I want to calculate the carrier mobility for a photocatalyst. If there is any simplest method for calculation of carrier mobility then please let me know.
You can go through the chapter 2 of the book http://www.amazon.in/Photochemical-Water-Splitting-Applications-Electrochemical/dp/1482237598. I can attach the required text soon
You can begin with the experimental crystallographic structure of the molecule. Then, use pair of molecules set at experimental molecular distances and run density functional theory calculations. This will give you coupling values for electrons (or holes) depending in your interest. However, you need to calculate reorganizing energy of the molecule as well to obtain Markus (charge) hopping rates (If that is your goal).
In case of electron mobility calculations four geometry optimization calculations have to be performed on a molecule to find the neutral ground state of the molecule (Eneutral), excited state (anion) energy of the molecule on its ground state geometry (Eanion(neutral geometry)), excited state geometry (Eanion) and neutral state energy of the molecule on its excited state geometry (Eneutral(anion geometry)). Then using the following equation you can calculate reoganizing energy.
λ = (Eanion(neutral geometry) - Eneutral) + (Eneutral(anion geometry) - Eanion)
Finally use the Makus-Hush equation (check it out from the text book) to calculate charge mobility. The advantage of this method is you need only reorganization energy and electronic coupling factor to calculate it. Anyway, do not forget to use correct units during the calculation!!
Many thanks..
But we can do in molecular level but how can we calculate in materials in VASP?
Can you elaborate your question? According to my knowledge DFT or MD methods cannot calculate device level properties. There is a limitation of size, which we can model from each method ranging from quantum chemistry to computational fluid dynamics through coarse graining methods.
One of the central tasks in the theoretical prediction of mobility is determining effective mass because carrier mobility varies inversely with carrier effective mass. The effective mass is proportional to the reciprocal of the second derivative of the band energy with respect to wave vector.
m* = (hbar)^2 (d^2E/dk^2)^(-1)
Carrier mass is therefore determined in theoretical calculations by finding the curvature of the highest energy valance band (hole effective mass) or lowest energy conduction band (electron effective mass) in k-space. This can be done numerically by computing the electronic structure with any of the numerous available band structure codes and fitting several points around the VBM/CBM to a parabola. Alternatively, some electronic structure codes include the option to compute the effective mass tensor directly.
Mobility is just the ratio of drift velocity to the applied electric field. To get from carrier mass to mobility requires the mean free time (average time between scattering events). A quick web search turned up this page: http://britneyspears.ac/physics/mobility/mobility.htm
The application of hopping theory to determine mobility has been suggested above (Jeffrey Roshan De Lile). There is a well-known paper by Deng & Goddard that shows a straightforward protocol for the application of hopping theory: [Deng, W.-Q.; Goddard, William A., III. Predictions of Hole Mobilities in Oligoacene Organic Semiconductors from Quantum Mechanical Calculations. J. Phys. Chem. B 2004, 108, 8614–8621] Hopping theory is a reasonable strategy for molecular crystals, but the OP asks about photocatalysts. Photocatalysts are often TM oxides, to which hopping theory generally isn't applicable.
Dear Jefferey,
I have one semiconducting two-dimensional material, in which I will discuss the photocatalysis on that system. I want to calculate the carrier mobility on that system to make that more potent. I never did this carrier mobility, so now I want to start this.
You can read following two review papers to get better understanding of the method (If you preferred to follow the Markus-Hush method).
- C. P. Hsu, Acc. Chem. Res., 2009, 42, 509
- Zhao Y, and Liang W-Z, 2012, Chem.Soc.Rev, 41: 1075-1087.
Zhao et al. had described the application of the method to solar cells. In addition, there are two good papers; one of which is calculated TiOPc (two dimensional transition metal containing phthalocyanine crystal) from Norton and Bredas J. Chem. Phys. 128(3): 034701. First principles method which I described above is extended to materials by Goddard et al. J. Phys. Chem. B 2009, 113, 8813–8819. Hope this may be of some help to you.
I have read one paper regarding carrier mobility which DOI no is as follows:
DOI: 10.1002/anie.201502107
They have calculated the carrier mobility but I have some doubt that how to calculate elastic constant for electron and hole individually?? They have applied strain in two directions and calculated elastic constant by fitting the plot. Moreover, they have given individual value of elastic constant for electron and hole
Hi Priyanka Garg
They have calculated the value of elastic modulus for the material, not individually for electron and hole. The value of electron and hole elastic constant is same for a particular direction.
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