Miniature electrical filters for single electron devices

In experiments on single electron devices, the electromagnetic noise from parts of the apparatus at temperatures higher than that of the device can dramatically increase the tunnel rates out of the Coulomb-blocked state and therefore increase the device error rate. The electrical lines must therefore be filtered adequately. We derive simple expressions for calculating the required attenuation coefficient. We describe a wide-band miniature dissipative filter functioning at cryogenic temperatures. The effective thermalization of an experiment at 30 mK can be obtained by placing four of these filters in series at temperatures ranging from 4 K to 30 mK.