Interference gating: a novel way for the dynamic investigation of switching semiconductor nanostructures by time-resolved electron holography

Abstract text (incl. figure legends and references)

Off-axis electron holography deepens TEM"s insight even further by providing access to amplitudes and phases of reconstructed electron waves. The latter contain spatially resolved information about projected electromagnetic potentials, making electron holography (EH) an excellent tool for the investigation of electric potential distributions in semiconductor nanodevices, especially when they are operated during investigations using special in situ specimen holders. Since existing methods for the realization of time-resolved measurements in a TEM by stroboscopic illumination have proven to be disadvantageous for EH [1,2], such investigations have so far been limited to static measurements.

Recently, a simple, yet promising approach to realize time-resolved measurements of periodic processes with nanosecond time resolution in an electron holographic setup by means of interference gating (iGate) was presented [3]. As shown in fig. 1a, the basic idea of interference gating is a synchronized destruction of the interference pattern, realized by introducing random phase shifts φ_g(t) to the electron wave, for a defined period of time during an interferometric measurement such as electron holography (EH). The holographic reconstruction process acts as a temporal filter that only retains the information of the undisturbed interferogram outside this period (fig. 1b). By shifting the undisturbed time interval ? (gate) along an synchronized externally controlled periodic process (e.g. due to an applied voltage signal), the whole period can be sampled in a pump-probe (or lock-in) manner.

In a first materials scientific application, interference gating was used to investigate dynamic electric potential distribution in an externally driven nanostructured general purpose silicon diode during switching in reverse-biased condition shown in fig. 2. An added value of this type of investigations is the simultaneous combination of high spatial and temporal resolutions. In the analysis of single frames of the investigated process (every 11.1 ns), different potential dynamics are revealed depending on the location. Thus, switching times in vacuum between free-standing electrodes (grey circles) correlate very well with the applied signal as measured in parallel by an oscilloscope (blue line), whereas switching delays (transients) appear as expected within the space charge region (red circles). Interference gating, thus, paves the way for the investigation of dynamic electrical effects in semiconductor nanostructures directly at the site of the event.

[1] A. Feist et al., Ultramicroscopy, vol. 176, pp. 63–73, 2017.
[2] F. Houdellier et al., Ultramicroscopy, vol. 186, pp. 128–138, 2018.
[3] T. Wagner et al., Ultramicroscopy, vol. 206, p. 112 824, 2019.

Figure 1: a) Dynamic phase shift φ_g(t) producing time-dependent electron hologram I_hol(r, t) (red and blue lines represent exemplary wave fronts for different times t). b) Dynamic phase sequence for generating time-resolved electron holograms with gating length ? and respective Fourier transformations of I_hol(r, t) (disturbed case: only centerband, undisturbed: also sidebands).

Figure 2: Plot of the control signal U_in(t) (blue line) applied to the prepared diode measured by the oscilloscope and plots of the phase slopes d/dx φ_el(x, tgi) (vacuum: grey circles, depletion region of the diode: red circles) calculated for 30 gate positions t_gi in two different areas with the standard deviation as error bars.