Kinetics of Charge Carriers across a Graphene-Silicon Schottky Junction

Abstract

We perform a comparative study on the transfer velocity of charge carriers across two-dimensional and (2D) three-dimensional (3D) graphene-silicon and 3D-3D $\mathrm{Au}$-silicon Schottky junctions. Within the framework of classical thermionic emission theory, the transfer velocity of carriers across the $\mathrm{Au}$-$\mathrm{Si}$ interface is determined as $\overline{v}\ensuremath{\sim}{10}^{7}$ cm/s that is thoroughly consistent with the average thermal velocity of carriers in silicon. In contrast, the graphene-$\mathrm{Si}$ interface discloses a much lower transfer velocity of $\overline{v}\ensuremath{\sim}{10}^{1}$ cm/s, i.e., nearly 6 orders of magnitude smaller than the thermal velocity of carriers in silicon. Utilizing the ${T}^{1}$ universal scaling law for vertical 2D-3D Schottky junctions, we determine the effective out-of-plane velocity of charge carriers in graphene as ${v}_{\ensuremath{\perp}}^{\ensuremath{\ast}}\ensuremath{\sim}{10}^{0}$ cm/s. This indicates current flow across the graphene-$\mathrm{Si}$ contact is substantially limited by ${v}_{\ensuremath{\perp}}^{\ensuremath{\ast}}$. Moreover, by analyzing experimental activation-energy data, we uncover a general correlation between the kinetics of charge carriers and the potential barrier at the graphene-$\mathrm{Si}$ interface. It is found that the transfer velocity increases almost exponentially with the Schottky barrier height, which cannot be explained in the framework of classical theory. Considering nonconserving ${\mathbf{k}}_{\ensuremath{\parallel}}$ scattering strength as an exponential function of Schottky barrier height, ${T}^{1}$ scaling theory leads to a comprehensive interpretation of experimental data. This study sheds light on the electronic processes across 2D-3D interfaces.