Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrödinger equation), and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams.

A new method has been devised for investigation by transmission electron microscopy of the electrostatic microfield associated with reverse biased $p-n$ junctions. By means of electron holography and optical interferometry it is possible to obtain on the reconstructed images two-dimensional representations of the projected potential distribution inside and outside the specimen.

We propose an improved type of holographic-plate suitable for the shaping of electron beams. The plate is fabricated by a focused ion beam on a silicon nitride membrane and introduces a controllable phase shift to the electron wavefunction. We adopted the optimal blazed-profile design for the phase hologram, which results in the generation of highly efficient (25%) electron vortex beams. This approach paves the route towards applications in nano-scale imaging and materials science.

A large thermoelectric power factor in heavily boron-doped p-type nanograined Si with grain sizes ∼30 nm and grain boundary regions of ∼2 nm is reported. The reported power factor is ∼5 times higher than in bulk Si. It originates from the surprising observation that for a specific range of carrier concentrations, the electrical conductivity and Seebeck coefficient increase simultaneously. The two essential ingredients for this observation are nanocrystallinity and extremely high boron doping levels. This experimental finding is interpreted within a theoretical model that considers both electron and phonon transport within the semiclassical Boltzmann approach. It is shown that transport takes place through two phases so that high conductivity is achieved in the grains, and high Seebeck coefficient by the grain boundaries. This together with the drastic reduction in the thermal conductivity due to boundary scattering could lead to a significant increase of the figure of merit ZT. This is one of the rare observations of a simultaneous increase in the electrical conductivity and Seebeck coefficient, resulting in enhanced thermoelectric power factor.