Sara Touhami
email: sara.touhami@centralesupelec.fr

Vinicius Alves Fernandes
email: vinicius.alves-fernandes@edf.fr

Fernando Lopez Caballero
email: fernando.lopez-caballero@centralesupelec.fr

STRUCTURE-SOIL-STRUCTURE INTERACTION ANALYSIS OF NUPEC TEST CASES

Keywords: structure-soil-structure interaction, earthquake ingineering, numerical modeling

This work aims to study the influence of the Structure-Soil-Structure Interaction (SSSI) on the seismic response of structures. It focuses on the characterization of the main factors influencing this phenomenon by studying the well-known and documented case NUPEC from 90s and by conducting different case scenarios with a linear model. The performed numerical simulations are able to capture the influence of the adjacent structure, which partly depends on the type of foundation soil. A parametric analysis was also performed to highlight the influence of some parameters (such as a distance between building, mass, height and embedded depth) on the response of the main structure.

INTRODUCTION

This work deals with the physical phenomenon of the structure-soil-structure interaction, that is, the interference through the support soil during an earthquake between two buildings located next to one another, and their influence on seismic response. This type of configuration is common in the case of nuclear power plants.

It is well known that the dynamic response of two adjacent structures is affected by the exchange of vibrational energy through soil. Such interaction is a function of the separation distance, the natural frequencies of the system and the properties of the soil around the foundations, among others. Therefore, the effects on the response spectra of one structure when considering the adjacent structures are not easily predicted. The objective is to emphasize the sensitivity of this phenomenon to the quantities which characterizes the system. To reach this objective, a simple case study is first performed in order to best characterize the Structure-Sol-Structure interaction. The numerical model chosen corresponds to the "Soil-Struction Interaction NUPEC" workshop organized in Japan NUPEC (NUclear Power Electric Corporation [START_REF] Clouteau | Calculation methods of structure-soil-structure interaction (3SI) for embedded buildings: Application to NUPEC tests[END_REF]). Indeed, NUPEC had set up a large experimental program to study this type of phenomenon by building a small scale buildings in areas of high seismicity. The buildings were instrumented by sensors and various configurations were tested. This test case was studied by Clouteau et al. [START_REF] Clouteau | Calculation methods of structure-soil-structure interaction (3SI) for embedded buildings: Application to NUPEC tests[END_REF].

NUMERICAL METHODS

The calculation method used for this study is based on the FEM-BEM (Finite Element Method -Boundary Element Method) using the Code Aster and MISS3D software coupling. The first method (FE) is adapted for problem solving with complex geometry and nonlinear behavior and is limited to bounded domains. Conversely, the second method (BE) allows resolution in unbounded domains, because on the one hand, it is based on the discretization of boundaries only (which reduces the dimension of the domain to be discretized), and on the other hand, it takes into account the conditions of radiation at infinity [START_REF] Pecker | Dynamique des Sols[END_REF][START_REF] Semblat | Waves and vibrations in soils: earthquakes, traffic, shocks, construction works[END_REF][START_REF] Clouteau | Miss 6.4: Manuel scientifique[END_REF].

This approach is based on a technique of decomposition of the field of study called "substructuring method". One of the sub-domains (far field), namely the soil (unbounded medium stratified horizontally and with homogeneous isotropic elastic behavior per layer), is solved with the method of boundary elements in the frequency domain using the code MISS3D. The resolution of the other subdomain (near field), which is the structure (bounded medium), is performed with the finite element method in the time domain using the Code Aster (Figure 1). Figure 1: Simplified modeling of the Soil-Structure interaction model based on the technique of decomposition of the field of study [START_REF] Nieto-Ferro | Interaction sol-structure non-linéaire en analyse sismique[END_REF] The equations of motions to be solved (by reference to the Figure 2) are thus :

M Ü + C U + KU = Q f (1)
M , C and K represent the mass, damping and stiffness matrices of the system. Q f is the loading vector. It is different from zero only on the external boundaries of the model because the source of the earthquake is generally not included in the model (Figure 2, left). In the absence of the structure, the equation of motion in free field is similar to the equation 1 (the index f corresponds to the only free field) :

M f Üf + C f Uf + K f U f = Q f (2)
Figure 2: Decomposition of soil-structure interaction problem [START_REF] Pecker | Dynamique des Sols[END_REF] The interaction displacement U i is defined such as :

U = U i + U f (3)
This displacement (U i ) satisfy the following equation:

M Üi + C Ui + KU i = -Q i (4)
The problem of soil structure interaction is decomposed into two parts: a free-field soil response problem (1) and a source problem [START_REF] Alves-Fernandes | Dynamic soil-structure interaction modeling strategies applied to kashiwazaki-kariwa nuclear power plant case-study[END_REF]. As for the total displacement, it is given by the equation (3). The loading vector Q i is determined from the free-field displacements.

In a first step, an analysis of the kinematic interaction is carried out by considering the sub-domain which includes the soil and the rigid foundation without mass. Acceleration at the soil-foundation interface is deduced from the seismic motion at the base of the soil. An analysis of the inertial interaction is then carried out in order to determine the dynamic impedance of the foundation. This impedance characterizes the dynamic forces imposed on the massless foundation when subjected to a harmonic stress of unit amplitude. The complex impedance functions which depend on the frequency of the applied load are calculated for each of the six degrees of freedom (three translations and three rotations) of the foundation (for rigid foundation). The real part corresponds to the stiffness of the soil-foundation system, while the imaginary part represents the damping ξ (equation 5). Finally, the dynamic response of the structure (which is connected to the soil and is subjected to the deduced seismic load) is determined.

ξ = Im(K * ) 2Re(K * ) (5)

CHARACTERIZATION OF THE STRUCTURE SOIL STRUCTURE INTERACTION

In this section, the structure-soil-structure (SSSI) phenomenon is studied by relying on the test case of NUPEC. After the presentation of the adopted model, the results of the calculations carried out to characterize the SSSI are discussed. Finally, the results of a parametric study in order to determine the quantities that most impact the interaction are presented. The developed methodology of SSSI is then applied to the industrial application case of the KKNPP by Alves-Fernandes et al. [START_REF] Alves-Fernandes | Dynamic soil-structure interaction modeling strategies applied to kashiwazaki-kariwa nuclear power plant case-study[END_REF].

Description of the NUPEC test

The model adopted for this study corresponds to the buildings used for the "NUPEC Interaction Sol-Structure" workshop which was organized by NUPEC (NUclear Power Electric Corporation) in Aomori, Japan during the mid-1990s [START_REF] Clouteau | Calculation methods of structure-soil-structure interaction (3SI) for embedded buildings: Application to NUPEC tests[END_REF]. These models of a scale of 1/5 of nuclear buildings were built in a zone of high seismicity, in order to have experimental data under real seismic loading. In the framework of this analysis, different configurations were studied :

• single building, used as reference case for comparisons;

• two identical reactor buildings to evaluate the influence of the presence of a building on the seismic behavior of the other;

• two different buildings, a turbine building and a reactor building to highlight the influence of several parameter. At each step of the analysis, it is studied the response of the reactor building.

Numerical models and mechanical characteristics

Building model

There are several elementary models allowing to model the structures, namely the discrete model called "stick" which was adopted and which is very classic in earthquake engineering. The buildings are modeled with masses concentrated on each floor, and massless beams of different types (Figure 4a). The mechanical characteristics of the elements of the model are given in Tables 2 and3 [START_REF] Clouteau | Calculation methods of structure-soil-structure interaction (3SI) for embedded buildings: Application to NUPEC tests[END_REF]. The buildings are made of reinforced concrete with the characteristics of Table 1.

Soil model

The buildings are based on 25m soil column previously to a bedrock condition (Figure 4b). The buildings are embedded of 5m in a sand layer as shown in Figure 4b. For this study two soil conditions were used: a rigid soil and a soft soil. The rigid soil is obtained from the elastic properties measured on site. Tables 4 and5 show respectively the mechanical characteristics of the different rigid and soft soil layers. It should be noted that the properties of the layer 1 have been modified to be the same as those of the layer 2 because in the NUPEC cases layer 1 is of poor quality.

Foundation model

The foundations that constitute the interfaces of SSSI between buildings and the ground are considered rigid and modeled by shell elements. Figure 5 shows the dimensions of these interfaces (left) and the model FE (right) used. The two juxtaposed buildings are spaced 60cm apart. It is interesting to note that the resonance peaks for soft ground are shifted towards the low frequencies compared to the rigid soil. However, the amplifications corresponding to these peaks are stronger for the soft ground than for the rigid one. Concerning the structures, Figure 7 shows the transfer functions obtained for the case of a single building for both types of soil. It illustrates first that considering the soil-structure interaction, the resonance frequency reduces compared to the first fundamental mode of the structure on rigid base (at 28.2Hz). As expected, the lower the rigidity of the soil, the higher is the reduction on the resonance frequency of the building. In addition, the same figure shows an amplification factor of 15 at 12Hz for a rigid ground and of 4.3 at 9.4Hz for the soft ground. As a result, a soft foundation soil has the effect of reducing the amplification of its response on the structure and shifting its fundamental frequency to lower frequencies. These figures show that for all two cases, the fact that buildings are based on a soft soil reduce the peak (by a factor of two in the case of two buildings). However, the impact on the amplitude of the transfer function relatively to the soil type for the building-foundation configuration is very low. On the other hand, the presence of the second building has two effects: a reduction in the amplitude of the peak more remarkably for the rigid soil than for the soft soil, and the apparition of a second peak which is more pronounced for the rigid soil.

Parametric analyses

In this section, the factors which have an influence on the response of structure-soil-structure interaction for the two soil profiles are investigated. By considering a simple SSSI model (Figure 9), the main aspects affecting SSSI were determined and then varied on the NUPEC model in order to study their influence on this phenomenon [START_REF] Zhang | Modélisation physique et numérique des interactions sol-structure sous sollicitations dynamiques transverses[END_REF][START_REF] Clouteau | Calculation methods of structure-soil-structure interaction (3SI) for embedded buildings: Application to NUPEC tests[END_REF].

Figure 9: Building model [START_REF] Alexander | A simple discrete model for interaction of adjacent buildings during earthquakes[END_REF] According to Alexander et al. [START_REF] Alexander | A simple discrete model for interaction of adjacent buildings during earthquakes[END_REF], the equation of motion in its matrix form can be expressed as follows:

      1 -h 1 r 1 0 0 -h 1 r 1 m2 m 1 + h 1 r 1 2 0 0 0 0 m 3 r 2 2 m 1 r 2 1 -h 2 r 2 m 3 r 2 2 m 1 r 2 1 0 0 -h 2 r 2 m 3 r 2 2 m 1 r 2 1 m 3 r 2 2 m 1 r 2 1 ( m4 m 3 + ( h 2 r 2 ) 2 )           ü1 ü2 ü3 ü4     +      ω 2 1 0 0 0 0 m 2 m 1 ω 2 2 + 2 0 -2 0 0 m 3 r 2 2 m 1 r 2 1 ω 2 3 0 0 -2 0 m 4 m 3 m 3 r 2 2 m 1 r 2 1 ω 2 4 + 2          u 1 u 2 u 3 u 4     =      1 h 1 r 1 - m 3 r 2 2 m 1 r 2 1 r 1 r 2 h 2 r 2 m 3 r 2 2 m 1 r 2 1 r 1 r 2      üg (6)
with :

ω 2 1 = k 1 m 1 , ω 2 2 = k 2 m 2 r 2 1 , ω 2 3 = k 3 m 3 , ω 2 4 = k 4 m 4 r 2 2 , 2 = k m 1 r 2 1
and :

m 1 , m 3 : masses of buildings 1 and 2 respectively m 2 , m 4 : soil/foundation masses underneath buildings 1 and 2 respectively k 1 , k 3 : stiffnesses of buildings 1 and 2 respectively k 2 , k 4 : rotational spring stiffnesses of soil beneath buildings 1 and 2 respectively r 1 , r 2 : soil/foundation masses radius of gyration of buildings 1 and 2 respectively h 1 , h 2 : heights of building 1 and 2 respectively u 1 , u 3 : non-dimensional relative displacement to ground of buildings 1 and 2 respectively u 2 , u 4 : rotation at base of buildings 1 and 2 respectively k : rotational interaction spring between building 1 and 2 Equation 6shows the terms that characterize the "soil-structure" system and which can in particular have an effect on the seismic response of the building. The parameters studied are the following:

• The distance separating the two buildings in order to see from which spacing it is enough to do an ISS modeling only. It is estimated that the variation of the distance separating the two buildings would have an effect on the soil which connects them and which is assimilated to a spring of a certain rigidity k. Indeed, this parameter will change the term (interaction circular frequency ratio parameter) which intervenes in the stiffness matrix of the equation of motion;

• The height and mass of the adjacent building (m 3 and h 2 ) that will change the frequency of this building (7);

f 2 = 1 2π k 2 m 2 (7)
• The embedded depth into the ground of the two buildings. This will change the mass of the embedded part of the structure (m 2 and m 4 ).

Influence of separation distance

In order to show the impact of the distance between two buildings on their coupling, and consequently the structure-soil-structure interaction, this parameter is varied as follows: 0.60m, 1m, 2m and 5m.

Figure 10 shows the influence of the spacing between the two buildings on the evolution of the transfer functions of the reactor building. Figures 10a and10b has been normalized relative to the case of a single building. For frequencies below the resonance frequency of the case of a single building, a de-amplification is observed which is more important for small distances. This trend is reversed beyond this frequency and the same remarks are noted in the case of the soft ground. It is also observed that the coupling between the buildings is all the smaller as the distance increases. With this evolution, it is also noted that the amplitude of the second peak decreases. The frequencies at which these peaks occur are always reduced. These remarks apply to both types of soil.

On the other hand, Figure 11 shows the evolution of the resonant frequencies of the reactor building. It is noted that as the distance increases, these frequencies tend towards an asymptote corresponding to the resonance frequency of the case of a single building. This confirms the remark above which is true for both soil types. Let "a = 8m" be the width of the foundation. It is estimated that, from 65% of this width, the buildings are weakly coupled. Indeed, for the two types of soil, the curve corresponding to a distance of 5 m (62.25% of a) approaches an amplitude equal to 1 which corresponds to the case of a single building (But the buildings are still coupled at this distance).

Influence of mass and height of adjacent building

To quantify the influence of the adjacent building mass (m 3 ), this parameter is varied by considering a lighter (0.5 × m 1 ) and heavier (1.2 × m 1 ) adjacent structure. The weight m 1 = 675 tons is the initial mass tested and is equal for the two buildings spaced 60 cm apart. The choice of these ratios was made taking into account the mass ratios between the reactor building and adjacent building found in the case of nuclear power plants.

Figure 12 reports the ratio of the transfer functions relatively to the case where the masses are equal, that for the rigid ground the difference is almost non-existent for frequencies below 10Hz, While for the soft ground the variation of the mass in one direction as in the other reduces the amplitude of the peaks, and this from 5Hz. From 14Hz for the rigid ground and from 10Hz approximately for the soft ground the difference is more visible. In the case where the second building is heavier, an amplification (more important for the rigid ground) takes place. For the other case, it is a deamplification that occurs. The comparison is made relatively to the frequencies of the case of two buildings with equal masses. To study how the height of the second building could influence the first one, we compared three cases of figures for a spacing between buildings of 60 cm. In the first case we increased the height by a ratio of 1.4; In the second we lowered this height to 0.8 of the initial height. Finally, we compared these two cases with the one where the height of the two buildings is the same (10.75m). As with considered mass variation, the choice of height ratios results from what can be observed in structures of interest. Figure 13 synthesizes the ratios of the transfer functions of the two cases where the height is changed relatively to the case where it is fixed. It is noted that the height of the second building has no influence on the building of interest (first building) before 5Hz for the rigid ground and 10Hz for the soft ground. The three curves are superimposed over a wide range of frequencies and in particular up to 10Hz for soft ground. Beyond these frequencies, in the case where the second building is higher, an amplification followed by a deamplification is observed. The same trend is to be noted for the case where the second building is lower. These remarks are also valid for soft ground but with lower amplitudes.

Influence of depth

For this parameter, two steps are performed:

• the embedded depth of both buildings evenly was modified. Three configurations were tested: surface buildings, embedded at 3m and 5m;

• then, this depth was shifted for both buildings.

Figure 14 illustrates the seismic response of the structure in the embedded situation is lower than that in the shallow situation, as expected. In addition, amplification decreases with depth. In parallel, a shift towards the high frequencies is observed, for both types of soil, in spite of the fact that the amplitude is not the same. On the other hand, Figure 14 shows that embedded depth in the soil has the effect of shifting the peak frequencies of the transfer functions to higher values and of modifying the amplitude of these peaks. In the figure 15 is reported the strange form of the transfer function of the case of the shifted depth 5m-3m. This form is probably the result of an error in the numerical calculation.

Finally, as for the previous analyzes, it is concluded that these differences are more visible in the case of soft soil.

CONCLUSIONS

The present study aims to characterize the SSSI phenomenon, which can be important for the paraseismic design of structures and to highlight the parameters that influence this interaction. To do this, a simple model (NUPEC buildings) was chosen to conduct the SSSI characterization study in the linear domain using the Code Aster and MISS3D coupling.

In the first part of the study, different configurations were analyzed (single building and two buildings) to compare their seismic behavior. For this analysis, two soil types were considered: soft soil and rigid soil. This comparison made it possible to show that for this case study, the SSSI reduces spectral acceleration in the building of interest. It is also founded that this influence was greater in the case soft foundation soil. On the other hand, to study the sensitivity of the SSSI phenomenon to the quantities characterizing the model, a series of parametric studies were carried out. They related to the distance between the two buildings, the mass and the height of the second building, and the depth of sinking into the ground. The main conclusions drawn from this analysis are:

• Distance : it was noticed that coupling reduces by increasing the distance;

• Mass : amplifies the response of the first building when it is larger and reduces this amplification when it is smaller;

• Height of the second building, whether larger or smaller, has an impact on the seismic response of the first building. The difference lies in the frequencies at which the peaks occur;

• Depth : the greater the embedded depth, the greater the interaction between the buildings and therefore the reduction of the spectral response. This reduction is higher as the foundation of the second building is deeper.

In perspective to this work, it would be interesting to study an analytical model where the ground between the buildings can be modeled by a spring, in order to compare it to the numerical simulations.

Figure 3 :

 3 Figure 3: Single embedded building (top) and two identical closely spaced embedded buildings (low)[START_REF] Clouteau | Calculation methods of structure-soil-structure interaction (3SI) for embedded buildings: Application to NUPEC tests[END_REF]

  (a) Stick models of the building [4] (b) Soil Stratigraphy

Figure 4 :

 4 Figure 4: Building and soil models

Figure 5 :

 5 Figure 5: Simplified model of NUPEC buildings

Figure 6

 6 Figure 6 displays the transfer functions for the two considered soil columns. Three peaks in the [0: 20] Hz frequency range for the two soil types are identified:• rigid soil : peaks at 6.5 HZ, 11 Hz and 19.5 HZ;• soft soil: peaks at 5 Hz, 8.3 Hz and 15 Hz.

Figure 6 :

 6 Figure 6: Transfer function of soil. The curve in blue represents the rigid soil and the curve in green represents the soft soil.

Figure 7 :

 7 Figure 7: Transfer function for a single building

Figure 8

 8 Figure8shows the transfer functions for the case of two similar buildings side by side. It is observed a peak of 7.6 at 13.3 Hz for a rigid soil and 3.6 at 11 Hz for the soft ground. The second peak is 2.2 at 28 Hz for the rigid soil. For the soft soil this second peak is very low, it is 1 at 22 Hz.

Figure 8 :

 8 Figure 8: Transfer function for two similar buildings

  Figure 10: Ratio of transfer function : influence of the distance

  Figure 12: Ratio of transfer function : influence of mass

  Figure 13: Ratio of transfer function : influence of height

  Figure 14: Transfer function : influence of depth (equal)

Table 2 :

 2 Masses characteristics of stick model. Masses Height (m) Mass (10 3 Kg) Massic iner. (10 3 Kg.m 2 )

	J xx	J yy	J zz

Table 3 :

 3 Beams characteristics of stick model Beam Area (m 2 ) Iner. momentum (m 4 ) Shear Coef. Twist Const. (m 4 )

		A	I z	I y	A y	A z	J x
	P1	59.50	341.33 341.33	0.93 0.93 682.70
	P2	8.28	39.51 54.77	2.94 1.47 94.30
	P3	63.19	341.33 341.33	0.99 0.99 682.70
	P4	19.78	148.34 149.14	2.13 2.11 297.50
	P5	64.00	341.33 341.33	1.00 1.00 682.70

Table 4 :

 4 Rigid soil properties

	Layer	Thickness (m) E(MPa) ρ(Kg/m 3 ) 2β(%) ν
	8	1.00	117.9	1770	10	0.386
	9	1.00	190.8	1770	10	0.279
	10	1.00	207.0	1770	10	0.265
	11	1.00	224.2	1770	10	0.251
	12	1.00	248.7	1770	10	0.272
	1	0.50	614.9	1940	10	0.371
	2	2.50	614.9	1940	10	0.371
	3	3.00	1 015.1 1940	4	0.415
	4	14.00	10 190.0 2210	4	0.386
	substratum 27.75	15 010.0 2210	4	0.343

Table 5 :

 5 Soft soil properties

	Layer	Thickness (m) E(MPa) ρ(Kg/m 3 ) β(%) ν
	8	1.00	78.6	1770	2.019 0.386
	9	1.00	100.0	1770	2.871 0.279
	10	1.00	81.4	1770	3.673 0.265
	11	1.00	73.3	1770	4.072 0.251
	12	1.00	71.4	1770	4.314 0.272
	1	0.50	496.3	1940	0.574 0.371
	2	2.50	481.5	1940	0.641 0.371
	3	3.00	819.5	1940	0.573 0.415
	4	14.00	10 178.6 2210	0.157 0.386
	substratum 27.75	15 010.0 2210	0.007 0.343

ACKNOWLEDGMENTS

The work carried out under the SINAPS@ project receives French funding managed by the National Research Agency under the program Future Investments (SINAPS@ reference No. ANR-11-RSNR-0022). SINAPS@ is a SEISM Institute project (http://www.institut-seism.fr/en/).

APPENDIX


A V Krivosheeva

V L Shaposhnikov

V E Borisenko

J.-L Lazzari

Electronic Properties of WS 2 /WSe 2 Heterostructure Containing Te Impurity: The Role of Substituting Position

Keywords: 2D heterostructure, dichalcogenide, electronic property, impurity, substituting position

An impact of the positions of Te atoms substituting W atoms in two-dimensional WS 2 /WSe 2 heterostructures on their electronic properties is investigated by theoretical simulation. The substitution of W by Te tends to reduce the energy band gap and can lead to metallic properties depending on the impurity position and concentration.

Introduction

Individual layers of transition metal dichalcogenides, contrary to their bulk form, are known to possess direct-gap properties. [1][2][3][4] Analogously, stacking of two monolayers (MLs) of different dichalcogenides may also provide the direct nature of the gap. Moreover, doping may change band gap values and related characteristics of such heterostructures. In order to investigate how Te atoms can influence on electronic properties of a two-dimensional heterostructure made of WS 2 and WSe 2 MLs, we have calculated electronic energy band structures of different variants of the Te atoms substituting metal atoms in such structures and compared with our previous results for the case when Te atoms substituted the chalcogen ones. 5 An impact of Te atomic positions was analyzed.

Method

The heterostructure considered was composed of MLs of two different materials, namely WS 2 and WSe 2 . We analyzed 2H phase with the space group P6 3 /mmc as the most stable polymorphic modification for this class of hexagonal layered two-dimensional crystals. 6 The layers were arranged in accordance with the bulk material. Electronic energy band structure and densities of states (DOSs) for WS 2 /WSe 2 heterostructure were calculated using the PAW-LDA approximation 7 within the density functional theory realized in the VASP code. 8 Characteristics of the heterostructures were modeled using optB86b-vdW optimized exchange functional of J. Klimeš,9 describing the van der Waals interaction between the monolayers, implemented in VASP code, which gives the structural parameters very close to experimental values.

We used 2×2 translational cell. The thickness of the vacuum spacer between the repeating layers was 15 Å. Three different positions of Te atoms were considered as illustrated in Fig. 1: 1) one Te atom in WS 2 layer; 2) one Te atom in WSe 2 layer; 3) Te atoms in both layers. These compositions correspond to 25 at.%, 25 at.%, and 50 at.% of Te concentrations, respectively. Atomic relaxation via minimization of the total energy of the heterostructures was stopped when the forces acting on atoms became less than 0.01 eV/Å. The energy cutoff was fixed at 380 eV. The 9×9×2 Γ-centered grid of k-points was used.

Results and Discussion

The electronic band structures of WS 2 /WSe 2 heterostructure and total DOSs for all the cases considered are presented in Fig. 2 and Fig. 3, respectively. It is obvious, that substitution of W atoms by Te ones strictly reduces the band gap, leading to an appearance of the electronic states at the Fermi level when Te substitutes Se and, thus, to a metallic behavior. This differs from the variant, when chalcogen atom was substituted, as described in our previous paper. 5 In that case the gap was reduced as well, but the heterostructure preserved its semiconductor properties. However, the most interesting thing occurs, when Te atoms are located in both layers. We observe the appearance of the energy gap and recovery of semiconducting properties (Fig. 2с), whereas the states near the Fermi level are determined by p-electrons of both S and Se atoms. Contribution of Te atoms in the gap forming states is quite negligible in all the cases and is well-observed only for far-lying states.

Conclusion

Substitution of W atoms by Te ones in WS 2 layer in WS 2 /WSe 2 heterostructure strictly reduces its energy band gap, but preserves the semiconducting properties. Analogously, the heterostructure with Te atoms both in WS 2 and WSe 2 layers possesses a small band gap, whereas the substitution of W atoms by Te ones only in WSe 2 layer leads to an appearance of new states at the Fermi level and to metallic properties.

2 AFig. 1 .

 21 Fig. 1. Top and side view of WS2/WSe2 heterostructure (a) and the heterostructure with three different positions of Te atoms (b-d). Dark small balls represent W atoms, light small balls stand for chalcogen atoms (S atoms in bottom layer, Se atoms in top layer), large dark balls represent Te atoms.

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 2. Electronic energy bands in WS2/WSe2 heterostructures with (a,b,c) and without (d) Te atoms substituting W ones. Zero on the energy scale corresponds to the Fermi level. The partial DOSs of undoped WS 2 /WSe 2 heterostructures are presented in Fig. 3. The main impact on the band forming states is determined by d-states of W and p-states of chalcogen atoms (s-states are not shown). Calculation of partial DOSs (not shown here) gave us a detailed information how the states are redistributed upon the substitution of W atoms by Te ones. When Te atom is located in WS 2 layer, the states near the Fermi level are determined by d-electrons of W and p-electrons of S. The substitution of W atom by Te one in WSe 2 layer leads to an appearance of p-electrons of Se and d-electrons of W at the Fermi A C C E P T E D M A N U S C R I P T Accepted manuscript to appear in IJN

Acknowledgments

This work was supported by the project No F17MC-017 of BRFFR and Belarusian State Scientific Program "Functional and Engineering Materials, Nanomaterials".