  To examine thermoelectric (TE) properties of a semiconductor nanowire (NW)
network, we propose a theoretical approach mapping the TE network on a two-port
network. In contrast to a conventional single-port (i.e., resistor) network
model, our model allows for large scale calculations showing convergence of TE
figure of merit, $ZT$, with an increasing number of junctions. Using this
model, numerical simulations are performed for the Bi$_2$Te$_3$ branched
nanowire (BNW) and Cayley tree NW (CTNW) network. We find that the phonon
scattering at the network junctions plays a dominant role in enhancing the
network $ZT$. Specifically, disordered BNW and CTNW demonstrate an order of
magnitude higher ZT enhancement compared to their ordered counterparts.
Formation of preferential TE pathways in CTNW makes the network effectively
behave as its BNW counterpart. We provide formalism for simulating large scale
nanowire networks hinged upon experimentally measurable TE parameters of a
single T-junction.
