  How to design silicon-based quantum wires with figure of merit ($ZT$) larger
than three is under hot pursuit due to the advantage of low cost and the
availability of matured fabrication technique. Quantum wires consisting of
finite three dimensional quantum dot (QD) arrays coupled to electrodes are
proposed to realize high efficient thermoelectric devices with optimized power
factors. The transmission coefficient of 3D QD arrays can exhibit 3D, 2D, 1D
and 0D topological distribution functions by tailoring the interdot coupling
strengths. Such topological effects on the thermoelectric properties are
revealed. The 1D topological distribution function shows the maximum power
factor and the best $ZT$ value. We have demonstrated that 3D silicon QD array
nanowires with diameters below $20~nm$ and length $250~nm$ show high potential
to achieve $ZT\ge 3$ near room temperature.
