Effect of polarization screening length on electron-pump cotunneling errors

Abstract

We have calculated cotunneling errors occurring in the electron pump, including the effects of polarization screening length as determined by the gate-to-junction capacitance ratio. Previous analyses have been done in the limit of very large screening length, or equivalently in the limit of a very small ratio of gate-to-junction capacitance, where cotunneling errors are at most of order (N-1) for an N-junction pump for a restricted range of end-to-end bias. Within this same range, we find that the calculated cotunneling errors can increase significantly with increasing capacitance ratios 0.15–0.3, which encompass those reported for several experimental pumps in the literature. With realistic parameters, the calculated first-, second-, third-, and fourth-order cotunneling errors increase the error of a five-junction pump by factors of between 2 and 10 over much of the range of end-to-end bias and by up to a factor of 5×${10}^3$ toward the negative end of the bias range. We discuss the implications of these results for recent experimental observations which are at least two orders of magnitude larger than calculations based on very small capacitance ratios.