Two-dimensional strain mapping in semiconductors by nano-beam electron diffraction employing a delay-line detector

Contemporary nanotechnological applications such as light emitting diodes^1,2 or field-effect transistors^3–6 (FET) for electronic switching or non-volatile data storage rely on the detailed understanding of electronic and structural properties at the scale of a lattice constant and below. In this respect, scanning transmission electron microscopy (STEM) has become a prominent tool for the characterization of composition,⁷ electric field,⁸ and strain^9–12 due to its high spatial resolution between 50 pm and a few nanometres, depending on the mode of operation. As to strain measurements by nano-beam electron diffraction where the STEM probe is rastered over the specimen and a diffraction pattern is acquired for each raster position, the limited speed of established detectors drastically constrains the raster to a few hundred probe positions for typical scintillator-based charge-coupled devices (CCDs). Currently, exploring the applicability of various ultrafast detectors¹³ for high-energy electron detection attracts high interest, particularly because the fast acquisition of four-dimensional datasets becomes vital for novel techniques to measure atomic electric fields¹⁴ or STEM ptychography.^15,16

Here, we report on a pilot experiment with a delay-line^17–20 detector (DLD) mounted on an FEI Titan 80/300 (S)TEM microscope to investigate strain in a GeSi/Si FET test structure. This pixel-free detector is capable of a time-resolved recording of the x- and y-coordinate of impinging 300 keV electrons, and thus provides a five-dimensional dataset $I(px,py,τ,rx,ry)$⁠: Two-dimensional diffraction-space intensities $I(px,py)$ as a function of time τ with a precision in the range of 150 ps and the two-dimensional position (r_x, r_y) of the STEM probe.

The functional principle of a DLD is illustrated in Fig. 1. Each channel of a Chevron microchannel plate (MCP) stack amplifies a single incoming electron to form an electron cloud at the back side of the MCP. This cloud is divergently accelerated by a small positive potential difference between the MCP stack and the detector anode containing two serpentine-shaped wire frames (delay-lines, blue and red). In the delay lines, electrical pulses are induced by capacitive coupling in multiple neighbored segments of the wire frames with a Gaussian amplitude distribution. As an example, Fig. 1 shows two conjunct pulses for each delay line. The pulse groups are travelling with dispersion to the four ends of the meanders where the four arrival times are measured by time-to-digital converters (TDCs). The time differences $Δt$ between conjunct pulses in one pulse group are finally averaged. This average is proportional to the center of mass of the initial pulse group, hence yielding the coordinate of the impinging electron. As illustrated in Fig. 1, the electron hits the detector centered on the x-axis but in the top half in y-direction. Thus, there is no delay in delay line x (blue) as both pulses travel equal distances in the meander. Contrary, we have $Δt>0$ for the red delay line y because the point of incidence is closer to the upper wire end than to the lower one.

According to the delay-line principle, position sensitivity is not achieved by a discrete (pixelated) registration but by time measurement, naturally being continuous. Nevertheless, the spatial resolution is limited: Theoretically, the point of incidence of an electron could be determined with an accuracy equal to the pore pitch size of the MCP, being 25 μm in the present setup. However, the spatial resolution of a delay line detector is mainly restricted by the time resolution of 14 ps of the TDCs vs. delay line length and by the signal-to-noise ratio of the pulses therein. Consequently, the lateral dimension of the DLD of 50 mm is relatively large to enhance position measurement precision and delay-lines are embedded in a dielectric, leading to a pulse speed of approximately 50% of the velocity of light. As to the reliability of the measurement of impinging coordinates of an electron we found a precision of approximately 48 μm, so that coordinate storage as 10-bit integers is sufficient. Be it that detector resolution is to be compared with conventional pixelated detectors, this translates to about 1024 × 1024 pixels.

Finally, Fig. 1 visualizes the two operation modes of the detector: In time stream mode, a continuous time stream of single events (gray) is recorded. From this data, a conventional frame can be obtained posteriorly by integration over arbitrary τ. For example, the colour-coded image in Fig. 1 depicts a convergent-beam electron diffraction (CBED) pattern with the beam at position (r_x, r_y) calculated via

corresponding to a frame time of 40 ms. In frame mode, this integration is performed already during acquisition similar to CCDs, however, not involving any dead time for read-out. Acquisition and frame delimiters can be triggered externally, for example, by tapping the raster signal of the STEM.

As one prominent application in current solid-state physics, we employed the delay-line detector to measure strain along the [110] and [001] directions in a Si-based FET via strain analysis by nano-beam electron diffraction.¹⁰ In particular, a 300 keV STEM probe with a semi-convergence angle of 2.8 mrad was rastered over a region containing the Si gate and the GeSi source/drain stressors inducing uniaxial stress along [110]. The DLD was operated in frame mode with frame times of 40 ms and 20 ms to record 10 000 diffraction patterns corresponding to a 100 × 100 raster of the STEM probe with 1.6 nm sampling. By evaluating the positions of the 004 and 220 reflection discs (see image in Fig. 1 for exemplary) using the radial gradient maximisation method,¹⁰ strain maps for $εyy=ε[001]$ and $εxx=ε[110]$ have been obtained as shown in Fig. 2(a) and 2(b), respectively, for the 40 ms data.

Salient features in both maps are the GeSi stressors in the source S and drain D areas as marked exemplarily by the dashed white line in Fig. 2(a). In particular, the stressors exhibit two regimes of strain with $εyy≈3%, εxx≈2%$ on the one hand and $εyy≈0.9%, εxx≈0.5%$ on the other hand which correspond to Ge contents of 37% and 25%, respectively. This is in agreement with energy-dispersive X-ray analyses performed with the FEI chemiSTEM system. As to electronic applications, the stressor-induced strain distribution in the region below the gate G is of primary interest. Here, we observe a slight elongation of the Si unit cells along $[001]$ of $εyy=0.7%$ and a strong compression of up to $εxx=−2%$ laterally along $[110]$ direction, the latter gradually increasing in growth direction towards the gate contact. These strain characteristics in and below the gate channel are clearly visible in Fig. 3 which shows profiles of $εxx$ and $εyy$ along [001]. As indicated in red in Fig. 2, the profiles correspond to lateral averages in a 35 nm wide region. Similar strain distributions around GeSi stressors have been measured by geometric phase analysis (GPA),²¹ off- and on-axis holography,^22,23 scanning confocal electron microscopy,²⁴ and conventional nano-beam electron diffraction.^25,26

In consequence of the delay-line principle, the detector is a single-counting device. This enables us to relate the precision of the strain measurement considering a certain reflection directly to the integral number of electrons that have been detected in this reflection. For the 40 ms frames evaluated in Fig. 2, we find an average number of approximately $1×105$ electrons and a strain precision of $1.2×10−3$ in terms of the standard deviation in an unstrained substrate part of the specimen. For twice the scan speed, i.e., the 20 ms frames, we obtain a precision of $1.8×10−3$⁠, corresponding to an average number of approximately $4.5×104$ electrons in the diffraction discs analysed here.

We finally characterised the DLD with respect to its quantum efficiency. To this end, we recorded the undiffracted beam without a specimen inserted as a function of the STEM probe current which we varied by changing the “spot number” of the microscope between 5 and 11 at a low extraction voltage of 2.6 kV for the field emission cathode of the STEM. This setting translates to currents between 0.3 and 2.7 pA. A total acquisition time of 10 s has been used for each setting. Since quantum efficiency equals the number of detected electrons divided by the number of electrons incident on the detector, we determined the latter independently by exploiting the single-electron sensitivity of our annular dark field detector (Fischione 3000) as proposed by Ishikawa.²⁷ As can be seen from Fig. 4, the quantum efficiency is approximately 50% for low currents of up to $2×106$ electrons/s (0.3 pA) and then drops gradually to 20% for a current of $17×106$ electrons/s (2.7 pA). Because MCPs are rather sensitive to beam damage, higher currents can lead to a degradation of the hardware. Actually the MCP contribute to the quantum efficiency significantly as the sensitive area effectively covers about 60%–80% of the detector, the signal amplification depends on the depth at which the primary electron hits a pore, an electron can pass a pore without interaction, and because a single pore takes up to 200 μs to recharge completely. In addition to the spatial resolution discussed above, a high pore density is hence also beneficial with respect to quantum efficiency, which is expected to improve further by contemporary MCP with 10 μm pore size. Eventually, the number of detectable electrons is limited inherently by the delay-line principle as pulses originating from different events in the meanders may not overlap which results in a dead time of approximately 15 ns and puts a theoretical limit of $65×106$ detectable electrons/s independently of the MCP.

For a comparison of detector performance with existing hardware, we initially consider conventional read-out CCDs which require several hundreds of milliseconds for read-out only, independently of the actual illumination time. For example, Wang et al.²⁸ report the acquisition of 5000 diffraction patterns in 75 min of which only 8 min correspond to the actual illumination of the CCD. Noting that the recording of the present dataset with these settings would have taken 2.5 h instead of 3–6 min, it is obvious that the DLD provides an efficient, simple, and fast principle to overcome read-out limited data acquisition. On the other hand, recent developments combine ultrafast read-out hardware with CCDs for direct electron detection^13,29 to achieve read-out rates in the order of 1 kHz with a quantum efficiency close to 1. Using Fig. 4, we can gauge a maximum of approximately $3×103$ detectable electrons in a millisecond frame of the delay-line detector which is a factor of 5 less than typically needed for strain analysis. Consequently, the present setup with 25 μm MCP pore size should be feasible for 5 ms frame time. However, we stress that an advantage of the delay-line detector over ultrafast CCDs is not the dynamic range or high-dose applications but its inherent capability of in-situ single-event processing. As described above, the signal of each detected electron is analysed by means of the centre of mass of the time delays within the pulse trains induced in each delay line. Contrary, each 300 keV electron recorded, e.g., with the direct electron pnCCD detector¹³ deposits its energy in traces of up to 10 pixels. In previous millisecond frame analyses,¹³ this point spread of the pnCCD was ignored as the detector was operated close to saturation to increase the signal, preventing single event analysis due to non-separable traces.

As to typical precisions for strain measurements by nano-beam electron diffraction^{9,11,12,28,30} our values are nearly an order of magnitude larger. However, one must keep in mind that the present data has partly been acquired more than an order of magnitude faster in comparison to conventional CCDs and that the precisions found here are still a factor of 2 better than in conventional high-resolution TEM.³¹ 

In summary, we have introduced a fast, pixel-free, and time-resolving delay-line detector to the field of (scanning) transmission electron microscopy and demonstrated its performance by means of two-dimensional strain mapping in a Si-based field effect transistor. In this pilot application, 10 000 diffraction patterns have been acquired in approximately 6.5 min to obtain a strain precision of $1.2×10−3$⁠, while a precision of $1.8×10−3$ could still be achieved for twice the scan speed. The ability of the detector to record four-dimensional datasets, that is, two-dimensional diffraction patterns as a function of a two-dimensional STEM raster in finite time has great potential in materials characterisation beyond strain mapping, e.g., the measurement of electric fields, acquisition of ptychographic data or recording STEM intensities as a function of scattering angle. Moreover, the present study focused on frame mode imaging for strain measurements while exploiting the full time stream at up to 150 ps time resolution is left as a promising future application.

K.M.-C. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) under Contract No. MU 3660/1-1.