Applications of energy flux and numerical analyses to the plasma etching of silicon deep trench isolation (DTI) structures

Nanoindentations carried out by a “virtual plasma indenter” has been proposed in this study to solve the plasma etchings of Si wafer and determine the deep trench isolation (DTI) profile with a high accuracy. The methods of finding the virtual Gaussian-like indenter profiler and the back load applied to the back surface of indenter corresponding to the given etching conditions have been developed. The values of these two controlling factors in combination with the ANSYS/LS-DYNA software and the Johnson-Cook (J-C) fracture model allow us to solve the DTI profiles formed at various penetration depths. Good agreement between the experimental and simulational DTI profiles has been achieved and the efficiency and validity of the models developed for various etching conditions have been confirmed. From the analyses by the present models, the real dominant controlling factors for the geometries of DTI structure can be identified clearly, and the choices in the plasma etching conditions for the desired DTI geometries become easy and efficient. The present models can provide us an efficient way to determine the etching conditions required for the fabrication of a desired DTI structure with a high accuracy.