= Solution
\b[Nanowires can increase $Z$ by reducing lattice heat conduction more strongly than they degrade useful electronic transport.] A wire diameter comparable to important phonon mean free paths introduces boundary scattering and reduces the lattice part of <thermal conductivity>. Interfaces, surface roughness and suitable nanostructure can suppress long-mean-free-path phonons while preserving shorter-mean-free-path carrier transport.
Electronic confinement or energy-dependent scattering can also change the <Seebeck coefficient> and <thermoelectric power factor>, but neither improvement is automatic. Surface depletion, disorder and contact resistance may instead reduce <electrical conductivity>; a smaller wire is not necessarily better. The necessary comparison is the complete ratio $S^2\sigma/(\kappa_e+\kappa_l)$ over the operating temperature range. The experimentally established benefit of nanostructuring is especially clear when it suppresses phonon heat conduction while retaining a useful power factor.<High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys by Bed Poudel and others>[2008, nanostructured-alloy thermal-conductivity and figure-of-merit measurements]{ref}
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