Tunneling and Polaron Charge Transport through Li2O2 in Li–O2

Oct 1, 2013 - In combination with a simple model, these imply that charge transport through Li2O2 in Li–O2 batteries at practical current densities ...
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Tunneling and Polaron Charge Transport through Li2O2 in Li−O2 Batteries A. C. Luntz,*,†,‡ V. Viswanathan,‡,§ J. Voss,‡ J. B. Varley,‡,# J. K. Nørskov,‡,§ R. Scheffler,⊥ and A. Speidel⊥ †

Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States SUNCAT, SLAC National Accelerator Laboratory, Menlo Park, California 94025-7015, United States § Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States ⊥ Volkswagen Group, Inc., Belmont, California 94002, United States # Lawrence Livermore National Laboratory, Livermore, California 94550, United States ‡

S Supporting Information *

ABSTRACT: We describe Li−O2 discharge experiments in a bulk electrolysis cell as a function of current density and temperature. In combination with a simple model, these imply that charge transport through Li2O2 in Li−O2 batteries at practical current densities is based principally on hole tunneling, with hole polaron conductivity playing a significant role near the end of very low current discharges and at temperatures greater than 30 °C. We also show that charge-transport limitations are much less significant during charging than those in discharge. A key element of the model that qualitatively explains all results is the alignment of the Li2O2 valence band maximum close to the electrochemical Fermi energy and how this alignment varies with overpotentials during discharge and charge. In fact, comparison of the model with the experiments allows determination of the alignment of the bands relative to the electrochemical Fermi level. SECTION: Energy Conversion and Storage; Energy and Charge Transport

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combined with the electrochemical kinetics predicted a sudden death under galvanostatic conditions because a bias Ubias across the film becomes necessary to aid the tunneling, and this potential loss determines Qmax. Even with the Ubias, tunneling is only possible for length scales of d ≈ 5−10 nm. Adding a phenomenological resistance or jR drop through the deposit to the MIM tunneling model gave excellent agreement with the observed discharge behavior at one current density.4 Several authors have suggested that charge transport is via hole polarons or charged defects or a combination of these via a thermally activated hopping mechanism, either diffusion or migration.5−7 It is, however, difficult to see how these mechanisms can account for the sudden death that is observed experimentally in galvanostatic discharges (Figures 1a and S2 (SI)), as also noted elsewhere.6 There are two important issues that determine the mechanism of charge transfer through Li2O2, (1) the alignment of the Li2O2 bands (valence band maximum [VBM] and conduction band minimum [CBM]) relative to the Fermi level εF in Li2O2 in the electrochemical cell and (2) the thermal populations of various charged carriers (polarons, vacancies, impurities) at the battery potential U and the mobility of these

ver the past several years, there has been much research activity into the nonaqueous Li−air (or Li−O2) battery because of its potential for high specific energy. The net electrochemical reaction in a nonaqueous Li−air battery is 2Li + O2 ⇄ Li2O2, with battery discharge described by the forward direction and charge described by the reverse direction. Despite their great promise, there are significant challenges to developing practical Li−air batteries.1,2 One is the electrical passivation of the cathode during discharge.3,4 This occurs because insoluble and insulating Li2O2 produced during discharge builds up as a deposit on the cathode surface and ultimately inhibits charge transfer to the Li2O2−electrolyte interface where the electrochemistry occurs. This manifests itself as a “sudden death” (rapid drop in the output potential U) of the discharge at some maximum discharge capacity, Qmax. What is particularly disturbing is that this sudden death occurs at lower and lower Qmax as the current increases (see Figures S1 and S2 in the Supporting Information (SI)). Therefore, although a high specific energy (high Qmax) is currently achievable at very low current, the Qmax is ∼50× less at more practical currents. Thus, there is currently an unsatisfactory trade-off between specific energy and power in current Li−O2 batteries. We have suggested previously that the dominant chargetransport mechanism at practical current densities j is tunneling of holes through the Li2O2 deposit.4 A first-principles Au|Li2O2| Au metal insulator metal (MIM) model of this tunneling © 2013 American Chemical Society

Received: September 7, 2013 Accepted: October 1, 2013 Published: October 1, 2013 3494

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studying this on the GC cathodes rather than in Li−O2 batteries is that the current density j is moderately wellknown because of the known electrochemically active Li2O2 surface area. In this letter, we present a wide range of new experiments probing the charge transport, for example, its dependence on j and temperature T. These allow an identification of the dominant charge-transport path at the various experimental conditions because tunneling has an exponential dependence on film thickness d (or Qdis) and no significant T dependence, while an Ohmic path is approximately linear with d and exponentially T-dependent. We also develop a simple semiclassical model that emulates the MIM tunneling charge transport but also adds an Ohmic path from thermally populated hole polarons. This model allows us to add a key aspect of the electrochemically active Li2O2−electrolyte interface not contained in previous models, that is, that overpotentials in the electrochemistry cause shifts in the band alignment of Li2O2 to εF. This causes a current-dependent change both to the tunneling barrier and the thermal concentration of polarons. With parameters of the model chosen from density functional theory calculations, qualitative agreement with all experimental results is obtained. We find that the polaron path is important only at very low current densities at higher temperatures, so that tunneling dominates at the higher current densities appropriate for practical roomtemperature batteries. Figure 1a shows galvanostatic discharges at various currents at 30 °C, as labeled in the figure (see the SI for experimental details). There are three important qualitative features, all of which are strongly current-dependent, an immediate drop in U due to the kinetic overpotential (ηdis), a linear decrease in output potential with Qdis (interpreted as a resistive jR drop), and finally a more sudden exponential decrease in output potential, or sudden death of the cell. The kinetic overpotentials and their current dependence have been described previously as the electrochemical growth/dissolution on already nucleated films (or nanoparticles) of Li2O2.12,13 The latter two properties are attributed to charge-transport limitations through the Li2O2. Figure S2 (SI) shows that qualitatively similar discharge behavior is also observed in typical Swagelok Li−O2 batteries. However, in these batteries, the jR drop is minimal or absent. In part, this is because of the smaller current densities due to the large surface area of the porous carbon cathodes (see Figure 1a). In addition, Qdis in the batteries is driven by continuously nucleating new nanoparticle growth on the C cathode, each with a minimal initial jR drop, rather than as a thickening continuous film of Li2O2 on the GC cathodes in the electrolysis cell.4 This is similar to the Gibbs phase rule applied to Li−O2 batteries, that is, that the output potential is constant during discharge for a multiphase material but varies with composition for a single-phase material. Figures S3 and S4 (SI) show that the need for a Ubias is completely absent at the outset of charge when the Li2O2 film is thickest so that there is no equivalent sudden death phenomenon in charging. This asymmetry has also been observed previously in Li−O2 batteries.14 We have previously argued that the potential rise during charging is simply a result of electrolyte decomposition products depositing at the Li2O2− electrolyte interface where the electrochemistry occurs.15 Thus, in contradiction to the common assumption that the potential rise during charging is due to a charge-transport issue, we argue that the charge-transport constraint is far less severe during charging than that during discharging.

Figure 1. (a) Experimental Li−O2 galvanostatic discharge curves (U versus Qdis) observed in a bulk electrolysis cell on a ∼1 cm2 area glassy carbon (GC) cathode with 1 M LiTFSI in DME as the electrolyte, ∼1 bar O2 pressure, and at T = 30 °C. The various curves for different discharge currents (1−500 μA and 1−2 mA) are labeled . (b) Theoretical galvanostatic discharge curves (U versus the thickness of the film d) under the same conditions as (a) and based on the simple tunneling + Ohmic polaron charge-transport model described in this Letter. The scale of the d axis is equivalent to the Qdis axis in (a) assuming a film growth of average thickness d with Qdis. The currents for the various theoretical discharge curves are the same as the corresponding colors in (a).

charged carriers. The interplay of these two determines which of many possibilities dominate charge transport. For example, if εF is near midband, then charge transport is only possible through extended defects such as grain boundaries or through migration of charged point defects or polarons (e.g., an Ohmic path) when the diffusion barriers are also small. When εF approaches the VBM or CBM, then charge transport is also possible either via a semiconducting mechanism (carriers in the bands caused by excitations to shallow traps) or through tunneling. We have discussed previously that the cathode electrochemistry occurring on planar glassy carbon (GC) cathodes of ∼1 cm2 area in a bulk electrolysis cell is identical to that occurring in Li−O2 batteries with large-surface-area carbon cathodes when proper account is made for the different microscopic j.8 The major difference between the two is simply the morphology of Li2O2 growth, that is, thickening continuous films on the GC and nanoparticle growth in the Li−O2 batteries. At very low discharge j, large toroids of Li2O2 are reported by several authors9−11 (although we have never observed these in our experiments at low j). However, at higher (and more practical) j on these same cathodes, small nanometer-scale nanoparticles or continuous films are formed with a thickness similar to that formed on the GC films at the same j.10 We have suggested previously that charge transport through Li2O2 films/nanoparticles of varying thickness d can be studied by measuring galvanostatic Li−O2 discharges (U versus Qdis) on GC in the electrolysis cell.4 The great advantage for 3495

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without and with a charged Li vacancy4 (and to be published). The barrier for tunneling of holes is given by the area bounded by εF and the VBM and the Li2O2 thickness d. Note that the location of εF relative to the VBM also defines the formation energy of the hole polarons E f (h p+ ) and hence their concentration (to be published). Figure 3b shows schematically the band alignment during discharge assuming quasi-equilibrium. Nearly the full discharge potential Udis = U0 − ηdis represents a potential loss at the electrolyte−Li2O2 interface, that is, a potential drop in the inner Helmholtz plane (IHP) of the electrolyte. In order to sustain electrochemical current density j, a potential step of ηdis from that already present at the IHP at U0 is induced. Because this additional potential step is not effectively screened within the Li2O2 (λD ≫ d), εF must experience nearly the same rigid shift in potential to maintain equilibrium across the interface. Note that this step implies no bias potential applied across the film so that the VB and CB bands remain fixed. This gives a simple qualitative interpretation of why the discharge capacity decreases strongly with j in galvanostatic discharges, that is, ηdis(j) increases with j, causing an increase in the tunneling barrier and in Ef(h+p ). The former leads to a smaller maximum tunneling length d or Qmax, while the latter gives a smaller equilibrium concentration of polarons and its conductivity. As the film thickens near sudden death, a potential Ubias is also applied across the film that helps to drive transport of holes to the C cathode. Because the carrier density is small, we assume a linear potential drop across the film, and this potential shifts the bands and εF, as shown schematically in Figure 3d. Note that the bias applied across the film decreases the average barrier for hole tunneling, and this is the fundamental reason that Ubias helps maintain galvanostatic discharge currents at higher d near sudden death. Figure 3c shows the equivalent quasi-equilibrium band alignment during charge. In this case, ηchg(j) is positive relative to the equilibrium Li−O2 redox potential, and this shifts εF closer to the VBM than in the equilibrium case. Therefore, the average barrier to tunneling decreases with ηchg(j) and hence j. In addition, Ef(h+p ) decreases so that the polaron concentration and its conductivity also increase exponentially. Therefore, at the d for sudden death of discharge, charge transport during charge is significantly longer range than that for discharge (and therefore does not need help in the form of a Ubias). This simple picture then qualitatively rationalizes the Ubias asymmetry in Figure S4 (SI). We previously ascribed the linear decrease in U with Qdis to a jR drop due to some indefinite scattering phenomenon during the hole tunneling that causes a resistance R4 and argue that this is due to Coulomb scattering from thermally populated positively charged vacancies or polarons (to be published). Despite the fact that the jR slope increases with current density j, R actually decreases dramatically with j, as shown in Figure S7a (SI). In Figure S7b (SI), we show that this decrease is roughly exponential with ηdis/kBT for a wide range of j, T, electrolyte concentration [Li+], and O2 pressure P. We discuss in the SI that this exponential dependence of R is consistent with incoherent scattering from a set of positively charged or, in some cases, neutral point defects whose populations depend exponentially on ηdis/kBT, that is, in the same manner as suggested in Figure 3b. In order to quantify the arguments above, we develop a simple one-dimensional (x) model for charge transport that assumes growth of a Li2O2 film on the GC with average

Figure 2a shows related galvanostatic discharges in the bulk electrolysis cell at 20 and 40 °C. There is a dramatic T

Figure 2. (a) Experimental Li−O2 galvanostatic discharge curves (U versus capacity) observed in a bulk electrolysis cell on a ∼1 cm2 area GC cathode with 1 M LiTFSI in DME as the electrolyte, ∼1 bar O2 pressure, and at T = 20 and 40 °C. The various curves for different discharge currents and T are labeled at the side. (b) Theoretical galvanostatic discharge curves (U versus the average thickness of the film d) under the same conditions as (a) and based on the simple model described in the Letter. The scale of the d axis is equivalent to the capacity axis in (a) assuming a uniform film growth of average thickness d. The currents and T for the various theoretical discharge curves are the same as the corresponding colors/styles in (a).

dependence of Qmax at the lowest discharge currents (3 and 5 μA), with much weaker T dependence at higher j that seems largely associated with the changes in the discharge kinetic overpotentials observed previously.13 Figure S5a (SI) shows related experiments at T = 30 and 50 °C with qualitatively similar behavior. Li2O2 is a wide-band-gap insulator and has only a modest density of mobile charged defects (to be published and ref 7) (otherwise it would have a higher conductivity at larger d), with a Debye length λD ≫ d. For example, we find λD ≈ 85 nm at j = 1 μA/cm2, and this increases substantially at higher j. Figure 3a shows our estimate of the band alignment for all cathode components at the Li−O2 equilibrium potential U0 after some discharge has occurred, that is, in the electrolyte, in the Li2O2 deposit, and at the C cathode. At equilibrium, the Fermi levels (EF or εF) of all cathode components are common, that is, the Li−O2 redox potential, which is the Fermi level in the electrolyte, εF in Li2O2, and of the approximate metallic C cathode. This defines the alignment of the Li2O2 bands (VBM and CBM) relative to the Li−O2 redox potential. Note that εF at equilibrium, εF(U0), in Li2O2 is only ∼0.35 eV above the VBM. We will argue elsewhere (to be published) that εF in Li2O2 is pinned near the VBM by the unoccupied LiO2 states at the electrolyte−Li2O2 interface, and this is a necessary requirement in order to fulfill the Li−O2 electrochemistry. This alignment of the Li2O2 bands relative to εF is also similar to that obtained in the Au|Li2O2|Au MIM structure, both 3496

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Figure 3. Schematic of the Li2O2 band alignment imposed by the electrochemistry in terms of the electron energy (upward) and hole energy (downward). Li−O2 redox is the Fermi level in the electrolyte, that is, U0 for 2Li + O2 = Li2O2, and EF is the common Fermi level in Li2O2 and the cathode. VB is the valence band maximum in Li2O2, and h+ denotes the tunneling holes through the barrier bounded by EF and VB. (a) Alignment at the equilibrium potential U0. (b) Alignment during discharge at the potential U = U0 − ηdis. (c) Alignment during charge at the potential U = U0 + ηchg. (d) Li2O2 band alignment for thick films near sudden death in the discharge. In this case, a potential Ubias is applied across the Li2O2 film to help tunneling by lowering the average barrier. Because of this potential drop, the Li2O2 bands and EF are not uniform throughout the film thickness. Here, we approximate this as a linear potential drop appropriate for an insulator.

electronic energy relative to εF because a free hole must first be created before it can self-trap as a polaron. The 3 × 1022 is simply the number of possible polaron sites/cm3 . In anticipation of applying this model to the experiments, we note that jt dies exponentially with d but that it supports very high currents at small d. On the other hand, jm will have a longer range because it dies as 1/d, but it may be very limited because n0 and D depend exponentially on −[Ef(h+p ) + Vdiff]/ kBT. In addition, while jt is independent of T, jm exhibits the strong exponential temperature dependence above. In terms of the experimental observable U as a function of Qdis, we anticipate a nearly T-independent exponential sudden death in U for tunneling and an exponentially strong T-dependent linear decrease in U for Ohmic polaron charge transport. Figures 2a and S5a (SI) then qualitatively suggest that hole polaron charge transport is important only at very low j and that tunneling dominates at all higher discharge currents. The fundamental charge-transport condition for galvanostatic discharge at current j is simply that jct ≥ j; jct depends on d, Ubias, and T as well as implicitly on j through ηdis(j). For discharge, we find Ubias as the minimum bias potential required to satisfy the condition jct ≥ j for the given Li2O2 film thickness d. For these calculations, εF(U0) = 0.35 eV is chosen to fit the experiments, and a tunneling hole mass mh = me is assumed, where me is the mass of a free electron. The value of εF(U0) that best fits the experiments depends somewhat on the assumptions for the parameters mh and Vdiff. However, the

thickness from 0 to d. The charge transport is composed in principle of three terms, tunneling jt, migration jm, and diffusion jdiff; jdiff = eD(dn/dx) and jm = eμn(x)(dUbias/dx), with n(x) as the concentration of mobile charged species (hole polarons) as a function of position relative to the Li2O2−electrolyte interface, D its diffusion coefficient, and the mobility μ = eD/ kBT. In principle, the migration and diffusive terms are coupled via the Nernst−Planck and Poisson equations. However, because jm/jdiff ≈ eUbias/kBT for the maximum contribution of each, migration dominates when Ubias > 25 mV, that is, over most of the discharge. Therefore, we neglect the diffusive term and consider n(x) as a constant n0. With a linear potential drop of Ubias through the film thickness, jm is simply Ohmic. Therefore, neglecting interactions between the terms, the total charge transport is jct ≈ jt + jm. Because simple trapezoidal tunneling barriers are assumed in Figure 3, jt can be estimated using a simple WKB approximation for tunneling well-known from MIM models of charge transport,16 jm = (e2D/kBT)n0 (Ubias/d), with D ≈ 2va2e(−Vdiff/kBT). Here, v ≈ 3 × 1013, a is a jump length of ∼2.7 Å, and Vdiff ≈ 0.38 eV is the diffusion barrier for hole polarons. Vdiff is simply chosen to give a contribution from the Ohmic term at very low j and higher T, as observed in the experiments, but is fully consistent with estimates from density functional theory.7 Here, n0 = 3 × 1022e[−Ef(h+p )/kBT], with Ef(h+p ) = εf (U0) + eηdis for discharge and Ef(h+p ) = εf (U0) − eηchg for charge. Note that Ef(h+p ) is defined by the formation energy of the free hole rather than its 3497

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Li2O2 to obtain simultaneously a high-capacity and high-power Li−O2 battery at room temperature.

experiments are qualitatively inconsistent with the model for any reasonable mh and Vdiff for the value of εF(U0) ≈ 2 eV suggested by Radin and Siegel.7 Figure 1b shows the discharge potential U = U0 − ηdis − Ubias − jR by application of this simple model to the discharge conditions appropriate to Figure 1a, with ηdis and jR taken from the experiments. The purely theoretical ηdis(j) from the DFT calculations13 slightly overestimates the experimental ηdis, and this lessens quantitative agreement of the model with the experiments, although qualitative agreement is still good (see Figure S10, SI). The d scale of the calculations is the average d assuming a Gaussian roughness in the thickness across the film of 1 nm standard deviation. This d is related to the experimental Qdis scale by assuming growth as an average thickening of the Li2O2 on the GC electrode with the roughness as described, both of which are observed in AFM experiments.4 Tunneling dominates throughout this range of discharges, and there is excellent qualitative agreement of the model with the experiment. Both the increase in the tunneling barrier with ηdis and the increase in the jR drop contribute about equally to the decrease in Qmax with j. In a similar manner, during charging, εF = εF(U0) − ηchg, and this lowers the tunneling barrier, increases n0, and decreases R with increasing j or ηchg. Thus, the simple model under charge conditions predicts absolutely no Ubias under any of the charge conditions of Figures S3 and S4, as shown in Figure S8 (SI). Figure 2b shows the application of the model to the experimental conditions of Figure 2a. The qualitative agreement is excellent. The model correctly shows the significant capacity at large d and low T for the lowest j (3 and 5 μA) that is absent at higher currents. Figure S9a (SI) shows the model with and without the polaron charge transport and demonstrates that the extended capacity at low j and high T is due to the polaron contribution to charge transport. Figure S5 (SI) shows the T dependence at 30 and 50 °C and its comparison to the model, again in excellent qualitative agreement with experiment. Figure S9b (SI) also separates the additional contribution of the polaron charge transport to the capacity. This model only considers charge transport through crystalline Li2O2, and we have shown that discharge produces some Li2CO3, LiHCO2, and other decomposition products as well in the cathode deposit.15,17 In addition to the incoherent scattering discussed in the SI that causes the jR drop, these impurities could induce other charge-transport limitations. For example, both tunneling15 and polaron charge transport6 through Li2CO3 are smaller than those through Li2O2. However, because ∼15−20 nm crystallinity is observed in Li−O2 batteries, these impurity effects on charge transport should be modest. In summary, we presented both experimental and theoretical evidence that hole tunneling generally dominates charge transport through Li2O2 in Li−O2 discharge at practical battery current densities and that this defines the j-dependent capacity of the Li−O2 battery at room temperature. At low j and high T, charge-transport contributions from an Ohmic polaron path significantly increase the discharge capacity. Therefore, operating a Li−O2 battery at higher temperatures could enhance the polaron charge transport and hence improve the specific energy-specific power trade-off. Unfortunately, given these mechanisms of charge transport in Li2O2, there seems little chance to obtain simultaneously higher current (power) and capacity from them at room temperature. Therefore, alternate conduction paths need to be introduced into the

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ASSOCIATED CONTENT

S Supporting Information *

Ten figures referred to in the text as Figure S1−10 are included. These provide further support to the arguments presented in the text, including the dependence of the capacity at sudden death as a function of current density, the galvanostatic discharge at different currents, the output potential during galvanostatic charging, the galvanostatic discharge followed by galvanostatic charge, experimental and theoretical galvanostatic discharge curves, plots of the galvanostatic discharge versus the current, the resistance of the Li2O2 film as a function of the discharge current density, the discharge and charge predicted by the charge transport model, comparison of the model with and without the polaron contribution, and theoretical galvanostatic discharge curves using the theoretical overpotentials. In addition, a discussion of the experimental details, the Simmons tunneling formula, and the origin of the jR drop prior to sudden death are included along with figures. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge partial support of this work from the U.S. Department of Energy, Chemical Sciences, Geosciences and Biosciences Division under Contract Number DE-AC0276SF00515 and the ReLiable project (# 11-116792) funded by The Danish Council for Strategic Research. We also wish to thank J. Hummelshøj, Don Siegel, and B. D. McCloskey for useful discussions.

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REFERENCES

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