In this master thesis, we have investigated the surface states of Bi1−xSbx with varying x and the thickness(number of slabs), and the importance of Rashba terms to obtain a Topological Insulator instead of trivial phase. We used the TB platform in order to reproduce the electronic band structure and DOS, the results that we have obtained match perfectly the experimental results, this gives more importance to this platform comparing to DFT for reproducing the electronic properties of a crystal, since it does not take much time technique as in the case of DFT.