Calculation of the SEI thickness

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compounds because it requires more lithium and the Li3PO4 formation sets in earlier. Only when after multiple lithium deposition steps enough lithium is present, Li3PO4 can be converted into the binary compounds. In a real battery system, the amount of Li3PO4 may be smaller than found during the XPS experiment. As lithium always needs to diffuse from the lithium metal anode into the electrolyte and is steadily hindered by the limited transport properties of the continuously growing SEI, it can still be expected to find a lithium–poor Li3PO4 layer in batteries with „LiPON“ electrolyte.

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surface. Therefore, any effects of surface roughness and compositional inhomogeneities are neglected. Moreover, for each deposition step the growing SEI overlayer is considered to be perfectly flat and as a homogenous mixture of its components. Assuming a thin overlayer with thickness d on a solid electrolyte substrate (SE), the intensities of the respective photoelectron signals of the elemental transition from a given subshell i from substrate (𝐼_{i, SE}) and transition j from overlayer (𝐼_j,SEI) can then be calculated as

I_{i, SE} = I_i,SE^∞ ∙ exp(_L^{– d}

i, SEI) (29)

I_j,SEI = I_j,SEI^∞ ∙ [1– exp( ^{– d}

L_j,SEI)] (30)

with L_{i,j, SEI} =EAL_{i, j,SEI}(KE)∙ cosϑ

EAL_{i, j,SEI}(KE) = energy–dependent effective attenuation length of photoelectrons from transition i or j in the SEI,

ϑ = photoelectron emission angle with respect to the surface normal (here 𝜗 = 45°).

I_{i, SE}^∞ and I_{j, SEI}^∞ denote signal intensities for the respective materials assuming infinite thickness and can be calculated as

I_{i, SE/SEI}^∞ = σ_i ∙ N_i,SE/SEI ∙ EAL_{i, SE/SEI}(KE) ∙ cosϑ∙ J_hυ ∙ T(KE) (31) The factors contributing to the signal intensities can be grouped to those affected by instrumental properties (J_hυ: X–ray flux density, T(KE): energy–dependent transmission function of the analyser), to those being governed by the transition itself (σ_i: elemental photoionization cross–section for transition i) and to sample dependent factors (N_i,SE/SEI: number of atoms of element i, EAL_{i, SE/SEI}(KE)∙ cosϑ: effective attenuation length for electrons of elemental transition i in the respective material). The number of atoms Ni can be calculated from the molar volume Vmol and the atomic concentration Xi.

In the following the signal intensities of the P 2p signal of different P–species from SE and SEI are used to calculate the SEI thickness as P solely originates from the solid electrolyte film and is not present in the chamber atmosphere. In this case i = j = P 2p and the energy dependence of the EALs can be neglected (L_{i, SEI}=L_{j, SEI}=L _{P 2p,SEI})

To extract d from equation 30, the ratio of both intensities can be used.

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I_SEI I_SE = ^ISEI∞

I_SE^∞ ∙

[1 — exp( ^{— d} LP 2p, SEI)]

exp( ^{— d} LP 2p,SEI)

(32)

After rearranging, the thickness d can be calculated according to [164] and [165]:

d = L_{P 2p,SEI} ∙ ln(^ISE∞

I_SEI^∞ ∙ ^ISEI

I_SE+ 1) (33)

with ^ISEI∞

I_SE^∞

=

N_{P 2p, SE}

∙

L_{P 2p, SE}

=

V_{mol, SEI}

∙

X_{P, SE}

∙

L_{P 2p, SE}

d = L_{P 2p,SEI} ∙ ln(^{Vmol, SEI}

V_{mol, SE}∙^{XP, SE}

X_P,SEI∙^{LP 2p, SE}

L_{P 2p, SEI}∙^ISEI

I_SE + 1) (34) The values V_{mol, SE}, X_{i, SE}, and L_{i, SE} depend on properties of the SE and are assumed to be constant for each SE sample in the course of the experiment. However, V_{mol, SEI}, X_{i, SEI}, and L_{i, SEI} are functions of the SEI composition and change in the course of the experiment. This equation is also valid for intermediate layers as in the case of an SEI between solid electrolyte and electrode. Equation 34 now allows for the calculation of the SEI thickness after each deposition step.

According to the results of the chemical analysis the SEI has to be described as a complex multi–component composite with increasing Li concentration toward the surface and with the lowest Li content at the SEI|SE interface. Moreover, the average molar volume of the SEI will obviously differ from that of the SE. Depending on the chemical nature of the SEI species, the interphase formation leads to a contraction or expansion of the material. Finally, for each subsequent deposition step, electrons from SE and SEI are attenuated differently.

The available data do not allow to determine a precise stoichiometry of the formed SEI as species close to the surface will always be detected with a higher intensity than species below.

Moreover, additional surface species lead to an overestimation of the Li2O content. Also the energy dependence of the EAL can lead to different relative intensities of the various reaction products and to a misinterpretation of the data. To address these complications, some assumptions can be made as SEI thickness and EALs for the relevant signals are both in the same range (2 – 3.5 nm): Firstly, an average SEI signal intensity is calculated as sum of the photoemission intensities from the respective species (Li3PO4 + LixPy+ Li3P) resulting in a

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single value for the SEI thickness. Moreover, this average SEI composition can be used for calculating V_{mol, SEI}, X_{i, SEI}, and L_{i, SEI}.

Figure 29 shows the evaluation of the SEI thickness in the course of Li deposition for all samples. Three main observations can be made at this point:

- The SEI thickness is about 2 – 3.5 nm for all samples (similar to Li7P3S11 [78]).

- The SEI thickness reaches a constant value (in the timeframe of the measurement, less than one day).

- LiPON–high forms a thicker SEI than the other two samples.

Figure 29: SEI growth in dependence of the deposition time for the different “LiPO(N)”

films.

It must be pointed out that dSEI as determined by in situ XPS describes the lower limit of the thickness and that the real SEI might be thicker. According to Wenzel et al. the in situ XPS experiment can only be used when the kinetics of the reaction fulfill certain requirements.

The kinetics of the experiment must be either very fast, so that the reaction is already completed when the measurement step after lithium deposition starts or the kinetics must be very slow so that no change of the sample occurs until the measurement is finished [48].

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However, as the experiment consisted of subsequent lithium deposition and analyzing steps, the reaction between the electrolyte and lithium does not necessarily have to be finished during the analyzing step and might still proceed during the measurement if enough lithium is present. To clarify whether the decomposition is an ongoing process, one would have to perform several measurements with different analyzing times between each lithium deposition step and see whether the intensity ratio changes over time.