Giant Isotope Effect of Thermal Conductivity in Silicon Nanowires

Isotopically purified semiconductors potentially dissipate heat better than their natural, isotopically mixed counterparts as they have higher thermal conductivity ($\kappa$). But the benefit is low for Si at room temperature, amounting to only $\sim 10\%$ higher $\kappa$ for bulk ${}^{28}\mathrm{Si}$ than for bulk natural Si (${}^{\mathrm{nat}}\mathrm{Si}$). We show that in stark contrast to this bulk behavior, ${}^{28}\mathrm{Si}$ (99.92% enriched) nanowires have up to 150% higher $\kappa$ than ${}^{\mathrm{nat}}\mathrm{Si}$ nanowires with similar diameters and surface morphology. Using a first-principles phonon dispersion model, this giant isotope effect is attributed to a mutual enhancement of isotope scattering and surface scattering of phonons in ${}^{\mathrm{nat}}\mathrm{Si}$ nanowires, correlated via transmission of phonons to the native amorphous ${\mathrm{SiO}}_2$ shell. The Letter discovers the strongest isotope effect of $\kappa$ at room temperature among all materials reported to date and inspires potential applications of isotopically enriched semiconductors in microelectronics.

Figure 1

Thermal conductivity of isotopically enriched (${}^{28}\mathrm{Si}$ at 99.92%) and natural Si NWs. (a) Optical image of a microdevice consisting of two suspended pads bridged by a Si NW. Inset: SEM image showing the Si NW FIB-bonded by Pt onto the underlying electrodes on the suspended pads. Scale bars: $10\mu \mathrm{m}$ (main panel); 100 nm (Inset). (b) Normalized Raman spectra of suspended Si NWs at a low and a high laser power. (c) Raman peak position as a function of the laser power. Inset: optical image of a suspended NW, where the blue spot shows the focus of the laser beam. Scale bar: $5\mu \mathrm{m}$. (d) Temperature-dependent thermal conductivity of Si NWs. Symbols are experimental data; curves with shaded thickness are theoretical predictions with 3 nm roughness and $6.5\pm 0.1$ ($5.1\pm 0.1$) nm correlation length for the isotopically enriched (natural) Si NWs. (e) Calculated (curves) and measured (points) thermal conductivity of Si NWs as a function of reciprocal diameter at 300K. (f) Comparison of room-temperature isotope effect of $\kappa$ of Si NWs compared with that of other isotopically enriched materials reported in the literature. Mass fluctuation parameter of elemental material ($A$) and compound ($AB$) is defined as $g_A={\sum }_i{c}_i{(1-M_i/M_{av})}^2$ and $g=[(g_A{M}_A^2+g_B{M}_B^2)/{(M_A+M_B)}^2]$, respectively, where $c_i$ is the atomic fraction of the $i$th isotope.

Figure 2

Schematic of phonon scattering on the $\mathrm{Si}/{\mathrm{SiO}}_2$ interface and structural characterization of the Si NWs. (a) Schematic of phonon scattering on the $c\text{−}\mathrm{Si}$ core/$a\text{−}{\mathrm{SiO}}_2$ shell interface of ${}^{28}\mathrm{Si}$ and ${}^{\mathrm{nat}}\mathrm{Si}$ NWs, where $\mathrm{\Delta }$ and $L$ indicate the roughness amplitude and physical correlation length, respectively. Phonon scattering back to the Si core occurs dominantly on the interface in ${}^{28}\mathrm{Si}$ NWs; in ${}^{\mathrm{nat}}\mathrm{Si}$ NWs, in contrast, a higher portion of phonon wave packets transmits into the $a\text{−}{\mathrm{SiO}}_2$ shell, effectively shortening the correlation length and significantly reducing the thermal conductivity of the NW. (b) and (c) high-resolution TEM images and fast Fourier transform (FFT, inset) of a ${}^{28}\mathrm{Si}$ NW and a ${}^{\mathrm{nat}}\mathrm{Si}$ NW. Surface roughness, highlighted by the red dashed line, is evident on the interface between the crystalline Si core ($c\text{−}\mathrm{Si}$) and the native amorphous ${\mathrm{SiO}}_2$ shell ($a\text{−}{\mathrm{SiO}}_2$). Scale bar is 4 nm in both (b) and (c).

Figure 3

Calculation of two-way coupled phonon dynamics involving surface roughness and isotope mass disorder in Si NWs. (a) Isotope scattering rates in a ${}^{\mathrm{nat}}\mathrm{Si}$ NW (90 nm diameter) by the “decoupled” model compared to the “coupled” model. In the energy range below 20 meV, the isotope scattering is remarkably enhanced by the presence of the surface ${\mathrm{SiO}}_2$. (b) Transmission coefficient spectrum of different phonon branches from $c\text{−}\mathrm{Si}$ to $a\text{−}{\mathrm{SiO}}_2$ for ${}^{28}\mathrm{Si}$ vs ${}^{\mathrm{nat}}\mathrm{Si}$. ${}^{\mathrm{nat}}\mathrm{Si}$ shows a higher transmission coefficient at low phonon energies, implying stronger roughness scattering at the $\mathrm{Si}/{\mathrm{SiO}}_2$ interface enhanced by isotopes.