Nanoelectronic primary thermometry below 4 millikelvin

We present measurements of nanoelectronic Coulomb Blockade Thermometers that are optimised for operation below 10 mK. Their design incorporates on-chip electronic filters and cooling fins with a high electron-phonon coupling. By immersing the devices in the 3He/4He mixture of a dilution refrigerator, and by minimising electrical noise in the measurement circuit, the on-chip electron temperature reaches a value of 3.7 mK, the lowest yet measured in any nanoelectronic device. Above 7 mK the devices are in good thermal contact with their environment and are not susceptible to self-heating. Below 7 mK the device continues to provide accurate thermometry of the on-chip electron temperature, which is seen to diverge from the ambient temperature. In this regime the device provides valuable information about noise and heat-leaks from the environment, which points the way towards cooling nanoelectronic structures to lower temperatures.