To other QTCAD users, the problem was found to be in the .geo file used in the simulation.
When generating a structure, it is very important to make sure that the mesh is conformal, i.e., it should be possible to draw a path on the mesh between any pair of nodes. Here is an example of a non-conformal mesh, taken from a very clear tutorial by Dr. Bertrand Thierry.
As can be seen in the picture, the green mesh and the orange mesh are independent meshes. What we want is a single conformal mesh, like this:
In the first picture, solving, say, Poisson's equation would result in two independent solutions on the two meshes. In the second picture, the green and orange meshes are connected at their intersections, and a single Poisson solution through the entire domain would be found.
In the example shared by byoungwookan, the 2D mesh defining the gates and the 3D mesh defining the simulation domain were disjoint (non-conformal). As a consequence, boundary conditions from the gates could not be enforced to the simulation domain when solving Poisson's equation. This lead the Poisson solver to crash.
To produce a conformal mesh, a straightforward approach is to use the BooleanFragments operation which is available when using the OpenCASCADE kernel of Gmsh instead of the Built-in kernel. This approach is described very clearly in Dr. Thierry's tutorial, above.
When observing that a solver crashes, it is always a good reflex to check if the mesh is conformal. This is an error that most Gmsh users make in the beginning (myself included).
Special thanks to @byoungwookan for reporting this issue, and thus giving us the opportunity to make this clarification.
