A delay-line detector is established for electron detection in the field of scanning transmission electron microscopy (STEM) and applied to two-dimensional strain mapping in Si-based field effect transistors. We initially outline the functional principle of position-sensitive delay-line detection, based on highly accurate time measurements for electronic pulses travelling in meandering wires. In particular, the detector is a single-counting device essentially providing an infinite time stream of position-resolved events so that acquisition speed is not hindered by detector read-outs occurring in conventional charge-coupled devices. By scanning the STEM probe over stressor- and gate regions of a field effect transistor on a 100 × 100 raster, 10 000 diffraction patterns have been acquired within 3–6.5 min, depending on the scan speed. Evaluation of the 004 and 220 reflections yields lateral and vertical strain at a spatial resolution of 1.6 nm. Dose-dependent strain precisions of 1.21.8×103 could be achieved for frame times of 40 and 20 ms, respectively. Finally, the detector is characterised as to quantum efficiency and further scopes of application are outlined.

Contemporary nanotechnological applications such as light emitting diodes1,2 or field-effect transistors3–6 (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 strain9–12 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-line17–20 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 (rx, ry) 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 (rx, ry) calculated via

I(px,py,rx,ry)=040msI(px,py,τ,rx,ry)dτ
(1)

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 εyy3%,εxx2% on the one hand and εyy0.9%,εxx0.5% 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 1.2×103 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 1.8×103, 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 detection13,29 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 diffraction9,11,12,28,30 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 1.2×103, while a precision of 1.8×103 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.

1.
S.
Nakamura
,
T.
Mukai
, and
M.
Senoh
, “
Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes
,”
Appl. Phys. Lett.
64
,
1687
1689
(
1994
).
2.
K.
Iso
,
H.
Yamada
,
H.
Hirasawa
,
N.
Fellows
,
M.
Saito
,
K.
Fujito
,
S. P.
DenBaars
,
J. S.
Speck
, and
S.
Nakamura
, “
High brightness blue InGaN/GaN light emitting diode on nonpolar m-plane bulk GaN substrate
,”
Jpn. J. Appl. Phys., Part 2
46
,
L960
L962
(
2007
).
3.
A.
Lochtefeld
and
D.
Antoniadis
, “
Investigating the relationship between electron mobility and velocity in deeply scaled NMOS via mechanical stress
,”
IEEE Electron Device Lett.
22
,
591
593
(
2001
).
4.
M.
Chu
,
Y.
Sun
,
U.
Aghoram
, and
S. E.
Thompson
, “
Strain: A solution for higher carrier mobility in nanoscale MOSFETs
,”
Annu. Rev. Mater. Res.
39
,
203
229
(
2009
).
5.
S.
Flachowsky
,
A.
Wei
,
R.
Illgen
,
T.
Herrmann
,
J.
Höntschel
,
M.
Horstmann
,
W.
Klix
, and
R.
Stenzel
, “
Understanding strain-induced drive-current enhancement in strained-silicon n-MOSFET and p-MOSFET
,”
IEEE Trans. Electron Devices
57
,
1343
1354
(
2010
).
6.
S.
Reboh
,
P.
Morin
,
M. J.
Htch
,
F.
Houdellier
, and
A.
Claverie
, “
Mechanics of silicon nitride thin-film stressors on a transistor-like geometry
,”
APL Mater.
1
,
042117
(
2013
).
7.
A.
Rosenauer
,
T.
Mehrtens
,
K.
Müller
,
K.
Gries
,
M.
Schowalter
,
P. V.
Satyam
,
S.
Bley
,
C.
Tessarek
,
D.
Hommel
,
K.
Sebald
,
M.
Seyfried
,
J.
Gutowski
,
A.
Avramescu
,
K.
Engl
, and
S.
Lutgen
, “
Composition mapping in InGaN by scanning transmission electron microscopy
,”
Ultramicroscopy
111
,
1316
1327
(
2011
).
8.
N.
Shibata
,
S. D.
Findlay
,
Y.
Kohno
,
H.
Sawada
,
Y.
Kondo
, and
Y.
Ikuhara
, “
Differential phase-contrast microscopy at atomic resolution
,”
Nat. Phys.
8
,
611
615
(
2012
).
9.
A.
Béché
,
J. L.
Rouvière
,
L.
Clément
, and
J. M.
Hartmann
, “
Improved precision in strain measurement using nanobeam electron diffraction
,”
Appl. Phys. Lett.
95
,
123114
(
2009
).
10.
K.
Müller
,
A.
Rosenauer
,
M.
Schowalter
,
J.
Zweck
,
R.
Fritz
, and
K.
Volz
, “
Strain measurement in semiconductor heterostructures by scanning transmission electron microscopy
,”
Microsc. Microanal.
18
,
995
1009
(
2012
).
11.
A.
Béché
,
J.
Rouvière
,
J.
Barnes
, and
D.
Cooper
, “
Strain measurement at the nanoscale: Comparison between convergent beam electron diffraction, nano-beam electron diffraction, high resolution imaging and dark field electron holography
,”
Ultramicroscopy
131
,
10
23
(
2013
).
12.
M. P.
Vigouroux
,
V.
Delaye
,
N.
Bernier
,
R.
Cipro
,
D.
Lafond
,
G.
Audoit
,
T.
Baron
,
J. L.
Rouvire
,
M.
Martin
,
B.
Chenevier
, and
F.
Bertin
, “
Strain mapping at the nanoscale using precession electron diffraction in transmission electron microscope with off axis camera
,”
Appl. Phys. Lett.
105
,
191906
(
2014
).
13.
K.
Müller
,
H.
Ryll
,
I.
Ordavo
,
S.
Ihle
,
L.
Strüder
,
K.
Volz
,
J.
Zweck
,
H.
Soltau
, and
A.
Rosenauer
, “
Scanning transmission electron microscopy strain measurement from millisecond frames of a direct electron charge coupled device
,”
Appl. Phys. Lett.
101
,
212110
(
2012
).
14.
K.
Müller
,
F. F.
Krause
,
A.
Béché
,
M.
Schowalter
,
V.
Galioit
,
S.
Löffler
,
J.
Verbeeck
,
J.
Zweck
,
P.
Schattschneider
, and
A.
Rosenauer
, “
Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction
,”
Nat. Commun.
5
(
5653
),
1
8
(
2014
).
15.
T. J.
Pennycook
,
A. R.
Lupini
,
H.
Yang
,
M. F.
Murfitt
,
L.
Jones
, and
P. D.
Nellist
, “
Efficient phase contrast imaging in {STEM} using a pixelated detector. Part I. Experimental demonstration at atomic resolution
,”
Ultramicroscopy
151
,
160
167
(
2015
), special Issue: 80th Birthday of Harald Rose; 2015 Third Conference on Frontiers of Aberration Corrected Electron Microscopy.
16.
H.
Yang
,
T. J.
Pennycook
, and
P. D.
Nellist
, “
Efficient phase contrast imaging in {STEM} using a pixelated detector. Part II. Optimisation of imaging conditions
,”
Ultramicroscopy
151
,
232
239
(
2015
), special Issue: 80th Birthday of Harald Rose; 2015 Third Conference on Frontiers of Aberration Corrected Electron Microscopy.
17.
H.
Keller
,
G.
Klingelhöfer
, and
E.
Kankeleit
, “
A position sensitive microchannelplate detector using a delay line readout anode
,”
Nucl. Instrum. Methods Phys. Res., Sect. A
258
,
221
224
(
1987
).
18.
M.
Lampton
,
O.
Siegmund
, and
R.
Raffanti
, “
Delay line anodes for microchannelplate spectrometers
,”
Rev. Sci. Instrum.
58
,
2298
2305
(
1987
).
19.
I.
Ali
,
R.
Dörner
,
O.
Jagutzki
,
S.
Nüttgens
,
V.
Mergel
,
L.
Spielberger
,
K.
Khayyat
,
T.
Vogt
,
H.
Bräuning
,
K.
Ullmann
,
R.
Moshammer
,
J.
Ullrich
,
S.
Hagmann
,
K.-O.
Groeneveld
,
C.
Cocke
, and
H.
Schmidt-Böcking
, “
Multi-hit detector system for complete momentum balance in spectroscopy in molecular fragmentation processes
,”
Nucl. Instrum. Methods Phys. Res., Sect. B
149
,
490
500
(
1999
).
20.
A.
Oelsner
,
O.
Schmidt
,
M.
Schicketanz
,
M.
Klais
,
G.
Schönhense
,
V.
Mergel
,
O.
Jagutzki
, and
H.
Schmidt-Böcking
, “
Microspectroscopy and imaging using a delay line detector in time-of-flight photoemission microscopy
,”
Rev. Sci. Instrum.
72
,
3968
3974
(
2001
).
21.
S.
Kim
,
Y.
Jung
,
S.
Lee
,
J. J.
Kim
,
G.
Byun
,
S.
Lee
, and
H.
Lee
, “
3D strain measurement in electronic devices using through-focal annular dark-field imaging
,”
Ultramicroscopy
146
,
1
5
(
2014
).
22.
C. T.
Koch
,
V. B.
Özdöl
, and
P. A.
van Aken
, “
An efficient, simple, and precise way to map strain with nanometer resolution in semiconductor devices
,”
Appl. Phys. Lett.
96
,
091901
(
2010
).
23.
Y.
Wang
,
J.
Li
,
A.
Domenicucci
, and
J.
Bruley
, “
Variable magnification dual lens electron holography for semiconductor junction profiling and strain mapping
,”
Ultramicroscopy
124
,
117
129
(
2013
).
24.
F.
Uesugi
, “
Strain mapping in selected area electron diffraction method combining a Cs-corrected TEM with a stage scanning system
,”
Ultramicroscopy
135
,
80
83
(
2013
).
25.
P.
Favia
,
M. B.
Gonzales
,
E.
Simoen
,
P.
Verheyen
,
D.
Klenov
, and
H.
Bender
, “
Nanobeam diffraction: Technique evaluation and strain measurement on complementary metal oxide semiconductor devices
,”
J. Electrochem. Soc.
158
,
H438
H446
(
2011
).
26.
F. H.
Baumann
, “
High precision two-dimensional strain mapping in semiconductor devices using nanobeam electron diffraction in the transmission electron microscope
,”
Appl. Phys. Lett.
104
,
262102
(
2014
).
27.
R.
Ishikawa
,
A. R.
Lupini
,
S. D.
Findlay
, and
S. J.
Pennycook
, “
Quantitative annular dark field electron microscopy using single electron signals
,”
Microsc. Microanal.
20
,
99
110
(
2014
).
28.
Y. Y.
Wang
,
D.
Cooper
,
J.
Rouviere
,
C. E.
Murray
,
N.
Bernier
, and
J.
Bruley
, “
Nanoscale strain distributions in embedded SiGe semiconductor devices revealed by precession electron diffraction and dual lens dark field electron holography
,”
Appl. Phys. Lett.
106
,
042104
(
2015
).
29.
V. B.
Ozdol
,
C.
Gammer
,
X. G.
Jin
,
P.
Ercius
,
C.
Ophus
,
J.
Ciston
, and
A. M.
Minor
, “
Strain mapping at nanometer resolution using advanced nano-beam electron diffraction
,”
Appl. Phys. Lett.
106
,
253107
(
2015
).
30.
K.
Müller
,
H.
Ryll
,
I.
Ordavo
,
M.
Schowalter
,
J.
Zweck
,
H.
Soltau
,
S.
Ihle
,
L.
Strüder
,
K.
Volz
,
P.
Potapov
, and
A.
Rosenauer
, “
STEM strain analysis at sub-nanometre scale using millisecond frames from a direct electron read-out CCD camera
,”
J. Phys.: Conf. Ser.
471
,
012024
(
2013
).
31.
F.
Hüe
,
M.
Hýtch
,
H.
Bender
,
F.
Houdellier
, and
A.
Claverie
, “
Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy
,”
Phys. Rev. Lett.
100
,
156602
(
2008
).