Atomic-level imaging observation along (100) plane
The pivotal criterion to get accurate and sufficient atomic-level structural information on Cu(I) occupations is the exposed plane aligning flawlessly with a-axis, i.e. (100) cleavage plane, as proposed in Fig. 1d. For this, the as-grown CIPS single crystal is precisely cut into nanosheet along a-axis by focused-ion-beam (FIB) technology (Figure S1). The low-dose integrated differential phase-contrast coupled scanning transmission electron microscopy (iDPC-STEM) is performed to achieve atomic-level imaging. Figure 2a shows a dark field (DF) mode image where all the Cu(I)/In/P/S atoms and their positions are clearly seen. Strikingly, the atoms between the InS6 octahedral skeletons are not solitary, but instead there occur obvious multiple lattice sites for Cu(I) occupations, e.g. Cu(I) ions occupy both position I and III (Fig. 2b-i); Cu(I) ions occupy simultaneously position I, II and III (Fig. 2b-ii). For convenience, we here refer to the local crystal configuration situation of Region I and Region II by Cu2InP2S6 and Cu3InP2S6, respectively. It is worth noting that the local structure CuxInP2S6 (x = 2, 3) only occurs in a tiny region but does not change the overall chemical formula of the CuInP2S6 single-crystal. The structural configurations with forming local CuxInP2S6 (x = 2, 3) can be universally observed from different areas or regions in CIPS (Figure S2), which is definitely attributed to the Cu(I) migration and multiple occupations under the electric field.
To gain the insights on the microscopical results, standard atomic structure and lattice occupations are compared. The theoretical angular/distance relationship between adjacent In ions, as the (001) plane demonstrated in Fig. 2c, is ∠ABC = 59.969 º (~ 60 º) and BC = 0.6099 nm, respectively. Experimentally, the projected distance between the two nearest In ions in a layer from the (100) plane is 0.5500 nm (highlighted by red line in Fig. 2a), which yields an actual distance of 0.55/cos(59.969/2) = 0.6350 nm according to the geometric relationship. This value is 4.12% larger than the theoretical In-In distance (i.e. BC = 0.6099 nm in Fig. 2c), which suggests the existence of the multiple Cu(I) occupations between the InS6 octahedral skeletons that thus leads to lattice expansion in the < 010 > direction. The occurrence of the atomic multi-occupation and lattice constant increase is to release the local stress and maintain the structural stability when the electron-beam irradiation continues.
Atomic distance relationships for P-P in one layer and In-In between adjacent two layers are further analyzed. As shown in Fig. 2d, the theoretical P-P distance is 0.2218 nm, almost analogous to the experimental value of 0.2256 nm (highlighted by blue line in Fig. 2a). The theoretical In-In distance between the nearest layers in Fig. 2e is 0.6812 nm, while the experimentally measured distance is 0.6812 nm (highlighted by yellow line in Fig. 2a). It is worth noting that the lattice constant c (= 1.3524 nm) experimentally determined also matches well the theoretical one (1.3623 nm). These percentage differences, i.e. 1.7% in P-P, 0.0058% in In-In in layers, and − 0.73% in lattice constant c, respectively, are small enough to be considered no variations in the c-axis direction. To conclude, the Cu(I) atomic multi-occupations do not cause the out-of-ab-plane structural fluctuations but apparent in-ab-plane structural expansion. Then, what is the structural reason?
This can be attributed to the sliding mis-arrangements for the CIPS layers. As indicated in Fig. 2f, the theoretical In ions between the CIPS layers should be arranged in a straight line from the perspective of the (100) plane, but the microscopical observation clearly exhibits that the In ions in CIPS layers are not situated in a straight line along the c-axis direction. The array paths of In ions are shown in Fig. 2b-iii dotted orange lines, which is a broken line, containing lines segment parallel to the c-axis. Accordingly, the sliding boundary position can be deduced, which is rightly the interface of the two adjacent CIPS layers, as indicated by the green line in Fig. 2a. This suggests that the smallest unit in which the glide occurs is a single cell, without compromising its double-layer structure. The sliding distance between the layers is carefully confirmed, and its magnitude is 1/6 lattice constant b. This further confirms that in order to keep the stability of the crystal structure induced by the Cu(I) multiple occupations, the interlayer sliding releases the lattice stress but does not cause changes in lattice constant c.
In addition to the atom positions or occupations, more atomic-level information e.g. atomic distribution/intensity/shift etc. are further extracted. To this, precise analysis and transformation are performed on the iDPC-STEM images (Figs. 3a, S3) by optimized Multiple-Ellipse Fitting method with the detailed calculations are seen in Supporting information section (Figures S3-7).22 The noise reduction image in Figure S3a is obtained by BM3D method and the position of the atoms are determined by threshold method.23 Fig. 3a and Fig. 3b show respectively the pseudo-color display raw image and fitting image that exhibit quite high matchiness, thus giving a very small difference in intensity, morphology and strength errors (Figs. 3c, S3) with all the fitting parameters can be obtained in Table S1). Accordingly, the 2D intensity distributions of Cu, In, P, and S based on the elemental mapping and statistical analysis (corresponding to the highlighted area in Fig. 3d, Figure S8) are deduced, as shown in Fig. 3e, and meanwhile, the distribution of the atom shift is also obtained (Fig. 3f).
With regard to the Cu(I) occupation, Cu(I) ions are present between the InS6 octahedral skeletons in the form of CuxInP2S6 (x = 2–3) local structure. As a matter of fact, the STEM image contrast predominantly depends on the atomic number (Z) and the atom count.24,25 The intensities of Cu(I) are primarily distributed in 5–7×106 and 9–16×106 for positions II and I & III, respectively in the intensity distribution histogram of Fig. 3e. These results show that Cu(I) in CIPS have their own filling rules: Under electron irradiation, Cu(I) will preferentially occupy positions I and III to form Cu2InP2S6 local structure. When positions 1 and 3 are filled, Cu(I) then will occupy position II to further form Cu3InP2S6 local structure. These results are very significant for the understanding of the kinetic process of copper ion occupation in CIPS.
The Cu(I) preferential occupation might induce the atom/ion shift/displacement in CIPS crystal structure, shown in Fig. 3f, which favors the understanding of lattice distortion and polarization. There occur two types of the atom shift (the shift vectors are highlighted by yellow arrows). One shifts along the < 010 > directions ([010] or [0–10]) distinguished from the middle position, which contributes to the lattice distortion by atomic multiple occupancies between the InS6 octahedral skeletons. The other shifts along < 001 > direction, which is due to the intrinsic out-of-plane (OOP) polarization in the lattice. Because the atomic shift vector in < 001 > direction is overall upward, it does not affect the lattice constant of the c-axis. The fitting result corresponding to the iDPC-STEM image indicates the dependability of the structural evolution process of Cu(I) multiple occupancies between the InS6 octahedral skeletons of CIPS under the electron-beam irradiation along < 100 > direction.
Dynamic and stability of Cu x InP 2 S 6 (x = 2–3) local structure
The above precise iDPC-STEM imaging and analysis prove the Cu(I) multiple occupations and the structural changes of CIPS under electron irradiation, but the dynamic process and stability for the local structural configurations on CuxInP2S6 (x = 2–3) remain to be investigated clearly. Herein, a facile strategy is devised to observe the CuxInP2S6 (x = 2–3) configurations. Specifically, a large current (50 pA) is used to irradiate partial region (red box in Fig. 4a) for 30 seconds, and EDS mapping is then carried out over a larger area with a small current (33 pA). The CuxInP2S6 (x = 2–3) configurations can be judged by the fluctuations in elemental contents in the red box. The resulting EDS mapping (Fig. 4b) shows that there is no clear distinction of element contrast. Another similar experiment by line scanning (Fig. 4c, d) for element mapping also gives the same conclusion, i.e. the electron-irradiated area exhibits the uniform elemental distribution. As a matter of fact, the Cu(I) contents (26.01% for Fig. 4a and 29.52% for Fig. 4c) are much higher than the theoretical value from the standard structure (Table S2 and Table S3), which means the occurrence of the Cu(I) multi-occupancy with forming CuxInP2S6 (x = 2–3). However, the CuxInP2S6 (x = 2–3) is quite unstable because of undergoing the extremely severe lattice distortion, unless continuous injection energy (electron-beam irradiation) maintains CuxInP2S6 (x = 2–3) configurations. Otherwise, when the energy (electron-beam irradiation) is removed, the Cu(1) would move back to its original position to retain the standard CuInP2S6 structure (Figure S9). This dynamic process that clearly uncovers locally structural configuration fluctuations i.e. is obviously a result of the Cu(I) migration under the electric field behavior.
The Cu(I) migration dynamics is further investigated by monitoring the elemental fluctuations during the continuous electron-beam irradiations. To figure out the energy dependence or threshold for the Cu(I) migration, the varied current dose rates are performed. Here Fig. 4e-h only show the cases of two typical current rates, i.e. 30 pA and 72 pA. Note that too small dose (e.g. 2 pA) can not drive the Cu(I) migration (Figure S9) while too large dose makes Cu(I) migration too quick for inaccurate detection. It can be seen that the detected elemental amounts exhibit different changes with increasing the irradiation time. Clearly from both the EDS imaging (Fig. 4e) and quantitive analysis (Fig. 4g), the Cu(I) amount gradually increases with the irradiation time at a low current (30 pA), from initial 25.9% to final 27.09% (irradiation for 30 mins) and keeping unchanged upon longer irradiation in atomic proportion. While, high current irradiation e.g. 72 pA (Figs. 4f and 4h), might be due to the quite fast Cu(I) migration, does not bring about any apparent fluctuations in elemental distributions that nearly undergo unchanged at about 28%.
The energy injected for Cu(I) migration induced crystal structure distortion is further quantified, which is referred to the current dose (D) that can be obtained by Eq. (1) is 50 e− Å−2 and 120 e− Å−2 for 30 pA (Fig. 4e) and 72 pA (Fig. 4f), respectively. Although the energy dose increases doubly, the Cu(I) content is not increased all the way, but finally fixed at about 28%. This is, again, indicative of the Cu(I) migration but the available positions in the lattice sites (i.e. positions I, II, III, IV illustrated in Fig. 1a) for Cu(I) occupation are in a certain level. Even if forming the Cu3InP2S6 structural configuration, Cu(I) has an atomic percentage content of 25%, still less than the value obtained from experimental determinations. One possibility is Cu(I) may occupy the interlayer position IV (Fig. 1a) that has been predicted by the theoretical calculation, but here from the atomic-level microscopy experiment, no direct evidence that Cu(I) could occupy the interlayer position.