Dynamic force microscopy (DFM) is by now well established, at least since Gross et al. at IBM Zurich attached a carbon monoxide molecule to the sharp tip of their AFM apparatus. By passivating and stabilizing the tip in this manner, the tip could approach closely enough to the substrate so that the electrons interacted without causing any chemical or physical modifications, either to the substrate or the tip. In this mode of operation, the electron orbitals of the CO molecule interact with those of the substrate by way of the Pauli exclusion principle.

We should compare with the earlier technique of scanning tunnelling microscopy (STM), which probes the tip/substrate interaction within a particular energy range. As the authors remind us, this means that in STM one usually obtains an image of the frontier molecular orbitals, which do not map easily onto atomic positions. Indeed, STM is often interpreted by way of quantum mechanical computations of the hypothesized substrate surface. That is, one needs to have a fairly good idea of what the surface looks like in terms of molecular orbitals in order to make sense of an STM image.

By contrast, DFM responds to the total electron density, and this normally corresponds directly to the “ball and stick” model with which we visualize molecules and surfaces. Now, that this mental model is based in classical physics sometimes leads us astray. That the force sensed in DFM is due to the Pauli exclusion principle means that it is fundamentally a quantum mechanical phenomenon. But there is little doubt that in most situations, we can make sense of the image without the heavy machinery of quantum mechanical calculations.

The paper presents a quite readable summary of Pauli’s exclusion principle and how it is used in imaging.

Reference: Jarvis et al., “Pauli’s principle in probe microscopy”, arXiv:1408.1026.

When we want to examine ultrafast, irreversible microscopic dynamics by electron microscopy, we are faced with instrumental limitations. Stroboscopic techniques, with repetitive system excitation and image formation, work well for reversible systems. Alternatively, using specialty scanning electronics and deflectors, one can examine a pulsed image in a manner similar to a streak camera. While suited to irreversible dynamics, the latter method seems to be limited to the nanosecond regime and slower.

Basklin, Liu and Zewail of Caltech have recently introduced a multi-cathode technique which promises to give picosecond regime imaging of irreversible phenomena. Their electron bunches are generated by multiple, spatially separated photocathodes, each triggered by one and the same UV pulse. Because of the cathode spatial separation, the respective electron images are also spatially separated at the detector. Because of the temporal separation, each electron image samples the dynamic process at a different point in time. Their experimental proof of principle shows 19 ps delay between two beams impinging on a photo-excited gold sample.

Reference: PNAS 111(2014)10479-84 (open access)

In ultra-high resolution electron microscopy, a major limitation is sample damage. Given the propensity of many samples to charge under e-beam irradiation, it is advantageous to use high-voltage e-beams in preference to low-voltage e-beams. Therefore, the only way to limit radiation damage is to lower the electron dose. Low dose unfortunately translates directly into small signals available for detection. This means that noise is increasingly important.

Another implication of increased beam voltage in (S)TEM is the drop-off of image intensity in ordinary phosphorescent detectors, along with reduced high-frequency modulation transfer function (MTF) due to long-range scattering within the phosphor. Industry has responded by introducing direct electron detectors in the form of back-thinned, monolithic active pixel sensors (MAPS).

With these developments in mind, a useful quality measure in addition to the MTF is the detective quantum efficiency (DQE). This is defined as

DQE = ( SNR_o / SNR_i )²,

where SNR_o is the detector output signal-to-noise ratio, and SNR_i is the corresponding detector input signal-to-noise ratio. DQE cannot exceed 1.0, but we would like to make it as close to 1.0 as possible.

McMullen et al. have undertaken a careful experimental study comparing the DQE and MTF of three commercial MAPS detectors, emphasizing the importance of DQE in choosing a low-dose detector. Their preprint is available on the arXiv.

Reference: McMullen, Faruqi, Clare, and Henderson, arXiv:1406.1389.

Whether one uses scanning probe microscopy to gather real-space images or one uses photoemission measurements to gather reciprocal-space images, only electron densities are experimentally accessible, all phase information being lost. (One exception is for simple molecules subjected to high-intensity femtosecond laser pulse excitation. In this case, one can gather intra-molecular interference information which permits phase recovery.)

In the January 14 issue of PNAS, researchers working at BESY II put forward an iterative refinement method for reconstructing slices through approximate single-electron molecular orbitals, based on ARPES momentum maps of molecular monolayers. Interestingly, the method can recover both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).

The method echoes the discovery by Sayre (1952) that Bragg diffraction under-samples diffracted intensity, and that over-sampling can lead to unique real space solutions.

References:

• Lüftner et al., “Imaging the wave functions of adsorbed molecules”, Proc NAS 111(2014)605-610
• “Coherent diffraction imaging“, Wikipedia