Measuring the temperature of a mesoscopic electron system by means of single electron statistics

We measure the temperature of a mesoscopic system consisting of an ultradilute two-dimensional electron gas at the Si/SiO2 interface in a metal-oxide-semiconductor field effect transistor (MOSFET) by means of the capture and emission of an electron in a point defect close to the interface. We show that the capture and emission by point defects in Si n-MOSFETs can be temperature dependent down to 800 mK. As the finite quantum grand canonical ensemble applies, the time domain charge fluctuation in the defect is used to define the temperature of the few electron gas in the channel.