# Measuring the Temperature of a Mesoscopic Electron System by means of Single Electron Statistics 

Enrico Prati and Matteo Belli 

Laboratorio Nazionale Materiali e Dispositivi per la Microelettronica, Consiglio Nazionale delle Ricerche - Istituto Nazionale per la Fisica della Materia, Via Olivetti 2, I-20041 Agrate Brianza, Italy ∗ 

Marco Fanciulli 

Laboratorio Nazionale Materiali e Dispositivi per la Microelettronica, Consiglio Nazionale delle Ricerche - Istituto Nazionale per la Fisica della Materia, Via Olivetti 2, I-20041 Agrate Brianza, Italy ∗ and Dipartimento di Scienza dei Materiali, Universita degli Studi Milano-Bicocca, 20125 Milano, Italy 

Dipartimento di Elettronica e Informazione, Politecnico di Milano, P.za Leonardo da Vinci 32, I-20133 Milano, Italy 

Giorgio Ferrari 

## Abstract 

We measure the temperature of a mesoscopic system consisting of an ultra-dilute two dimen- sional electron gas at the Si/SiO$_{2}$ 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. Contrarily to previous reports, 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. 

