  The thermoelectric properties of a semiconduct quantum dot chain (SQDC)
connected to metallic electrodes are theoretically investigated in the Coulomb
blockade regime. An extended Hubbard model is employed to simulate the SQDC
system consisted of {\color{blue}N=2,3,4, and 5} quantum dots (QDs). The charge
and heat currents are calculated in the framework of Keldysh Green's function
technique. We obtained a closed-form Landauer expression for the transmission
coefficient of the SQDC system with arbitrary number of QDs by using the method
beyond mean-field theory. The electrical conductance ($G_e$), Seebeck
coefficient (S), thermal conductance, and figure of merit (ZT) are numerically
calculated and analyzed in the linear response regime. When thermal conductance
is dominated by phonon carriers, the optimization of ZT is determined by the
power factor ($pF=S^2G_e$). We find that the optimization of ZT value favors
the following conditions:(1) QDs with low energy level fluctuations, (2) QD
energy levels lie above the Fermi level of electrodes, (3) $\Gamma < t_c \ll
U_0$, where $t_c$, $U_0$, and $\Gamma$ are electron interdot hopping strength,
on-site electron Coulomb interaction, and tunneling rate, respectively, and (4)
$\Gamma_L=\Gamma_R$ with $\Gamma_L+\Gamma_R$ kept constant, where $\Gamma_L
(\Gamma_R)$ is the left (right) tunneling rate. It is predicted that high ZT
values can be achieved by tailoring above conditions.
