  We report thermoelectric (TE) properties of topological surface Dirac states
(TSDS) in three-dimensional topological insulators (3D-TIs) purely isolated
from the bulk by employing single crystal Bi$_{2-x}$Sb$_x$Te$_{3-y}$Se$_y$
films epitaxially grown in the ultrathin limit. Two intrinsic nontrivial
topological surface states, a metallic TSDS (m-TSDS) and a gap-opened
semiconducting topological state (g-TSDS), are successfully observed by
electrical transport, and important TE parameters (electrical conductivity
(${\sigma}$), thermal conductivity (${\kappa}$), and thermopower ($S$)) are
accurately determined. Pure m-TSDS gives $S$=-44 {\mu}VK$^{-1}$, which is an
order of magnitude higher than those of the conventional metals and the value
is enhanced to -212 {\mu}VK$^{-1}$ for g-TSDS. It is clearly shown that the
semi-classical Boltzmann transport equation (SBTE) in the framework of constant
relaxation time (${\tau}$) most frequently used for conventional analysis
cannot be valid in 3D-TIs and strong energy dependent relaxation time
${\tau}(E)$ beyond the Born approximation is essential for making intrinsic
interpretations. Although ${\sigma}$ is protected on the m-TSDS, ${\kappa}$ is
greatly influenced by the disorder on the topological surface, giving a
dissimilar effect between topologically protected electronic conduction and
phonon transport.
