Thermal design of superconducting digital circuits for milliKelvin operation

Niobium based rapid-single-flux-quantum (RSFQ) digital circuits generally operate at temperature 4 K. It is desirable to develop RSFQ circuits for operation at much lower temperatures, in particular to use as control and interface circuitry for superconducting qubits, and eventually for a full scale quantum computer. The total heat load is moderate - current designs generate 0.5 (mu)W per bias resistor, so simple RSFQ integrated circuits are easily compatible with commercial helium dilution refrigerators, and this power can readily be reduced by several orders of magnitude for complex future designs - but thermal conductivity will be a bottleneck. We present a simple model of heat flow through standard RSFQ structures. We find that circuits designed for 4 K operation can be used with little or no modification below one Kelvin. At lower temperatures however the heat generated on chip cannot be removed, and the temperature of a working circuit will rise. We suggest fabrication design rule changes to address this problem.