Ordered SnO2 nanotube arrays of tuneable geometry as a lithium ion battery material with high longevity

Ordered arrays of straight, parallel SnO2 nanotubes are prepared by atomic layer deposition (ALD) on inert ‘anodic’ aluminum oxide porous membranes serving as templates. Various thicknesses of the SnO2 tube walls and various tube lengths are characterized in terms of morphology by scanning electron microscopy (SEM), chemical identity by X-ray photoelectron spectroscopy (XPS) and phase composition by X-ray diffraction (XRD). Their performance as negative electrode (‘anode’) materials for lithium-ion batteries (LIBs) is quantified at different charge and discharge rates in the absence of additives. We find distinct trends and optima for the dependence of initial capacity and long-term stability on the geometric parameters of the nanotube materials. A sample featuring SnO2 tubes of 30 µm length and 10 nm wall thickness achieves after 780 cycles a coulombic efficiency of >99% and a specific capacity of 671 mA h g−1. This value represents 92% of the first-cycle capacity and 86% of the theoretical value.


Introduction
Owing to environmental concerns (global warming and pollution) associated with the exploitation of fossil fuels, renewable energy sources such as wind and solar energy have provided an increasing contribution to the energy mix. 1 Their inherently intermittent nature and unequal geographic availability render the storage of energy crucial. 2 Water electrolysis [3][4][5] and batteries [6][7][8] represent adequate storage technologies.In particular, rechargeable lithium-ion batteries (LIBs) [9][10][11] are attractive for various applications, 12,13 especially mobile and portable devices.Increases in the specic capacity of commercial LIBs have been mostly based on the positive electrode ('cathode'), whereas the negative counterpart has remained carbon-based in the past several years.Thus, replacing carbonaceous material with alternatives offering a signicantly improved specic capacity would represent a step change in electrochemical energy storage. 12,14mong the promising alternatives for the negative electrode, silicon and SnO 2 feature prominently.Both materials actually base on the same set of reversible lithiation/delithiation events, described (for Sn) in eqn (1): 9,[15][16][17] Sn + xLi + + xe À / Li x Sn, (x # 4.4) (1) Oen, however, the starting material used in the preparation of the electrode is not metallic Sn but the decently conductive oxide SnO 2 , instead.Therefore, the following irreversible reduction must take place in the rst cycle (or over the rst few cycles), eqn (2): 9,[15][16][17] SnO 2 + 4Li + + 4e À / Sn + 2Li 2 O (2) Considering the faradaic current associated with the reversible lithiation, eqn (1), and reporting it to the mass of SnO 2 originally present yields a value of 782 mA h g À1 for the theoretical specic capacity oen cited: This value dwarfs graphite (372 mA h g À1 ) despite the fact that the mass of oxide is considered (not only the pure element). 7,18,19Despite the advantageous capacity number, Snbased (and Si-based) electrodes have been hampered by their lack of stability so far. 12,20Indeed, they suffer from the large volume variation of $300% that occurs upon lithiation and delithiation. 12,21,22The strong internal stresses caused by it within the electrode material fracture the solid particles and cause the disintegration of the electrode upon repeated charge and discharge.This is associated with drastic capacity losses over tens or hundreds of cycles.0][31][32][33][34] Table 1 summarizes the state of the art for SnO 2 -based electrode materials.This comparison shows that the current best systems exhibit signicant capacity losses unless the total number of charge-discharge cycles performed is limited and/or the rates of charge and discharge are reduced signicantly.The various types of nanostructuring explored so far have not been sufficiently well controlled in order to allow for the signicant volume changes without deleterious pulverization of the solid.
In this work, we introduce arrays of parallel SnO 2 nanotubes (Fig. 1), fabricated by atomic layer deposition (ALD) in 'anodic' aluminum oxide (AAO) membranes as inert templates.Anodization not only yields a high quality of cylindrical, straight and ordered pores, it also allows the experimentalist to vary the pore geometry accurately: the pore diameter depends on anodization voltage and electrolyte, and the pore length on the anodization duration. 47][50][51] This design presents several advantageous features for a systematic study of how geometry affects performance and stability.Firstly, the straight geometry of the tubes denes a continuous electron transport path from the electrical contact to any point of the electroactive solid, thus rendering additives such as graphite (mostly used in other studies) unnecessary.This simplies the analysis and interpretation of the results signicantly.Secondly, the void internal volume of our SnO 2 nanotubes serves to take up the volume expansion occurring during lithiation, thus allowing the material to better endure the volume variations caused by charge and discharge.Thirdly, the transport distances for lithium from the electrolyte interface to any point of the solid are short and controllable by the tube wall thickness.We will show in the following that this geometry yields signicant improvements in stability over systems published so far (see Table 1).

Deposition of thin lms
Deposition of the thin SnO 2 layer along the inner walls of the AAO template pores to build up SnO 2 nanotubes was performed by ALD in a commercial Gemstar-6 XT ALD reactor from Arradiance at 200 C with tetrakis(dimethylamino)tin(IV) (TDMASn) and hydrogen peroxide (30% aqueous solution) as precursors.
TDMASn and H 2 O 2 were maintained in stainless steel bottles at 60 C and at room temperature, respectively.Subsequently, a thin gold contact layer (approximately 50 nm) was sputtered onto one side of the sample in a torr CRC 622 sputter coater.The loading of SnO 2 was determined as a difference by mass measurements of the sample before and aer ALD with an analytical balance (Sartorius micro, nominal accuracy AE0.001 mg, observed reproducibility AE0.003 mg).The accuracy of the mass determination of loading is evaluated to be AE0.005mg.For example, the sample with L ¼ 30 mm, ' ¼ 10 nm has 0.650 mg of SnO 2 in 4.062 mg of AAO membrane.

Characterization
The thicknesses of SnO 2 layers were determined on Si(100) wafers by spectroscopic ellipsometry with a SENPro from SEN-TECH.Scanning electron microscopy (SEM) and energydispersive (EDX) spectroscopy were implemented with an Jeol JSM 6400 upgraded with a LaB 6 cathode and SDD X-ray detector.
The crystal structure of the samples was investigated by X-ray diffraction (XRD) with Cu Ka 1 radiation (l ¼ 1.54056 A) on a Bruker D8 Advance diffractometer equipped with a LynxEye XE-T detector.The measurements were performed in the regular Bragg-Brentano geometry for porous samples and in grazing incidence (0.6 ) for planar ones.X-ray photoelectron spectroscopy (XPS) was carried out with monochromatized Al Ka X-ray photoelectron spectroscopy (PHI Quantera II, Japan).

Electrochemical studies
The nanostructured SnO 2 with AAO template were laser-cut with a GCC LaserPro Spirit LS Laser from their Al frame and into smaller pieces.The samples were then glued onto Cu foil by using double-sided adhesive and conducting Cu tape.The area of the sample was dened by a circular window laser-cut into chemically resistant and electrically insulating polyamide tape (Kapton®).They were complemented with a Li foil and 1.0 M Gold is sputtered as a thin electrical contact (yellow).The sample is then glued on Cu foil (brown).Every geometric parameter of this ordered structure is independently tunable: outer tube diameter D, wall thickness ', length L.
LiPF 6 in 50 : 50 (v/v) ethylene carbonate and diethyl carbonate, which was purchased from Sigma Aldrich, in CR2032 coin cells (from MTI Corporation) for galvanostatic charge/discharge curves at different current rate in a range of 0.02 V to 2.8 V.
Voltammetry and impedance spectroscopy datasets were recorded with an additional lithium metal reference electrode in a three-electrode conguration in a cell from EL-cell.Cyclic voltammograms were performed at a scan rate of 0.1 mV s À1 in the potential range 0.02 V to 2.8 V, while galvanostatic electrochemical impedance spectroscopy measurements were completed with an amplitude of 0.99 mA over the frequency range of 0.1 Hz to 1 MHz aer different cycling numbers.

Results and discussion
The preparative procedure towards ordered arrays of straight, cylindrical SnO 2 nanotubes by atomic layer deposition (ALD, 50 to 250 cycles corresponding to 10 nm to 50 nm) 48,49,52 in anodic aluminum oxide (AAO) membranes as templates is presented in Fig. 2. In short, the outstanding ability of ALD to coat deep pores (for the electroactive material) is complemented by the property of physical deposition methods (sputtering) of only coating one sample face (for the electrical contact).For this study, we will consider of SnO 2 nanotube lengths of 30 mm to 150 mm obtained by anodizing for 10 h to 50 h.We maintain a constant tube outer diameter (D) of 390(AE10) nm for a centerto-center distance of 450 nm.Fig. 3a and b compares the macroscopic appearance of an AAO membrane before and aer SnO 2 ALD coating (10 nm as determined by spectroscopic ellipsometry on a planar reference sample).The slightly yellow color of the semiconductor is evident and homogeneous across the full sample diameter (12 mm).Of course, thicker coatings result in darker shades of yellow.The high structural quality of the samples on the microscopic scale is presented on Fig. 3c, where the regularly ordered AAO pores, coated with SnO 2 , are evident in top view.The presence of the SnO 2 layer is proven by EDX spectroscopy (Fig. 3d).
The homogeneity of SnO 2 ALD coating along the pore length is proven by an EDX prole recorded along the cross-section of the SnO 2 sample, Fig. 4. The Sn signal is continuous from one side of the sample to the other, albeit not perfectly constant.It stands in stark contrast, however, to the Au signal associated with the electrical contact, which is nicely located on one sample surface only.
Further insight into the chemical identity of our ALDdeposited material is provided by X-ray photoelectron spectroscopy (XPS, Fig. 5).The survey spectrum (Fig. 5a) exhibits the elements Sn and O as expected, in addition to the weak C 1s peak always present at 284.8 eV for samples handled in air.No other impurities are observed.The ratio between Sn and O is found to be 1 : 2.7, larger than the value of 2 expected for SnO 2 .The XPS Sn 3d line (Fig. 5b), however, is a perfect spin-split doublet at 486.52 eV and 494.94 eV, the position expected of SnO 2 .Thus, tin centers are homogeneously in oxidation state +IV and bonded to oxygens.The O 1s region, in contrast to this, must be tted with two distinct species.The peak at 530.70 eV perfectly corresponds to perfectly stoichiometric SnO 2 .The broader peak at higher energies falls into the range expected of -(OH) groups. 55,56These observations are consistent with a partial hydration of SnO 2 in the surface-near region.
Further conrmation of the identity of the ALD material is provided by X-ray diffraction (XRD).Fig. 6 reveals that crystalline SnO 2 is obtained from ALD without annealing necessary, as has been reported before for layers of sufficient thickness and depending on deposition temperature and substrate. 57,58herefore, the amount of hydrated material (presumably amorphous) is low in the bulk.The very broad signal stretching from 20 to 40 and evident of a large amount of amorphous can be attributed to the alumina matrix, since it is absent of data recorded for planar lms on silicon wafers in grazing incidence (0.6 ).The three sharp peaks marked by stars at 45 , 65 and 78 in the porous sample diffractogram (dark green in Fig. 6) are due to the Al frame of the AAO membrane.
These SnO 2 nanotubes can be exploited as lithium ion battery materials aer addition of a gold electrical contact, without the need to remove them out of the matrix or to complement them with any electron and/or ion conducting additives as is usually performed.The conditions for it are a high electrical conductivity 57,59 and a continuous, straight transport pathway along the tube axis.Fig. 7 demonstrates that indeed, such a sample is electrochemically active as is.Starting from +2.8 V vs. a lithium foil in LiPF 6 electrolyte, the rst cyclic voltammogram exhibits the irreversible reduction peak of SnO 2 to metallic Sn at 1.38 V (eqn (2) in the Introduction), which is very characteristic and well established in the eld 9,16,17 The complete disappearance of this reaction over the subsequent two cycles is indicative of an outstanding accessibility of all SnO 2 present to both electrons and lithium ions.An additional irreversible feature that disappears over the rst few cycles is the shoulder observed at 0.48 V.This feature is also precedented in the SnO 2 literature and has been attributed to the formation of the solid-electrolyte interface (SEI) via electrolyte decomposition. 17he peaks attributed to the reversible lithiation of Sn (eqn (1) in the Introduction) are observed at 0.22 V and 0.08 V during the rst cathodic sweep, and they shi somewhat to more positive potentials over the rst ve cycles. 9,16Both the potential values and this slight shi are consistent with SnO 2 -based electrodes studied so far. 9,16The corresponding anodic features are found at approximately 0.40 V, 0.50 V, 0.60 V and 0.90 V for delithiation. 9,16We note that the aluminum oxide matrix is inert electrochemically, as demonstrated by a reference measurement performed in the absence of SnO 2 (dashed black line on Fig. 7), at least aer completion of the rst few cycles.
The voltage proles obtained from galvanostatic measurements performed in the same potential range display stages of low slope at the peak positions in the voltammograms, as expected.The fact that perfectly horizontal plateaus are replaced by low-slope sections is due to the rather fast charge/discharge rate (one full charge within 2 hours or 0.5C) used for the galvanostatic measurements.The galvanostatic curves allow us to quantify the degree of irreversibility caused be SEI layer  formation at the early stages (over the rst three cycles) to 8%, yielding (equivalently) a coulombic efficiency of 92%.The rstcycle absolute capacity of 0.235C translates to an areal capacity of 1870 mC cm À2 or 0.519 mA h cm À2 and to a gravimetric specic value of 1284 mA h g À1 .This value is larger than the theoretical reversible capacity of 782 mA h g À1 on the basis of SnO 2 (as dened in the Introduction) and is in line with the observation that in the rst few cycles a signicant amount of irreversible processes take place.The development of these values over time, that is, over large numbers of charge and discharge, will be described later as it depends on charge rates and geometry.
Galvanostatic electrochemical impedance spectroscopy measurements carried out (in a three-electrode conguration) over the frequency range of 0.1 Hz to 1 MHz aer 0, 1, 2, and 20 charge-discharge cycles are presented in Fig. 8 as Nyquist plots.The data consist of a semicircle and a straight line at lower frequency range, attributed to charge transfer impedance at the electrode/electrolyte interface and transport of Li + , respectively. 27First of all, the series resistance is reasonably low (<10 U), indicating a good electrical contact.The curve changes most signicantly from before the rst cycle to aer it, as expected based on the irreversible chemical changes (reduction to Sn metal and SEI layer formation) that occur during it as discussed above.
The quantitative EIS parameters presented in Table 2 derive from ts according to the equivalent electrical circuit model shown in Fig. 8 and adapted from literature precedents. 31,32,44e x the a values of constant-phase elements to 0.8 for Q SEI and 0.9 for Q dl .The SEI-related elements are ignored for the pristine sample, which does not exhibit any SEI yet.Aer the rst cycle, the values of Q SEI and R SEI remain fairly constant, which indicates a stable SEI layer.R ct decreases aer cycling, again signifying properties that are stable (or even improving) upon repeated cycling (eqn (1)).The behavior of Q dl seems to indicate a signicant roughening upon initial cycling, followed by a slow but steady smoothening subsequently.Fig. S1 † presents the EIS data recorded at various potentials and from SnO 2 nanotubes with different wall thicknesses for completeness.
For the systematic investigation of how electrochemical performance (specic capacity and stability) depends on geometric parameters, we need to generate samples with various geometries.Fig. 9 displays how the tube wall thickness ', on the one hand, and the tube length L, and the other hand, are controlled experimentally.The former is adjusted via the number N of ALD cycles performed but is also accessible experimentally via direct gravimetric measurements.The graph (Fig. 9a) shows how the SnO 2 loadings determined directly increase linearly with N and correlate with the values expected based on geometric considerations-for a given value of L. Independently of this, L can be varied for a constant ' as displayed by the low-magnication micrographs of Fig. 9b.The  gravimetric determinations of SnO 2 loadings are associated with an absolute uncertainty of approximately 0.005 mg, which translates to an experimental error of AE1% for the samples with the thickest coatings and AE3% for their thinnest counterparts.However, the linearity of ALD lm growth can also be used to check the validity of the gravimetric determinations, as is especially useful for the thinnest (10 nm) samples.Further conrmation of the numbers has been provided by quantitative element analysis using inductively coupled plasma optical emission spectroscopy (ICP-OES) aer complete dissolution of a test sample.
The behavior of samples with various SnO 2 tube wall thicknesses ' over the rst 30 charge/discharge cycles at 0.5C is presented in Fig. 10a.Note that in this paper, we always base Crate denominations on the theoretical specic capacity of SnO 2 mA h g À1 ).Thus, 0.5C represents 391 mA per gram of SnO 2 as determined gravimetrically aer ALD.Note also that repeating measurements on nominally identical samples allows us to evaluate the experimental uncertainty to roughly AE17% (caused to a large extent by the gravimetric determination of SnO 2 amount), but Fig. 10 displays the data recorded on one individual batch.
All samples exhibit sub-unity coulombic efficiency and a concomitant signicant capacity loss that stabilizes gradually.The most striking difference between the samples is in the gravimetric specic capacity values, with the thinnest tubes performing best.This must be due to the excellent accessibility of the full volume of electroactive material to lithium insertion.Of course, the values beyond theoretical capacity recorded for this sample over the very rst cycles do not represent the reversible lithiation/delithiation of Li x Snthey contain all additional, irreversible processes (SnO 2 reduction to Sn, SEI layer formation, all further decomposition reactions) and are associated with a signicant relative uncertainty caused by the gravimetric determination of SnO 2 loading as described above.
The data presented in Fig. 10b, recorded on fresh samples with nominally identical geometric parameters, feature their   rate stability.The loss of accessible capacity from 0.5C to 2C varies between 7.60% and 48.60%, but in most cases cycling at high rates does not permanently damage the material as it recovers its capacity in subsequent, slow cycles.Fig. 11 shows the reason for the capacity loss.A change in morphology is observed aer the completion of many hundreds of cycles from perfect, hollow tubes to particles.This ration is particularly apparent for the tubes with thicker walls (Fig. 11f), where the large particles generated over time may even clog the pores, thus rendering some of the electroactive material inaccessible to the electrolyte.In contrast to this, thin tubes become rougher aer cycling but never generate such large, separate particles (compare Fig. 11a taken aer 783 cycles with Fig. 11f taken aer only 100 cycles).Thus, the nanotube strategy of improving stability is most appropriate with thin walls (as expected).
Not only the wall thickness ' but also the tube length L can be varied.Fig. 12 shows data obtained for a series of samples with various L: they differ in absolute capacities but converge when described in units of specic capacity (Fig. S2 †), demonstrating that even with the thinnest tubes and in the absence of any conductive additive, all of the material is accessible and electroactive, as designed.Indeed, the absolute capacity increases with loading (as varied with L at constant ') in a roughly linear manner.The behavior of the capacity loss over the initial cycles, however, is somewhat differentiated.Although each sample behaves in an individual manner, the general observation is that shorter tubes tend to reach a steady state faster.This could be due to the ohmic voltage drop present from the current collector to the top tube extremity, which spreads all processes, including the irreversible ones that have to occur in the initial cycles, over the voltage axis.
Let us nally turn to the long-term stability of our electrodes.Fig. 13 displays the variations in specic capacity and reversibility exhibited by a sample (L ¼ 30 mm, ' ¼ 10 nm) over 783 cycles at 0.5C (391 mA h g À1 ).Its behavior is representative of all samples presented above.As expected, the irreversible reactions leading to non-unity coulombic efficiency are completed within the rst 30 cycles or so, aer which the coulombic efficiency values are essentially 100% and the charge storage fully reversible.The capacity also drops by about 51% over the rst 70   cycles, aer which it not only stabilizes but even increases very slowly again.In fact, it almost reverts back to its original capacity (664 mA h g À1 of 724 mA h g À1 ).This unusual behavior is not specic to one particular sample or geometry but is observed in a qualitatively similar manner for all systems investigated.Similar behavior has been observed before in SnO 2 -based systems, without explanation being provided so far. 26,27,44Our hypothesis concerning the origin of this phenomenon is the following.In the initial stages of the material's lifetime, the initially continuous SnO 2 layer is converted to a heterogeneous Sn/Li 2 O mixture in which the electrically conductive phase (Sn) may be holey, or even patchy.This increases ohmic losses and may even isolate some fraction of the electroactive material.Upon the effective kneading that occurs during subsequent charge/discharge cycles (with their associated volume changes), individual Sn particles or islands may well reconnect, thereby improving the electrical conductivity and the completeness of the conductive network.This scenario is consistent with the behavior observed for Q dl over the course of 20 cycles.

Conclusions
Taken together, the data presented establish the applicability of ALD in combination with 'anodic' porous substrates for the preparation of battery electrode materials in parallel nanotubular shape.Such arrays of parallel SnO 2 nanotubes are active as a negative LIB electrode material in the absence of any additive.The nanotube structure is designed to have sufficient space for volume expansion during lithiation and shrinking upon delithiation and enables the experimentalist to explore systematically the geometric effects on performance and longevity.In this respect, the results are most convincing for thinner tube walls.The stabilized specic gravimetric capacity is highest (on the basis of SnO 2 ) for tubes with 10 nm wall thickness.Not only does the presence of a void central space allow for volume changes without deleterious cracking and pulverization, it also seems to promote a slow recovery of electroactive material particles that may have lost contact with the bulk in the early stages of electrochemical cycling.
Our best samples compare positively with the state of the art for SnO 2 -based electrodes (Table 1), with a coulombic efficiency > 99% and a specic capacity of 671 mA h g À1 aer 783 cycles.This represents a 92% retention of the initial capacity, and 86% of the theoretical value on the basis of SnO 2 .Since the best results on this scale are obtained for the samples that feature the thinnest walls, the areal specic capacity is low, as well as the overall gravimetric one (including the Al 2 O 3 matrix).In other words, the highly tunable nature of this system allows the user to choose for each application the optimal geometry with either maximized longevity or maximized areal specic capacity, or a balance of both.In principle, the alumina matrix could even be removed aer ALD generation of the electroactive material: this would cause a loss of order (since the tubes would tend to collapse), but would equate the gravimetric SnO 2 -only capacity (and energy density) with the overall gravimetric capacity of the negative electrode.These properties pave the way towards real-world applications of SnO 2 in the lithium ion batteries of portable devices.

Fig. 1
Fig. 1 Schematic presentation of the nanostructured SnO 2 electrodes studied in this work.ALD-SnO 2 nanotubes (pale orange) are embedded within an anodic aluminum oxide (AAO) matrix (gray).The void space in the center of each nanotube allows for the volume expansion of the electroactive material upon lithiation (salmon color).Gold is sputtered as a thin electrical contact (yellow).The sample is then glued on Cu foil (brown).Every geometric parameter of this ordered structure is independently tunable: outer tube diameter D, wall thickness ', length L.

Fig. 2
Fig. 2 Preparation of SnO 2 nanotubes: (a) two-step anodization of Al foil (defining the tube length L) and subsequent wet chemical removal of metallic Al.The length of the AAO membranes was defined by this step.(b) Wet chemical Al 2 O 3 barrier layer removal and pore widening (defining the outer tube diameter D).(c) ALD of SnO 2 (defining the tube wall thickness ').(d) Sputter-coating of Au.(e) Laser-cutting of the sample and gluing with conductive Cu adhesive tape.

Fig. 3
Fig. 3 (a) Macroscopic photograph of a transparent, bare AAO membrane before ALD.(b) Same sample after SnO 2 ALD.(c) SEM micrograph of a sample in top view after all preparation steps of Fig. 2. (d) EDX spectrum exhibiting the presence of Sn.

Fig. 4
Fig. 4 Element analysis of a sample by EDX spectroscopy.(a) SEM micrograph of the cross-section analyzed, displaying the profile analyzed as a red arrow.(b) EDX profile for the elements Al, O, Sn and Au along the path defined in (a).

Fig. 5 X
Fig. 5 X-ray photoelectron spectra of a SnO 2 film (10 nm) on a clean Si (100) surface.(a) XPS survey spectrum indicating the presence of all expected elements.(b) XPS Sn 3d region fitted by one single spin-split doublet.(c) XPS O 1s region fitted by two peaks.

Fig. 6 X
Fig. 6 X-ray diffraction patterns of 30 nm of SnO 2 deposited on an AAO substrate and a planar Si wafer.Light green: grazing-incidence XRD (GIXRD) of the planar film recorded under 0.6 incident angle.Dark green: regular (Bragg-Brentano) XRD of the nanotube sample.The peaks associated with metallic aluminum are marked by a star.The positions of peaks expected of SnO 2 (COD 2101853) are marked.

Fig. 7
Fig. 7 Initial electrochemical properties (three cycles) of a SnO 2 nanotube electrode (' ¼ 10 nm, L ¼ 30 mm, 4 mm macroscopic sample diameter).(a) Cyclic voltammograms recorded at a scan rate of 0.1 mV s À1 in the potential range 0.02 V to 2.8 V. (b) Voltage profiles recorded under a constant current of 19.8 mA (corresponding to a rate of 0.5C).

Fig. 8
Fig. 8 Nyquist plots of galvanostatic electrochemical impedance spectroscopy (EIS) measurements recorded of SnO 2 nanotube electrodes (' ¼ 10 nm, L ¼ 30 mm, 4 mm macroscopic sample diameter) in their delithiated state after 0, 1, 2, and 20 charge/discharge cycles (spectra are plotted in dots).The equivalent electrical circuit model shown in figure is used to fit the data, whereas the Q SEI /R SEI element is abandoned for the dataset recorded before cycling.W: Warburg diffusion; Q dl : constant-phase element due to double layer; R ct : charge transfer resistance; Q SEI , R SEI : constant-phase element and resistance due to the solid/electrolyte interface (SEI) layer; R s : series resistance.

Fig. 9
Fig. 9 Geometric control of SnO 2 nanotube electrodes.(a) Demonstration of varying ' via the number N of ALD cycles: the graph shows the SnO 2 loading determined gravimetrically and compared to the values calculated based on geometric considerations.(b) Demonstration of varying L via the anodization duration: the micrographs present cross-section views of the samples.

Fig. 10
Fig. 10 Charge-discharge behavior of SnO 2 nanotube electrodes with various wall thicknesses between 10 nm and 50 nm.(a) Thirty cycles performed at a constant rate of 0.5C calculated based on the theoretical capacity value of 782 mA h g À1 .(b) Performance at various C-rates.

Fig. 12
Fig. 12 Galvanostatic charging and discharging curves of SnO 2 nanotube electrodes with 10 nm wall thickness.The length of SnO 2 nanotubes has been varied.

Table 1
Summary of the performance and longevity of nanostructured SnO 2 or SnO 2 composites as negative electrode materials for lithium ion batteries

as received. Aluminum plates (0.5 mm thick) were provided by Smart Membranes. Water was puried in a Millipore Direct-Q System. Au target for sputtering was supplied by Stanford Advanced Materials. Silicon wafers coated with an oxide layer were from Silicon Materials Inc. CR2032 cases, stainless steel spacers and springs were purchased from
MTI Corporation.Celgard 2325 separators were from EL-Cell GmbH.CrO 3 in 6 wt% H 3 PO 4 ) was added to the beakers to remove the irregularly grown aluminum oxide nanopores for 24 h at 45 C. The second anodization was carried out at +195 V and at 0 C, rst for 1 h in 0.5 wt% H 3 PO 4 and subsequently for an adjustable duration in 1 wt% H 3 PO 4 .The duration of this second anodization determined the length of the AAO matrix pores.The aluminum substrate was later removed with 0.7 M CuCl 2 in 10% HCl. 10 wt% H 3 PO 4 solution was used to remove the barrier layer of the AAO membrane at 45 C (35 min from the back side) and perform pore widening (full immersion in H 3 PO 4 for another 35 min).Finally, laser-cut circles of AAO templates were dried overnight at 45 C.
4for another 23 h.The anodization was performed in a two-electrode system, in which the aluminum plates were sandwiched between a PVC beaker with O-ring on top and a Cu plate underneath, used as the electrical contact.The PVC beaker contained the H 3 PO 4 solution and was covered by a cap 53,54

Table 2
Parameters fitted from EIS spectra in Fig.8recorded after various numbers N of charge-discharge cycles