Ion Implantation and Synthesis of Materials - Studium

1.4 Atomic and Planar Densities 5(a)(b)Fig. 1.5. Schematic representation for (a) a single-crystal with crystallographic planesperpendicular to the surface and (b) a polycrystalline layer on a single-crystal1.4 Atomic and Planar DensitiesTo understand the description of ion implantation and ion doses, one must knowthe atomic density interplanar distance between planes and the number ofatoms cm −2 on a given plane. In cubic systems with an atomic density of Natoms cm −3 , the crystal lattice parameter, a c , is given byac⎛atoms/unit cell ⎞= ⎜ ⎟⎝ N ⎠1/3,(1.1)where, for systems with one atom per lattice point, there are four atoms per unitcell for a face-centered-cubic lattice (Al, Ag, Au, Pd, Pt) and there are eight forthe common semiconductors germanium (Ge) and silicon (Si), which have thediamond cubic structure. Aluminum has an atomic density of 6.02 × 10 22atoms cm −3 , so that the lattice parameter isac 221/3⎛ 4 ⎞−8= ⎜= 4.05 × 10 cm.6.02 × 10 ⎟⎝ ⎠(1.2)The atomic volume can be calculated without the use of crystallography. Theatomic density N of atoms cm −3 is given byAN = NAρ,(1.3)