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Impurity doping is one of the important means to control the physical properties of intrinsic semiconductors. By combining data mining and first principles calculation, a series of potential dopable elements in GaN were predicted by Shannon radius and probability model methods in this study. The Shannon radius difference and replacement probability were used as the criterion to screen the dopable elements and a total of 36 dopants were predicted. Then the structural stability and electronic structure of these doped structures were systematically studied by the first principles calculations. Among these dopants, the defect formation energy of 14 kinds is less than 3 eV, namely ON, ZrGa, TiGa, SiGa, FN, GeGa, NbGa, SN, SeN for n-type and BeGa, MgGa, CaGa, ZnGa and MnGa for p-type. In these potential doping systems, the changes of electronic structure can be divided into two types according to whether the impurity energy level is introduced or not. The doping of TiGa, NbGa, FN and MnGa can introduce significant impurity levels in the band gap, the electrons of which are directly involved in the carrier transition. For other dopants, no obvious impurity energy level is introduced in the band gap. Compared with the undoped GaN, the electronic density of states of the doped systems are significantly enhanced at the conduction band minimum. These results are expected to provide an effective theoretical reference for the experimental screening of appropriate GaN dopants

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