Planar array of semiconducting nanotubes in an external electric field: Collective screening and polarizability

We study theoretically the charge separation in a planar array of semiconducting nanotubes (NTs) of length, 2h, placed in an external electric field, F, parallel to their axes. By employing the conformal mapping, we find analytically the exact distribution of the induced charge density for the arbitrary ratio of the gap, E(g), and the voltage drop, eFh, across the NT. We use the result obtained to (i) trace the narrowing of the neutral strip at the center of the NT with increasing F, (ii) analyze the polarizability of the array as a function of E(g), and (iii) study the field enhancement near the tips.