Coulomb blockade and cotunneling in single electron circuits with on-chip resistors: Towards the implementation of the R pump

We report on the investigation of Al single electron structures equipped with miniature (8 um long) on-chip Cr resistors of R > R_k = h/e^2 = 25.8 kOhm. From the measurement of the Coulomb blockade in single-junction structures we evaluated the self-capacitance of our resistors per unit length, c = 62 aF/um. We demonstrate that the cotunneling current in the transistor samples in the Coulomb blockade regime obeys the power law, $I \propto V^{3+(R/R_k)}$, predicted by Odintsov, Bubanja and Sch\"on for a transistor having pure ohmic-resistance leads. The concept of the three-junction single electron pump with on-chip resistors (R-pump) is developed. We demonstrate that the implementation of the R-pump with a relative accuracy of the electron transfer of 10^{-8} is quite feasible with the technology available.