Ballistic bipolar junctions in chemically gated graphene ribbons

The realization of ballistic graphene pn-junctions is an essential task in order to study Klein tunneling phenomena. Here we show that intercalation of Ge under the buffer layer of pre-structured SiC-samples succeeds to make truly nano-scaled pn-junctions. By means of local tunneling spectroscopy the junction width is found to be as narrow as 5 nm which is a hundred times smaller compared to electrically gated structures. The ballistic transmission across the junction is directly proven by systematic transport measurements with a 4-tip STM. Various npn- and pnp-junctions are studied with respect to the barrier length. The pn-junctions are shown to act as polarizer and analyzer with the second junction becoming transparent in case of a fully ballistic barrier. This can be attributed to the almost full suppression of electron transmission through the junction away from normal incidence.


I. CALCULATION OF THE TRANSMISSION PROBABILITY
The calculation of the transmission probability is carried out for electrons with an energy E which is half of the potential step (E = V 0 2 = 300 meV ). In our case this assumption is sufficiently close to our experimental conditions since the difference in the chemical potential of the n-and p-type doped areas is comparably small (about 50 meV). In figure S1 the transmission probabilities for smooth and sharp potential steps are plotted against the incident angle. In the case of a sharp potential step (k F t << 1) the transmission probability is given by T = cos 2 (φ) [1,2]. As obvious, a preference for normal incidence is given by this transmission function. However, the transmission probability is relatively high for all angles except those close to 90 • . In the case of a smooth potential step (k F t >> 1) the transmission probability is T = exp(−πk F tsin 2 (φ)) [1,2]. As for the sharp potential step T (0) = 1, but decreases rapidly to zero for larger angles in contrast to the sharp potential step. This is the reason for the strong collimation effect of a smooth potential step, basically no other particles than those with an incidence angle close to 0 are transmitted.
In our experimental setup, the width of the potential step is in the transition region between a sharp and a smooth step since k F t ≈ 0.7. The corresponding transmission probability is calculated under the assumption that the formula given above for the smooth potential step is still valid. The result is shown in figure S1 and reflects the transitional character between a smooth and a sharp potential step.

II. SHEET RESISTANCE AND CARRIER MOBILITIES
In order to discriminate the contribution of the pn junctions from the background, the Hence, from the two resistances R A and R B , the sheet resistance can be directly calculated without the need for any geometrical correction factors [3].
The IV-curves recorded exhibit linear (ohmic) behavior and the corresponding resistance is deduced by a linear fit. In fig. S2b) the sheet resistances of a p-doped and an n-doped area with respect to the probe spacing are shown exemplarily for a measurement taken at room temperature. No variation of the sheet resistance with the probe spacing is observed for neither of the two doping levels, a typical signature for two dimensional transport behavior.
The mean sheet resistance of the p-doped area (782 Ω) is slightly higher than on the n-doped area (729 Ω). The temperature dependence of the sheet resistance is rather weak as can be seen in fig. S2c). Both areas show an almost identical small decrease of the sheet resistance with decreasing temperature. The sheet resistance of the p-doped area is decreasing to a minimum value of 502 Ω at 32 K while the minimum value for the n-doped area is slightly higher (520 Ω at 32 K). The temperature dependence can be described by a simple model taking into account scattering processes with surface phonons [4] as obvious from the fit in fig. S2c). The corresponding mobilities are extracted using the Drude model where FIG. S1: Transmission probability T as a function of the incidence angle across a potential step for an electron energy of half the potential step. Three cases are shown: a sharp potential step (k F t << 1), a smooth step (k F t >> 1) and an intermediate case (k F t ≈ 0.7). The formulas for each step type are given in the main text. FIG. S2: a) The two setups used for the dual configuration measurements to deduce R A and R B . b) Sheet resistance of n and p doped areas as a function of probe spacing at room temperature. c) Sheet resistances and mobilities of n and p doped graphene areas as a function of temperature.