We calculate the depletion length, W(R), at the surface of a cylindrical nanostructure of radius R and show that W(R) satisfies the inequality Wp less than or equal to W(R) less than or equal to R-c, where W-p = root2epsilonPhi / (e(2)N(d)) is the depletion length at a planar interface (Phi is the surface potential energy barrier, epsilon is the dielectric constant and N-d is the doping density), and R-c = root2W(p) is, as we show, a critical radius below which, for R less than or equal to R-c, the structure is fully depleted. The standard result W-p therefore underestimates the depletion length in a finite structure, The discrepancy between W(R) and W-p becomes significant when the dimensions of the structure becomes comparable to the depletion length, as can occur in nanostructure devices. (C) 2002 Published by Elsevier Science Ltd.