Control Charge Transfer in Graphene by an Electric Field

Graphene is one of the strongest, lightest and most conductive materials that have ever been discovered. Graphene is stronger and stiffer than diamond, yet can be stretched by a quarter of its length. Graphene properties are attractive for scientists and electrical engineers for great deal of reasons. For example, it can provide us with circuits that are smaller and faster than what we have in silicon or we can have many other useful devices like super small computers.In this work, we have discussed a method in which we can control the charge transfer in graphene by using an electric field existed by a kind of variable external bias perpendicular to the graphene surface. This vertical electric field makes a rectangular barrier. The electrons go through the barrier in different angles. By solving the Dirac equation in different areas, the components of the Dirac spinor can be achieved. Finally, by applying the boundary conditions, we have evaluated the electronic transmission coefficient and probability.Our results show the complete transmission at the normal incident angle without being affected by the barrier height or length. While as the incident angle increases from zero, we can observe different values for the transmission probability including special angles at which we have resonances. Besides, the transmission probability has an oscillatory behavior as a function of barrier length which is related to quantum behaviors of the system. In addition, our calculations show that by manipulating the adjustable electric barriers on graphene, it is possible to control angle-dependent electronic transmission. In other words, we can control the electron transmission by manual tuning the external gate voltage from zero to unit. This formalism can be used in designing graphene base nano electeronic divices including field effect transistors.