Modelling background charge rearrangements near single – electron transistors as a Poisson process

– Background charge rearrangements in metallic single–electron transistors are modelled in two–level tunnelling systems as a Poisson process with a scale parameter as only variable. The model explains the recent observation of asymmetric Coulomb blockade peak spacing distributions in metallic single–electron transistors. From the scale parameter we estimate the average size of the tunnelling systems, their density of states, and the height of their energy barrier. We conclude that the observed background charge rearrangements predominantly take place in the substrate of the single–electron transistor. Introduction. – The metallic single–electron transistor (SET) [1,2] is a possible building block of future electronics, based upon the controlled transfer of individual charges onto and off small isolated electrodes, called islands. However, due to the extreme sensitivity of SETs to charges close to these islands, a static background charge arrangement is essential for proper device operation [3, 4]. On the other hand, this very high sensitivity makes the SET an excellent device to investigate background charge rearrangements, e.g. in nearby two–level tunnelling systems (TLTS) [5,6]. One issue of this paper is to determine the location of TLTSs within the device. In recent experiments [7, 8] on Al/AlOx/Al SETs it was shown that the distribution of nearest–neighbour spacings (NNS) between Coulomb blockade oscillation peaks is influenced by such charge rearrangements: they generate a pronounced tail in the NNS distribution towards smaller spacings (see left inset of fig. 1). Here, we propose a quantitative model for this tail. We argue that background charge rearrangements can be interpreted in terms of a Poisson process. This way, we can fit the shape of the NNS distribution tail, with a single scale parameter. From this fit, we find an average hopping distance in the TLTS of about 4 nm and conclude that the charge rearrangements do not occur in the tunnel barriers of the SET.