  The Landauer approach provides a conceptually simple way to calculate the
intrinsic thermoelectric (TE) parameters of materials from the ballistic to the
diffusive transport regime. This method relies on the calculation of the number
of propagating modes and the scattering rate for each mode. The modes are
calculated from the energy dispersion (E(k)) of the materials which require
heavy computation and often supply energy relation on sparse momentum (k)
grids. Here an efficient method to calculate the distribution of modes (DOM)
from a given E(k) relationship is presented. The main features of this
algorithm are, (i) its ability to work on sparse dispersion data, and (ii)
creation of an energy grid for the DOM that is almost independent of the
dispersion data therefore allowing for efficient and fast calculation of TE
parameters. The inclusion of scattering effects is also straight forward. The
effect of k-grid sparsity on the compute time for DOM and on the sensitivity of
the calculated TE results are provided. The algorithm calculates the TE
parameters within 5% accuracy when the K-grid sparsity is increased up to 60%
for all the dimensions (3D, 2D and 1D). The time taken for the DOM calculation
is strongly influenced by the transverse K density (K perpendicular to
transport direction) but is almost independent of the transport K density
(along the transport direction). The DOM and TE results from the algorithm are
bench-marked with, (i) analytical calculations for parabolic bands, and (ii)
realistic electronic and phonon results for $Bi_{2}Te_{3}$.
