TY - JOUR
T1 - Penetration of external field into regular and random arrays of nanotubes
T2 - Implications for field emission
AU - Sedrakyan, T. A.
AU - Mishchenko, E. G.
AU - Raikh, M. E.
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - We develop an analytical theory of polarization of a vertically aligned array of carbon nanotubes (NTs) in external electric field. Such arrays are commonly utilized in field-emission devices, due to the known electrostatic effect of strong field enhancement near the tip of an individual NT. A small ratio of the NT radius to the separation between neighboring NTs allows us to obtain asymptotically exact solution for the distribution of induced charge density along the NT axes. For a regular array, this solution allows us to trace the suppression of the field penetration with increasing the density of NTs in the array. We demonstrate that for a random array, fluctuations in the NT density terminate the applicability of our result at distances from the NT tips much larger than the field penetration depth, where the induced charge density is already exponentially small. Our prime conclusion is that, due to collective screening of the external field by the array, the field-emission current decreases drastically for dense arrays compared to an individual NT. We argue that the reason why the strong field emission, described by the Fowler-Nordheim law and observed in realistic arrays, is the strong dispersion in heights of the constituting NTs.
AB - We develop an analytical theory of polarization of a vertically aligned array of carbon nanotubes (NTs) in external electric field. Such arrays are commonly utilized in field-emission devices, due to the known electrostatic effect of strong field enhancement near the tip of an individual NT. A small ratio of the NT radius to the separation between neighboring NTs allows us to obtain asymptotically exact solution for the distribution of induced charge density along the NT axes. For a regular array, this solution allows us to trace the suppression of the field penetration with increasing the density of NTs in the array. We demonstrate that for a random array, fluctuations in the NT density terminate the applicability of our result at distances from the NT tips much larger than the field penetration depth, where the induced charge density is already exponentially small. Our prime conclusion is that, due to collective screening of the external field by the array, the field-emission current decreases drastically for dense arrays compared to an individual NT. We argue that the reason why the strong field emission, described by the Fowler-Nordheim law and observed in realistic arrays, is the strong dispersion in heights of the constituting NTs.
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U2 - 10.1103/PhysRevB.73.245325
DO - 10.1103/PhysRevB.73.245325
M3 - Article
AN - SCOPUS:33745215645
SN - 1098-0121
VL - 73
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 24
M1 - 245325
ER -