Thermal Modeling of Rapid Single Flux Quantum Circuit Structures

Abstract

The operation of rapid single flux quantum (RSFQ) circuits depends upon the superconductive properties of the Josephson junctions (JJs) and metal layers, which are highly dependent on the temperature. Increasing densities and frequencies of JJs in RSFQ circuits have created a need to accurately model the local ambient thermal environment. In this article, an analytic thermal model of RSFQ circuit structures targeting the MIT Lincoln Laboratory SFQ5ee 10 kA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> technology is presented. The model is based on a network of thermal resistances, representing the heat generation and thermal paths within an RSFQ circuit. An error of less than 0.22% between the model and a numerical solver is achieved. To reduce the computational complexity, the sparsity of the matrix of thermal resistances among the nodes is increased by exploiting the effective radius of the heat spreading behavior. Ignoring the thermal effects of the heating elements outside of a target radius reduces the number of thermal resistances by 50%, increasing the maximum error of the model to only 0.26%.