Sub-microradian angular detection limits for field mapping by Lorentz 4D scanning transmission electron microscopy on a Si p–n junction

Abstract

We have examined a focused ion beam prepared silicon p–n junction lamella with different thicknesses by Lorentz 4D scanning transmission electron microscopy using center-of-mass (CoM) analysis. Using convergence semi-angles of 992, 207, and 83 μrad, we demonstrate diffraction limited spatial resolution combined with deflection detection limits on the sample as good as 0.49 μrad. We assess electron beam deflection detection limits away from the p–n junction, as well as the variation along the junction, and compare these with the variation in a vacuum region. With the larger semi-convergence angle of 992 μrad, a rigid shift of the transmitted disk was observed in the junction, while using smaller angles, a redistribution of intensity in the transmitted beam occurs, leading to an underestimation of the electric field related to the larger electron probe size. It is shown that electric field detection limits as good as 0.033, 0.0072, and 0.0051 MV cm−1 could be obtained for decreasing semi-convergence angles (at 376 nm sample thickness), equivalent to angular detection limits of 3.2, 0.68, and 0.49 μrad, respectively. For an optimal detection limit, we show that about 50 counts per pixel within the diffracted disk are needed for all settings, allowing rapid acquisition of diffraction maps, mitigating sample drift and beam damage issues. Moreover, we demonstrate that the CoM shift increases linearly with electrically active sample thickness, as must be the case for a quantitative signal.