Direct and Indirect Band-to-Band Tunneling in Germanium-Based TFETs

Germanium is a widely used material for tunnel FETs because of its small band gap and compatibility with silicon. Typically, only the indirect band gap of Ge at 0.66 eV is considered. However, direct band-to-band tunneling (BTBT) in Ge should be included in tunnel FET modeling and simulations since the energy difference between the Ge conduction band edges at the L and Γ valleys is only 0.14 eV at room temperature. In this paper, we theoretically calculate the parameters A and B of Kane´s direct and indirect BTBT models at different tunneling directions ([100], [110], and [111]) for Si, Ge and unstrained Si_1-xGe_x. We highlight how the direct BTBT component becomes more important as the Ge mole fraction increases. The calculation of the band-to-band generation rate in the uniform electric field limit reveals that direct tunneling always dominates over indirect tunneling in Ge. The impact of the direct transition in Ge on the performance of two realistic tunnel field-effect transistor configurations is illustrated with TCAD simulations. The influence of field-induced quantum confinement is included in the analysis based on a back-of-the-envelope calculation.