Dielectric films, generally oxides, are key elements in all microelectronic devices (1,2). The basic computing unit of the modern, information-based economy, the transistor, contains a dielectric film at its heart, as does the simple capacitor. Such films are also the switching component in the resistive random access memory (RRAM) elements that might soon constitute much of fast digital storage (2)(3)(4) and neuromorphic processors (3,5). Depending on the application, conduction in nominally insulating dielectric films can be central to device function (RRAM) or failure (gate dielectrics, capacitors). The reliability of computing hardware, present and future, thus depends critically on the detailed mechanisms underlying controlled and uncontrolled dielectric breakdown (DB) in these insulators.
Because RRAM devices feature controlled DB (2,(6)(7)(8)(9) that can be switched ON and OFF repeatedly, they represent an ideal target for a study of DB. For oxide-based RRAM (known as valence change memory -VCM-or OxRAM) in particular, many details about the switching process are poorly understood. Unsettled issues involve the filament growth direction (toward the cathode (4,(10)(11)(12) or away from it (13,14)), the filament conduction method (15), and the filament morphology (8,15). Incomplete understanding of the physics and chemistry that drive switching in VCM is the main obstacle to its optimization and commercialization (3,15,16).
Direct imaging of DB in VCM has the potential to reveal critical details about the switching mechanisms, but visualizing a dynamic and fundamentally electronic process occurring inside a bulk solid is extremely challenging (5). DB has been imaged using SPM (17)(18)(19)(20)(21), SEM (22)(23)(24), X-rays (25,26), and TEM (12,14,20,22,(27)(28)(29)(30)(31). Standard SPM, SEM, X-ray, and TEM imaging are sensitive to physical structure: the arrangement of atoms (22,24,27), and perhaps their chemical identities (12,20,(25)(26)(27)(28)(29)(30)32). But the changes to the physical structure of an insulator can be millions of times smaller -and thus more difficult to visualizethan the changes to its electronic structure. For example, doping at a level of 10 -5 can change the conductivity by a factor of 10 3 (33). Thus standard imaging techniques show DB in the limit where marked changes to the physical structure occur, such as bubbling (17,18,22,24), clustering (20,29,32), and crystallization (20, 22-24, 27, 31). This physically-stressed limit is not necessarily the regime of interest, especially in the case of RRAM, where the DB must be controlled and reversible (24,27).
Electronic signatures of DB can be visualized with modified versions of the standard imaging techniques. Conductive atomic force microscopy (CAFM) (8,20), scalpel scanning probe microscopy (19), scanning tunneling microscopy (21), in situ TEM holography (14), and electron beam-induced current imaging (EBIC) in an SEM (23) have been used to image changes to the local conductivity and electric fields associated with DB. However, these imaging technique struggle with poor perspective (spatial or temporal), imaging artifacts, and/or low contrast (5). To date it has not been possible to perform high-contrast imaging of cycling in a clean VCM device at nm-scale resolution.
To address these issues we fabricate Pt/HfO 2 /Ti VCM devices in a slant-vertical architecture (Fig. 1) and then image them using STEM EBIC. Since its implementation as a high-κ gate dielectric in 2007, HfO 2 (hafnia) has been considered perhaps the preferred dielectric for transistor, flash memory, and RRAM applications (7,16). The slant-vertical architecture maintains a realistic RRAM device topology while simultaneously allowing good TEM imaging access. This architecture has previously revealed the movement of Cu atoms (atomic number Z = 29) in Cu/Al 2 O 3 conductive bridge memory (CBRAM) over multiple switching cycles (34). However, the oxygen atom (Z = 8), or, more precisely, vacancy movement thought to mediate VCM switching (6,7,9,15) is too subtle to be detected in an Hf (Z = 72) background with standard TEM imaging. We therefore also image the slant-vertical VCM devices using STEM electron beam-induced current (EBIC) imaging. STEM EBIC imaging has two important contrast modes: the standard mode, which generates its contrast based on electronhole pair separation (35,36), and a recently-developed mode that generates contrast via the emission of secondary electrons (SEEBIC) (37). Because standard EBIC and SEEBIC imaging are sensitive to local electric fields (35,36) and to the local conductivity (37,38), respectively, these imaging modalities are uniquely suited for mapping the effects of DB at high spatial resolution (39).
As detailed below, we observe DB proceeding in two steps. Increasing the Ti-Pt bias voltage from zero first produces a volatile, or "soft", filament. This structure, which we attribute to charge injection into existing oxygen vacancies, vanishes when the bias voltage is removed. Further increasing the bias voltage eventually produces a non-volatile, or "hard", filament. The hard filament, which we attribute to the production and aggregation of new oxygen vacancies, remains if the bias voltage is set to 0 V, but it can be dissolved by reversing the voltage bias. The hard filament conducts ohmically, while the soft filament conducts via the Poole-Frenkel mechanism. A complete filament puts the VCM device in the ON state and consists of distinct hard and soft filaments arranged in series, with the latter limiting the net electrical transport via PF conduction. These filaments can be associated with regions of hard and soft DB (40), respectively.
A slant-vertical Pt/HfO 2 /Ti VCM device (Fig. 1) imaged in plan-view affords a side-on perspective of the switching region (34). The top (Ti) and bottom (Pt) electrodes are both completely encased in HfO 2 , with a continuous HfO 2 layer separating them (see Methods). This architecture avoids the focused ion beam (FIB) sample preparation (12,14,22,28,29,32) often used to create cross-sectional TEM samples, which introduces additional, compromising interfaces, structural damage, and chemical (e.g. gallium) contamination that have the potential to alter the DB process under study (5). Thus we have good STEM imaging access in clean, microfabricated devices with a realistic (i.e. vertically stacked) topology.
We cycle a device up to a potential just below the switching potential and then back to zero (Fig. 2, Movie #1). While the bias current is initially small, it is easily measured and increases exponentially, from 5 pA at 1 V, to 20 pA at 20 V, in this device (see also Fig. 4). Annular dark field (ADF) STEM imaging of the device essentially maps the proton column densitythe Pt (Z = 78) electrode generates more signal than the Ti (Z = 22) electrode (Fig. 2, top row). (The Si 3 N 4 and HfO 2 are very and mostly uniformly distributed, respectively, across this field of view.) Unsurprisingly, standard STEM ADF imaging of the device shows no changes as the device begins to conduct. Although cation motion has been observed in valence change chemistries (21), the absence of ADF contrast changes like those seen in Ref. 34 with a similar device architecture indicates that few, if any, of the heavy nuclei in the sample are relocating as a result of the applied potential.
STEM EBIC imaging (Fig. 2, second row), on the other hand, reveals the VCM device's changing conductivity and connectivity landscape (37). In the device's OFF state the Pt electrode is well-isolated from the Ti and thus is only connected to the transimpedance amplifier (TIA) that measures the EBIC. When the beam is incident on the Pt, secondary electrons (SEs) are ejected from the sample, the holes left behind reach the TIA, and this positive current gives bright contrast. When the beam is incident on the Ti, SEs are also ejected, but the corresponding holes go to ground through the Ti. While the TIA does not register these holes, a portion of the emitted SEs are recaptured (37) in the Pt and the resulting negative current in the Pt produces dark contrast. When the beam is not incident on an electrode, few SEs are produced and the contrast resulting is a neutral gray.
Even subtle, pre-switching electronic changes are immediately visible with STEM EBIC imaging. (Fig. 2, second row). With no applied bias the Pt electrode has the same shape whether viewed with ADF or with EBIC, but as the bias is increased, the Pt electrode, viewed with EBIC, swells. With a 10 V bias, a bright region grows from the Pt edge towards the Ti. With 17.5 V applied, this bright region grows even closer to the Ti electrode, with an especially bright feature appearing at the apex of the protrusion slightly to the right of frame center. When the bias is removed, the bright structure disappears and the electrode, as viewed with STEM EBIC, reverts to its initial configuration. This structure is thus both conducting and volatile.
Line profiles (Fig. 2, bottom) extracted from these images and others not shown present these results more quantitatively. The ADF data (both images and line profiles) show no contrast changes as a function of increasing bias, other than some small shifts attributable to sample drift over the 90 s image-acquisition period. The corresponding EBIC data, however, show a conducting region that extends farther and farther into the gap, reaching almost halfway across at the final high bias of 17.5 V before disappearing entirely when the bias is returned to 0 V. These volatile conducting structures ("soft" filaments) that form prior to switching (see also Figs. 3, S3, and S7 and Movies #1-5) appear under both Ti-Pt bias polarities and always grow from the cathode to anode (low to high potential), as expected for electron-charge injection. With the Pt held at virtual ground, for example, a soft filament grows from the Pt under positive Ti bias and from the Ti under negative Ti bias (Fig. S7).
In the STEM EBIC images discussed above, the contrast is dominated by SEEBIC, which is generated by secondary electron emission. Standard EBIC contrast, on the other hand, is generated by the separation of electron-hole pairs in a local electric field E. As the soft filament extends across the gap, the local E-field increases like V /d, where V is the applied potential and d is the width of the remaining gap (Fig. 3). At low potentials, SEEBIC dominates the contrast and shows the soft filament extending from the cathode (e.g. Fig 2 and first two columns of Fig. 3). At high potentials the device is ON and cannot be EBIC-imaged under bias because the much-larger device current swamps the EBIC. However, in a very narrow, intermediate potential range, the E-field is large enough to separate electron-hole pairs, and yet not so large that device conduction saturates the TIA (Fig. 3, third column). Here standard EBIC contrast dominates the SEEBIC contrast (see Figs. S4-S5), vividly highlighting the large E-field in the region extending from the tip of the soft filament to the Ti electrode. (See also Figs. S6, S7, S9, and Movies #2-5.) Line profiles show that the peak EBIC, and thus the peak E-field, is in fact at the Ti interface (Fig. 3, bottom). Up to this point in the switching cycle, the observed changes are all volatile, in that returning the applied bias to 0 V causes the filamentary structures observed to disappear (Fig. 3, fourth column).
Applying just over 20 V bias to the Ti electrode of the Fig. 2 device causes it to transition from the high-resistance state (HRS) (rightmost Fig. 2 = leftmost Fig. 4) to the low-resistance state (LRS) (Fig. 4 middle). The device current accordingly jumps to the pre-programmed current limit of 50 nA (Fig. 4 plot) (34). Continuing the STEM EBIC image series of Fig. 2 then becomes impossible because at high bias the ON-state device current saturates the TIA. Therefore we reduce the device bias voltage to zero for imaging.
While (again) no changes are seen with ADF, even without the applied bias STEM EBIC reveals that the transition to the LRS is accompanied by a change in the HfO 2 : a new, conducting region electrically connected to the Pt electrode now extends into the gap. Since it appears at 0 V, by definition this change is non-volatile, or "hard", and it appears where the soft filament generates its most intense SEEBIC signal (Fig. 2). The hard filament does not bridge the entire gap between electrodes (see also Figs. S8, S10, S11, and S14).
After a -10 V RESET, the device returns to the HRS and the hard filament is almost en- Pt Ti OFF ON OFF |current| (A) voltage (V) PF fit to READ (ON) STEM EBIC ADF STEM HfO 2 I FORM ON READ (ON) RESET READ (OFF) SET 25 nm tirely dissolved (Fig. 4 rightmost images). During subsequent cycles the hard filament reappears in the same region in the ON state and disappears (though perhaps incompletely) in the OFF state (Fig. S8).
The current-voltage (I-V ) plot (Fig. 4) shows a typical FORM/ON/READ/OFF/READ/SET cycle for this device. In the LRS, the transport is well-fit (see SI) by the Poole-Frenkel (PF) conduction model (9,41,42). Evidence of PF conduction also appears when we image an ON-state device with STEM EBIC while floating the Ti electrode. We image a device after a RESET, after a SET, and again immediately afterward (Fig. 5). For all three images the device is under no applied bias and the Pt electrode is connected to the TIA. The Ti electrode is grounded when the device is nominally OFF (Fig. 5, left column) and floating when nominally ON (Fig. 5, center and right columns). After the RESET (SET) the Ti electrode is dark (bright) in the EBIC image, indicating that the Ti is not (is) connected to the Pt. However, the contrast on the floating Ti electrode, and only on the Ti electrode, is streaky when the device is ON (see also Figs. S10 and S11).
The streaking in the Ti is indicative of the device's nonlinear I -V relationship. As the beam rasters across the floating Ti electrode, pixel-by-pixel from left to right and line-by-line from top to bottom, SE ejection causes the Ti to charge positively. Eventually the charging produces a potential sufficient for PF conduction, and the Ti electrode then discharges into the Pt to produce positive (bright) EBIC. Immediately after a discharge the EBIC returns to a smaller value (gray). This charge/discharge cycle continues across the entire Ti electrode.
Imaging with the frame rotated 180 • (i.e. starting the raster on the Pt instead of the Ti) does not produce similar streaks on the Pt, which is directly connected to the TIA. (With the rotated scan direction the Ti appears dark for reasons to be discussed shortly.) While a hard filament is visible in this device (see also Fig. S11), this intermittent conduction is not consistent with an ohmic connection between electrodes. The voltage-dependent conduction is indicative of soft breakdown: this device is conducting through a PF soft filament in series with the ohmic hard filament during the first half of the ON-state images (Fig. 5, second column).
To a degree not seen in Cu/Al 2 O 3 CBRAM elements (34), the VCM devices are beam sensitive, which suggests that this VCM chemistry may be unsuitable for radiation-hard applications and also provides clues as to the mechanisms underlying the ON state conduction. As the beam rasters through the gap (Fig. 5, second column), SE emission produces holes that annihilate the injected electrons constituting the soft filament. As a result, images acquired immediately afterward (Fig. 5, third column) and subsequent transport measurements show the device to be OFF. We find that electron beam exposure steadily increases the device resistance, eventually switching an ON device OFF (Fig. S13). Even a few seconds of exposure, as occurs while pre-viewing the field of view prior to the longer EBIC image acquisition, typically returns a device in the LRS to the HRS. The change is especially rapid when the beam is imaging the region between the electrodes (Fig. S12). Transport in the beam-induced HRS more closely resembles the higher-resistance pre-forming state than the voltage-induced (i.e. deliberate RESET) HRS. The device can then be "re-formed" into the ON state and will subsequently cycle normally.
Hard filaments are relatively robust to repeated EBIC image acquisition (Fig. S14). While an I -V shows that imaging an ON device switches it OFF, a second EBIC image shows the hard filament to be almost unchanged. The sensitivity of the device conductance to the beam, combined with the relative insensitivity of the hard filament to the beam, suggests that the beam primarily affects the soft portion of the ON-state filament. Imaging the filament with an electron beam ejects SE, leaving holes behind that annihilate trapped electrons ( 16) and destroy the soft filament, which RESETs the device. Devices which receive a large electron dose eventually fail into a persistent LRS; the Figs. 2, 4 device switched reliably over dozens of cycles, failing after 40 EBIC images, each of which represents a dose of 3 × 10 6 e/nm 2 .
We understand our observations in terms of the following model (Fig. 6). In a pristine device, the low density of oxygen vacancies in the ALD-deposited HfO 2 does not support electrical conduction between the Pt bottom electrode and the Ti top electrode (43). The oxygen vacancies are present in a variety of charge states and aggregation numbers (44,45). Applying a positive voltage bias to the top electrode injects electrons from the bottom electrode into nearby pre-existing vacancies (42,46). These vacancies PF-conduct and constitute the soft filament, which grows (Fig. 2) from the cathode (here the bottom electrode) independent the electrode materials. With sufficient positive voltage bias, the soft filament eventually approaches the top electrode, producing a large electric field across the remaining gap (Fig. 3). In this field some Ti is oxidized, creating new, positively-charged oxygen vacancies (8,15,26,44). These positively-charged vacancies are especially mobile in the HfO 2 and are likely doubly- 14). STEM EBIC imaging visualizes all of this switching process's key features: the soft filament (Fig. 2), the hard filament (Fig. 4), the strong electric fields immediately preceding SET (Fig. 3), and the chargesensitive conduction mechanism (Fig. 5).
charged (8,44,45). They drift in the E-field through the dielectric until they establish ohmic contact with the bottom electrode, where they are reduced. In sufficient concentration these oxygen vacancies dope the HfO 2 into ohmic conduction (15,26) and constitute the hard filament, which, like the soft filament, also grows up from the bottom electrode (Fig. 4). This conducting filament growth resulting from positively-charged vacancies moving from the anode to the cathode is directly analogous to that seen with metal cations in CBRAM (15,34). The cathode-to-anode growth direction indicates that the oxygen exchange rate at the Ti is slow compared to the vacancy migration through the HfO 2 (15). The vacancy transport and PF conduction currents generate Joule heating, which accelerates the transport and reaction rates and leads to positive feedback (8,15). The creation of the hard filament, which generally does not span the entire gap between the electrodes, completes the forming process. With a current limit, as in VCM, the hard filament growth is regulated and the DB is controlled. With a voltage limit, as in a transistor or capacitor, positive feedback can produce uncontrolled, runaway DB and a catastrophic failure.
With hard and soft filaments in series, a small positive potential can drive an electrical current and the VCM device is in the ON state (Figs. 45). Zeroing the applied bias causes the soft filament to retract from the top electrode as electrons return to the bottom electrode. Reversing the applied bias injects electrons from the other side, causing a soft filament to grow from the top electrode towards the bottom. Larger negative bias oxidizes the hard filament starting at its tip (8), producing a RESET. Post-forming SET occurs at a lower voltage than the initial FORM (Fig. 4) because of both trapped charge and the remaining hard filament.
This picture of DB in VCM makes a physical distinction between hard and soft breakdown, which historically have been difficult to distinguish (2): the former involves the motion of atoms, ions, or vacancies, while the latter involves the motion of electrons or holes. As the motion of electrons is more easily reversed, to achieve the controllable, reversible DB required for memory function, at least part of the conducting filament in VCM should be soft. Thus the ideal VCM ON-state represents an intermediate condition between the soft and hard breakdown limits; larger currents lead to harder breakdown, with thermal runaway and an unswitchable VCM device at the endpoint (24). This DB picture moreover provides a clear theoretical framework that offers specific directives on how to optimize VCM switching parameters such as speed, retention, and longevity. During device fabrication the oxide density and its doping, for instance, might be independently tuned to separately address the ionic transport and electronic conduction, respectively, allowing direct control of the critical hard/soft filament length ratio. This model of DB is broadly consistent with previous findings, not only in HfO 2 (13,14,17), but also in other binary oxides such as TiO 2 and Ta 2 O 5 (18,(47)(48)(49).
Within the broader field of DB generally, these results provide a framework for understanding the distinction, or lack thereof, between hard and soft breakdown on the one hand, and (possibly time-dependent) progressive breakdown on the other (2,3,8,50). With high-contrast, high-resolution imaging, hard and soft breakdown are physically distinguishable as described here, but without such imaging DB appears to occur on a progressive continuum, where the progression is measured by the unseen relative lengths of hard and soft filaments arranged in series. We fabricate electron-transparent VCM devices on thin Si 3 N 4 membranes framed by 200 µmthick silicon chips (Figs. 1, S1, S2). Ti/Pt (5/25 nm) leads patterned with optical lithography extend from contact pads at an edge of a mm-scale chip to the edges of the Si 3 N 4 membrane window in the center of the chip (37). An initial 8-nm thick layer of atomic-layer-deposition (ALD) HfO 2 serves as an adhesion layer for the 30-nm thick Pt bottom electrodes (patterned with electron-beam lithography) that follow. The next 8 nm of ALD HfO 2 , the switching layer, is followed by 30-nm thick Ti top electrodes (also patterned via electron-beam lithography) and an 8-nm thick capping layer of ALD HfO 2 . This metal-insulator-metal deposition (Pt/HfO 2 /Ti) order is the same as that of a standard vertical device, but here the geometry is 'slant-vertical' (34). By adjusting the horizontal gap between the Pt and Ti electrodes this architecture can be deformed continuously to allow for good STEM imaging access (positive gap), or to duplicate a commercial device (negative gap, with the electrodes overlapping). The conformal layer 1 METHODS
Figure S2: STEM and EDS images of the Fig. 5 device in plan-view. These images show a device (and its elemental composition) as it is actually used in the experiments described. The "top" electrode is Ti, and the "bottom" electrode is Pt. The adjectives "top" and "bottom" thus give correct descriptions in two ways: these images are oriented such that the Ti is above the Pt, and the Ti is deposited after the Pt in the device fabrication process. These images also show the ALD HfO 2 to be conformal, as Hf can be seen coating the sidewalls of the electrodes (i.e. the electrodes appear wider in the Hf image than in the Pt or Ti images).
1 METHODS of oxide between the two electrodes ensures that any electrical conduction must penetrate the second HfO 2 layer; no interface connects the two electrodes. The ALD HfO 2 process uses tetrakis (dimethylamino) hafnium precursor and water as the oxygen source. After each round of ALD, HfO 2 in regions away from switching region is removed with reactive ion etching to allow contact between the optically-defined Ti/Pt leads and the Pt and Ti electrodes that extend over the membrane. The completed, TEM-ready devices feature a protected layer of HfO 2 between the electrodes that is uncompromised by any mechanical polishing or ion milling (Figs. 1, S1, S2).
Electrical transport is measured with a Keithley 6430 sourcemeter, and imaging is performed in an FEI Titan 80-300 TEM in STEM mode. All images are acquired using an 80 kV accelerating voltage to minimize beam damage and promote secondary electron (SE) production. Beam currents are 50 ± 30 pA. STEM EBIC and standard STEM (e.g. BF, ABF, and ADF) images are acquired simultaneously by digitizing in parallel the signal from the transimpedance amplifier (FEMTO DLPCA-200) and the signals from the standard STEM detectors. Typical STEM EBIC images are 256 × 256 pixels and acquired with a ∼100 s frame time.
Figures 4, S9, S10, and S11 show fits to the Poole-Frenkel model for electronic conduction,
where j = I/A is the electrical current I per area A, E is the electric field, σ 0 is the zerofield conductivity, k B T is the thermal energy, and ϵ is the dielectric constant. Taking E = V /d and R 0 = d/(Aσ 0 ), we fit the I(V ) data with Eq. 1, treating the zero-field resistance R 0 and one of either d, T or ϵ as free parameters. (The form of Eq. 1 prevents the concurrent fitting of more than one of the three parameters d, T and ϵ.) In all cases we fit over the voltage domain indicated by the extent of the red curve. The magnitude of the power dissipation IV is such that the temperature change due to Joule heating is likely < 1 K. Thus we expect k B T to have a room-temperature value of 25 meV, d to be about the measured minimum electrode separation, and ϵ to be about 20ϵ 0 ≃ 1 e/(V•nm). The fits return d or ϵ about five times the expected value, or T about √ 5 times the expected value, when the other two are fixed at their expected values. Thus this crude implementation (e.g. A, T , E constant along the length of the filament) manages to fit, to within a factor of order unity, the E exp[ √ E]-dependence characteristic of the Poole-Frenkel model over a broad voltage range using only two adjustable parameters. We conclude that the PF picture of trapassisted electron transport provides a reasonable explanation of the rate-limiting step in the ON-state electronic conduction through these VCM devices. Ti Pt HfO 2 50 nm I I STEM EBIC ADF STEM Choosing to measure the EBIC on the anode, as opposed to the cathode, does not change the conclusions, only the signal-to-noise ratio. These four images represent two separate acquisitions on the device of Fig. 3. For both acquisitions the Ti is biased to 10 V relative to the Pt. The ADF STEM images (top) show the same view of the device. The STEM EBIC images (bottom), on the other hand, are radically different (Fig. S5) because the preamplifier has been moved. The lower left image (reproduced from Fig. 3) shows the EBIC measured on the Pt. The lower right image shows the EBIC measured on the Ti. At the Ti edge the two EBIC images show equal and opposite EBICs, indicating standard EBIC contrast (i.e. pair separation). Away from the Ti edge the contrast is generated by SEEBIC (i.e. secondary electron emission). In this case the polarity is also reversed, but the magnitudes are unequal (Fig. S5). Not all secondary electrons emitted by one electrode are recaptured by the other, so the signal-to-noise ratio is better on the electrode attached to the TIA. We generally choose to attach the TIA to the cathode, as this arrangement gives the best signal-to-noise ratio for the structures that appear during switching (growing from the cathode). Here each line profile (using the STEM EBIC data from Fig. S4) is acquired from the region indicated by the box outlined with the same color and dashing. Unfortunately, these images are not acquired simultaneously, so this illustration is imperfect. However, at the "intense spot" (dashed boxes) the EBIC is opposite and of approximately equal magnitude in the two EBIC channels, as expected for standard EBIC. Meanwhile, the EBIC produced by the Pt electrode (solid boxes) is 4× larger in magnitude when measured as a hole current from the Pt electrode than when measured as an electron current from the Ti electrode, as expected for SEEBIC.
Very generally, a given EBIC can sometimes be identified as "standard EBIC" or "SEEBIC" based on its size and the material system. Usually standard EBIC is larger than SEEBIC, with the former at times comparable to the beam current and the latter only a few percent of the beam current. Standard EBIC is expected only in regions that have a local electric field, and where it is present it dominates.
In cases where the EBIC mode may be ambiguous or mixed, it can identified quantitatively by measuring the EBIC from two opposing electrodes, ideally simultaneously. In standard EBIC, each hole reaching one electrode has a corresponding electron reaching the other electrode: the EBICs measured at the two electrodes are equal and opposite. In SEEBIC many of the ejected secondary electrons (see "recapture" discussion of Ref. (37)) reach ground without passing through a preamplifier. Thus the SEEBIC hole current is larger than the SEEBIC (recaptured) electron current. As the bias voltage increases, an increasing current that is independent of the imaging electron beam is measured by the TIA. By definition this current is not an EBIC, but it produces an offset, constant at a given voltage, in the EBIC images. We could subtract this small offset, but in this paper we have elected to show the raw data in all line profiles. The streaks in the lower half of the 12 V image indicate that the device is approaching its switching point; the device current is beginning to swamp the EBIC. -5 0 5 10 15 10 -14 10 -12 10 -10 10 -8 |current| (A) voltage (V) HRS LRS READ (ON) PF fit to READ (ON) RESET/READ (OFF) 50 nm OFF ON 5 V I STEM EBIC ADF STEM I I Ti Pt Figure S9: A small electrode gap changes little but the imaging access. In this device the apparent separation between the two electrodes is only a few nanometers. However, it shows electrical transport similar to that seen in devices with larger gaps. Standard STEM imaging shows no significant changes as a function of voltage or the device ON/OFF state. At pre-SET voltages STEM EBIC imaging shows bright contrast growing from the Pt electrode (the soft filament) and very bright contrast at the edge of the Ti electrode (large E-fields). In the final STEM EBIC ON-state image, holes generated in the (grounded) Ti electrode always have an easy, direct path to ground; the Ti electrode never charges at all, PF conduction cannot occur, and the Ti electrode appears dark regardless of its ON/OFF state. The small gap prevents us from seeing a hard filament. While the small electrode separation gives relatively poor imaging access, all indications are that physics of the switching process is fundamentally unaltered. 4 Conduction signatures revealed by STEM imaging 50 nm OFF ON OFF OFF ON ON -10 -5 0 5 10 15 20 25 10 -13 10 -12 10 -11 10 -10 10 -9 10 -8 10 -7 HRS LRS READ (ON) PF fit to READ ON RESET/READ (OFF) |current| (A) voltage (V) n.c. n.c. n.c. ADF STEM STEM EBIC 25 nm Figure S12: Exposing the filament specifically (as opposed to the whole device) to the electron beam produces a RESET. These images, some of them partial, are shown in their order of acquisition from left to right. The device is SET before the first image, the TIA is connected to the Pt electrode and the Ti electrode is floating. In the first two images the STEM acquisition is interrupted before the rastering beam reaches the gap. Both images show streaking on the Ti electrode, indicating intermittent PF discharges: the device is still in the ON state. For the third image the acquisition is allowed to run to completion, and streaking is evident on the Ti electrode. However, the subsequent (fourth) image shows no streaking on the Ti. Evidently, when the beam rastered across the gap during the third image it switched the nominally ON-state device into its OFF state. 0 1 2 0 100 200 300 400 500 0 100 50 beam off beam on time (s) current (pA) bias (V) 50 nm 5 Supplementary Movies Included with this report are 5 movies showing VCM devices as visualized by standard STEM and STEM EBIC imaging. (Bright field (BF), annular bright-field (ABF), and annular darkfield (ADF) STEM are all examples of standard STEM.) Apart from some distortions created by sample drift, the applied voltage, and perhaps change of focus, BF, ABF, and ADF STEM imaging show no significant changes to the VCM devices as a function of the applied bias. STEM EBIC imaging, on the other hand, shows the region electrically connected to the Pt electrode growing toward the Ti as the soft filament develops. Captions specific to the individual movies follow: • Movie #1: Soft filament in the Figs. 2, 4 device (BF STEM, ADF STEM, and STEM EBIC imaging). Here biases varying from 0-17.5 V and then back to 0 V are applied to the Ti (top) electrode relative to the Pt (bottom) electrode. At biases ≤ 10 V the EBIC image contrast is generated by SEEBIC. At biases ≥ 15 V the device is almost ON, and intermittent device current produces streaking over the Pt electrode in the EBIC image.
The last frame shows that the voltage-induced changes are volatile: the device returns to its initial state when the bias returns to 0 V.
• Movie #2: Soft filament and large E-field in the Fig. S7 device (BF STEM, ADF STEM, and STEM EBIC imaging). Here biases varying from 0-20 V are applied to the Ti (top) electrode relative to the Pt (bottom) electrode. At biases ≤ 16 V the EBIC image contrast is generated by SEEBIC. At biases 18 V the large E-field at the tip of the soft filament creates standard EBIC contrast that intensifies with increasing voltage.
• Movie #3: Soft filament and large E-field in the Fig. 3 device (BF STEM, ADF STEM, and STEM EBIC imaging). Here biases varying from 0-12 V and then back to 0 V are applied to the Ti (top) electrode relative to the Pt (bottom) electrode. At biases ≤ 5 V the EBIC image contrast is generated by SEEBIC. At 10 V the large E-field at the tip of the soft filament creates strong standard EBIC contrast. At the highest bias, 12 V, the device is almost ON and intermittent device current produces streaking over the Pt electrode in the EBIC image. The last frame shows that all of these bias-induced changes are volatile: when the bias returns to 0 V, the device returns to its initial state.
• Movie #4: Soft filament and large E-field in a device with a fabrication defect (BF STEM, ABF STEM, ADF STEM, and STEM EBIC imaging). Here biases varying from 0-12.5 V are applied to the Ti (top) electrode relative to the Pt (bottom) electrode. This device has a point that, because of the device geometry, looks particularly vulnerable to DB. At biases 8 V the EBIC image contrast is generated by SEEBIC. At biases ≥ 9 V the large E-field at the tip of the soft filament creates standard EBIC contrast that intensifies with increasing voltage. At biases ≥ 12 V the device is almost ON and intermittent device current produces streaking in the EBIC image, especially when the STEM beam is rastering through the gap between the electrodes.
• Movie #5: Soft filament and large E-field in another device (BF STEM, ABF STEM, ADF STEM, and STEM EBIC imaging). Here biases varying from 0-15.5 V and then back to 0 V are applied to the Ti (top) electrode relative to the Pt (bottom) electrode. At biases 11 V the EBIC image contrast is generated by SEEBIC. At biases ≥ 12 V the large E-field at the tip of the soft filament creates standard EBIC contrast that intensifies with increasing voltage. At biases ≥ 13 V the device is almost ON and intermittent device current produces streaking in the EBIC image, especially when the STEM beam is rastering through the region with the large E-field.