A profound increase in can be achieved when we consider the more realist case, in which we allow for electrons and phonons to undergo boundary scattering in addition to phonon scattering. The figure of merit in this case is shown in Fig. 6.3, (Fig.6.3-a for -type nanowires and Fig. 6.3-b for -type nanowires). The anisotropy, and the main features observed with diameter scaling are not altered significantly compared to Fig. 6.2. , however, increases by almost a factor of with the introduction of boundary scattering, both for -type and -type nanowires (the phonon-scattering only results of Fig. 6.2-a are shown in Fig. 6.3-a for reference). varies from to for -type nanowires ( at larger diameters), also in agreement with other theoretical studies . For -type nanowires it reaches a maximum of for the nanowires of smaller diameters.
This increase in indicates that the boundary scattering reduces the thermal conductivity by a factor of more than it reduces the power factor. As explained in Ref. , the introduction of surface roughness (SR) scattering, degrades the electrical conductivity significantly, but improves the Seebeck coefficient slightly. The degradation in the power factor, therefore, is dominated by the decrease in the electrical conductivity. Fig. 6.3 shows, however, that even in geometries with ultra-small feature sizes, in which the electrical conductivity is strongly degraded due to enhanced electron-phonon and electron-SR scattering, the thermal conductivity even stronger degrads. It suggests that phonon engineering techniques that further increase phonon scattering can help in the improvement of . This was considered to be the case for nanowires of larger diameters , but it appears to be the case also for nanowire diameters as thin as a few nanometers.