Kinetics of charge carriers across a graphene–silicon Schottky junction

How fast can charge cross from a 2D sheet into a 3D crystal? Comparing graphene–silicon and gold–silicon contacts, we found that carriers cross the graphene interface about a million times more slowly, limited by how slowly electrons in graphene move out of its plane.

• Carrier transfer velocity across Au–Si is about 10⁷ cm/s, matching the thermal velocity in silicon.
• Across graphene–Si it is about 10 cm/s, nearly six orders of magnitude smaller.
• The effective out-of-plane velocity of carriers in graphene is about 1 cm/s.
• Transfer velocity rises almost exponentially with Schottky barrier height, explained by T¹ scaling theory with barrier-dependent scattering.