cermets), the bulk percolation limit (when the slope is zero) ranges from 0.40 to 0.65 for

Transcription

1 SUPPLEMENTARY INFORMATION A size-dependent nanoscale metal-insulator transition in random materials Supplementary Information Albert B. K. Chen *, Soo Gil Kim *, Yudi Wang *, Wei-Shao Tung & I-Wei Chen Department of Materials Science & Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA * These authors contributed equally to this work. A. Percolation Limits in SiO 2 :Pt and Perovskite Solid Solutions In Fig. S1 the sheet resistance of several SiO 2 :Pt films is shown as a function of temperature. The sign of the slope changes from negative at f=0.3 to slightly positive at f=0.4 signals a metal/insulator transition (with zero slope) at slightly below f=0.4, which may be regarded as the bulk percolation limit. (Macroscopic lengths of conduction paths, several mm long here, were used in these experiments.) For perovskites forming solid solutions, the R(T) curves also undergo similar changes in slope, although at very low temperatures there tends to be an uptick in resistance toward 0K due to localization effects. In Figure S1 R-T curves of SiO 2 :Pt films. Sheet resistance per four-point method normalized by the room temperature value. Pt % indicated next to the curve. Metal has a positive slope, insulator a negative slope. With macroscopic MIT identified with the zero slope, such composition is used as bulk percolation limit. LaFeO 3 :SrRuO 3 ceramics, the change is between f=0.8 and f=0.9, 1 as in LaCoO 3 :SrRuO 3 nature nanotechnology 1

2 supplementary information ceramics. 2 In SrTiO 3 :SrRuO 3 films, their sheet resistance (again considered bulk) sees a change in sign between f=0.61 and f= In SrZrO 3 :SrRuO 3 ceramics, our unpublished data found the transition between f=0.7and f= In granular metals (also called cermets), the bulk percolation limit (when the slope is zero) ranges from 0.40 to 0.65 for some eight amorphous-oxide:crystalline-metal two-phase systems, as reviewed by Abeles. 5 The bulk percolation limit of SiO 2 :Pt is close to the low end of the same range, that of conducting oxides in solid solutions is above the high end of this range. From these considerations we have estimated the bulk percolation limits shown in Table 1 of the main text. Note that these experimentally observed bulk percolation limits are higher than the theoretically predicted ones for three-dimensional lattices using the bond percolation model: they lie between 0.39 and 0.12, decreasing with the coordination number of the lattice (diamond, simple cubic, body centered cubic, and face centered cubic); these limits are slightly higher if the site percolation model is used. 6 The percolation limits in two-phase materials are higher than these predictions because the shapes of the conducting and the insulating phases are not the same. 5 They are even higher in oxide solid solutions because small atomic clusters may not be conducting. B. Metal-Insulator Transitions in Random Solid Solution Thin Films 2 nature nanotechnology

3 supplementary information In Fig. S2 the I-V and R-V curves of six solid solutions with identical top (Pt) and bottom (SRO) electrodes are presented. The four perovskite solid solutions have similar V set (2.2 V), Si 3 N 4 :Pt has a higher V set (2.8 V) and SiO 2 :Pt has the highest V set (4.2 V). The reset proceeds in several steps but always at lower voltages than the V set. All the R-V hysteresis curves are anticlockwise. For comparison, in Fig. S3 we present additional R-V curves with the following top/bottom electrode pairs, Ag/SRO and Au/SRO, for LAO:12.5%LNO, and Mo/SRO, Pt/Mo, Pt/Ta and Ag/Pt for SiO 2 :25%Pt. Referring to Table S1, Figure S2 I-V and R-V curves of solid solution films. 20 nm films with identical top (Pt, 80 m diameter) and bottom (SRO) electrodes. (a) CZO:SRO, (b) LAO:SRO, (c) CZO:LNO, (d) LAO:LNO, (e) SiO 2 :Pt, and (f) Si 3 N 4 :Pt. Arrowed circles indicate directions of R-V hysteresis loops. nature nanotechnology 3

4 supplementary information we find whenever the top electrode has a larger work function than the bottom electrode (Pt/SRO, Au/SRO, Pt/Mo and Pt/Ta), the hysteresis loop is anticlockwise. Conversely, whenever the top electrode has a lower work function than the bottom electrode (Ag/SRO, Mo/SRO and Ag/Pt), the hysteresis loop is clockwise. Perovskite thin films on STO substrates of different orientations (001, 011 and 111), thus having different film orientations and growth strains, show the same electrical characteristics (data not shown), as are films of SiO 2 :Pt on Si substrates of different orientations (100 and 110). Figure S3 Electrode effect on R-V curves of 20 nm films. (a-b) LAO:12.5%LNO and (c-f) SiO 2 :25%Pt solid solutions with various top/bottom electrode pairs. (a) Au/SRO, (b) Ag/SRO, (c) Mo/SRO, (d) Pt/Mo, (e) Pt/Ta, (f) Ag/Pt. Arrowed circles indicate hysteresis directions. In Fig. S4 the effect of UV irradiation on the HR is illustrated for five solid solutions. In all cases, the resistance decreased promptly after UV irradiation. UV has no effect on the LR. 4 nature nanotechnology

5 supplementary information Figure S4 UV induced transitions. Resistance of HR state promptly decreases upon UV irradiation. (a) CZO:SRO, (b) LAO:SRO, (c) CZO:LNO, (d) LAO:LNO and (e) SiO 2 :Pt. To probe the stability of the trapped electrons in the HR state, we performed accelerated retention tests by holding samples at 150 o C, cooling them to room temperature at set times to measure the resistance, then holding them again at 150 o C. In Figure S5 Retention tests. Resistance of HR state versus time for a perovskite (CZO:SRO) and a SiO 2 :Pt sample held at 150 o C. nature nanotechnology 5

6 supplementary information Fig. S5 the change of the HR resistance with time is shown for a perovskite and a SiO 2 :25%Pt sample. The long retention indicates that the trapped electrons have a low probability to escape in the absence of an electrical field or UV field. Additional unpublished data on perovskite solid solutions, including -f maps and -f-t independent switching voltages, were summarized in the PhD thesis of Yudi Wang (University of Pennsylvania, 2008.) C. LR and SrRuO 3 Bottom Electrode The R-T data of 20 nm films of CZO:5.5%SRO and LAO:12.5%LNO between a 80 mdiameter Pt top electrode and a SRO bottom electrode are compared with those of an SRO film in Fig. S6. Figure S6 Temperature dependence of resistance. Two-point resistance of 20 nm films of CZO:5.5%SRO and LAO:12.5%LNO between a 80 m-diameter Pt top electrode and a SRO bottom electrode. Also shown are data of SRO film in fourpoint-probe configuration. They all display a kink at about 160 K, the ferromagnetic Curie temperature of metallic SRO, below which there is reduced scattering from spin fluctuation. 7 Therefore, the spreading resistance of the SRO bottom electrode dominates the resistance of the LR state. A sheet conductor of a thickness with a cell contact area a 2 located at a distance L from the nearest edge electrical contact has a resistance of the order of SRO ((1-a/L) ) - 6 nature nanotechnology

7 supplementary information 1 ln(l/a), which is of the order of 250 for a 20 nm thick SRO film ( SRO =162 cm at room temperature) in this configuration (a = 80 mm and L = 2 mm.) D. Charge Trapping and Detrapping We use perovskite as an example. A schematic electronic band structure of perovskites is shown in Fig. S7. Both LAO and CZO are insulators with a similar band gap of 5.6 ev. 8,9 They may constitute a tunneling barrier for entering and leaving isolated trapped sites that are adjacent to electron s (0K) diffusion path in Anderson s picture, 10 or lie just outside the mobility edge in Mott s picture. 11 The barrier height is estimated from the electron affinity (EA) of the insulator and the work function (WF) of the electrode. The EA is 2.5 ev for LAO and the same for CZO if the value of BaZrO 3 is adopted. 8 The WF of SRO and Pt is 5.0 ev Figure S7 Electronic band diagrams. Energy of an isolated trap site between Pt top electrode and SRO bottom electrode. (a) Before contact, (b) after contact, at V=0, (c) with a trapped electron. and 5.6 ev, respectively. For LNO, a commonly used electrode, its work function should be slightly less than that of Pt. 12 For simplicity, we let the EA= 2.5 ev for both insulators. The energy of the trapped state is less certain but we let it be 5 ev first. We then draw the nature nanotechnology 7

8 supplementary information band diagrams in Fig. S7a and b for all the perovskite films with a Pt top electrode and a SRO bottom electrode. It is clear that the barrier is lower on the SRO side. The band diagrams allow Fowler-Nordheim tunneling (FNT) 13 from SRO when the SRO potential is raised (positive bias) by V set =2.5 ev. The tunneling rate can be calculated using a triangular shaped barrier with a height of 2.5 ev. Since the tunneling barrier to Pt is higher on the left by WF=0.6 ev, once the electron enters the trap, it will not continue tunneling through the second barrier to the Pt side. So after FNT the electron is trapped. The above consideration is incomplete because it ignored the increase in energy (by Hubbard energy, U) of the trapped electron due to localization. 14 With this taken into account, successful trapping then requires U<0.6 ev. The device is non-volatile because when the applied voltage is removed, the trapped electron still cannot detrap given the barrier height on both sides much more than U. Detrapping occurs when a reverse voltage of V reset =2.5 V U/e is applied (Fig. S7c). Therefore, V set V reset =U/e. Due to the statistical distribution of barrier height in a random structure, the most penetrable barrier should be below WF-EA. The lowest such barrier is the one where trapping first occurs. Subsequently, the influence of Coulombic repulsion of the trapped charge can lower the other barriers, so the barrier height in operation should be lower than WF-EA in general. However, the difference V set V reset is still maintained due to U. For a localization length of 1 unit cell (0.4 nm) in perovskite and a dielectric constant of 5, the electrostatic contribution to U is 0.34 ev, which is close to the estimate from the experimentally observed V set V reset. The statistical distribution of barrier width also explains why, even at a large positive bias, the HR state still remains: as the trapped 8 nature nanotechnology

9 supplementary information electron escapes to the Pt side at higher voltage, more electrons become trapped at other sites with a thicker barrier on the Pt side thus providing HR. (These latter sites were not accessible at a lower voltage because a thicker barrier on the Pt side implies less tunneling on the SRO side.) In summary, V set is determined by the difference of EA and the WF of the less noble electrode, the polarity of the set voltage is determined by the relative WF of the electrodes, and V set V reset =U. This explains (a) why all perovskite films have similar V set and V reset ; (b) the counterclockwise rotation of the R-V hysteresis loop when the WF of the top electrode exceeds that of the bottom electrode, and vice versa; (c) the retention of the HR state at 0 V and at 150 o C; and (d) why V set is the highest in SiO 2 (EA=0.95 ev being the smallest) and less so in Si 3 N 4 (EA= 2.1 ev). E. Reduced Activation Energy of Resistivity of the Intermediate States While the Ohmic LR state is clearly metallic, there is also evidence of nanometallicity in the intermediate HR states. The small-signal (±0.2 V) resistance of the intermediate states probed in Fig. 5b is replotted here in Fig. S8a. Although the resistance initially rises with decreasing temperature, it saturates at low temperatures. Therefore, electron conduction at sufficiently low temperature is not thermally activated an indication of metallicity. This is consistent with the reduced activation energy in Fig. S8b, W=-dlnR/dlnT, which rises with temperature indicating a metallic behavior. 15 As mentioned in the main manuscript, the conductance of these states can be explained in terms of fluctuation induced tunneling which is consistent with metallicity with weak tunneling barriers. 16 Cells having a much higher HR value with a steeper nature nanotechnology 9

10 supplementary information Figure S8 Reduced activation energy W. 20 nm film of LAO:12% LNO. Logtemperature dependence of (a) resistance and (b) its logarithmic derivative W at various states 0-3, arrested on the I-V curve in the inset of (a) at about -1.5 V. In (b), metallic conduction corresponds to a rising W, weak localization to constant W and variable range hopping to a decreasing W with a power law dependence on T. In computing W, the resistance of data set 4 (the LR mostly due to the bottom electrode) was first subtracted from the total R to obtain net R. Also shown are data (*) from another sample with a more resistive HR. temperature dependence at low temperatures also exist, one example marked by * is shown here, which has an entirely different temperature dependence for W indicating an insulating behavior. Here we found their conductivity is controlled by variable range hopping between localized states of an energy difference kt. 11 Between the above two limits, there are also states (not shown) with a constant W between 0.3 and 1 at low temperatures (thus R~T W ), a case referred to as the weak localization behaviour of a bad metal 17 found especially commonly in conducting polymers. 15 In all, many paths with various degrees of nanometallicity contribute to the transport in the intermediate HR states. Such bad metals and partially conducting insulators often manifest a hybrid optical property with coexisting features of insulator-like vibrational modes and freeelectron-like oscillations (a signature of conductor) similar to our observation in Fig. 2b 10 nature nanotechnology

11 supplementary information of the main text. 18 Such optically driven electron oscillations described by Drude s model indicates (in our case, localized) AC conduction; this is commonly termed optical conductivity. 18 (a) Perovskite films F. Material Preparation and Experimental Procedures Perovskite thin films were deposited by pulse laser depositions using a KrF laser ( = 248 nm) with a laser energy of 200 mj at a repetition frequency of 1-10 Hz in an O 2 pressure of mtorr. Mostly, (001) SrTiO 3 (STO) was used as substrates but (011) and (111) STO substrates were also used. The bottom electrode is always SRO for these films. The top electrode is mostly sputtered Pt, but thermally evaporated Au and Ag were also used to vary the work function. The film thickness, orientation and crystallinity were determined by a four-circle x-ray diffractometer (Bruker-AXS D8) using Cu K radiation, and the surface morphology was observed by atomic force microscopy (AFM). Single-TiO 2 -terminated STO (001) substrates were prepared following the procedures in the literature, 19,20 with some modification. The treated substrate surface has evenly distributed step edges and atomically flat terraces with a 0.4 nm height difference. Epitaxial SRO films (20 nm) were next deposited to provide the bottom electrode and an atomically smooth interface for growing the nanometallic film. The SRO films were atomically flat with a step structure of one unit-cell height. High resolution x-ray analyses indicated the SRO film was almost fully pinned to the STO (lattice parameters: out of plane nm, in plane nm) and was highly crystallized. (The full width at half maximum of the rocking curve was o, similar to that of the single crystal substrate, nature nanotechnology 11

12 supplementary information 0.03 o, around the (002) reflection). The crystal structure of SRO thin films including the in-plane domain structure was studied by off-axis azimuthal scan of a non-degenerate orthorhombic (221) reflection of SRO. It indicated a low content of secondary domains in the films, which were of a nearly single-crystal quality, being epitaxial with the substrate. The films had excellent electrical property: the resistivity at room temperature was 162 cm, which is comparable to that of single crystal. 7 The procedure for depositing CZO-SRO and LAO-LNO films on SRO/100-STO was given elsewhere. 21,22 To provide another example, here we give some details for the LAO:SRO layer. Because of the considerable strain in the solid solution layer, the x-ray diffraction peak of LAO:SRO films (labeled as LAO in Fig. S9b) is relatively weak. The solid solution of LAO:10%SRO has a lattice constant of nm, giving a biaxial Figure S9 20 nm LAO:10%SRO film. (a) AFM view of smooth surface. (b) X-ray diffraction pattern (Cu-K radiation) with the substrate reflection labeled as STO, bottom electrode as SRO, and solid solution layer as LAO. (c) Rocking curve showing comparable FWHM of substrate, bottom electrode and solid solution layer. tensile misfit strain of 2.7%. Crystalline, crack-free films of a thickness of 30 nm were obtained at o C and an oxygen pressure of mtorr. These films have a 12 nature nanotechnology

13 supplementary information smooth surface (Fig. S9a) and a small FWHM (Fig. S9c). Other solid solution layers were also prepared using laser ablation, and each was synthesized to achieve high crystallinity and smooth surfaces. (b) SiO 2 :Pt and Si 3 N 4 :Pt films One set of these films used Si substrates (100 or 110 orientations) covered with PLD deposited polycrystalline SRO (50 nm). The surface roughness of SRO was about 1.5 nm, compared to the roughness of the substrate of 1 nm, over 10 m 10 m. It contributed to a two-point resistance of about 200 to the resistance of an 80 m (diameter) cell. Another set of films used sputtered Mo as the bottom electrode. The surface roughness of the Mo film was about 1 nm and the Figure S10 TEM micrograph of SiO 2 :0.2 Pt film. The wormlike microstructure in this 12 nm film is similar to the one seen by Abeles for unannealed amorphous SiO 2 :W film. 5 Mo bottom electrode contributed to a resistance from 200 to 1000 depending on thickness. Top electrodes were sputtered Pt or Mo, or thermally evaporated Ag. Other samples with bottom electrodes of Pt and Ta were prepared by sputtering. Solid solution films of SiO 2 :Pt were deposited by RF sputtering using SiO 2 and Pt targets in Ar; films of Si 3 N 4 :Pt were similarly deposited by using Si 3 N 4 and Pt targets. All electrodes are crystalline but the SiO 2 :Pt and Si 3 N 4 :Pt films are amorphous according to x-ray diffraction. Sputtered SiO 2 and Si 3 N 4 films are known to be microporous unless a large negative bias is applied to the substrate. 23,24 The porosity is indicative of low atomic nature nanotechnology 13

14 supplementary information mobility on the surface, and the mobility appears to be further decreased by co-sputtering Pt, which increased porosity. This helps to prevent Pt segregation and crystallization. The film composition was measured using Rutherford backscattering in conjunction with direct thickness determination by AFM. Additional films were deposited onto carbonized TEM (transmission electron microscopy) grids and were directly examined using a TEM (JOEL 2010F) operating at 199 kv. One such micrograph is shown in Fig. S10 (same as the inset of Fig. 1a, but covering a larger area.) Another set of films were deposited onto Si substrates (without a bottom electrode) and examined using x-ray diffraction (Fig. S11). They showed amorphous SiO 2 and no evidence of Pt crystallization until f~0.6. Figure S11 X-ray diffraction pattern of SiO 2 :Pt films. Reflections of Pt are marked by lines, all (c) Electrical measurements other unlabeled peaks are reflections of Si. Electrical properties were measured using several meters (Keithley 237 current/voltage source-measure unit, Agilent 81104A pulse generator, HP 4192A impedance analyzer and Keithley 7001 switch system) on a Signatone S-1160 probe station for ambient measurements, on a Lakeshore TTP6 probe station and in several cryostats (PPMS and Janis ST-100H) for low temperature measurements. Sheet resistance was measured by the four-point method and cell characteristics were measured as two point resistance/impedance. Samples used for low temperature measurements typically had either lithographically or shadow-mask defined cells of various sizes ( µm 2 ), again with a Pt top electrode connected to the measurement circuits via a gold wire. To remove the inductance and resistance contribution of the measuring circuits, the 14 nature nanotechnology

15 supplementary information measured AC impedance of two shorted probes were subtracted. The remaining data were fitted using RC circuits. Retention and UV irradiation experiments were performed in air. In the retention experiment, the sample was first switched to either the HR or the LR state, then heated to a set temperature. The sample was removed from the heater from time to time to measure the room temperature resistance at a low voltage (0.2 V). In the UV experiment, a light source with a continuous energy spectrum spanning from 2.8 to 4.1 ev was illuminating from the bottom side of the sample, through the transparent (single crystal SrTiO 3 ) substrate and penetrating the relatively thin and less absorbing bottom electrode SRO. Since Si substrate is not transparent, solid solution films of SiO 2 :Pt deposited on quartz were used for the UV experiments. (d) Data analysis using fluctuation induced tunneling 16 We fit the tunneling conductance (R -1 ) to Sheng s equation, 16 G(0) = G o exp(- T 1 /(T+T 0 )), obtaining T 0 and T 1. According to Sheng, wa E 2T 2k w , T0 T 2 8 mv0 h 3V ew B 2, E0 where A and w represent the area and width of the gap, respectively, e and m are the electron charge and mass, respectively, V B is the barrier height, h is Planck s constant and 0 is the dielectric permittivity of vacuum. Since A and w are the only unknowns above, they can be obtained from T 1 and T 0, respectively. (d) Optical measurements nature nanotechnology 15

16 supplementary information Optical reflectivity and transmittance were measured using several SiO 2 :Pt thin films of various thickness on various substrates in order to avoid interference effects, excessive absorption, or substrate absorption bands in certain wavelength ranges. Fused silica substrates and 40 nm film thickness were used for UV-Vis measurements (Cary 5000 spectrometer from Varian); KBr substrates and nm thickness were used for IR measurements (Nicolet 8700 FTIR from Thermo Scientific.) All reflectance data were calibrated using an aluminum mirror with a known reflectance. According to the Mie theory, plasma resonance of Pt nanoparticles in an SiO 2 matrix occurs when Pt +2 SiO2 reaches a minimum, where Pt and SiO2 are the dielectric functions of Pt metal and the SiO 2 matrix, respectively. From this we estimate the resonance at 270 nm using dielectric functions of metallic Pt and insulating SiO 2 in the literature. 25,26 The free electron contribution to IR reflectivity was fitted using Drude s formula for dielectric constant, =1 2 p / ( +i/ ), from which we found the plasma frequency p and carrier concentration ( o m 2 p /e 2 ). 18 Data fitting of both transmittance and reflectance used a commercial code (TECompanion version 3.4) that allowed the selection of composite models (e.g., Maxwell Garnett) to simulate porosity and nanoparticles to compare with the experimental data as in the case of UV range. Likewise, it allowed the selection of both the Drude model and Lorentz models to simulate bond vibrations and free electron oscillations as in the case of IR range. The Lorentz peaks of SiO 2 glass are at 9.5 mm for the stretching mode, 12.5 mm for the bending mode, and 22.5 mm for the rocking mode. 27 Only the stretching mode shows a major distortion/splitting due to Pt addition. 16 nature nanotechnology

17 supplementary information Table S1 Work functions of electrode materials. Figure S1 R-T curves of SiO 2 :Pt films. Sheet resistance per four-point method normalized by the room temperature value. Pt % indicated next to the curve. Metal has a positive slope, insulator a negative slope. With macroscopic MIT identified with the zero slope, such composition is used as bulk percolation limit. Figure S2 I-V and R-V curves of solid solution films. 20 nm films with identical top (Pt, 80 m diameter) and bottom (SRO) electrodes. (a) CZO:SRO, (b) LAO:SRO, (c) CZO:LNO, (d) LAO:LNO, (e) SiO 2 :Pt, and (f) Si 3 N 4 :Pt. Arrowed circles indicate directions of R-V hysteresis loops. Figure S3 Electrode effect on R-V curves of 20 nm films. (a-b) LAO:12.5%LNO and (c-f) SiO 2 :25%Pt solid solutions with various top/bottom electrode pairs. (a) Au/SRO, (b) Ag/SRO, (c) Mo/SRO, (d) Pt/Mo, (e) Pt/Ta, (f) Ag/Pt. Arrowed circles indicate hysteresis directions. Figure S4 UV induced transitions. Resistance of HR state promptly decreases upon UV irradiation. (a) CZO:SRO, (b) LAO:SRO, (c) CZO:LNO, (d) LAO:LNO and (e) SiO 2 :Pt. Figure S5 Retention tests. Resistance of HR state versus time for a perovskite (CZO:SRO) and a SiO 2 :Pt sample held at 150 o C. Figure S6 Temperature dependence of resistance. Two-point resistance of 20 nm films of CZO:5.5%SRO and LAO:12.5%LNO between a 80 m-diameter Pt top electrode and a SRO bottom electrode. Also shown are data of SRO film in four-point-probe configuration. nature nanotechnology 17

18 supplementary information Figure S7 Electronic band diagrams. Energy of an isolated trap site between Pt top electrode and SRO bottom electrode. (a) Before contact, (b) after contact, at V=0, (c) with a trapped electron. Figure S8 Reduced activation energy W. 20 nm film of LAO:12% LNO. Logtemperature dependence of (a) resistance and (b) its logarithmic derivative W at various states 0-3, arrested on the I-V curve in the inset of (a) at about -1.5 V. In (b), metallic conduction corresponds to a rising W, weak localization to constant W and variable range hopping to a decreasing W with a power law dependence on T. In computing W, the resistance of data set 4 (the LR mostly due to the bottom electrode) was first subtracted from the total R to obtain net R. Also shown are data (*) from another sample with a more resistive HR. Figure S9 20 nm LAO-10%SRO film. (a) AFM view of smooth surface. (b) X-ray diffraction pattern (Cu-K radiation) with the substrate reflection labeled as STO, bottom electrode as SRO, and solid solution layer as LAO. (c) Rocking curve showing comparable FWHM of substrate, bottom electrode and solid solution layer. Figure S10 TEM micrograph of SiO 2 :0.2 Pt film. The worm-like microstructure in this 12 nm film is similar to the one seen by Abeles for unannealed amorphous SiO 2 :W film. 5 Figure S11 X-ray diffraction pattern of SiO 2 :Pt films. Reflections of Pt are marked by lines, all other unlabeled peaks are reflections of Si substrate. Cu-K radiation, Pt % indicated on the right. 18 nature nanotechnology

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