Single-Shot MeV Transmission Electron Microscopy with Picosecond Temporal Resolution

Pushing the limits in temporal resolution for transmission electron microscopy (TEM) requires a revolutionary change in the electron source technology. In this paper, we study the possibility of employing a radio-frequency photoinjector as the electron source for a time-resolved TEM. By raising the beam energy to the relativistic regime, we minimize the space-charge effects which otherwise limit the spatiotemporal resolution of the instrument. Analysis and optimization of the system taking into account the achievable beam brightness, electron flux on the sample, chromatic and spherical aberration of the electron optic system, and space-charge effects in image formation are presented and supported by detailed numerical modeling. The results demonstrate the feasibility of 10-nm–10-ps spatiotemporal resolution single-shot MeV TEM.

Figure 1

Comparison of 1.6-cell and 1.4-cell guns for (a) the output kinetic energy and energy spread (10-ps-long, low-charge electron beam) and (b) the acceleration gradient seen by the beam.

Figure 2

(a) LPS of the beam before (blue dot) and after (red dot) the $X$-band cavity. The correlated energy spread $\delta \gamma /\gamma$ is reduced by 150 times. (b) LPS at the sample position. The vertical axis is zoomed in by 20 times compared to that of (a).

Figure 3

(a) Cartoon concept of the single-shot picosecond MeV TEM. (b) The rms spot size ${\sigma }_x$ and normalized emittance ${\epsilon }_n$ along the beam line. The inset plot shows ${\sigma }_x$ evolution close to the sample location at $z=0.75\mathrm{m}$. (c1) The $x\text{−}y$ profile and (c2) $x\text{−}{x}^{\prime }$ distribution of the electron beam at the sample position. Within a $2.0\text{−}\mu \mathrm{m}$-diameter area, indicated by white dashed lines, the beam has quasiuniform position and angular distributions.

Figure 4

gpt-tracking results of the dependence of the FW50 image size (a) ${\sigma }_x/M$ and (b) ${\sigma }_y/M$ of a point source, on its FW50 relative energy spread $\delta \gamma /\gamma$ (Gaussian distribution) and the objective collection semiangle $\beta$ (uniform angular distribution).

Figure 5

(a) radia model of a 3-mm-thick PMQ magnet and (b) the calculated on-axis focusing gradient of a 3-mm and a 6-mm PMQ. Dashed lines indicate the physical boundaries of the 3- and 6-mm-thick PMQs.

Figure 6

Image disk profiles of a point source modeled by using (a) the hard-edge ideal quadrupole models and (b) the 3D field map from radia. The collection semiangle is 2 mrad, and FW50 beam energy spread is $1.5\times 10^{-5}$. Transverse dimensions have been referred back to the object plane.

Figure 7

Simulated electron beam images of the test target under beam illumination flux levels of (a) $200e/(10\mathrm{nm}{)}^2$, (b) $50e/(10\mathrm{nm}{)}^2$, and (c) $12.5e/(10\mathrm{nm}{)}^2$.

Figure 8

(a) rms spot size ${\sigma }_x$ and ${\sigma }_y$ and (b) charge density evolution in the first stage of the column of the full beam ($2\text{−}\mu \mathrm{m}$ initial diameter, black line) and a transversely scaled beam (100-nm initial diameter, red line). The blue rectangles represent PMQ positions of the objective lens.

Figure 9

(a) Comparison of the spot size obtained (black dashed line) directly by using the spacecharge3dmesh method and (red dotted line) the one using superposed PMQ and space-charge field map without turning on any $e\text{−}e$ effects in gpt. The result (blue dash-dotted line) with only the PMQ field is also shown. (b) Spot size evolution of a point source (black dotted line) with only the PMQ field tuned at imaging at $z_i=20\mathrm{cm}$, (blue dashed line) after including the smooth space-charge field, and (cyan dash-dotted line) with only the linear component of the smooth space-charge field. (Red solid line) The PMQ triplet is retuned to image at $z_i$ again with the new space-charge field calculated under the new PMQ setting.

Figure 10

(a) Field gradients of the linear part in the space-charge field. (b) Nonlinearity $s$ of the space-charge field. The field gradient $E_x^s/x$ at two positions where nonlinearity is (b1) low and (b2) high is shown.

Figure 11

Simulated image of the test target for (a) $200e/(10\mathrm{nm}{)}^2$ and (b) $50e/(10\mathrm{nm}{)}^2$ illumination flux, with smooth space-charge effects taken into account.

Figure 12

(a) Histogram of the image of a point source (red solid line) and $w$ disk of a full-transverse-size beam (black dotted line) tracked in the smooth space-charge field, together with the $w$ disk of a full-transverse-size beam tracked by using the first-principle pairwise $e\text{−}e$ interaction model (blue dashed line). (b) $w$ disk of a full-transverse-size beam tracked by using the first-principle pairwise $e\text{−}e$ interaction model with divergence and illumination flux of (red solid line) 3 mrad, $50e/(10\mathrm{nm}{)}^2$, (black dotted line) 2 mrad, $50e/(10\mathrm{nm}{)}^2$, and (blue dashed line) 2 mrad, $200e/(10\mathrm{nm}{)}^2$.

Figure 13

Images of the test target simulated with first-principle pairwise $e\text{−}e$ interaction model, for a beam divergence and illumination flux of (a) 2 mrad, $200e/(10\mathrm{nm}{)}^2$, (b) 2 mrad, $50e/(10\mathrm{nm}{)}^2$, and (c) 3 mrad, $50e/(10\mathrm{nm}{)}^2$.