Polymeric materials are widely used to cover on a carbon nanotube for producing the n-type semiconductor. However, understanding of structural polymerization of polyethyleneimine (PEI) warped on carbon nanotubes is poor. To approach the structural, all of calculations are treated with the package based on Density Functional Theory correcting with vdW correction. As a result, the functionalized carbon nanotube coated with PEI explicitly leads to n-type when such PEI performs as trans-trans-trans conformer and number of unit of polymer is over 3. Increasing of number of polymers in interacting process also dramatically improves the irreversible absorptions.