Thermal Magnetic Field Noise Limits Resolution in Transmission Electron Microscopy

The resolving power of an electron microscope is determined by the optics and the stability of the instrument. Recently, progress has been obtained towards subångström resolution at beam energies of 80 kV and below but a discrepancy between the expected and achieved instrumental information limit has been observed. Here we show that magnetic field noise from thermally driven currents in the conductive parts of the instrument is the root cause for this hitherto unexplained decoherence phenomenon. We demonstrate that the deleterious effect depends on temperature and at least weakly on the type of material.

Figure 1

Experiment to evaluate the effect on the image contrast. (a) Beam path with low ($A$) and increased ($B$) sensitivity from objective lens to the selected area (SA) plane used for the measurements. The focal length of the objective lens $f$ and the aperture magnification $M$ are indicated. (b) Sketch of the TEM column extension with vacuum recipient and liquid nitrogen cooler which accommodates the test tube. The position of the Pt100 temperature sensor is shown. (c) Stainless steel test tube with an outer diameter of 3.0 mm (top) and stack of $Ø=7.0\mathrm{mm}$ permalloy test tubes (bottom) both with an inner bore of $Ø=2.7\mathrm{mm}$. (d) Copper cooler and vacuum recipient before integration.

Figure 2

Diffractograms from images with tilted illumination. (a) Recorded with low beam path $A$. (b) Recorded with beam path $B$ and empty cooler. (c),(d) Recorded with beam path $B$ at $\overline{T}\approx 120\mathrm{K}$ and a stainless steel (c) and permalloy (d) test tube, respectively. (e),(f) Identical beam path $B$ at room temperature and a stainless steel (e) and permalloy (f) test tube. All images have the same Nyquist frequency of $g_{\mathrm{Ny}}=(33\pm 0.8)/\mathrm{nm}$, the diffractograms are cropped at $g_{\mathrm{Ny}}/2$.

Figure 3

Evaluation of the diffractograms. (a) Gradual reduction of contrast along an achromatic circle with (blue) and without (green) image spread from the test tube. The blue curve is compared to the green one multiplied by an envelope function corresponding to different image spreads $\sigma$ (light blue). A best fit is obtained for an image spread $\sigma$ of 67 pm. (b) Temperature and material dependence of the variance of the magnetic field noise times the correlation length $\xi$ as evaluated from the experiments (B1)–(B3) shown in Fig. 2. The least-squares fits (solid lines) are done for the data of the experiments (B2) and (B3) and are extrapolated. The experiment (B1) with the empty cooler has been placed at $\overline{T}=0\mathrm{K}$. All the data points are intentionally displaced by 1 K with respect to each other to make the vertical error bars better visible.

Figure 4

Initial experiments with tilted illumination. (a) Diffractogram recorded with a beam tilt of 1.6° demonstrating contrast transfer up to about $g=14/\mathrm{nm}$. The area used for the ring-shaped line scan in the evaluation and the corresponding vector of the spatial frequency $g$ are depicted in red. (b) Same situation with rotated azimuth of beam tilt. (c) Diffractogram recorded for cold permalloy test tube showing significantly reduced contrast transfer due to image spread. (d) Same situation with rotated azimuth of beam tilt. All corresponding images have the same Nyquist frequency of $g_{\mathrm{Ny}}=(33\pm 0.8)/\mathrm{nm}$, the diffractograms are cropped at $g_{\mathrm{Ny}}/2$.