Determination of Mean Inner Potential and Inelastic Mean Free Path of ZnTe Using Off-Axis Electron Holography and Dynamical Effects Affecting Phase Determination

Abstract

The mean inner potential (MIP) and inelastic mean free path (IMFP) of undoped ZnTe are determined using a combination of off-axis electron holography and convergent beam electron diffraction. The ZnTe MIP is measured to be 13.7±0.6 V, agreeing with previously reported simulations, and the IMFP at 200 keV is determined to be 46±2 nm for a collection angle of 0.75 mrad. Dynamical effects affecting holographic phase imaging as a function of incident beam direction for several common semiconductors are systematically studied and compared using Bloch wave simulations. These simulation results emphasize the need for careful choice of specimen orientation when carrying out quantitative electron holography studies in order to avoid erroneous phase measurements.

Determination of the mean inner potential of cadmium telluride via electron holography

“…Another established methodology 5 involves (i) utilizing Doyle-Turner atomic scattering factors; (ii) estimating an upper limit by assuming that the lattice is composed of distinct, non-bonded, neutral atoms (the "isolated atom" or "non-binding" approximation); and (iii) estimating a lower limit by applying an empirically derived correction factor (the "Ross-Stobbs" approximation). Applying this methodology to CdTe, in the same fashion as for ZnTe, 13 yields an upper value of 14.2 V and a lower value of 10.3 V. The experimental value certainly falls within this range, but it is clear that the experimental distribution is centered very close to the non-binding value. This lends weight to the assumption that the non-binding approximation yields accurate values for covalently bonded materials.…”

“…11,12 Additionally, Gan et al recently measured the mean free path of ZnTe (a rather similar material to CdTe) to be 46 nm (Ref. 13) via holography amplitude measurements. Therefore, to place the CdTe value in a wider context, it is important to clarify the definition of mean free path, and the electron scattering processes that underpin it.…”

“…The theoretical background and pertinent experimental considerations have been explained in detail. 20,21 The ZnTe measurements by Gan et al 13 utilized a very small aperture of 0.75 mrad, presumably resulting in significant scattering absorption. Considering both of these effects, it is therefore logical that the holographic measurements of mean free path, as reported by Gan et al for ZnTe, are much shorter.…”

“…15 It is a complex phenomenon, which can cause very significant electron wave phase shifts that vary dramatically with only slight lattice orientation or thickness changes. 13 It has been studied systematically by Lubk et al, 22 who explored the effect of dynamical diffraction on the mean inner potential measurements, as a function of simulation methodology, microscope parameters and specimen thickness, orientation, and composition. They found that dynamical scattering results in a systematic underestimation of the mean inner potential, and that the dynamical contribution was reduced as a function of tilt away from low-index crystallographic zone axes.…”

“…18,19 A more systematic study of the contributions of dynamical diffraction would also be beneficial. 13,22 The roles of synthesis method, crystal quality, and trace impurities should also be investigated. Measurements could also be acquired at multiple accelerating voltages, temperatures, electron dose rates, and specimens with different specimen geometries, to obtain a fuller picture of the mean inner potential for this semiconductor material.…”