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Because of its large Fermi velocity, leading to a great mobility, graphene isexpected to play an important role in (small signal) radio frequencyelectronics. Among other, graphene devices based on Klein tunneling phenomenaare already envisioned. The connection between the Klein tunneling times ofelectrons and cut-off frequencies of graphene devices is not obvious. We arguein this paper that the trajectory-based Bohmian approach gives a very naturalframework to quantify Klein tunneling times in linear band graphene devicesbecause of its ability to distinguish, not only between transmitted andreflected electrons, but also between reflected electrons that spend time inthe barrier and those that do not. Without such distinction, typicalexpressions found in the literature to compute dwell times can give unphysicalresults when applied to predict cut-off frequencies. In particular, we studyKlein tunneling times for electrons in a two-terminal graphene deviceconstituted by a potential barrier between two metallic contacts. We show thatfor a zero incident angle (and positive or negative kinetic energy), thetransmission coefficient is equal to one, and the dwell time is roughly equalto the barrier distance divided by the Fermi velocity. For electrons incidentwith a non-zero angle smaller than the critical angle, the transmissioncoefficient decreases and dwell time can still be easily predicted in theBohmian framework. The main conclusion of this work is that, contrary totunneling devices with parabolic bands, the high graphene mobility is roughlyindependent of the presence of Klein tunneling phenomena in the active deviceregion.

Implications of the Klein tunneling times on high frequency graphene devices using Bohmian trajectories