Let's consider an example of a 3x3x1 supercell of WS2 monolayer which has 9 W atoms. If we substitute two of them with 2 dopants, the concentration will be 2/9 which equals approximately 22%. Will this still be called doping? Is it OK to go for it?. If no, what is the maximum concentration allowed for doping?
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What is the maximum allowed doping concentration?
It really depends on what you want to study. The doping concentration can be changed from 0 to $100\%$. Taking the primitive monolayer of MoS$_2$ as an example, if you substitute the S atom with Se, then you obtain the MoSSe alloy (alloy engineering method in the field of 2D materials), which can be viewed as $50\%$ doping concentration. Furthermore, if you substitute Mo with W then you actually realize the $100\%$ doping concentration. But that makes no sense, you just calculate WS$_2$ monolayer. For other doping concentrations, you may need to build a supercell. Importantly, how to build the supercell is dependent on what you want to study.
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Let me start with this, I have a FCC unit cell with one light impurity at interstitial. Is it enough for solution energy of impurity or I have to take larger cell (2x2x2). If I am taking 1 periodic unit cell then concentration is 20%, if later case case then it is 3.03% .First thing we need to consider whether interstitials are interacting with each other or not. Interaction may occur from periodic boundary condition or within same simulation cell. you can verify this by checking your solution energy in different size simulation cell.Basically if your solution energy is not changing means individual doping are independent and not affecting already present defect(interstitial). Other way to check this is to analyze PDOS, and it is easy to notice that in case of interaction between dopants peak broadening or shifting occurs. Now you consider whether your doping is changing system characteristics or not will put a limit on solubility/concentration. Even we are doing computer simulation and we have multiple option for a dopant to be inside system doesn't mean that basic characteristics of host material or system should change drastically, if it happen then we are analyzing some other system. Apart from this kindly check your mechanical and dynamical stability of system if possible.
