Reversible migration of silver on memorized pathways in Ag-Ge 40 S 60 films

Reversible and reproducible formation and dissolution of silver conductive filaments are studied in Ag-photodoped thin-film Ge40S60 subjected to electric fields. A tip-planar geometry is employed, where a conductive-atomic-force microscopy tip is the tip electrode and a silver patch is the planar electrode. We highlight an inherent “memory” effect in the amorphous chalcogenide solid-state electrolyte, in which particular silver-ion migration pathways are preserved “memorized” during writing and erasing cycles. The “memorized” pathways reflect structural changes in the photodoped chalcogenide film. Structural changes due to silver photodoping, and electrically-induced structural changes arising from silver migration, are elucidated using Raman spectroscopy. Conductive filament formation, dissolution, and electron (reduction) efficiency in a lateral device geometry are related to operation of the nano-ionic Programmable Metallization Cell memory and to newly emerging chalcogenide-based lateral geometry MEMS...


I. INTRODUCTION
The structure and physico-chemical properties of silver-doped thin-film amorphous chalcogenides have been extensively studied in connection with their application as optical elements, 1 inorganic resists, 2 ion-selective electrodes, 3 thin-film ionic batteries, 4 and photonic devices. 5n the present work, the main focus is on the use of amorphous chalcogenides in the solid-state memory variously known as nano-ionic, 6 programmable metallization cell, PMC, 7 or conductivebridging random-access memory, CB-RAM. 8In such devices, the memory cell typically has top silver and bottom inert (Pt, W, Au, Ni...) electrodes.Writing is by formation of conducting filament(s) (CF) of metallic silver within the cell on application of a voltage (silver anode, inert cathode) leading to the ON state.Erasing is by dissolution of the metal on reversal of the potential difference (OFF state).The ON state stability depends on the smallest lateral size of the CF.Writing can already be achieved at low voltage but then the ON state can have poor stability if the CF has a very small diameter or is discontinuous.The width of the CF has been estimated to be in the order of tens of nanometers (assuming a cone-shaped CF, with growth limited by compliance current), 9 and it is supposed that only one CF is formed in each memory cell in the ON state. 10The morphology of CFs is explored in more detail in this paper.
Amorphous Ag-photodoped Ge x S 100−x and Ge x Se 100−x (x = 25-40 at.%) are the usual choice for PMC. 11The electrodeposit growth rate in PMC is estimated to be 1 m s −1 . 7The resistance ratio R OFF /R ON is typically ∼10 5 . 12The PMC is a low-power device, requiring switching energy ∼10 −15 J, three orders of magnitude lower than for example in phase-change memory (also chalcogenide-based), and the ionic switching takes ∼50 ns. 13 An attraction is that memory based on structural changes should be non-volatile: ON-state data retention in PMC is estimated to be >10 yrs at room temperature; 8 and recently retention up to 10 5 minutes at 200 • C has been demonstrated for Ge-S-based PMC. 14 On the other hand, damage accumulation can limit the endurance; beyond 10 11 cycles is claimed with 20% decrease in ON current after 10 16 cycles. 15PMC memory is highly scalable, including 3-D porous alumina templating. 16Contact sizes down to 20 nm have been achieved, 8 but technology at this scale is not yet applicable because of poor endurance and data-retention.
Given these characteristics, chalcogenide-based ionic memory is attractive for portable devices, and has found a niche application, because of its good resistance to X-rays and short-term high-temperature stability, in medical environments with strict sterilization requirements.PMC also shows promise beyond von-Neumann computing. 17Still early in its development, and with clear prospects for scaling down, PMC performance is likely to improve significantly in next-generation devices.
In the present work, we examine some of the issues associated with the reversible growth of CFs in Ag-photodoped Ge 40 S 60 films in a lateral configuration.The dissolution of silver must involve volume changes and high local stresses.How do these affect the structure of the electrolyte, the nature of the reversibility (for example, does the CF follow a different path for growth in each successive ON state?) and the endurance of the device?In the writing cycle, there is a leakage current through the electrolyte that does not contribute to Ag + migration and metal deposition.When the CF is established, further current is superfluous.In erasing, similarly, there are currents along the CF (at the start) and through the electrolyte (later) that do not contribute to the dissolution of the Ag filament.With the energy of device operation in mind, it is clearly of interest to study what may be termed the electron efficiency of writing and erasing.Such issues of electrolyte structure and efficiency are difficult to examine in commercially relevant memory cells.We use conductive atomic-force microscopy (C-AFM) 18 to study micrometer-scale Ag dendrites in Ge 40 S 60 films, and Raman scattering to understand structural changes in Ag-photodoped films and samples with filaments.The lateral growth in these films, similarly to Refs.19-21, contrasts with the vertical growth in PMC, but the configuration in the present study does permit detailed and direct examination of the CF.C-AFM studies on vertical samples show I-V characteristics relevant for PMC memory operation, but such studies do not provide direct access to the full CF morphology, which is typically inferred from topographic swelling on the surface caused by CF growth. 22,23The role of stresses in interdiffusion in an amorphous phase has been analyzed for example by Greer et al. 24 In the present work, the larger length-scales and the longer time-scales (s rather than ns), imply a reduced role of stresses, but the observations still have points of relevance for understanding the operation of commercial chalcogenide-based PMC memory.
The studied sample geometry is of direct relevance for a newly emerging Ag-photodoped chalcogenide lateral devices, of the similar micrometer length-scales, used as visible light and radiofrequency switches, 25 high-Q tunable MEMS resonators, microvalves 11 and omnidirectional microphone for tunable hearing aids suiting individual patients' needs. 26A lateral device geometry may sound arbitrary chosen just for its simplicity, but for example radiofrequency switch has to have lateral configuration with only electrode edges facing one another, otherwise the (OFF state) isolation would be very poor at GHz frequencies due to high capacitance. 25All these devices rely on the same basic ionic-switching mechanism as in PMC with alike issues such as meagre repeatability and ON-like state stability.The reversible CFs growth/dissolution is exploited in bringing new functionalities.MEMS have been demonstrated using thin-film Ag-Ge-Se, compositions similar to those used in PMC, as the main solid-state electrolyte.These devices are at early stages of development beyond the established memory technology.The present work not only takes advantage of the experience with PMC, but also attempts to establish a basis for the evolving lateral technologies.
C-AFM may be helpful in mass screening of different samples to observe trends and compare electrolyte performance in a simple but effective lateral geometry.

II. EXPERIMENTAL SECTION
Amorphous Ge 40 S 60 films (thickness ∼300 nm) were deposited by magnetron sputtering on Si 3 N 4 (50 nm)/silicon wafers at argon pressure 2.5 Pa and power 10 W, the substrates, initially at room temperature, heated by < 10 K during deposition.Silver was deposited on top of as-prepared Ge 40 S 60 films by thermal evaporation, under a background pressure of ∼10 −4 Pa, at a rate of ∼0.2 nm s −1 .The multilayer stack was illuminated by a halogen lamp to optically induce silver diffusion into the amorphous film. 4The residual silver on top of the film was removed by dissolving in Fe(NO 3 ) 3 .9H 2 O (8 g/100 ml H 2 O) solution.
The AFM (Veeco 3100), equipped with an electronic tunneling module (TUNA) to extend current sensitivity, was used to induce electrodeposit formation and dissolution under ambient conditions.The cantilevers, of standard n-type Si (spring constant ∼0.2 N m −1 , maximum tip radius 25 nm), coated with a 20 nm film of Pt/Ir, had to be replaced regularly due to significant wear.The topographic images were recorded immediately after the induced dendrite growth/dissolution using the same tip in contact mode.The AFM data were processed using Gwyddion software. 27While the C-AFM tip itself served as one electrode, the other electrode was a silver conductive pad painted on the shorter side edge of the 1.0×0.5 cm cut sample (Fig. 1) with a typical tip to planar electrode distance of 200-500 µm.CF growth was achieved by scanning down a 50×50 nm area of the sample at a scan rate of 2 Hz while applying a constant DC voltage from +2 V up to +10 V, typically for 130 s.No detectable change in topography was observed for voltage biases lower than +2 V.
The entire dendritic shape of the deposited CFs was evaluated using a fractal dimension (D f ) analysis. 28,29The built-in FracLac plugin for the ImageJ 30 was used for D f calculations via local-connected-fractal-dimension (LCFD) analysis.This method was tested on a standard Koch snowflake giving a reproducible value of D f = 1.25; the LCFD does not allow evaluation of lacunarity.Outlined images were used for fractal analysis, therefore ignoring the internal morphology of the dendrites.
Compositional analysis used a FEG SEM CamScan MX2600 (20 kV) equipped with silicondrift detector (Oxford Instruments), and X-ray data were collected using a Bruker D8 diffractometer equipped with position-sensitive detector.Micro-Raman spectra of the films on Si substrates were collected using a Renishaw Ramascope-1000 spectrophotometer (cut-off at ∼200 cm −1 ) equipped with a He-Ne laser (λ = 633 nm); a photon energy of 1.96 eV (bandgap) and power output ∼7 mW were used (Ge 40 S 60 bulk has an optical bandgap energy ∼2 eV).No photo-induced changes in the films were observed during the micro-Raman measurements.The off-resonant Raman spectrum of the Ge 40 S 60 bulk glass was recorded with a Fourier-transform Raman set-up, (excitation at λ = 1064 nm; the photon energy of 1.165 eV).The scattered intensity below 120 cm −1 is attenuated by the instrument notch filter.

III. RESULTS AND DISCUSSION
The amorphous structure of the as-prepared and the silver photo-doped thin films was confirmed by X-ray diffraction.The composition of the as-prepared thin films was Ge 40 S 60 (±0.5 at.%).The doped chalcogenide film was found to contain ∼16 at.%Ag (Ge/S atomic ratio 2:3).

A. C-AFM -Ag CF growth and dissolution
The electric-field induced migration of silver in Ag-G 40 S 60 films leads to formation of dendrites on the surface with complex branched morphology that depends on the applied voltage (Figs.2(a and 2(b)).There are small "electrodeposits" up to ∼20 nm in height (Fig. 2(c)), between the main branches, corresponding to the topography of the as-prepared sample after removal of residual Ag.There is no detectable change in topography outside the effective area of dendritic growth.It is therefore assumed that silver ions originate from the surface and sub-surface layers adjacent to the propagating dendrites.Hsu et al. 31 have also shown, in a similar lateral device configuration, that silver CFs in Ag 2 S solid electrolyte are predominantly formed close to the surface and also propagate along it.The Ag + ions in the electrolyte, migrating in response to the electric field, deposit on the growing dendrite with a sticking coefficient ∼1.The dendrites thus grow outwards from the C-AFM tip (cathode) through the reduction reaction Ag + + e − → Ag at the newly formed CF tip/electrolyte interface.When the first silver deposits are formed, at tip-film contact, the electric field is higher at that point and the silver migration and electrodeposition are accelerated, with the first Ag particles serving as nucleation centers for further growth.There has been no detectable role of irreversible processes, such as germanium oxidation, 32 as any grown dendrite could be fully dissolved by exposure to light.
The fractal dimension D f increased linearly with increasing voltage from 1.20 to 1.30 ± 0.02, at +2 V and +10 V, respectively.The D f neglects the internal morphology of the dendrites, which was found to be independent of the applied voltage (Figs.2(a) and 2(b)).It is clear that the morphology of the dendrites depends on the applied voltage: at higher voltage, the dendrite arms grow initially thinner and then are more branched.There is a loose analogy here with dendritic growth in other contexts, such as the solidification of metallic alloys; at greater melt supercooling (corresponding to greater voltage in the present case) dendrites grow faster, have sharper tips and thinner arms, and are more branched. 33In solidification dendritic growth can occur in steady state, but that is not possible in the present case because of the complex roles of chemical diffusion, and mixed ionic and electronic conductivities.The interpretation of D f in a lateral device and its relationship with PMC memory are not straightforward.The growth kinetics and final shape of the dendrites must depend on the composition of the solid-state electrolyte and not only on silver content.For exploring a wide range of systems, however, a fast and simple technique such as C-AFM, could be particularly attractive.Mitkova et al. 21observed the morphology of Ag dendrites in Ge x Se 100−x films (x = 20, 30, 33 and 40 at.%.) by sweeping the applied voltage from 0 to +5 V.As the Ge concentration in the matrix increased, the dendrites became more fragmented.This was attributed to local Ag-rich particles/clusters serving as nucleation centers.Fractal analysis of the dendritic growth in lateral samples could provide insights on dendrite sharpening and branching, dependent on the sample and its initial structure, and on the electrical conditions driving dendrite growth.The degree of branching, related to dendrite-arm thickness, is likely to be important for memory applications: thinner arms grow faster, but are less stable. 34n co-planar type lateral devices, further apart the electrodes are, the longer the time is, and the more branched dendrites may grow for a given voltage.For example, the tunable reflectance of the visible-light frequency switch, 11 via the surface metallic electrodeposit, can be in first approximation, taken as an effective-medium approximation (percentage of the surface coverage), and therefore branching and dendrites width will have pronounced influence on the complex dielectric function.
The electron efficiency η e of the electrodeposition process relates the actual amount of Ag metal in the CFs to the theoretical value according to Faraday's law assuming that all the charge transport corresponds to reduction of Ag + .Calculation of η e was possible in the regime of constant current flow during stable dendrite growth (writing), where measured currents were in the range 10 −8 to 10 −6 A for +2 V to +10 V, respectively.Two limiting cases of η e were calculated.The lower limit was calculated by taking electrodeposit volume above the surface only, neglecting any complex internal morphology and sub-surface deposit, which cannot be imaged by AFM.The η e was ∼9% for +2 V and dropped below 1% at higher voltages.The upper limit could be estimated by assuming dendritic growth through the entire thickness of the film (the projected area of the dendrite taken throughout the entire sample thickness ∼300 nm), then η e was ∼25% for +2 V and dropped below 5% at higher voltages.The low η e of CF bridge formation has also been noted for PMC memory. 35Some losses originate from the entire circuit, but most of the current just flows through the low-resistance electrolyte.The η e will depend on device size, and must be higher for devices in which the electrodeposited CF occupies a larger fraction of the volume and cross-section of the memory cell.After the CF touches the top electrode, the rest of the current is superfluous, short-circuiting through the CF; the electrodeposition then slows down and further deposition is at very low values of η e .
Reproducibility and reversibility of growth (writing) and dissolution (erasing) have been tested over 10-20 cycles by switching the applied voltage between +7 V and −7 V (Fig. 3).In the dissolution phase, the dendrites dissolve from the branch tips towards the center, in other words in what is a close approximation of a time-reversal of the growth process.Dissolution leaves behind some fragments of undissolved Ag.In detail, two types of dissolution have been observed: (i) usually, there is partial dissolution of the dendrite (Fig. 3(b)), similar to that seen in oxide-based devices; 36 and (ii) more rarely, there is a complete dissolution of the dendrite when the voltage bias is reversed.An analogous distinction was found in oxide electrolytes, 37 where CF dissolution is mostly partial.It should be noted, though, that the origin and mechanism of reset are different in this case (being thermally assisted and therefore dependent on power density, unlike in PMC).A dual dissolution characteristics, resulting in a different morphology of broken-and continuous-shaped CF, has been observed in the oxide-based CB-RAM. 38The particular CF shape could be assigned to different I-V erasing curve.Again, highlighting the importance of CF morphology on the device performance.
In the present set-up, the growth ∼0.3-0.6 µm s −1 at +7 V was 6-7 times slower than the dissolution, and the current ratio I growth /I dissolution was ∼10 2 .In PMC devices, the ratio of the writing/erasing currents is 1-10 at maximum because the limiting compliance current is used to prevent later growth of CF during the writing cycle. 7he growth and dissolution of dendrites occurs along the same pathways ("memory effect") during cycling, with the last metallic electrodeposit to grow being the first to dissolve.It is tempting to assume that a similar mechanism operates in real PMC memory.The reproducible re-growth cannot be simply because of the sample geometry, which lacks any 2-D directionality, or any substrate templating.The dendritic deposits slightly resemble the 'four-fold' symmetry (Fig. 2) that would be associated with crystallography, but in fact the entire shape is rather random, without defined orientations.That the same shape is re-formed (Fig. 3(c)), in the absence of the geometrical effects and any substrate templating, provides evidence for the memorized pathways in the films.Modeling predicts that a CF dissolves first at the contact with the Ag top electrode, 39 and the memory immediately switches to the OFF state.When the bias is reversed, the Ag electrode being positive, the CF can quickly be restored in a repeatable and reproducible way due to "memorized" pathways in the electrolyte.The successful formation of CFs in PMC memory could also be indicated by the threshold initialization voltage being higher than subsequent writing voltages, e.g.+0.20 V and +0.15 V, respectively for a bottom electrode in an amorphous Ag-Ge-Se thin film. 40The difference between the threshold initialization and subsequent writing voltage is even more pronounced for oxide-based memory (Cu-WO 3 ). 41part from PMC devices, the "memorized" pathways could potentially be beneficial for quantitative liquid pumping in microvalve technology, 11 if the same volume of the liquid can always be restored inside a microchannel.
Unlike in the PMC technology, ionic transport enhanced on cycling via structurally memorized pathways can have pronounced negative effects in some contexts.This is likely in the case of lithium batteries, where swelling and shrinking of graphite electrode anode associated with (de)lithiation leads to battery degradation and failure through dendrite formation. 42

B. Micro-Raman spectroscopy -elucidating structural changes in the thin films
Micro-Raman spectroscopy was employed to reveal the origin of the structural differences between the as-deposited films (Fig. 4(a)), the Ag photo-doped films (Fig. 4(b)) and films in the area of a dendrite (Fig. 4(c)).The Raman spectra include sharp peaks of the Si substrate located at 300 cm −1 and 520 cm −1 ; the former was subtracted from the presented normalized Raman spectra, after proper scaling, to achieve more reliable fitting. 435][46] Ag photodoping induces structural modifications evidenced from changes in the Raman spectra.The breadth of the peaks makes the quantitative analysis of the Ag-Ge-S spectra dubious.
The off-resonant Raman spectrum of the Ge 40 S 60 bulk glass is added in Figure 4(a) for comparison.This spectrum bears a close resemblance to that recorded from the sputtered film, confirming that the sputtered film not only has a composition that is close to nominal but also its structure is very similar to the bulk glass structure as no sharp bands, representative of molecular species, appear in the film spectrum.The bands in the high-frequency envelope (300-450 cm −1 ) represent predominantly Ge-S stretching vibrations.Considering that the chemically ordered network model applies here (namely, assuming the satisfaction of the 8-N rule) the structure of the nonstoichiometric Ge 40 S 60 glass must be composed of a mixture of interconnected GeS n Ge 4−n (n = 0, 1, 2, 3, 4) tetrahedra.The relative proportions of these tetrahedra at the S:Ge ratio = 1.5 are: 31.64%GeS 4 ; 42.18% GeS 3 Ge; 21.09% GeS 2 Ge 2 ; 4.69% GeSGe 3 ; and 0.39% GeGe 4 . 47Only one third of the tetrahedra are GeS 4 units with full tetrahedral, T d , symmetry.The reduction of the T d symmetry to C 3v and C 2v in GeS 3 Ge 1 and GeS 2 Ge 2 units lifts the degeneracy and causes the appearance of bands in addition to those expected for the GeS 4/2 tetrahedra, complicating the interpretation.The main stretching Ge-S vibrations of the corner sharing (CS) GeS 4/2 tetrahedra in the stoichiometric glass GeS 2 are at ∼342 cm −1 (symmetric stretching, v 1 (A 2 )) 47 and at ∼394 cm −1 (antisymmetric stretching, v 3 (F 2 )). 45Edge-sharing (ES) tetrahedra are also structural motifs in Ge-S glasses with their main band at 372 cm −1 , known as the companion line, A c 1 .The origin of the band at ∼435 cm −1 is discussed below.
The best-fit deconvolution of the spectrum of the as-deposited Ge 40 S 60 film was performed with six Raman peaks.The four bands in the high-frequency envelope (300-450 cm −1 ) resemble the four bands noted above in connection with stoichiometric amorphous GeS 2 , and are highlighted by arrows.The band at ∼347 cm −1 is assigned to the symmetric stretching Ge-S modes of GeS 4/2 and GeS 3 Ge tetrahedral units, which compose the majority of tetrahedral and tetrahedral-like species for this composition.The band at ∼405 cm −1 is near the 395 cm −1 band of the stoichiometric GeS 2 compound, which, using scaling analysis, has been attributed to the asymmetric stretching mode of GeS 4/2 and GeS 3 Ge tetrahedral units. 45The band at 379 cm −1 originates from ES (companion line A c 1 ) GeS 4/2 tetrahedra. 45,47Finally, the fit has revealed a band at ∼435 cm −1 whose interpretation is still controversial.Several studies (Ref.44 and references therein) consider this to arise from S-S vibrations (short chains or cluster terminations).This assignment can be excluded based on the Raman spectrum of crystalline and liquid S where the most intense bands of both molecular (S 8 rings) and polymeric (S n chains) sulfur species, not expected in Ge-rich glasses, lie at 474 and 463 cm −1 respectively. 48In an alternative explanation, the 435 cm −1 mode has been associated with the highest mode in the ES clusters using ab initio calculations. 49he bending modes of the tetrahedral units and the Ge-Ge homonuclear bonds form a rather structureless continuum of vibrational modes in the range 200-300 cm −1 .The band associated with Ge-Ge bonds, at ∼230 cm −1 , appears as soon as the Ge content exceeds even slightly the 33.33% stoichiometric level in GeS 2 , and becomes dominant for Ge 40 S 60 . 45Lucovsky et al. 47 suggested that around 230 cm −1 , symmetric Raman modes of GeS 3 Ge and GeS 2 Ge 2 mixed tetrahedral units are expected.
The introduction of silver makes the interpretation of Raman spectra even more difficult.Deconvoluting the Raman spectrum is, then, highly uncertain as a multiplicity of Gaussian lines can result in equally good fits, and the spectral changes can be discussed only qualitatively. Figure 4(b) shows an appreciable change of the relative band intensities between the high (300-450 cm −1 ) and low (300 cm −1 ) frequency ranges.The intensity of the high-frequency band (Ge-S stretching modes) decreases after Ag addition in relation to the low frequency intensity.Ag seems to cause network degradation through the rupture of Ge-S-Ge bridges.The formation of Ag-S bonds, which bear more ionic character than the covalent Ge-S bonds, exhibit low Raman cross-sections.Indeed, Ag-S modes appear in Raman spectra at frequencies below 300 cm −1 as broad weak bands. 50Therefore, the shape of the Raman spectrum of the Ag-doped Ge-S glass (Fig. 4(b)) provides evidence for significant network degradation caused by silver atoms.This 'opening' of the structure may provide channels for fast migration of Ag + ions.
The spectrum recorded from the electrodeposited dendrite region (Fig. 4(c)), where Ag concentration is much higher than the surrounding area, can be accounted for along the same lines.The increased Ag concentration is responsible for Ge-S network damage evidenced by the weakening of the high-frequency spectral area, corresponding to Ge-S stretching modes.As a result, the intensities of low-frequency bands increase over the high-frequency Raman bands.

IV. CONCLUSIONS
While the length-scales, time-scales, geometry and reduced role of stresses in conductivefilament growth in lateral thin-film samples are different from those in PMC memory, the C-AFM observations in the present work are useful in permitting the imaging of the formation/dissolution of conductive paths in metal-doped thin-film amorphous chalcogenides.The growth of metallic silver dendrites in Ge 40 S 60 films is found to show an effect, where Ag migration pathways are "memorized" after erasing, allowing easier re-growth in subsequent cycles.The open structure of the Ge-rich sulfides further promotes fast silver diffusion under applied bias.
Whereas the PMC has been so far the most promising commercial technology, the "memorized" effect and lateral sample geometry is directly important for the new emerging thin-film MEMS technologies based on Ag-photodoped chalcogenides, which are specifically designed to operate in a lateral geometry.
Description of dendritic structures via fractal analysis is promising for assessment and comparison of chalcogenide solid-state electrolytes for potential use in both vertical, PMC, and lateral devices.A lateral geometry such as that in the present work, is useful in developing and understanding of how the shape of conducting filaments depends on the solid-state electrolyte and on the electrical conditions for their growth.The lateral geometry, unlike the fabrication of PMC devices, would allow mass (i.e.multi-parameter) screening to guide the selection of chalcogenide electrolyte and metal electrode for optimized memory-device performance.

FIG. 1 .
FIG. 1. Schematic of a C-AFM configuration for tip-sample DC biased current flow measurements during writing (not to scale).
FIG. 2. AFM topography images showing dendritic growth on an amorphous Ag-Ge 40 S 60 film after application of a DC voltage: (a) +2 V, no appreciable growth was observed below this voltage; and (b) +10 V, upper limit of the set-up.(c) The surface between two main branches in (b) corresponding to the topography of the as-prepared sample after removal of residual Ag.The original tip position was always at the center-point of the dendritic growth.

FIG. 3 .
FIG. 3. AFM topography images of reversible: (a) writing at +7 V; (b) erasing at −7 V; and (c) rewriting at +7 V.The arrows show the directions of growth (a,c) and dissolution (b).Once the conductive filament is established in the first cycle, then growth along the same (memorized) pathways is facilitated in subsequent cycles.

FIG. 4 .
FIG. 4. Normalized deconvoluted Raman spectra from: (a) the as-deposited amorphous thin film, and bulk glass for comparison; (b) the Ag photo-doped thin film; and (c) the region around a dendrite.The open symbols show experimental data after background and Si substrate Raman bands subtraction.The dashed-blue lines in (a) show the Gaussian peaks and the solid-red line through the experimental data is the best fit result.See text for further discussion on the importance of the high-frequency modes.