Estimation of the Neutralization Current from the Gas Environment 100

In presence of gas (here 99% helium and 1% water) incident electrons undergo inelastic scattering events with gas atoms or molecules resulting in a fractional ionization of the gas particles. Such ionization processes are accompanied by the emission of SE from gas atoms/molecules, so-called environmental secondary electrons (ESE). All ESE generated near the PCMO surface are attracted by the beam induced electric potential in PCMO and thus contribute to charge compensation. Furthermore, SE emitted from PCMO

4.6 Supporting Information might be captured by water molecules due to dissociative electron attachment. This results in the generation of negatively charged OH⁻, O⁻ or H⁻ ions which represent an additional contribution to charge neutralization. [207] The possible charge neutralization channels from gas, i.e. ESE capture and charge transfer from negative ions, are schematically shown in Fig. 4.11. Due to the decay of the electric field outside the PCMO specimen the neutralization currents of ESE and negative ions are generated within a finite interaction volume with radius s_i. It depends on the sample geometry, sample potential, kinetic energies and mean free paths of the respective particles. Kinetic energies of ESE and negative ions are small (<5eV). In the following we assume that ESE and negative ions generated at s > s_i do not contribute to charge compensation whereas all ESE and{H₂O}⁻ ions generated ats < s_i are captured by PCMO.

FIG. 4.11Scheme of the contribution of gas environment to neutralization currents. Inelastic collision of beam electron with gas molecules leads to ESE emission and generation of positive gas ions (here helium). ESE as well as negative gas ions due to dissociative electron attachment to water can diffuse to the sample for distancess < si (gray shaded area), wheresidenotes the range of the electric field in the vacuum. The yellow area represents the beam diameterd.

We get a rough estimate of the ESE-yield for He gas pressure p = 0.3 mbar and a typical ionization cross section σ_ion(E_i)∼10⁻¹⁹ cm² via

Y_He^ESE =n_gas·σ_ion(E_i)·2s_i ≈5·10⁻⁸−10⁻⁶ (4.15) for s_i in a range of 500 nm - 10 µm. Y_He^ESE is only 10⁻³−5·10⁻⁵ of the SE-yield Y₀ of PCMO. For a beam current of I_p = 11 nA the resulting backflow current in the order of I_b = 10 fA. Even for much larger s_i, I_b is much below the SE emission currents. Thus, the backflow from gas limited by the number of ESE is much too small to be taken into

account for neutralization.

Cross sections for dissociative electron attachment are even smaller than for ionization.

Considering for example H2O, σdiss < 10⁻²¹ cm² for ESE energies < 5 eV is more than 2 orders of magnitude smaller than σ_ion(E_i) ≈ 10⁻¹⁹ cm² . Moreover, the water partial pressure is a factor 10² smaller than the He partial pressure. Thus, we can easily disregard all charge neutralization channels involving H2O and He. [193]

The negligible impact of the gas environment on neutralization of sample charging in the ETEM seems to be in contradiction to environmental SEM (ESEM), where gas is used for charge neutralization of insulating samples. In contrast to ETEM, an external potential between the sample (which is negatively charged due to the absorption of beam electrons) and the electron detector is applied in ESEM. The applied potential gives rise to an acceleration of ESE and, thus, a drastic interaction volume between ESE, gas ions and sample. Furthermore, in environmental SEM the emitted SE’s are accelerated to the detector which is at positive bias. Thus, they gain kinetic energy leading to multiple inelastic scattering events of one single SE with gas species and resulting cascade generation of positively charged gas ions. This cascade effect is absent in TEM. [208]

4.6.7 Neutralization Current from the MgO Back Contact

In order to estimate the contribution to the neutralization current coming from the nominally insulating MgO section of the TEM lamella clued to the Cu grid by an electron beam deposited Pt/C mixture, we have measured current-voltage characteristics using a Nanofactory TEM holder equipped with a piezo-driven Pt/Ir tip for biasing.

The dimensions of the MgO lamella and the PCMO/MgO lamella shown in Fig. 4.8 are comparable, i.e. both have a thickness of 50 nm and a height of about 3 µm. The height is defined as the distance from the Cu grid back contact to the surface which can be contacted by the Pt/Ir tip. In the experiment shown in Fig. 4.12, we obtain a total resistance of R = 10⁹ Ω for kUk ≤ 1 V. Using the STM holder for resistance measurements at metallic TEM samples, the contribution of interface and feed line resistances can be estimated to be in the range of 15−20 Ω. Even contact resistance between the Pt/Ir tip and highly conducting oxides such as Nb:STO is below 100 Ω.

Consequently, we estimate a resistivity of about ρ ≈ 2· 10³ Ωcm for the MgO TEM lamella which is 12 orders of magnitude smaller than ideal single crystal values of ρ ≈ 10¹⁵ Ωcm. [192] Due to the non-linear current-voltage characteristics, the resistivity further decreases with increasing voltage.

It is well known that FIB preparation of TEM lamellae induces defects in the MgO, such as Ga implantation and oxygen vacancies due to atomic displacements. Oxygen vacancies can act as donors and generate electronic states within the band gap. [209] The same may apply for implanted Ga. In addition, surface contamination by C can enhance the electric conductivity.

4.6 Supporting Information

FIG. 4.12 Measurement of the electric characteristics of a MgO TEM lamella prepared by FIB. (a) Measurement configuration showing the electron transparent MgO, the Pt/Ir tip in contact with the lamella and the TEM aperture used for defining the illumination area. (b) Current-voltage curve with blanked beam (black circles), and under illumination (red circles) with a total beam current ofI = 10 nA. Inset: Frenkel-Poole fit to the potential dependence of the resistance.

Considering a semi-circular PCMO region of radius Rˆ = 200 nm illuminated by a beam current of I_p = 11 nA, and assuming a beam induced potential of 2 V where the poten-tial dependent yield is Y(V) = 0.0015, the balance-of-currents equation 4.7 in the main manuscript indicates that a neutralization current of I_n(V) = 17pA is sufficient to reach a stationary state. Using the measured resistivity for MgO would allow for neutralization currents of the order ofI_n(2V)≈100 pA in this geometry, which is more than enough to insure a steady state.