but from Fourier transform (between x and q) or uncertainty principle, I think
Q = 1/(Size of defect: distance between the defect and its neighboring atoms).

I did not look carefully yet to your reference (I will do later today) , but just brievely looked at some graphs. Did you see the page 37 ?

 

[asheg]

Yes I saw that figure and it made me unsure about what "Configuration coordinate diagram" means? E-Q (page 35) or E-x (page 37)?

 

[mendes]

Yes I saw that figure and it made me unsure about what "Configuration coordinate diagram" means? E-Q (page 35) or E-x (page 37)?

You can maybe have a look at this :

http://www.sciencemag.org/content/281/5379/945.full

Extract:

The configuration coordinate (CC) diagram provides a powerful framework (36) for interpreting Chadi and Chang's model. The total defect energy is plotted as a function of a generalized coordinate, which is an overall measure of all the changes in the defect atom and its neighbor's coordinates. The CC diagram for the DX center described by the model of Chadi and Chang is shown in Fig. 7. At low pressures or AlAs mole fractions, the CC diagram to the left applies. The shallow-donor configuration is stable, but DX coexists in metastable form. Optical excitation can lead to DX formation. At modest temperatures, the small energy barrier separating the two defect structures is easily overcome, returning the center into its stable form. At pressures ≥20 kbar or at AlAs mole fractions ≥22%, the DX configuration is stable. The material is insulating despite the presence of dopants. During band edge light illumination free electrons and holes are generated, leading to the standard photoconductivity. However, DX centers are also optically pumped into the shallow-donor configuration. If the crystal is kept cold, the shallow-donor configuration is trapped by the energy barrier between the two configurations. The donors are very shallow and remain ionized, that is, the conductivity persists, no longer because of photon illumination but because of the photon-induced defect configuration change.

It looks like the plot for the harmonic oscillator potential energy versus displacement, where the energy minimum points towards the equilibrium displacement value.

 

[tuyuan]

hello,mendes. I am Tu Yuan from CHina,I have much question about the configuration-coordinate diagrams.so do you understand it completely now?

 

[tuyuan]

my main trouble is ,the ground state and excited state are two defect levels.so I don't know how to get the equilibrium positions of the atoms ,so I can't calculate the energy levels with first-principle calculations.