Dominant scattering mechanisms and mobility peak in cryogenic 2D electron transport in Silicon (110) confinement by high-k oxides

Abstract

The performance of silicon nano-devices at cryogenic temperatures is critical for quantum computing technologies. Through multi-valley Monte Carlo simulations of Si (110) systems, we reveal a fundamental shift in electron transport physics at low temperatures. Phonon scattering becomes negligible, and mobility is instead dictated by a competition between remote Coulomb scattering (RCS) at low carrier densities and surface roughness scattering (SRS) at high densities. This competition creates a distinct peak in electron mobility. Furthermore, we demonstrate a critical design trade-off for high-$κ$ dielectrics like $\mathrm{HfO_2}$: while enhancing gate control, they introduce strong remote phonon scattering, which can suppress mobility. These findings provide essential guidelines for the material selection and design of next-generation cryogenic nano-devices.

Figures (4)

• Figure 1: Scattering rates with electron energy. (a) Acoustic phonon. (b) Optical phonon. Intravalley and inter-valley transitions are included. (c) Remote phonon. The dashed lines are the result that $\mathrm{HfO_2}$ is the dielectric, and the solid lines show that $\mathrm{SiO_2}$ is used. (d) Surface roughness. The surface roughness parameters $\lambda$ is 1.0 nm and $\Delta$ is 0.5 nm. (e) Remote Coulomb. The fix-charge density in the oxide is $\mathrm{2.0 \times 10^{13}}$$\mathrm{cm^{-2}}$ and the charges position is 1 nm away from the interface. (f) Impurity. The ionized impurity concentration is set as $\mathrm{5.0 \times 10^{11}}$$\mathrm{cm^{-2}}$.
• Figure 2: (a) Surface roughness scattering rate ($\lambda$ = 1.0 nm and $\Delta$ = 0.5 nm) with different inversion layer concentrations ($\mathrm{N_{inv}}$). (b) Remote Coulomb (solid lines, fix-charge concentration = $\mathrm{2.0 \times 10^{13}}$$\mathrm{cm^{-2}}$) and ionized impurity scattering (dash lines, impurity concentration = $\mathrm{5.0 \times 10^{11}}$$\mathrm{cm^{-2}}$) rates with $\mathrm{N_{inv}}$. (c) Mobility with various $\mathrm{N_{inv}}$ and $\mathrm{SiO_2}$ is the dielectric. (d) Mobility with various $\mathrm{N_{inv}}$ and $\mathrm{HfO_2}$ is the dielectric. In (c) and (d), the same surface roughness parameters and fix-charge and impurity concentrations as (a) and (b) are set.
• Figure 3: (a)$\sim$(b) Scattering rates (electron energy = 0.001 eV) with temperatures and $\mathrm{SiO_2}$ and $\mathrm{HfO_2}$ are used as dielectric, respectively. (c)$\sim$(f) Scattering rates with $\mathrm{N_{inv}}$. $\mathrm{SiO_2}$ and $\mathrm{HfO_2}$ are used as dielectric at 4K and 300K, respectively. The same parameters in FIG. 2 are set.
• Figure 4: (a) and (b) represent the field-dependent velocity results that $\mathrm{SiO_2}$ and $\mathrm{HfO_2}$ are used as dielectric and the $\mathrm{N_{inv}}\sim\mathrm{5.0 \times 10^{12}}$$\mathrm{cm^{-2}}$. (c) and (d) are the scattering events ratios of the main mechanisms when $\mathrm{HfO_2}$ is the dielectric at 4K and 300K. The same parameters in FIG. 2 are set.