Visualization of different carrier concentrations in n-type-GaN semiconductors by phase-shifting electron holography with multiple electron biprisms.

Phase-shifting electron holography (PS-EH) using a transmission electron microscope (TEM) was applied to visualize layers with different concentrations of carriers activated by Si (at dopant levels of 1019, 1018, 1017 and 1016 atoms cm-3) in n-type GaN semiconductors. To precisely measure the reconstructed phase profiles in the GaN sample, three electron biprisms were used to obtain a series of high-contrast holograms without Fresnel fringes generated by a biprism filament, and a cryo-focused-ion-beam (cryo-FIB) was used to prepare a uniform TEM sample with less distortion in the wide field of view. All layers in a 350-nm-thick TEM sample were distinguished with 1.8-nm spatial resolution and 0.02-rad phase-resolution, and variations of step width in the phase profile (corresponding to depletion width) at the interfaces between the layers were also measured. Thicknesses of the active and inactive layers at each dopant level were estimated from the observed phase profile and the simulation of theoretical band structure. Ratio of active-layer thickness to total thickness of the TEM sample significantly decreased as dopant concentration decreased; thus, a thicker TEM sample is necessary to visualize lower carrier concentrations; for example, to distinguish layers with dopant concentrations of 1016 and 1015 atoms cm-3. It was estimated that sample thickness must be more than 700 nm to make it be possible to detect sub-layers by the combination of PS-EH and cryo-FIB.