  We present results of a systematic study of the c axis lattice dynamics in
single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer
Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both
experimental data obtained by spectral ellipsometry on single crystals and
theoretical calculations. The calculations are carried out within the framework
of a classical shell model, which includes long-range Coulomb interactions and
short-range interactions of the Buckingham form in a system of polarizable
ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and
Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes
of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve
good agreement between the calculated A2u eigenfrequencies and the experimental
values of the c axis TO phonon frequencies which allows us to make a reliable
phonon mode assignment for all three Bi-based cuprate superconductors. We also
present the results of our shell model calculations for the Gamma-point A1g
symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is
based on the published experimental Raman spectra. The
superconductivity-induced phonon anomalies recently observed in the c axis
infrared and resonant Raman scattering spectra in trilayer Bi2223 are
consistently explained with the suggested assignment.
