  Superconducting nanowire cryotrons (nTrons) are expected to be used as
interfaces for super-high-performance hybrid devices in which superconductor
and semiconductor circuits are combined. However, nTrons are still under
development, and diverse analyses of these devices are needed. Accordingly, we
have developed a numerical technique to simulate the three-terminal operation
of an nTron by using the finite element method to solve the time-dependent
Ginzburg-Landau (TDGL) equation and the heat-diffusion equation. Simulations
using this technique offer understanding of the dynamics of the order
parameter, the thermal behavior, and the characteristics of three-terminal
operation, and the TDGL model reproduces qualitatively the results of nTron
experiments. In addition, we investigated how some geometric and physical
parameters (the design elements) affect the operation characteristics. The TDGL
model has far fewer free parameters compared with the lumped-element
electrothermal model commonly used for simulating superconducting devices.
Furthermore, the TDGL model provides time-dependent visual information about
the superconducting state and the normal state, thereby offering insights into
the relationship between nTron geometry and three-terminal operation. These
simulation results offer a route to nTron optimization and the development of
nTron applications.
