Electron tunnel rates in a donor-silicon single electron transistor hybrid

We investigate a hybrid structure consisting of $20\pm4$ implanted $^{31}$P atoms close to a gate-induced silicon single electron transistor (SiSET). In this configuration, the SiSET is extremely sensitive to the charge state of the nearby centers, turning from the off state to the conducting state when the charge configuration is changed. We present a method to measure fast electron tunnel rates between donors and the SiSET island, using a pulsed voltage scheme and low-bandwidth current detection. The experimental findings are quantitatively discussed using a rate equation model, enabling the extraction of the capture and emission rates.