Electrostatic depolarization in clusters of emitters regularly spaced and with uniform height causes the emission to concentrate on the outer corners, suppressing the relative emission contribution from center emitters. In this Letter, we performed extensive three-dimensional computer simulations to show that profiling the height distribution of the emitters significantly compensates for the electrostatic depolarization and homogenizes the emitted current per emitter. Importantly, a minimum standard deviation on the currents from individual emitters shows the route to find the ellipsoidal height profile to achieve optimized conditions. This implies a maximized macroscopic current extractable from the device since every emitter contributes approximately the same before burning out. Our findings are expected to guide developments on new field electron emission devices.

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