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.


Introduction
Nanostructures of compound semiconductors find extensive application in optoelectronics (light emitting diodes, photodetectors and solar cells), biosensors, and field-effect transistors [1][2][3][4].These devices rely on the presence of electrical junctions and associated built-in potentials derived from carrier diffusion.However, methods for the accurate assessment of dopant impurity concentration and associated carrier activation are difficult or limited.One of the most direct methods Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
for the evaluation of nanoscale junctions is via the application of electron holography (EH) in a transmission electron microscopy [5,6].
EH detects changes in the phase of high energy electrons after they pass through a sample.Assuming a non-magnetic material, the phase shift is proportional to the internal electric potential (or index of refraction) experienced during the transit.While a solid might appear neutral from the outside, the inside potential varies depending on the degree of nuclear screening that occurs from within the electron distribution.Each solid has a characteristic mean inner potential (MIP), defined as the volume average of the electrostatic potential in the material.Since the positive nuclear cores are localized compared to the distributed electrons, the MIP is typically a net positive quantity with respect to vacuum [7][8][9] (10-20 V).Given a positive MIP, the electron speed increases within the sample and, its phase has shifted with respect to vacuum when it exits the thin sample, in proportion to the thickness and internal potential [10].
Knowing the bulk MIP for a given semiconductor means that additional internal potentials at junctions [11], material defects [12], electrostatic charge, and or strain [13] can be distinguished, helping to evaluate, for example, the effectiveness of added dopant impurities in a device design.Any impurity present at fractional atomic percent levels, has a negligible effect on the bulk MIP but can form p-n junctions with built-in potentials, V bi , on the order of volts.
There are various theoretical approaches to calculating the MIP [14].The simplest is to treat the crystal as a superposition of isolated atoms or ions, a method known as the independent-atom approximation [15].More recent studies have used density-functional theory (DFT) which can account for the effects of bonding interactions [16][17][18].Assuming the surface is at zero potential, the calculated material potentials are peaked positive near each nuclei, decreasing towards a minimum in between.The resulting MIP has a weak dependence on increasing mass density as the number of electrons increases, with other effects on electron distribution including degree of ionic bonding, and surface termination modifying the MIP up or down [16,19,20].
The first experimental measurements of the MIP were based on its relationship to the electron index of refraction, and obtained from bulk single crystal diffraction observed at glancing incidence (and relatively low electron energies, 30 keV) [7,8,21].While there are bulk MIP values reported for many semiconductors [16,20] in many cases, the value is obtained from a theoretical calculation, or the range of measured values exceed the expected device junction potentials that are of interest.In particular, the local measurement of dopant activation in Zn-based semiconductor nanowire junctions would benefit from a careful reassessment of their reported bulk MIP values [22][23][24].Since the initial measurements of zincblende (ZnS) and ZnO in the 1930's, only a limited number of experimental MIP measurements for Zn-VI semiconductors have been reported [7,[25][26][27][28][29].
In this work, we have grown undoped nanowires and or nanoribbons of ZnS, ZnSSe, ZnSe, ZnTe, and ZnO and used off-axis EH to measure their MIPs.The nanostructures have uniform thicknesses over large dimensions, meaning that the experimental evaluation of electron phase shifts via EH can be more accurately measured, since they do not need to be thinned to be electron transparent.The data is then compared to results from previous reports and theoretical calculations.

EH
Imaging in the transmission electron microscope (TEM) can be explained using the framework of wave optics [30].When an object is illuminated with a plane electron wave, the electron wave passing through an object is modulated in phase and amplitude.The recorded image wave that can be represented as: where A is the amplitude and ϕ is the phase.In conventional TEM the image recorded represents a spatial variation of intensity of the image wave given by: This results in the loss of phase and amplitude information about the object.EH recovers this information as separate phase and amplitude images, from the Fourier analysis of the intensity variations in a hologram [31].
EH is based on the use of an electrostatic biprism developed by Möllenstedt and Duker in 1956.The biprism is nothing but a submicron-diameter, conducting wire inserted in the microscope perpendicular to the beam.A schematic diagram of an EH setup with a biprism in an electron microscope can be found in [30,32].A monochromatic, spatially-coherent electron beam is a fundamental criterion for holography.This is provided by the small diameter emission sources that appear to emit plane waves when viewed at large distances compared to the electron wavelength.
When a voltage is applied to the biprism, this leads to the deflection of each electron wave such that it forms an interference pattern (hologram).This can be considered equivalent to a young's double slit experiment, except that we have virtual coherent sources.When you increase the voltage to the biprism, this is equivalent to increasing the spacing between the virtual sources and also, the deflection angle, meaning an increased hologram width.However, detecting interference between the virtual sources requires sufficient spatial coherence of the electrons [32].The spatial coherence length is simply the distance over which the actual spherical wave looks planar, meaning a constant phase at the sample.Therefore, fringe contrast eventually decays at the edges of a hologram above a certain applied voltage.
The fringe spacing determines the spatial resolution of the reconstructed amplitude and phase images, and the fringe contrast is a measure of the electron coherence, influencing the reconstructed image precision.The optimal choice of biprism voltage is a compromise between competing forces.Although a higher biprism voltage will expand the width, giving perhaps a larger observable region, it also results in a smaller fringe spacing, and less hologram visibility.An interference fringe must contain at least 4 pixels to be adequately resolved by the digital camera.Narrower fringes mean fewer camera pixels per fringe and a reduced hologram visibility.The maximum hologram width is also limited overall by the spatial coherence of the electron source and hence even with a better camera eventually the fringes do not occur.
In this work, we have used a Lorentz lens for the holography experiments with the objective lens turned off.While this lens is primarily useful for investigations of magnetic materials, it also allows operation at a low magnification, with an increased field of view (FOV).The FOV must include a volume of sample and vacuum for reference.
The hologram is Fourier analyzed to extract the phase and amplitude images.The inverse Fourier transform results in a central spot with two sidebands.A second inverse Fourier transform of one of these sidebands, gives a complex image with real (Re) and imaginary (Im) parts from which the amplitude and phase information is calculated separately.
In the absence of magnetic fields, junctions, or strong diffraction, the phase shift ϕ, (obtained from the hologram) of an electron beam passing through a specimen is linearly related to the mean inner potential, V 0 , and thickness, t, following: where C E is a constant depending on beam energy (7.29×10 6 rad V −1 m −1 for 200 kV and 6.52 ×10 6 rad V −1 m −1 for 300 keV).

Experimental
Nanostructures of ZnS, ZnSe, ZnTe, and an alloy, ZnS x Se 1−x , were grown by the vapor-liquid-solid (VLS) method [33].A polished silicon wafer was used as the substrate onto which a thin gold film of 2-3 nm was deposited.The substrate and source powder (ZnS, ZnSe, ZnTe, or a combination of the first two) were placed in separate ceramic 'boats' in a quartz tube inside a tube furnace.The source material was placed at the center of the furnace at a temperature of 1000 • C while the substrate was placed farther away in a lower temperature zone of 600 and (700 • C-800 • C), respectively.Argon was used as the carrier gas and was allowed to flow through the tube for at least 30 min prior to deposition to purge it of oxygen.The deposition took place for 30 min except for ZnTe which was 10 min, and the substrate was removed after the furnace was allowed to cool to room temperature.ZnO nanowires were grown on sapphire substrates by metalorganic vapor phase epitaxy at 600 • C and 700 Torr using dimethylzinc and nitrous oxide under a nitrogen carrier gas [34].
The nanostructures in each case, were transferred from the substrate to a lacey carbon TEM grid by swiping the grid on the sample.The sample was observed in a scanning transmission electron microscope (STEM) equipped with a Lorentz lens, a biprism positioned in the selected area aperture (SAD) holder, and a field-emission gun, at an acceleration voltage of either 200 kV (point-to-point resolution 0.23 nm) or 300 keV (pointto-point resolution 70 pm, aberration-corrected).
In most cases, nanowires were obtained with cylindrical sidewall geometries, such that their widths in TEM images were assumed to be equal to the thickness in the beam direction.In the case of ZnSe, both nanowire and nanoribbons were obtained.The thickness of ZnSe nanoribbons analyzed were measured using electron energy loss spectroscopy (EELS) using the log-ratio method (beam collection angle β was 2.96 mrad) [35].Spectra from the zero-loss through the plasmon-loss region at 16.5 eV were obtained from five spots (each averaging 10 frames, exposure time 0.1 s, 100 nm spacing) and the inelastic mean free path, λ, was calculated theoretically to be equal 129 nm [35].The effect of native oxides on the measured diameters was not considered.
Holograms were acquired in Lorentz mode, at a biprism voltage of 140 V with, with a FOV of 500 nm, and an exposure time of 1.2 s.Beam damage leads to sample density variations and did occur, so exposure was kept to a minimum.
Nanostructures with at least two contacts to the carbon support were used to avoid charging during holography acquisition.Regions of strong diffraction were avoided.The condenser lens was tuned to obtain an elliptical illumination to create larger coherence in the direction perpendicular to fringes.A reference hologram was obtained at a distance of 1 micron away from the sample, equal to the distance between double images seen on the screen.This is considered the optimum distance from the specimen to obtain a reference hologram that avoids stray fields from the specimen [36].The holograms obtained had a fringe contrast of 20% and a fringe spacing of 4 nm at 200 kV or (30% contrast and a fringe spacing of 2.5 nm at 300 kV, aberration-corrected).The holograms were reconstructed to obtain the corresponding phase and amplitude images using Digital Micrograph scripts, ASU Holography [37,38] and Holo3 [20].
Figures 1(a) and (c) show low magnification examples of an object and reference holograms, respectively, from a ZnSe nanoribbon (200 keV).The large period fringes at the two edges of the hologram occur as a result of interference by the beam passing the biprism (0.7 micron diameter, Fresnel).The frequency of these are easily distinguished from the desired MIP fringes seen in the magnified images (b) and (d) where finer fringes are visible.The Fresnel fringes generate a streak in the Fourier transform that can be subtracted during hologram reconstruction.The hologram shown in figure 1 was taken at a beam energy of 200 kV.

Results and discussion
A major limitation found while working on ZnS and ZnSe was movement and bending of samples, presumably due to heating by the beam.Especially in the case of wires with diameters smaller than 50 nm, and those at the edge of the carbon support on the grid, they often moved from the field of view during observation.Nevertheless, those that perhaps had better adherence to the grid could be successfully maintained for the time required to set up the NW for the collection of a hologram.The ZnTe nanowires with the largest diameter compared to all other NWs were the most stable under the beam.The ZnO NWs were often found in clumps rather than individual NWs and were also more susceptible to changes in appearance well known to be due to beam damage [39].
Multiple ZnSe morphologies, including wires, sheets and ribbons, apparently grew simultaneously, as they were all visible on each TEM support grid from the sample.A typical bright field (BF) TEM image and SAD of ZnSe is shown in figure 2(a).The strong contrast is due to diffraction with some of the variations partially due to bending in these thin membranes.The SAD revealed the nanoribbon phase and orientation to be (011) zincblende (ZB) with the longer, in-plane direction as [112].Most regions were free from visible defects except for line defects visible on one edge of many of the nanoribbons.A lattice image at the border between the defectfree and faulted regions in the ribbon is shown in figure 2(b) obtained from the area marked by the yellow box in figure 2(a).The yellow arrow points to a twin boundary between two mirror planes consistent with the double spots in the SAD pattern.
The crystals in figure 2(a) with a narrow morphology were predominantly wurtzite (WZ) ZnSe nanowires.Figure 2(c) shows a bright field TEM image from one of them showing contrast from many stacking faults perpendicular to the [0002] growth direction.From the inset SAD pattern, it can be deduced that the beam direction in this case was [01 10].A higher magnification TEM image of the same wire obtained from the region marked by the white box, is shown in figure 2(d).Lattice fringes are visible indicating the presence of both WZ and ZB structure.Such structure are commonly reported in the literature for ZnSe [40,41].Gold catalyst particles were found at one end of each wire and ribbon (not shown), indicating the growth direction.
Figure 2(e) shows a BF-TEM image and associated SAD pattern from a typical ZnS NW, indexed along a [01 10] beam direction.The crystal is also predominantly WZ structure with short regions of ZB crystal.The growth direction is [0001] or the equivalent cubic {111} direction.An HR-TEM image is shown in figure 2(f) where the presence of both WZ and ZB structure is clear from the 2 and 3 layer stacking number, respectively.
Growth with a combination of ZnS and ZnSe powder sources produced ZnSSe alloy NWs that were also predominantly WZ structure.Figures 3(a    nanoribbon from EELS was 47 ± 2 nm, a larger percentage error, 4%.Thus, combining these errors, the ZnSe ribbon MIP is 12.8 ± 0.6 V. Figure 4(c) shows a phase image from a ZnSe NW.A radial profile obtained by averaging data from the indicated area is shown in figure 4(d).A cylindrical function fits best the increase in phase from a flat vacuum background.There was no sign of faceting in this case.The maximum phase shift corresponding to the thickest part of the wire was 3.92 ± 0.04 radians, a 1% error.The average diameter of this nanowire, 41 nm, was obtained from the width of its bright field image.
The region shown in the figure is primarily WZ and is free from stacking faults.However, the wire is 3 microns long and stacking faults were found in other parts of the wire.Regions with no SFs were chosen for the measurement of phase shift so as to avoid the effects of diffraction contrast from the SFs.MIP calculations from stacking fault-free regions of 4 wires gave an average value of 12.9 ± 0.2 V, a 2% error.This result is equal to the MIP obtained from the ZB ZnSe nanoribbons, to within experimental error.
Similar phase images were obtained from the other Zn semiconductors.Figure 4(e) shows a phase image example  for ZnS and phases images of ZnS 0.3 Se 0.7 , ZnTe, and ZnO nanowires are shown in figures 5(a)-(c), respectively.In each case, the phase shift from the thickest part of each NW was obtained through a cylindrical fit to the profile.At least 5 NWs were averaged to obtain each MIP.For any of these semiconductors, one might expect to see a hexagonal thickness profile.However, it was found that for all of the nanowires, including ZnO, the best fit was cylindrical.
Table 1 lists experimental and theoretical MIP values, V 0 , as a function of Zn-VI semiconductor molecular atomic number Z mol and mass density, ρ m .The same information is shown graphically in figure 6. Theoretical MIP values using isolated Table 1.Properties of Zn-VI compound semiconductors including molecular atomic number, Z mol , mass density, ρm, their mean inner potentials, MIP, V 0 : calculated assuming an isolated atom approximation, (V 0 IA ), or density functional theory, DFT (GGA approximation) (V 0 DFT ) [17,18] or measured, (V 0 Exp ), from this work and literature [7,[25][26][27][28][29].  atom approximation (V 0 IA ) or DFT assumptions (V 0 DFT ) [17,18] are listed.The MIP from the isolated atom approximation (IA) [43] were calculated based on atomic scattering factors assuming neutral non-interacting atoms [15].The DFT calculations were conducted using the WIEN2k code, which implements the full potential linearized augmented plane wave (FPLAPW) method.Wave functions and potentials were represented using spherical harmonics within a sphere of radius RMT (the muffin tin radius) which is set to RMT = d NN/2 , where d NN is the nearest neighbor distance.Either a local density approximation (LDA) or a general gradient approximation (GGA) was applied for MIP calculations.The LDA assumes that the exchange-correlation energy density is the same at every point, similar to a uniform electron gas, whereas a GGA considers a gradient in density to account for inhomogeneities.[17].
It can be seen that the general trend, both theoretically and experimentally is for the MIP to increase with density as has been predicted from theoretical calculations for elemental solids [16].This makes sense since an increased mass density moves atoms closer together increasing the Coulombic force, and reducing the effectiveness of the same electron distribution to screen the positive nuclei.However, for a given density the MIP varies significantly, partially due to variations in bonding and surface termination [19].We confirm that ZnS has the lowest MIP followed by a slight increase for ZnS 0.3 Se 0.7 , and ZnSe, a rapid increase for ZnTe and finally a much larger increase for ZnO, with the highest density.
Perhaps not surprisingly, our experimental results as seen in table 1, agreed with the DFT calculations to within experimental error (0.2-0.3 V) better than those obtained from the isolated atom approximation.The calculation of MIPs using atomic scattering factors in isolated atom approximation neglects any effects due to a redistribution of electrons in the bonds resulting in an overestimation of the MIP in contrast to the computation with DFT considered the redistribution of electrons due to atomic bonding [17].
We found both WZ or ZB structure in our Zn sulfide and selenide nanostructures.Since the density of ZnSe is slightly higher in the WZ structure compared to ZB, this is expected to cause an increase in the MIP.Using an IA approximation this means a change of perhaps 0.5 V [42].We found that the ZnSe nanoribbons were ZB, while the wires were primarily WZ, but the larger experimental error on the measurement of the ZnSe ribbon thickness (±0.6 V) meant that we were unable to distinguish whether there was such a difference.
Our MIP results for the WZ nanowires ZnS, ZnS 0.3 Se 0.7 and ZnSe showed an increase with Se fraction by a small degree above the experimental error.Previous reports for ZnS were found only for the ZB phase.We agreed with the value obtained via glancing incidence diffraction (1934) [7,8] of flat crystals while a much smaller value was reported for an evaporated thin film (1959) [25] using a direct interferometric measurement.This smaller value may have been caused by poor stoichiometry due to the evaporation preparation.
Experimental MIP of ZnO obtained in this work and reported by others, were more scattered and significantly smaller than those predicted by DFT calculations.This may be related to the greater susceptibility to electron beam damage as mentioned.ZnO was also observed to be more prone to charging compared to other wires as seen by potential gradients visible within the vacuum regions adjacent to the wire.Care was taken to choose only those wires with less to no charging for our MIP measurements.
A similar trend is apparent when one compares the MIP of other semiconductor families, including the Ga and In-based III-V semiconductors.A plot of MIP values as a function of density from DFT and experiment for a selection are shown in figure 7. Similar to ZnO in the Zn series, GaN (InN) has the largest density and MIP significantly greater than the other compounds in the corresponding series.

Conclusions
Off-axis EH was carried out on a series of nominally-undoped Zn-VI semiconductor nanowires: ZnS, ZnS 0.3 Se 0.7 , ZnSe, ZnTe and ZnO.They were all grown by a vapor-liquid-solid method using Au catalysts, except for the ZnO nanowires which were grown by MOCVD without catalysts.Their crystal phases were either, or both, zincblende and wurtzite, with many planar defects in some cases.
Phase images obtained from holograms of each nanostructure were used to measure the mean inner potential (MIP) of these materials.In general, the MIP increased with increasing density from the lowest (12.4 V) for ZnS, to the highest (14.8 V) for ZnO.Overall, the measured MIPs were in good agreement with the DFT predicted values with the exception of ZnO which showed a variation of 1 V.No effects of crystal phase or defects on the measured MIPs were detected, to within an experimental error of 5%, primarily limited by sample thickness estimates.The MIP of ZnO deviated most from the expected theoretical behavior likely due to greater rates of beam damage.

Figure 1 .
Figure 1.Holograms from a ZnSe nanoribbon (200 keV) (a) object and (c) reference.Images (b) and (d) are magnified views obtained from the white square of the (a) and (c) images, respectively.The fringe spacing in (d) is 4 nm.
) and (b) shows a HR-TEM image, lattice image of the indicated white square region, and associated EDS spectrum.The (0001) lattice spacing is 0.646 nm indicating a ZnS 0.3 Se 0.7 alloy composition based on Vegards law.(The (0001) lattice spacing for ZnS and ZnSe are 0.626 and 0.654 nm, respectively.)A similar value was obtained through EDS analysis.ZnTe was ZB while the ZnO was again WZ. Figure 3(c) shows BF-TEM images and SAD patterns (beam direction [11 2]) of ZnTe, while image (d) is from ZnO NWs with growth again along a [0001].The ZnO NWs had faceted sidewalls and tip surfaces.

Figure 4 (
a) shows a phase image from a ZnSe ribbon obtained after reconstruction of a hologram like the one in figure 1.The color scale ranging from blue to yellow shows a phase change of 7 rads.Averaged phase profiles obtained perpendicular to the long direction along the white arrow are shown in figure 4(b).In the shorter dimension, the profile has an abrupt increase in ϕ at the sample edges with respect to vacuum that remains constant within the sample region.The phase measured in the vacuum away from the ribbon is flat on both sides indicating the absence of varying external or local electric fields originating from charging of the ribbon.If no potential gradients are detected in the vacuum, the ϕ shift is entirely due to the V MIP of the material.The profile shows a uniform phase shift of 4.39 ± 0.06 rads.The noise signal indicates a small phase variation of 1%.The thickness of this

Figure 2 .
Figure 2. (a) BF TEM image of ZnSe nanostructures on the grid support with an indexed SAD pattern from the indicated ribbon.The zone axis is [011].(b) HR-TEM image of the region marked by the yellow box in (a).The yellow arrow indicates a twin boundary.(c) BF image and corresponding SAD pattern of a ZnSe nanowire.(d) HR-TEM image from the white box area indicated in (c).(e) ZnS nanowire BF-TEM image and associated SAD pattern with a HR-TEM image in (f).

Figure 3 .
Figure 3. (a) High magnification TEM images of ZnSSe alloy with (b)an EDS spectrum and lattice spacing in the inset.(c) BF image and SAD pattern of a ZnTe NW (d) BF image of ZnO NWs with SAD pattern from the long NW in the inset.

Figure 4 .
Figure 4. Phase images of ZnSe (a) nanoribbon and (b) nanowire, and (c) ZnS nanowire, each with a radial line profile region of averaging indicated, and plotted in (d), (e), and (f), respectively.The solid lines in the plots are fits to the data.

Figure 5 .
Figure 5. Nanowire phase images (a) ZnO, (b) ZnTe, and (c) ZnS 0.3 Se 0.7 with line profiles indicated and plotted in (d), (e), and (f), respectively.The solid lines are fits to each profile.

Figure 6 .
Figure 6.Plot of experimentally measured and calculated MIPs versus density for Zn-VI semiconductors.This work , other experimental reports , and DFT , and IA , theoretical calculations.

Figure 7 .
Figure 7. Plots of experimentally measured and calculated MIPs versus density for Ga-V and In-V semiconductors.DFT values are shown by crossmark [44] and experimental reports in literature are shown by solid circles.[44-47].