Introduction

Remarkable interfacial phenomena such as ferromagnetism at CaRuO3 paramagnetic/CaMnO3 antiferromagnetic, topological superconductivity at LaAlO3 insulator/SrTiO3 insulator and the magneto-electric effect at La0.5Sr0.5MnO3 ferromagnetic/BaTiO3 ferroelectric can provide a new avenue to realize artificial multifunctional materials which show physical properties that are not present in either of the constituent layer’s bulk materials1,2,3,4. Together, they have exposed a wealth of phenomena at the boundaries where compounds with different structural instabilities and electro-magnetic properties meet, providing unprecedented access to new physics emerging at oxide interfaces. After a report (Wang et al. ref. 5) of room temperature electric and magnetic polarizations in a BiFeO3 antiferromagnetic/SrRuO3 paramagnetic heterostructure, there have been numerous studies identifying the origin of these enhanced properties as either epitaxial strain5 or doping induced altered BiFeO3 (BFO) crystal symmetries6. With recent advances in deposition techniques, the BiFeO3 heterostructure spans a wide range of crystalline structures and plays host to an incredible variety of physical phenomena. Recent studies show that using X-ray reciprocal mapping, neutron scattering and temperature-dependent scanning probe-based studies, the growth temperature, thickness and substrate symmetry-dependent evolution of complex BiFeO3 phases7, 8 range from distorted monoclinic (MA and MC phases) to tetragonal and eventually parent rhombohedral structure. However, the exact origin for these significant properties has remained elusive. Previously, our group has worked extensively with various SrRuO3 metal/SrTiO3 insulator, (BiPb)FeO3 antiferromagnetic/SrRuO3 paramagnetic and (BiPb)FeO3 antiferromagnetic/SrTiO3 diamagnetic heterostructures of interest9,10,11,12. Doping of Pb ion plays a vital role in stabilizing single phase BiFeO3 with weak ferromagnetic order while dramatically reducing leakages, which gives correlation between the processing crystal structure, magnetic properties and magnetoelectric couplings8, 13. In the recent study9, we used reciprocal space mappings (RSMs) to demonstrate structural expansion (from cubic to tetragonal, and finally a mixture of two tetragonal phases) and suppression of spiral spin state in Pb doped BiFeO3 ((BiPb)FeO3) layers with varying growth temperature (650–700 °C). However, results of electron paramagnetic resonance study are unclear in terms of whether the other secondary tetragonal structure observed in RSM is due to (BiPb)FeO3 or is due to the presence of some defects or other nonmagnetic impurity. In another study11, we have shown an inverse effect in (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures, with an increase in thickness of the top (BiPb)FeO3layers (50–400 nm), and an anomalous decrease in unit cell volume of the bottom SrRuO3 (fixed thickness ~100 nm) layer. Usually, the properties of the subsequently grown top layers of heterostructures are affected by the interface formed between it and the preceding layer.

In order to comprehend these altered properties and new (BiPb)FeO3 phases, in-depth knowledge of interfacial phenomena of heterostructures is required before discovering devices. Although high-resolution X-ray reciprocal maps, transmission electron microscopy (HRTEM) and Raman spectroscopy have been the most preeminent techniques to study structural properties in terms of their lattices, it is generally difficult to apply the technique at an elemental level. In literature, commonly the best BiFeO3 films were obtained in the growth temperature range 600–700 °C either by PLD or sputtering14,15,16, and therefore it’s imperative to study these films at elemental level in order to get in depth knowledge of interfacial mixing or inter-diffusion of elements otherwise their stoichiometry will be remained doubtful. In most of the cases RSM and HRTEM gives crystal lattices which may lead to a wrong conclusion about exact crystal structures, because of the various nearly similar (BiPb)FeO3 crystal symmetries and twining present in the films. Here, we highlight new interface phenomena in (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures grown at critical growth temperature range 650–700 °C by using Rutherford backscattering as a probe to identify the phases of each layers. We further propose a mechanism for the observed secondary phase that provides insight into the competing nature of the phases in this system.

Results

The (BiPb)FeO3 layers were grown on SrRuO3 coated SrTiO3(100) substrates at growth temperature, T g  = 650–700 °C, by a sputtering system9, 12. While Raman scattering has been employed to investigate the phase transformation and soft modes in the bulk BiFeO3, Raman spectra from (BiPb)FeO3 layers are in general difficult to obtain since an underlying perovskite SrRuO3/SrTiO3 structure overwhelms the scattering signal emanating from the top (BiPb)FeO3 layers. By subtracting the contributions arising solely from the SrRuO3/SrTiO3 structure, it is possible to obtain the contribution of the (BiPb)FeO3 layer in the Raman signal17. Figure 1a shows one of the representative Raman spectra of the (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure grown at T g  = 650 °C (x) as well as the base SrRuO3/SrTiO3 (y) structure. Figure 1b shows the difference in spectra between curves x and y for the (BiPb)FeO3 layer (x-y). Applying this same method, the Raman spectra of other (BiPb)FeO3 layers grown at T g of 665–700 °C are given in the same figure. These Raman spectra show prominent bands at 140.2, 175, 370.4, and 540.3 cm−1 slightly higher than rhombohedral bulk BiFeO3 energy values18, which correspond to BiFeO3 modes of A1(1TO), A1(2TO),E(TO) and E(TO), respectively. This shift in Raman bands can be ascribed to the Pb doping which may create minor changes in chemical bonds that surround the dopants. This also results in fewer number of Raman mode compared to the 13 Raman-active modes for bulk R3c rhombohedral BiFeO3 symmetry18. Although the fewer Raman modes in our (BiPb)FeO3 layers may reflect a space group with higher symmetry than the bulk R3c, we can still compare the spectra qualitatively to obtain some insight into (BiPb)FeO3 symmetry change with T g . The Raman spectra of the T g  = 650 °C (BiPb)FeO3 layer is slightly different from the other 665–700 °C layers. As T g increases, small variances in Raman spectra are visible between the (BiPb)FeO3 layers. Indeed, in T g  = 665 °C films, the 175 cm−1 band starts appearing, and is completely developed in the T g  = 675 °C films, similar to bulk R3c BiFeO3. At high T g of 700 °C, these two 140 and 175 cm−1 bands overlap again and become broad peaks, which gives an indication of mixing of phases or inter-diffusion of elements. The “pre-edge” before 140 cm−1 for 650 and 700 °C films is a cut-off result for the filter to avoid the tail effect of original incident beam.

Figure 1
figure 1

Raman spectroscopy and high resolution X-ray reciprocal space mapping of (BiPb)FeO3/SrRuO3/SrTiO3 hetero-structures. (a) Raman spectra of (BiPb)FeO3/SrRuO3/SrTiO3 hetero-structure for T g  = 650 °C (x) and the bottom SrRuO3/SrTiO3 structure (y). (b) Raman spectra represent only contributions from (BiPb)FeO3 layers (x-y) at different T g , showing only a few Raman modes when compared to bulk BiFeO3. (c: 1–4) RSMs around (103) planes of (BiPb)FeO3 layers9 and bottom SrRuO3/SrTiO3 structure; with increasing T g , the (BiPb)FeO3 peak splits into two peaks (indicated by vertical red arrow).

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Any changes in crystal symmetry due to applied strains caused by the substrate or a Pb doping-related effect results in either a shift in the frequency of Raman modes or a merging of Raman modes. For this purpose, X-ray RSMs can be an optimal tool to compute exact crystal lattices. The RSM images of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures grown at different T g , collected around asymmetric (103) SrTiO3 planes is shown9 in Fig. c1–4. All topmost (BiPb)FeO3 layers exhibit large in-plane lattices (a = 4.08–3.99 Å) compared to the SrRuO3 (a = 3.926 Å) and SrTiO3 (a = 3.905 Å), as shown in Table 1. In-and out-of-plane lattices of SrRuO3 layers are almost independent of T g . The strain relaxation, i.e., (a BiPbFeO 3 – a SrTiO 3 )/a SrTiO 3 , in (BiPb)FeO3 peaks (indicated by red bended dashed arrow) decreases with T g from 650 °C (~5%) to 700 °C (~0.5%), approaching R3c bulk BiFeO3 symmetry, as is shown in the Raman spectra. For the T g  = 675 °C sample, one can see three SrTiO3 substrate peaks located at the (103) plane position, which simply indicates a substrate imperfection that propagates deeper into the (BiPb)FeO3/SrRuO3 structure. Surprisingly, at a high T g of 700 °C, the films exhibit one new peak adjacent to the main (BiPb)FeO3 peak and exactly beneath the SrTiO3 substrate peak (indicated by vertical red dashed arrow). Raman data of this film also show an unusual merger of three 140, 220 and 275 cm−1 bands. At this stage, we are uncertain whether these are mixed phases of BiFeO3 and/or splitting of the BiFeO3 layer or impurity phases. However, this case differs from Kim et al.14, where splitting of BiFeO3 peaks was observed when thickness increased from 70 nm to 980 nm, which resulted in the transformation of the tetragonal phase to the original R3c BiFeO3 phase. Another study by Bea et al.15 also shows the splitting of BiFeO3 peaks with an increase in thicknesses from 70 nm to 240 nm which were attributed to a monoclinic-to-tetragonal phase transformation. However, their results strictly cannot be compared to ours, because neither study changed the growth temperature nor used Pb doping. Hence, since using only Raman modes and lattice parameters is insufficient to determine the exact stoichiometry of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures, some local probe is necessary to investigate the elemental level deficiency/vacancy of the selected materials.

Table 1 Composition and thickness (t) of each layers of (BiPb)FeO3/SrRuO3/SrTiO3 hetero-structures deduced from simulated RBS spectra at different T g. Lattices parameters (a and c) estimated by RSM are also given in the Table.
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We rigorously deployed Rutherford backscattering spectra for random and aligned cases on (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures and the buffer layer SrRuO3/SrTiO3. RBS data was first analyzed qualitatively and then quantitatively. Figure 2 shows Rutherford backscattering (RBS) spectra taken in random and aligned modes. The leading edges from the Bi/Pb and Sr/Ru and Fe atoms in the films and those from the Sr, Ti and O atoms in the substrate are clearly seen. As shown in Fig. 2, Rutherford backscattering ratios (χ min  = 34 to 100%) yielded from aligned to random spectra near surface regions of top (BiPb)FeO3 layers (blue triangle). It indicates the degradation of crystalline quality with increasing T g . At T g  = 650 °C, the count of the aligned spectra of (BiPb)FeO3 slowly increases up to the top surface region of χ min  = 34%, indicating a possible presence of Bi/Pb and Ru vacancies. As T g increases to 665 °C, a significantly large count is observed at the (BiPb)FeO3/SrRuO3 interface (χ min  = 64%), which decreases gradually to the top surface value (χ min  = 46%). A higher density of defects at the (BiPb)FeO3/SrRuO3 interface is mainly due to the additional lattice misfit strain apart from vacancies, which tends to become lower towards the top (BiPb)FeO3 surface, similar to the conventional strain-relaxation process19. Furthermore, at T g  = 675 °C, the count of χ min  = 67% increases in the sample and can be preliminarily explained as the introduction of extra crystal imperfections into the SrTiO3 substrate (as depicted in Fig. 1c). Surprisingly, at high T g  = 700 °C, we do not see any difference between random and aligned spectra, i.e., χ min  = 100%, which implies the presence of a large amount of defects/distortions/inter-diffusion which can enhance maximum backscattering even in (001) aligned configurations. We can also see the gradual diminishing of Fe peaks with increasing T g , indicating the presence of Fe vacancies in the (BiPb)FeO3 layer.

Figure 2
figure 2

Random and aligned RBS spectra for (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures. Random (red) and aligned RBS spectra (along [001] direction) (black) for (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures. RBS ratio (χ min : 34 to 100%) (blue triangle) at (BiPb)FeO3 surfaces clearly indicates crystalline quality degradation and eventually completes an overlap of aligned to random spectra at high T g . Inset shows RBS experimental sketch.

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Discussion

In order to perform quantitative elemental analysis, the random RBS data for (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures were simulated by using the Simulation Program (SIMNRA)20, and two of the representative sample plots (T g of 650 and 700 °C) are given in Fig. 3. These random and simulated curves are in good agreement. The accurate determination of the Bi and Pb concentrations independently is difficult, because the contribution of Bi and Pb atoms to the RBS spectrum cannot be distinguished from each other. For convenience, the (Bi,Pb)x concentration will be referred here as Bi concentration. The compositional analysis and thickness of each layers of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures from simulated spectra, as shown in Table 1, suggests four important features. First, we observe a severe deficiency of Fe element in top (BiPb)Fe1−δO3±δ layers with increasing T g . The Fe deficiency increases rapidly from 7% to 23% for films grown at 665 °C and 675 °C, respectively, and then increases further up to 35% for 700 °C films. Obviously, the extremely high deficiency cannot support a stable structure unless some other ions, such as Bi, Pb or O, can move to fill in the Fe ion vacancies. However, these high T g films retain a crystalline structure with slightly smaller lattices compared to other films. Second, Ru vacancies in the bottom SrRuO3 layer, similar to the sample without the top (BiPb)FeO3 layer (shown in the inset of Fig. 3b), can be clearly observed. The Ru vacancy concentrations in all films are as high as Fe deficiency. Third, their structural integrity is maintained due to the interdiffusion of (BiPb) in the layer as well as the excess of oxygen filling in the Ru vacancies. The oxygen is the lightest element in the compound and is very difficult to quantify. Its concentration can be easily altered automatically in order to accommodate for any deficiency or vacancies of other elements. Instead of listing the exact quantities of oxygen, we use 3 ± δ to indicate its complexity. Interestingly, the Bi and Pb element inter-diffuses through the SrRuO3 layer and then penetrates even further into SrTiO3 substrates with T g to form a very thin interlayer at the SrRuO3/SrTiO3 interface. For the 700 °C film, the interdiffusion of (BiPb) into the interlayer is estimated to be 0.087 mole. The fourth notable feature is that, along with the significant Ti vacancies, the interlayer of the 700 °C film obviously forms a crystal structure different from the pure SrTiO3 and becomes tetragonal with strained in-plane and relaxed out-of-plane lattices. This distinct interlayer contributes to the extra peak right below the SrTiO3 peak, as marked by a vertical dashed line, and by the SrTi(BiPb)O3 peak in Fig. 1c-4.

Figure 3
figure 3

Elemental analysis of each layer of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures and bottom SrRuO3/SrTiO3 structure. RBS simulated data (solid lines) for (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures of (a) T g  = 650 °C and (b) T g  = 700 °C are in good agreement with random data (symbols). Variation in different edges of Pb, Bi and Fe indicate composition and thickness changes with T g . Inset of Fig. 3(b): Random and simulated spectra of bottom SrRuO3/SrTiO3 structure with Ru vacancies at surface of SrRuO3 layer.

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Further support about Bi and Pb inter-diffusion into SrTiO3 substrate, we have performed TEM EDS analysis across the  (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure with T g of 700 °C, as shown in bright field STEM image (Top left Fig. 4). Compositional analysis Tables (Right Fig. 4) for each selected points from 1 to 8, are indicative that (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure suffers Bi and Pb interdiffusion. On Auger electron depth profiling  spectra of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure (Bottom left Fig. 4), it demonstrates undoubtedly a significant interdiffusion of Bi and Pb elements at the (BiPb)FeO3/SrRuO3 and SrRuO3/SrTiO3 interfaces. But it is understood that TEM EDS shows only local reading while Auger  plot shows average reading of a large area of sample. However, the thicknesses (x-axis) in Auger plot was estimated using  SiO2  etching rate which may not take as a correct number. The inter-diffusion of Bi and Pb elements was also observed 21 in 0.7BiTiO3–0.3PbTiO3 films, when laser ablated on Pt/TiOx/SiO2/Si substrate. The Bi and Pb move through the entire porous Pt bottom electrode and sit just above the TiOx adhesion layer. Although, SrRuO3 buffer layer was introduced  to prevent this interdiffusion between the substrate and the film, the Bi still appears to readily segregate from the other elements in the film towards the substrate. In our case, vacancies of Ru in SrRuO3 bottom layer facilities this inter-diffusion further deep into SrTiO3 substrate. With increasing (BiPb)FeO3 layer thickness11, the Bi and Pb inter-diffuses more rapidly into SrTiO3 substrate, which can be supported from fact that bottom SrRuO3 layer recovered their original bulk unit cell volume due to refilling of Ru vacancies by Bi and Pb elements. Therefore, it appears that inter-diffusion of Bi and Pb does take place, irrespective of method of deposition, however, inter-diffusion rate might be different like in RF-sputtering, sputter materials have higher kinetic energy compared to PLD and MBE processes. Thus, due to identical nature of Bi and Pb, both normally start inter-diffusion depending upon growth conditions and in-situ/ex-situ heat treatments, and the normal trigger point for inter-diffusion is above 600 °C. Study on interdiffusion (Bi and Pb) and vacancies (O and Ru) in the (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure is crucial, as many novel properties like a switchable diode22 and photovoltaic23 effect and ferroelectric resistive switching22 phenomena can be tuned by controlling the oxygen vacancy migration. In the present (BiPb)FeO3 layers, more complicated phenomena are involved like interdiffusion, or doping, of Bi and Pb and the Fe vacancies. The former one, the doping of Pb, is responsible for generating O vacancies24 and must provide a very tight binding between them. For the later one (Fe vacancies), it can provide a path way for O vacancies to migrate under applied electric field. However, the migration of O vacancies will alter the fine balance of electricity and the polarization of (BiPb)FeO3 layer. Therefore, based on overall effects, a relatively higher driving force, or electric field, is expected to initialize the O vacancies migration. Our previous study25 indicating a subtle carrier accumulation at (BiPb)FeO3/SrRuO3 interface reflects a different band bending effect which causes the polarization vector of (BiPb)FeO3 pointing towards the interface at zero bias. How these different phenomena may affect the diode and photovoltaic effect are worthy to explore in near future.

Figure 4
figure 4

Compositional analysis of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures. Top left: STEM bright field image of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure with T g  = 700 °C, Bottom Left: Auger electron spectroscopy depth profiles with colour assigned to the different elements throughout the (BiPb)FeO3/SrRuO3 and SrRuO3/SrTiO3 interfaces11. This gives clear evidence of Bi and Pb inter-diffusion. Right: TEM EDS analysis across the points 1 to 8 shown on the bright field image.

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The combined effects of inter-diffusion of (Pb and Bi) elements into SrRuO3 (which is paramagnetic at room temperature and ferromagnetic well below T c of 150 K), as well as possible reduction in canted magnetism of (BiPb)FeO3 due to Fe vacancies, can be clearly seen in M–H loops (taken at 5 K) of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures grown at T g  = 650 °C and T g  = 700 °C, as shown in Fig. 5. The inset of Fig. 5 shows significant drop in the coercivity value, H C for the T g  = 700 °C films compared to the T g  = 650 °C films as well as the H C of the bare SrRuO3 layer around 0.2 T. Normally, the magnetization of both (BiPb)FeO3 and SrRuO3 layers are expected to decrease because of Fe and Ru vacancies in respective layers. However, presence of Bi and Pb may trap in part of Ru vacancies, and excess of Bi and Pb and Ru vacancies can distribute randomly in the SrRuO3 layer, creating local distortions that vary the angle and distance of Ru(site)–O–Ru(site) bonds and frustrate the long-range magnetic coupling11, 12. The Fe vacancy effect is more directly visible at 300 K, where SrRuO3 is in a paramagnetic state and the canted magnetic moment only arises from (BiPb)FeO3 being reduced drastically9 by 75% when T g changes from 650 °C to 700 °C.

Figure 5
figure 5

Low temperature magnetic properties of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures. M–H loops measured at 5 K in out–of–plane configuration for (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures grown at T g  = 650 °C and T g  = 700 °C. Bare SrRuO3 layer M–H loop is also given for comparison. Inset shows decrease in coercivity H C with T g compared to the bare SrRuO3 layer.

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In summary, Rutherford backscattering spectroscopy  (RBS) is demonstrated to be a powerful technique for investigating the compositional analysis at the elemental level of each layer of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructures. The RBS simulation analysis offers various recurring features, such as the formation of Fe and Ru vacancies in respective (BiPb) FeO3 and SrRuO3 layers, as well as robust inter-diffusion of Pb and Bi elements not only into bottom SrRuO3 layers but also deep into surface of SrTiO3 substrates. Beyond these, the inter-diffused element (Pb and Bi) coupled with Ti vacancies near SrTiO3 surfaces can modify the SrRuO3/SrTiO3 interface, which causes an additional thin inter layer of “SrTi(BiPb)O3”. This so-called thin layer of tetragonal crystal structure (similar to that of SrTiO3 substrate but with elongated c-axis) basically shows an additional peak in RSM, which is not a secondary phase of (BiPb)FeO3. This is a remarkable result, since, generally, observing the lattice without knowing the actual elemental compositions can mislead about the phases of same crystalline structure. These changes also drastically affect the magnetic properties of SrRuO3 and (BiPb)FeO3 layers.

Methods

Sample fabrication

The (BiPb)FeO3 layers were sputtered from a ceramic BiFeO3 (doped by 10% Pb) target at RF power of 200 W using a standard off-axis magnetron sputtering technique. Phase pure BiFeO3 (doped by 10% Pb) target was prepared by standard solid state reaction rout (shown in Supplementary Fig. S1 and Fig. S2). The (BiPb)FeO3 layers were grown at growth temperature, T g  = 650–700 °C under Ar/O2 (2/1) gas flow9. The bottom SrRuO3/SrTiO3(001) structure12, having in-plane lattices that match well with bulk BiFeO3, was used (grown at 690 °C, 200 W and Ar/O2 = 2/1) in order to minimize the strain effect on top (BiPb)FeO3 layers. SrTiO3(001) substrates were cleaned by the process described elsewhere11 prior to deposition. After deposition, the heterostructures were annealed under oxygen pressure of 250 Torr at 700 °C for 1.5 h to reduce possible oxygen deficiencies.

Sample characterization

Raman spectra were recorded at room temperature by using a Jobin Yvon dispersion Raman microscope equipped with a CCD detector and a 16 mW He–Ne laser (633 nm) and were collected in backscattering configuration along the growth direction of the films. The spectra were measured in the range of 10–1200 cm−1 within an accuracy of 0.1 cm−1. It was confirmed that the laser power did not heat or modify the sample. Structural properties were measured by a Bede D1 high resolution X-ray diffractometer. Scanning transmission electron microscopy (STEM) images in bright field mode and energy dispersive x-ray spectroscopy (EDS) was performed with a field emission gun transmission electron microscope [(FE-TEM), FEI E.O Tecnai F20 G2] operated at 200 kV. An Auger electron spectroscopy depth profile was performed to analyze the composition of (BiPb)FeO3/SrRuO3/SrTiO3 heterostructure. The magnetic properties were measured with an out-of-plane configurations in superconducting quantum interference device. The diamagnetic contributions from the SrTiO3 substrate, glue/tapes and sample holder were subtracted from magnetization data by measuring the high-field magnetic susceptibility.

Rutherford backscattering spectroscopy (RBS)

The compositional analysis of the (BiPb)FeO3/SrRuO3/SrTiO3heterostructure was carried out by Rutherford backscattering spectroscopy (RBS). A 2 MeV helium (4He+) beam was directed at the sample and the energy of the backscattered helium ions is measured at a back scattering angle of 165°. To minimize the possible charging effect at the top insulated (BiPb)FeO3 film, the sample were grounded by an C-tape. The RBS data analyses were performed by the simulation of the spectra using the Simulation Program20.