Independent control of electrical and heat conduction by nanostructure designing for Si-based thermoelectric materials

The high electrical and drastically-low thermal conductivities, a vital goal for high performance thermoelectric (TE) materials, are achieved in Si-based nanoarchitecture composed of Si channel layers and epitaxial Ge nanodots (NDs) with ultrahigh areal density (~1012 cm−2). In this nanoarchitecture, the ultrasmall NDs and Si channel layers play roles of phonon scattering sources and electrical conduction channels, respectively. Electron conductivity in n-type nanoacrhitecture shows high values comparable to those of epitaxial Si films despite the existence of epitaxial NDs. This is because Ge NDs mainly scattered not electrons but phonons selectively, which could be attributed to the small conduction band offset at the epitaxially-grown Si/Ge interface and high transmission probability through stacking faults. These results demonstrate an independent control of thermal and electrical conduction for phonon-glass electron-crystal TE materials by nanostructure designing and the energetic and structural interface control.


II. Dopant surface-depth profiles, carrier profiles, and activation rate
The surface-depth profile of dopants is shown in Fig. S1(a). We find little difference between calculation and SIMS result except for P small sharp peaks in SIMS. This suggests that SRIM calculation is applicable to these nanostructures implanted at different primary ion energies and that P diffusion during the rapid thermal annealing is negligible. The black and red dashed curves are corresponding to depth-integral curves of the surface-depth profiles measured by SIMS and calculated by SRIM. Both integrated curves are saturated (~99.5%) at a certain depth (276 nm), which is distant from the peak by about twice the standard deviation of the Gaussian depth-distribution. In the present study, this depth is called as "implanted depth". We calculated the implanted depths under other conditions in Table S1 and confirmed that the implanted depth is smaller than the film thickness in any cases. This indicates that in our experiments, our electrical measurements were done within the nanostructure films, not in the substrates.
Assuming a constant activation rate of implanted ions, the carrier concentration n is proportional to dopant concentration. Then, n has the same surface-depth profile shape as that of dopant concentration. Therefore, we defined that the carrier conduction layer thickness, L as the aforementioned implanted depth. The sheet carrier concentration, n S is obtained by Hall measurements. We defined the average carrier concentration, n A by setting the product of n A and carrier conduction layer thickness to be the n S value as shown in Fig. S1(b). The n surface-depth profile can be also determined because the integral of n surface-depth profile is equivalent to n S .
The activation rate can also be obtained by the ratio between the n S and dopant ion dose (=the integral of dopant surface-depth profiles). In the main text, the n A represents the carrier concentration of the samples.

III. Validity of n A in terms of electrical conductivity and Seebeck coefficient
In chapter II, we defined L and n A . In this chapter, we confirmed the validity of the n A definition in terms of electrical conductivity , and Seebeck coefficient, S.
The carrier mobility  and  have the n-dependence: namely depth-dependence. We calculated surface-depth profile of  using  with n-dependence of bulk Si as shown in Fig. S2(a). This is a similar surface-depth profile to that of n. We compared the difference of the L obtained from n surface-depth profile (chapter II) and the saturated depth in  surface-depth profile, at which integrated curve of  surface-depth profile is saturated (~99.5%). The difference is very small (usually ~6-7%). This indicates that the depth-dependence of  and  does not influence the determination of the conduction layer thickness.
To show the validity of this definition in terms of electrical conductivity , and Seebeck coefficient, uniformly-doped bulk Si [S1-S3] as shown in Fig. 3b and 3d. This proved that we can evaluate the  He , S, , and n A under this definition.

IV Structural characters of the nanoarchitecture
Our nanoarchitecture has the following structural characters as shown in Figs. S3 and S4. Figure S3 shows the random position of Ge NDs in the nanoarchitecture with thin Si layer in one cycle structure, indicating reduction of structural anisotropy. Figure S4 shows ansyses of the fast Fourier transformation (FFT) patterns around Ge NDs in the high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of the stacked structure. The lattice spacing analyses of FFT patterns suggest that Ge NDs, with 4% lattice mismatch, are fully relaxed, as reported in our previous work [S5], and that Si layer is elastically strain-relaxed just above Ge NDs within a typical distance of ~ 1 nm. The same strain distribution was also observed in the samples after carrier doping of P, indicating carrier doping does not affect the structural properties of nanoarchitecture. This is applicable to the case of carrier doping of B because of the same dose. Also, strain effect should be considered when we discuss the conduction band offset at Si/Ge NDs and it complicates the energy band diagram [S6]. However, we considered that this effect could be negligible in our case of non-strained Si layer except for the ultrasmall regions (<~1-nm distance from Ge NDs).  The error in FFT pattern analysis is ~3px corresponding to ~0.66% error.