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The finite element simulation program COMSOL Multiphysics® was used to simulate the emission efficiency of a silicon tip electron source in triode configuration for different geometries and electrode potentials. The simulation predicts a maximum emission efficiency of 84% for an optimized structure. In a second simulation a gate electrode was concentrically arranged above a single CNT column. Here, the efficiency was simulated as a function of gate hole geometry, electrode potentials and distances between the electrodes. The simulation shows that a conical shape of the gate hole results in an efficiency up to nearly 100%.