In this context, global energy minimum means that your structure is at the geometry that minimizes the total energy. There are a few main ways to check this:
- If there are large forces on atoms, the structure needs geometry optimization (force minimization).
- If you chenge the length of the device central region just a little bit, and then relax the atoms, you will see if this leads to a lower total energy.
The 1DMIN method does the above automatically, but is not always needed. In particular, if the device was carefully made from relaxed "building blocks" you probably don't need to consider the central region length, so perhaps only relax forces on atoms.