In general terms, how we select a material for doping? While doping, is it necessary to have a element with low ionic radius in to the host material having ionic radii larger than the dopant.
Although neither atoms nor ions have sharp boundaries, it is useful to treat them as if they are hard spheres with radii. In this way, the sum of ionic radii of a cation and an anion can give us the distance between the ions in a crystal lattice.
Different dopants have different radiuses. They deform the lattice. The result is that different dopants have different donor (acceptor) energies. Thus to have shallow donors , you must have a dopant that has approximately the same radius as the atom that replaces in the lattice.
For Si and Ge you have these energy leves of the donors and acceptors
From my experience, there is a critical role for the ionic radius of the acceptor dopant on the stability, sinterability, and proton conductivity of barium zirconate. In Particular, when dopants such as, (Al, Sc, In, Lu, Tm, Y, Gd, Sm, Nd, and La) are added to zirconate, the lattice mismatch between the ionic radii of the dopants and Zr ion is critical.
Dear Anna, Yes, the ionic radius (dopant) is the most important factor to change their material properties. In general, we have selected doping ions based on application properties.
For example, if you select low ionic radius element is introduced into host material (high ionic) to alter its original properties (you can find your material like low bandgap, increase crystallite size, low peak intensity, etc.,) it only enhance some kind of applications properties on the other hand if you select higher ionic radius element is introduced into host material (low ionic) to alter its original properties (you can find your material like higher energy gab, decrease crystallite size, high and low peak intensity, etc.,) it only enhances other kinds of applications properties.