Electron thermalization in metallic islands probed by Coulomb blockade thermometry

We describe a systematic series of experiments on thermalization of electrons in lithographic metallic thin films at millikelvin temperatures using Coulomb blockade thermometry (CBT). Joule dissipation due to biasing of the CBT sensor tends to drive the electron system into non-equilibrium. Under all experimental conditions tested, the electron-electron relaxation is fast enough to ensure thermal electron distribution, which is also in agreement with the theoretical arguments we present. On the other hand, poor electron-phonon relaxation plays a dominant role in lifting the electron temperature above that of the bath. From a comparison of the results with the theoretical current-voltage characteristics of the thermometers we precisely determine the electron-phonon coupling constant for the common metals used. Our experiments show that it is a formidable task to attain thermal equilibrium with the bath using single-electron devices under non-zero bias conditions at 20-50 mK temperatures that are typically encountered in experiments. The conclusion concerning Coulomb blockade thermometry is more optimistic and two-fold: (1) One can now correct the errors due to bias heating in a satisfactory manner based on known material properties and the size of the metal films in the sensor. (2) Reliable thermometry down to 20 mK requires islands whose volumes are > 10(-15) m(3), which is still acceptable both from the parameter (capacitance) and fabrication points of view.