The Large Electron Multipliers (LEMs) are key components of double phase liquid argon TPCs. The drifting charges after being extracted from the liquid are amplified in the LEM positioned half a centimeter above the liquid in pure argon vapor at 87 K. The LEM is characterised by the size of its dielectric rim around the holes, the thickness of the LEM insulator, the diameter of the holes as well as their geometrical layout. The impact of those design parameters on the amplification were checked by testing seven different LEMs with an active area of 10$times$10 cm$^2$ in a double phase liquid argon TPC of 21 cm drift. We studied their response in terms of maximal reachable gain and impact on the collected charge uniformity as well as the long term stability of the gain. We show that we could reach maximal gains of around 150 which corresponds to a signal-to-noise ratio ($S/N$) of about 800 for a minimal ionising particle (MIP) signal on 3 mm readout strips. We could also conclude that the dielectric surfaces in the vicinity of the LEM holes charge up with different time constants that depend on their design parameters. Our results demonstrate that the LAr LEM TPC is a robust concept that is well-understood and well-suited for operation in ultra-pure cryogenic environments and that can match the goals of future large-scale liquid argon detectors.
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