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Dependence of optimal spacing on applied field in ungated field emitter arrays
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29. Assuming we are operating at spacings that are comparable to the emitter height.
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33.This quantity is often referred to as the transconductance in gated field emitters, in which the change in applied field is due to a change in the gate voltage rather than the anode-cathode field considered here. See, J.P. Calame, H.F. Gray, and J.L. Shaw, J. Appl. Phys. 73, 1485 (1993).
34. The effect in 2-dimensional arrays can be seen in Ref. 1 in the curves labeled “1” for the square and triangular arrays. This curve of β(b) included only the central emitter and the nearest neighbors, and while not completely accurate due to the use of the same fitting constants for both the inboard and outboard emitters, it does replicate the minimum observed in the 1-dimensional arrays.
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In ungated field emitter arrays, the field enhancement factor β of each emitter tip is reduced below the value it would have in isolation due to the presence of adjacent emitters, an effect known as shielding or screening. Reducing the distance b between emitters increases the density of emission sites, but also reduces the emission per site, leading to the existence of an optimal spacing that maximizes the array current. Most researchers have identified that this optimal spacing is comparable to the emitter height h, although there is disagreement about the exact optimization. Here, we develop a procedure to determine the dependence of this optimal spacing on the applied electric field. It is shown that the nature of this dependence is governed by the shape of the β(b) curve, and that for typical curves, the optimal value of the emitter spacing b decreases as the applied field increases.
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