Mean Inner Potential Research Articles

Comparing the mean inner potential of Zn-VI semiconductor nanowires using off-axis electron holography

The mean inner potential (MIP), V 0, for a series of Zn group VI semiconductor nanostructures were measured experimentally using off-axis electron holography. Values for ZnS, ZnTe and ZnO were remeasured and new values were added for ZnSe and ZnSSe nanowires. We confirm that the MIP increases non-linearly with mass density beginning at 12.4 ± 0.2 V for the lowest density ZnS and slowly increasing with composition to 12.9 ± 0.2 V for ZnSe, more rapidly for ZnTe and with a significant increase to 14.8 ± 0.3 V for ZnO with the highest density. Published results from DFT calculations compared well to these measurements with similar trends apparent for other cation families such as the Ga-III-V.

The Mean Inner Potential of Hematite α-Fe2O3 Across the Morin Transition.

We measure the mean inner potential (MIP) of hematite, α-Fe2O3, using electron holography and transmission electron microscopy. Since the MIP is sensitive to valence electrons, we propose its use as a chemical bonding parameter for solids. Hematite can test the sensitivity of the MIP as a bonding parameter because of the Morin magnetic phase transition. Across this transition temperature, no change in the corundum crystal structure can be distinguished, while a change in hybridized Fe-3d and O-2p states was reported, affecting ionic bonding. For a given crystallographic phase, the change in the MIP with temperature is expected to be minor due to thermal expansion. Indeed, we measure the temperature dependence in corundum α-Al2O3(112¯0) between 95 and 295 K showing a constant MIP value of ∼16.8 V within the measurement accuracy of 0.45 V. Thus, our objectives are as follows: measure the MIP of hematite as a function of temperature and examine the sensitivity of the MIP as a bonding parameter for crystals. Measured MIPs of α-Fe2O3(112¯0) above the Morin transition are equal, 17.85 ± 0.50 V, 17.93 ± 0.50 V, at 295 K, 230 K, respectively. Below the Morin transition, at 95 K, a significant reduction of ∼1.3 V is measured to 16.56 ± 0.46 V. We show that this reduction follows charge redistribution resulting in increased ionic bonding.

Mean inner potential of graphite measured by electron holography: Probing charge distribution and orbital diamagnetic susceptibility

The mean-inner-potential (MIP) of a crystal is the average electrostatic Coulomb potential within a crystal with respect to vacuum.We conducted off-axis electron holography experiments on highly-oriented-pyrolytic-graphite (HOPG) in a transmission-electron-microscope to measure the MIP from nanometer-scale volumes of Bernal graphite oriented with respect to the electron beam, along the principal-axis or directions in the basal plane. These MIP were related to mean orbital electron radii and diamagnetic susceptibilities in perpendicular planes.These measurements are interesting compared to magneto-transport measurements, which report large anisotropy. Along the principal-axis, the susceptibility is highest amongst diamagnetic materials. However, those measurements vary significantly depending on type, size, and thickness of samples, indicating that the signal is significantly extrinsic due to defect induced interfaces. Indeed, structural examination of HOPG show stacking-faults and planar rotations around the principal-axis, such that measuring intrinsic properties requires probing a volume of ∼102 × 102 × 102 nm3.Experiments on such individual graphite crystals with (0001) basal, or (1–100), (2-1-10) prismatic planes, resulted in MIP of 10.16 ± 0.40V, 11.37 ± 0.35V, 12.66 ± 0.41V, respectively. First-principles calculations confirm these anisotropic measurements with 11.72V, 13.65V, 14.56 V, respectively.These measured MIP enable to determine projected mean-radii of electron orbitals and volume susceptibilities at 0.704 ± 0.015 Å, (−1.99 ± 0.08) × 10−5; 0.744 ± 0.015 Å, (−2.23 ± 0.07) × 10−5; 0.785 ± 0.015 Å, (−2.48 ± 0.08) × 10−5.

Measuring the mean inner potential of Al2O3 sapphire using off-axis electron holography

The mean inner potential (MIP) of a single crystal α-Al2O3 sapphire was measured using off-axis electron holography. To measure the MIP, we use mechanically polished wedge specimens for transmission electron microscopy (TEM). This approach also enabled us to measure the plasmon mean free path for inelastic scattering (IMFP). The wedge specimen, chosen here at an angle of approximately 45°, allows to determine the MIP by measuring the gradient of phase variations of the reconstructed electron wave over extended regions across the sample. The angle of the wedge was measured to an accuracy of better than 1° by two methods: first, perpendicular sectioning in a focused ion beam for direct measurement by TEM and second, by a non-destructive approach of confocal optical microscopy. The validity of this methodology was examined on a single crystal Si(001) sample showing that the mechanically polished wedge approach can be applied to a wide range of materials. Our measurements concluded that the MIP of sapphire is V0 = 16.90 ± 0.36 V. Furthermore, the IMFP of sapphire was measured at 136 ± 2 nm for 197 keV electrons with a collection angle of 18mrad. The measured MIP of sapphire reflects its degree of ionicity, which lies between theoretical calculations based on electron scattering factors of charged and neutral isolated atoms obtained by Dirac–Fock calculations. Our MIP measurements tend to the expected value for this predominantly ionic material. To account for chemical bonding and the role of the crystallographic plane at the surface of the sample, we compared the experimental measurements to density-functional-theory calculations of the MIP. Calculations of α-Al2O3 slabs cut along (0001) and (1–100) planes obtained MIP values of 15.7 V and 16.7 V, respectively.

Correlative micro-diffraction and differential phase contrast study of mean inner potential and subtle beam-specimen interaction

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22 V and 14.15 ± 0.22 V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

Publisher’s note

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22V and 14.15 ± 0.22V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

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

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.

Imaging of three-dimensional (Si,Ge) nanostructures by off-axis electron holography

Quantitative phase mapping in transmission electron microscopy is applied to image the three-dimensional (3D) morphology of (Si,Ge) islands grown on Si substrates. The phase shift of the transmitted electrons induced by the crystal inner potential was recorded by using off-axis electron holography. The analysis of the experimental data requires the knowledge of the mean inner potential (MIP) of the (Si,Ge) solid solution. The MIP was calculated using different models of isolated or bonded atoms, which are based on the interpolation of first principle data. The results are compared with structure modeling and related MIP calculations applying classical molecular dynamics (MD) simulations. For MD simulations bond order potentials were applied, which can take into consideration both electronic effects and elastic relaxations. The calculated mean inner potential is used to transform the phase shifts into thickness mapping for the reconstruction of the 3D island morphology. Both, phase shift due to dynamical electron diffraction and structural relaxation influence the resulting 3D reconstruction.

Chemical diffusion: Another factor affecting the magnetoresistance ratio in Ta/CoFeB/MgO/CoFeB/Ta magnetic tunnel junction

This letter investigates the microstructure and mean inner potential (MIP) profile of Ta/CoFeB/MgO/CoFeB/Ta magnetic tunnel junctions (MTJs) by high resolution transmission electron microscopy (HRTEM) and electron holography, respectively. The inconspicuous crystallization of MgO barrier is confirmed by HRTEM in the post-annealed sample at 250 °C. An obvious MIP difference is displayed in the Ta layers between the top and bottom of the MTJ, and elemental content difference of them is confirmed by energy dispersive spectroscopy. These results imply that the chemical diffusion can also give rise to a lower tunnel magnetoresistance ratio besides the inconspicuous crystallization of MgO barrier.

Electron holography characterization as a method for measurements of diameter and mean inner potential of hollow nanomaterials

In this paper, we provide a method for the simultaneous measurement of the inner diameter of nanotubes with a regular shape and calculation of their mean inner potential (MIP) using electron holography. This method contains 4 steps: (i)phase profile characterization from electron holography; (ii) shape assumption from prepared data; (iii) thickness simulation from a shape assumption and fitting method; (iv) calculation of MIP of the simulated and fitted parameters. By this method, as an example, the shape and the outer and inner diameters of a tube formed from C(60) molecules were characterized. The MIP of the tube was also calculated through this method. The MIP calculation from another nano whisker formed from C(60) molecules supports the feasibility of our method and it could be extended to other nanomaterials. This work provides a convenient method for morphology characterization of hollow nanomaterials, such as diameter measurements and cross-sectional shape determination, which are the most basic and important characteristics of the nanomaterials. In addition, it also provides a method for MIP calculation without a thickness measurement if the samples have relatively regular shapes. Thus this method should be more convenient for closely combining the tomography and physical properties of samples, which could be essential for in situ TEM studies of nanomaterials.

Towards automated electron holographic tomography for 3D mapping of electrostatic potentials

Electron-holographic tomography (EHT), that is, the combination of off-axis electron holography with electron tomography, was successfully applied for the quantitative 3D mapping of electrostatic potentials at the nanoscale. Here we present the first software package (THOMAS) for semi-automated acquisition of holographic tilt series, a prerequisite for efficient data collection. Using THOMAS, the acquisition time for a holographic tilt series, consisting of object and reference holograms, is reduced by a factor of five on average, compared to the previous, completely manual approaches. Moreover, the existing software packages for retrieving amplitude and phase information from electron holograms have been extended, now including a one-step procedure for holographic tilt series reconstruction. Furthermore, a modified SIRT algorithm (WSIRT) was implemented for the quantitative 3D reconstruction of the electrostatic potential from the aligned phase tilt series. Finally, the application of EHT to a polystyrene latex sphere test-specimen and a pn-doped Ge ‘needle’-shaped specimen are presented, illustrating the quantitative character of EHT. For both specimens the mean inner potential (MIP) values were accurately determined from the reconstructed 3D potential. For the Ge specimen, additionally the ‘built-in’ voltage across the pn junction of 0.5 V was obtained.

Mapping the potential of graphite nanotubes with electron holography

The technique of transmission electron holography has been employed to investigate the nanoscale features of graphitic nanotubes (buckytubes) and their particulate derivatives. Reconstructed phase images of holograms offer a quantitative means to calculate the mean inner potential (MIP), thickness profiles, and three-dimensional morphology for multi-/single shell buckytubes, their ‘‘tips’’ and other enclosed structures. It is demonstrated that electron holography is also sensitive to the defect nature of termination and bending in buckytubes and their particulate derivatives. Phase sensitivity of about 0.1 rad is demonstrated for single-layer buckytube, which corresponds to change in phase due to two monolayers of carbon.

Calculation of the mean inner potential

The mean inner potential (MIP) has been calculated for a number of elements and compounds by using the atomic electrostatic potential of Sanchez del Rio (1977). Four models have been assumed for the solid and comparisons with experimental measurements are made. The results have also been compared with the computations of the MIP made by using electronic density data from Moruzzi et al. (1978).

Messung des Mittleren Inneren Potentials von Natriumchlorid, Kaliumbromid und Kupfer mittels Elektronenbeugung

Electron diffraction patterns were taken from plain surfaces of sodium chloride, potassium bromide and copper in reflection. Displacements of the spots compared with the BRAGG position were observed. From these displacements the mean inner potential (MIP) of NaCl, KBr and Cu was obtained to 8.24, 9.05 and 19.00 Volts, respectively. During these experiments heat treated surfaces and cleavage surfaces of NaCl revealed the same value of the MIP. With KBr, cleavage surfaces were used. By investigation of electropolished (100) or (111) surfaces of copper single crystals always the same value of the MIP was obtained.

Methode zur Berechnung des Mittleren Inneren Potentials und deren Anwendung auf NaCl, KBr und Cu

From recently published analytic approximations to X-Ray scattering factors which were obtained from improved wave functions, the mean inner potential (MIP) was calculated according to the BETHE formula. With sodium chloride, potassium bromide and copper the values 7.33, 8.32 and 18.43 Volts, respectively, were obtained. All these values are smaller than the experimental values of 8.24, 9.05 and 19.00 Volts, respectively, which were published recently 3. The procedure delivers good results with respect to the comparatively simple method of calculation and it has the advantage of being applicable to all kinds of ions and atoms. Furthermore, a method of calculation is given for the case, that the charge cloud covers a greater region than that of one ion.