Voltage and temperature dependence of silicon high-order Laue zone line positions

Abstract

Two fast-electron quantum states are highly excited for crystal orientations close to the Si<111> zone axis, manifesting themselves as pairs of lines associated with each high-order Laue zone (HOLZ) reflection. The electron wave-vector k is determined from absolute positions of deficit lines in the zeroth-order beam, where full account is taken of dynamically induced displacements compared with positions determined from kinematic (geometrical) theory. Geometrie results approximate experiment provided that k is modified by Δk, equivalent to a voltage shift ΔE. The two excited Bloch states provide an independent assessment of Δk. Changes in HOLZ line position with inereasing temperature are due to delocalization of the projected potential and corresponding shifts in eigenvalues. The displacement of HOLZ lines due to thermal lattice dilation is three times smaller than shifts due to delocalization of the elastic potential. A nominal 300 kV accelerating voltage of a Philips CM30 electron microscope is measured to be 302–75 ± 0*_d2 kV.