I am investigating diffusion of Cu in In2S3 layers with and without chlorine and the activation energies and pre-exponential factor D0 are different for the two sets of layers. Structural properties are similar though. How can one interpret and explain this different in Ea and D0?
The stoichiometry of a semiconductor is very important particularly for its electrical properties. Slight nonstoichiometry can induce defects in the system and change these parameters particularly activation enrgy and pre-exponential factors drastically. I suggest you to do some theoretical investigation through DFT band structure calculations with GGA for different kinds of defects in this system. Then you can correlate your parameters with the DFT (GGA) results.
The diffusion mechanisms in semiconductors, especially the compound semiconductor is extremely complex due to the existance of the vacancy defects. You should refer to an early book written by Tuck: Diffusion in semiconductors. An extremely complication theory called interstial-substitutional mechnism can explain Zinc diffusion in GaAs semiconductor perfectly. this theory was developed for 15 year starting early 60s. The essenance is impruity using interstitial as the the diffusion path; but the dopant depends on the substtional solubility in the host semiconductor, which in turn depends on vacancy contratration; and which also depends on the stoichiometric defects in the host crystal.
Therefore the activation energy and pre-exponential constant is not as simple as common diffusion theory can explain. It depsnds on a series of equation. Some time up-hill diffusion could occur; mostly non-Gaussion distribuion will be resulted.
Go get Tuck's book and read it. You will understanding the compexity.
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Tiwari, thank you for the suggestion. I would like to know if there is any publication discussing a similar case from a theoretical point of view. I am not in a position to do DFT simulations because of time constraints and expertise but I would like to understand these effects from what others have done and relate it to my results.
Shie, I will look for the book by Tuck. thank you.
Add to all this that the Fermi level can change according to the local doping. This leads to a change in the population of charged interstitial and vacancy defects and consequently, to an induced electric field, and so on...Not trivial !
Christophe, do you know how the concentration of the Cl in In2S3 could change the population of interstitial or vacancy defects?
With a concentration of between 7 and 14 at.% of Cl in In2S3 the activation energy stays at about 0.7 eV and the diffusion prefactor is 6x10^-6 cm^2/s compared to 0.3eV activation energy and 2x10^-11cm^2/s prefactor for stoichiometric In2S3 layers. I am looking for a way to discuss the diffusion mechanisms in these two cases and if possible a model.
Sorry, I'm not familiar with this system. I guess it should depend on how much Cl is active (acts as dopant) and contribute to conductivity. In Si it was possible to calculate the population of I0, I+ and I++ this way, knowing the ionization energies between each pair of species, and assuming that the interchange of charges is quasi-instantaneous in comparison to diffusion processes. Also, for these Cl concentrations, don't rule out any interaction between Cl and Cu. To be checked. Also, is there any interaction between Cl and point defects ? But again, I don't know this system. Good luck.
This study may give you some idea on the effect os stoichiometric change on the diffusion of an impurity (dopant).
Holmes, R. J. & Smyth, D. M. Titanium diffusion into LiNbO3 as a function of stoichiometry. Journal of Applied Physics 55, 3531–3535 (1984).
The diffusivity of Ti into LiNbO3 has been measured as a function of crystal orientation and Li/Nb ratio in the temperature range 980–1112 °C. The Li/Nb ratios of single crystal samples were adjusted by vapor phase equilibration with fixed Li2O activities. No anisotropy of diffusivity with crystal orientation could be detected. The diffusion constants for Ti in LiNbO3 decrease with increasing Li2O content. At 1050 °C, the values decrease from 2.60×10−12 cm2/s at the Li2O‐deficient phase boundary (48.1 mol % Li2O) to 1.06×10−12 cm2/s at the congruently melting composition at (48.6 mol % Li2O) to 0.4×10−12 cm2/s at the Li2O‐rich phase boundary (50.0 mol % Li2O). It is suggested that enhanced lateral diffusion observed for stripe geometry Ti sources results from increased diffusivity in a surface layer formed by Li2O outdiffusion.
In most cases the diffusing (foreign) atom uses a vacancy mechanism. Then, in many cases the diffusion constant is proportional to the vacany concentration as a rough estimation. In your case foriegn atoms and off-stoechiometry atoms may bind vacancies, which neans that the vacancy formation energy in the neighbourhood of such atoms is lower than in the undisturbed crystal. Anyway, the vacancy concentration is higher and so the diffusion coefficient is larger.
I investigated several metal B2(CsCl) type structures, where on one side of the stoechiometric composition the lacking atoms are replaced by vacancies. then there is an interesting diffusion mechanism, the 6-step (or Elcock-McCombie) mechanism which drives the diffusion processes.
.G. Frohberg (emeritus) / TU Berlin / Metal Physics
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