Tellurization of Pd(111): absence of PdTe$_2$ but formation of a TePd$_2$ surface alloy

In a recent publication [2D Materials, 8, 045033 (2021), arXiv:2103.11403], it was reported that the growth of a monolayer PdTe$_2$ in ultra-high vacuum could be achieved by deposition of tellurium on a palladium (111) crystal surface and subsequent thermal annealing. By means of low-energy electron diffraction intensity (LEED-IV) structural analysis, we show that the obtained $\left(\sqrt{3}\times \sqrt{3} \right)\textrm{R30}^\circ$ superstructure is in fact a TePd$_2$ surface alloy. Attempts to produce a PdTe$_2$ layer in ultra-high vacuum by increasing the Te content on the surface were not successful.

Our experimental and theoretical methods, LEED-IV, scanning tunneling microscopy (STM), and density functional theory (DFT), are described in great detail in our previous publications [4,6].By comparison with these systems, we were also able to precisely determine the amount of Te evaporated onto the clean Pd(111) crystal.All experiments were performed under UHV conditions (p < 2 • 10 −10 mbar).The Pd(111) substrate was cleaned by standard sputtering and annealing cycles.For structural analysis of the Te-induced Pd(111) √ 3 × √ 3 R30 • superstructure 0.33 monolayer of Te was evaporated onto the Pd(111) surface held at 90 K.We define one monolayer (ML) to correspond to an adsorbate surface density equal to the atomic density of the underlying substrate (15.3 nm −2 ).To induce the surface reaction and the formation of the wellordered √ 3 × √ 3 R30 • superstructure an annealing temperature of at least 720 K was necessary.The structural order could be improved slightly by annealing to temperatures up to 1070 K. Beyond that temperature, decomposition sets in and the √ 3 × √ 3 R30 • reflexes vanish.We note that Liu et al. [7] also report on the formation of the √ 3 × √ 3 R30 • superstructure after annealing to 470 • C (743 K).Liu et al. characterized the Te amount deposited from XPS electron attenuation lengths and stated a Te thickness of approximately 4 Å which may correspond to a full monolayer of Te.From our experiments (see below) we find that any Te in excess of 0.33 ML desorbs from the surface starting at 540 K.With these observations, we believe to have prepared the same system as [7].
In the work presented here, we used the newly developed ViPErLEED package [9] which provides a sophisticated tool for LEED-IV data acquisition and manages a modified and parallelized TensErLEED code [10] for full-dynamical calculation of intensity spectra and parameter fitting.Experimental LEED-IV data were recorded at normal incidence for energies from 50 eV up to 600 eV in steps of 0.5 eV and stored for off-line evaluation.The temperature of the substrate during LEED-IV data taking was 110 K, consequently we used as lattice parameter of the Pd(111)-(1x1) the value of 2.755 Å determined at that temperature in [11].We tested the suggested PdTe 2 on Pd(111) by Liu et al. [7], the simple Pd(111)- • -TePd 2 substitutional surface alloy against our experimental data.
The analysis was backed by DFT structural energy relaxations using the VASP package [12] and the PBE-PAW general gradient approximation [13].For that, √ 3 × √ 3 -Pd(111) slabs were set up consisting of eight layers of which the three lowest were kept fixed at bulk positions.Repeated slabs are separated by at least 1.5 nm of vacuum.The STM images were simulated based on the Tersoff-Hamann approximation [14].

III. RESULTS
Not surprisingly, our LEED data looks the same as that presented by Liu et al. [7] (Fig. 1(a)).For the STM image (Fig. 1(b)) we chose data with a slightly different appearance than that in [7] but depending on tip state and tunneling bias also a regular hexagonal pattern of maxima was observed.We aim to convey to the readers that relying solely on STM and DFT is insufficient sometimes for determining a specific surface structure.While fine details in the DFT may lead to the identification of the correct model (here the substitution of Te in the surface), the dependence of such images on tip state on the experimental side and on parameters of the DFT Tersoff-Hamann simulations can make agreement or disagreement fortuitous.
In By using simple LEED imaging the unit cell is determined only.In many cases, this is a redundant information if STM is also available.What would be more important is to provide a selection of images at different electron energies that track characteristic intensity variations.By this it can be verified that upon repetition of an experiment, the same surface phase and not only a phase with the same surface unit cell was prepared.An example is shown in Figs.2(a) and (b).The system as we prepared it, shows distinctively different intensities of the (1|0) and (0|1) spots at 151 eV and rather similar intensities at 162 eV.Likewise the ( 2 /3| 2 /3) and ( 1 /3| 4 /3) spots are brighter at 151 eV than the (0|1) spot and dimmer at 162 eV.
The essence of LEED-IV structural analysis is now to record the intensity of (ideally all) accessible spots, and compare it to the theoretically expected intensity.The comparison is governed by the Pendry R-factor [15] which is R = 0 for perfect agreement and R = 1 completely unrelated spectra.A level R < 0.2 is commonly considered to indicate the correct structural model.
In a first step it was tried to find agreement between experimental and calculated spectra by varying atomic z-coordinates in rather rough steps of ∆z = 3 pm and ∆xy = 5 pm.For the adsorbate model we find R = 0.57, for the honeycomb model R = 0.29, for the substitutional surface alloy R = 0.14, and R = 0.55 for the compressed PdTe 2 layer.Models in hcp stacking were worse than those in fcc stacking.Due to the much better R-factors, only the substitutional surface alloy and the second-best honeycomb model in fcc stacking were considered for fine fits also including non-structural parameters (particularly vibrational amplitudes).Note that the two models differ by one additional Pd atom in the surface layer only.The fine fit produced an excellent R-factor of R = 0.06 for the substitutional surface alloy model Fig. 1(e) as final result of the LEED-IV analysis.At that R-factor level, there is no doubt that the correct model has been found.In contrast, variation of parameters of the honeycomb model did not lead to a better agreement with experiment than R = 0.25.In Fig. 2(c) and (d) we show two exemplary spectra showing the significance by which the two models can be discriminated against the experimental data.The agreement between experiment and calculated spectra is considerably worse for the honeycomb model.Note that the Pendry R-factor is particularly sensitive to the energetic positions of minima and maxima due to its dependence on the logarithmic derivative of spectra [15].
For the analysis we used an accumulated data base of 3.7 keV which allowed us to fit the 17 structural and non-structural parameters with a redundancy of ρ = 10.8 (for the relevance of this see [6]).The structural parameters and the comparison to those obtained from the DFT structural analysis are shown in Fig. 3.By virtue of the low R-factor, the error margins of the atomic z-positions in the first 4 layers are less than ±1 pm, while those for the x,y positions are ≈ ±2 pm (see supplement for details [16]).When the DFT results are scaled from the theoretical (2.786 Å) to the experimental lattice parameter, the atomic positions agree perfectly within these error margins.The LEED results indicate maximal lateral shifts of 1.5 pm from a perfect bulk crystal structure where allowed by symmetry.
We notice that among the three models with 0.33 ML Te the DFT total energy calculations also found the substitutional model to be energetically favorable by 190 -320 meV with respect to the adsorbate or honeycomb structure in fcc (more favorable) or hcp stacking.All detailed comparisons between experimental and calculated spectra, a list of parameter definitions, values, and their error ranges of the model parameters are provided in the

Fig. 1 (
c)-(f) we show the structural models that we tested in our LEED-IV analysis and the corresponding DFT image simulations.The simple Te-adsorbate model (c), the TePd-honeycomb (d), and the PdTe 2 layer (f) were also tested in hcp stacking sequence.All models led to converged DFT structures and the DFT simulated images could serve to explain the experimentally observed contrast, although the interpretation of which atoms appear as bright features would be different depending on model.

FIG. 2 .
FIG. 2. (a) (b) experimental LEED at two further energiesdemonstrating the idea of using LEED pattern of a set of particular energies as "finger prints" of a particular surface structure (see text).(c) Comparison of the experimental LEED-IV spectra (red) and calculated spectra using for the substitutional model (Fig.1 (e)) after final fine fitting.(d) The same level of fine fitting procedures applied to the honeycomb model introduced in Fig.1(d).Note that the two models differ by one additional atom only.

FIG. 3 .
FIG. 3. Structural parameters as found by LEED-IV and comparison with those found by DFT structural relaxation.On the left layer distances and on the right bucklings are given in pm.The statistical errors of the shown parameters determined by LEED amounts to less than ±1 pm.The full list of varied parameters and their errors is given in the Supplement.