Direct measurement of the charge distribution along a biased carbon nanotube bundle using electron holography

Nanowires and nanotubes can be examined in the transmission electron microscope under an applied bias. Here we introduce a model-independent method, which allows the charge distribution along a nanowire or nanotube to be measured directly from the Laplacian of an electron holographic phase image. We present results from a biased bundle of carbon nanotubes, in which we show that the charge density increases linearly with distance from its base, reaching a value of $∼0.8electrons/nm$ near its tip.