  We have developed a material specific theoretical framework for modelling
scanning tunneling spectroscopy (STS) of high temperature superconducting
materials in the normal as well as the superconducting state. Results for
$Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi2212) show clearly that the tunneling process
strongly modifies the STS spectrum from the local density of states (LDOS) of
the $d_{x^2-y^2}$ orbital of Cu. The dominant tunneling channel to the surface
Bi involves the $d_{x^2-y^2}$ orbitals of the four neighbouring Cu atoms. In
accord with experimental observations, the computed spectrum displays a
remarkable asymmetry between the processes of electron injection and
extraction, which arises from contributions of Cu $d_{z^2}$ and other orbitals
to the tunneling current.
