Critical Voltage Effect in Tungsten ECP

Abstract

The critical voltage effect is caused by an accidental degeneracy between two Bloch waves at a certain energy, Vc, and results in a disappearance of a particular reflection in the Kikuchi pattern. The effect until now has only been detected in this way via high voltage transmission electron microscopy, mainly because for most materials Vc is several hundred keV. Since the predicted critical voltage for the (220) reflection in tungsten is 22 keV, we attempted, with success, to detect the effect in an SEM by looking at the tungsten electron channeling pattern (ECP) as a function of accelerating voltage, E0. The critical voltage effect was evident in the (220) ECP line as an anomalous narrowing of the line near Vc and inverted contrast of the line for E0 > Vc. Vc was determined by measuring the voltage where the (220) linewidth was at a minimum to be Vc = 10.50 ± .05 keV. This experimental Vc was used in a many beam diffraction calculation to refine the first order Fourier lattice potential coefficient. The shape of the line narrowing curve in the vicinity of Vc was used to estimate the depth of ECP information for the (220) line in tungsten. Details of the experiment and subsequent calculations will be discussed. The measurements were done on a single crystal of tungsten in a modified version of an ISI Super III-A scanning electron microscope. The linewidth of the (220) ECP line was measured in the range 10-15 keV from specimen current line profiles using a signal gating and averaging technique to improve the signal to noise ratio. The (220) line becomes too broad to be visible above 15 keV which is in agreement with line-width calculations using simple two beam diffraction theory. An example ECP and line profile are shown in Figure 1 for E0 = 12.25 keV. The micrograph is a differentiated image of the backscattered electron signal. The dark (220) line was of opposite contrast to the rest of the (110) series of lines which were light. The (220) line shape is circled in the line profile. Its line-width, △θ, is defined as the angular distance between the maximum and minimum.