In this master thesis, the silicon (001) surface is studied from first-principles using a local-basis method. This surface, which was discovered back in the eighties and has generated since then a large number of publications, still continues to fascinate scientists. Its technological importance added to the physical richness of the possible reconstructions are probably at the origin of this continuous interest.

As for most semiconductors, the silicon (001) surface reconstructs in order to lower its surface energy. Different reconstruction models have been proposed and this subject still remains controversial. \\
In this work, different models are first analysed from a structural point of view. The relaxed atomic positions are obtained for the different reconstructions before comparing them through a relative stability study. Initially, the silicon (001) surface presents two dangling bonds per surface atom. By forming surface dimers, this number is reduced to one and rows of dimers are formed. Symmetric dimers are unstable with respect to buckling which leads to asymmetric dimers with one atom going up while the other goes down. Larger reconstructions can be achieved by alternating dimers inside a given row or between adjacent rows. The relative stability study shows that the effects of alternation are far less important than the ones induced by forming a dimer. Indeed, larger reconstructions permits to lower the surface stresses but no other bonds are created.

The electronic properties of the different reconstructions are then obtained and compared. With symmetric dimers at its surface, the system is metallic. It becomes semiconducting once the dimers are buckled. The semiconducting gap is computed for each case and the bandstructure is obtained. The contribution to surface states is analysed using the projected density of states. It is shown that the upper dimer atom contributes significantly to the total DOS for valence states while the lower dimer atom contributes more to empty states.\\
The silicon (001) surface is further studied by means of simulated STM images. The important parameters are investigated and the study of the bias, which is the most important one, sheds light on the strong differences between the symmetric dimer and the other reconstructions. The spectroscopic study permits to distinguish between the bonding and antibonding character associated to surface atoms.\\
Preliminary results are presented regarding the adsorption of ammonia on the silicon (001) surface. The possible perspectives are sketched for this surface and for the scanning tunnelling microscope.
