Estimation of the theoretical SEI thickness
4.1.4 Electrochemical properties of the „LiPON“ SEI
From the latest findings of SEI formation on various different electrolytes, the question arises, why there has been little evidence of the SEI formation in the cycling data of batteries.
Simple mathematics show that finding electrochemical evidence of the interphase formation is rather challenging as its properties make it difficult to distinguish between the interphase and the electrolyte. In most cases the electrolyte has a thickness of more than 1 µm, whereas the SEI is suggested to have a thickness of roughly 10 nm and, according to the calculations in this work, is even thinner than that. The interfacial contribution to impedance spectra is rather small and highly depending on the properties of the interphase itself as will be shown below.
The peak frequency 𝜔P of a RC semicircle in the Nyquist plot is the reciprocal value of the time constant τ and depends on the ohmic resistance R and the capacitance C of the sample.
ωP = RC1 = 1τ (43)
108
If one assumes geometric relations for both R and C (𝑅 = 1σ ∙ l
A and equation 22 for C), the peak frequency is independent from the sample geometry and only depends on the conductivity and the permittivity of the film. There are no precise values of the permittivity of most battery materials given in literature but if 𝜀r is assumed to be in the range of 10 – 100 for most battery materials, the peak frequency for the interface between lithium and
„LiPON“ can be estimated.
If Li3PO4 reacts with lithium, the major component of the SEI will be Li2O with around 62 % of the SEI volume. If Li2O is the major contributor to the SEI conductivity, the conductivity of the SEI layer will be in the range of 10–8 – 10–10 S/cm resulting in a peak frequency of
ωP = 10–9 S/cm ε0 ∙ 1
εr=113 Hz
εr (44)
An interphase with Li2O will be influencing the impedance of the system in the range of a few dozen Hz, depending on the value of εr. If the SEI is thick enough, it should be visible as a contribution in the impedance spectrum; if not, it will most likely be hidden in the electrolyte contribution.
However, if the nitrogen content in the „LiPON“ film is high enough and the combined volume fractions of Li3N and Li3P are high enough to form a percolating network, the conductivity of the interface will be in the range of 10–3 S/cm resulting in a peak frequency of 107 – 109 Hz which cannot be seen with most impedance devices. If the thickness of the SEI is assumed to be in the range of 1 nm – 3 nm as calculated from the XPS measurements, for the present sample geometry, the resulting resistance would be 3.3 kΩ – 10 kΩ for Li2O and 5 mΩ – 15 mΩ for Li3N/Li3P. That means the interphase will only be visible if very thin films are prepared as its contribution to the overall resistance will only be around 1 %. Very thin films, which fully cover the substrate, are very hard to prepare.
If the interphase contains a lot of nitrogen, the fraction of Li3N formed in contact with lithium will be much higher. The interphase will have a higher ionic conductivity than the electrolyte and its contribution will not be visible in the common frequency ranges. Even if
109
the conductivity is lower, the smaller thickness may result in a transport process, which cannot be seen in the spectrum as it might overlap with the ionic transport across the electrolyte. These values explain why „LiPON“ has been considered to be stable in contact with lithium metal. The reaction layer was usually so thin that the most common detection methods were not able to detect the interphase.
However, there are a few evidences of the „LiPON“ SEI reported in literature. Larfaillou et al. examined thin–film batteries containing „LiPON“ solid electrolyte [171]. They compared commercial batteries consisting of LiCoO2, „LiPON“ and a lithium metal anode with batteries of the same scheme prepared in the lab. Their impedance analysis showed that the interface between lithium and „LiPON“ led to a contribution to the impedance spectrum, which was much bigger when aged cells, which had been stored in the fully charged state at 60 °C for 60 h were used. They found that this contribution was formed during a first charging of the battery suggesting that the transport of lithium across the electrolyte led to a modification of the interface. They also suggested that this modification was partly reversible as lithium deposition during a subsequent battery cycle led to a decrease of this contribution in the impedance spectrum. However, they did not take into account that these batteries were assembled at an indefinite point before the testing. In accordance with Schwöbel et al.
the interface between „LiPON“ and lithium was already passivated. Probably the cycling of the battery led to breaking of the SEI or lithium plating underneath the SEI and ongoing SEI growth.
Schichtel et al. prepared all–solid–state thin–film batteries based on lithium titanate Li4Ti5O12 (LTO) and „LiPON“ as an electrolyte. They performed various experiments to determine the different elements present in the impedance spectra of this system. One of their findings was a contribution in the high–frequency range caused by the transport of the ions across an interface between the lithium electrode and the „LiPON“ solid electrolyte.
They performed impedance measurements at different states of charge and after different
“cycling properties” and found out that this contribution at high frequencies was independent from the state of charge and the applied C–rate, suggesting that the interphase is stable [172].
An ideal SEI that only consists of Li3P and Li3N should not be visible in the impedance spectrum as its contribution is too small to be resolved. However, the effectiveness of the
110
interface passivation may be visible by the absence of a contribution of the reaction layer between the electrolyte and lithium to the impedance spectrum. If P3N5 can be successfully applied as interlayer, its effect may have to be derived from cycling data rather than impedance measurements.
111