Review—Electronic Properties of 2D Layered Chalcogenide Surfaces and Interfaces grown by (quasi) van der Waals Epitaxy

The bulk electronic structure of layered transition metal dichalcogenides is described in Refs. 49–51. A detailed discussion of interlayer interactions will be given below). Electronic interactions across the van der Waals-gap, or across a heterointerface with a van der Waals-surface, are due to electronic states, which orbitals are directed perpendicular to the layers. These states will be referred to as z-states. In addition to the z-states there are pure x, y-states^a but also xz, yz-states according to different combinations of the chalcogen p_x and p_y states. In Fig. 2 the x, y-states are labelled as x⁺-states and the xz and yz-states as x⁻-states.^b Within the P6₃/mmc space group, which is appropriate for the group VIb transition metal dichalcogenides (except WTe₂), the x⁺-states have the same symmetry properties as the metal ${d}_{{x}^{2}-y2}$ and d_xy-states and the x⁻-states have the same symmetry as the metal d_xz and d_yz-states (for more details see Ref. 52). The x⁺, x⁻ and the corresponding z-states are symmetrized according to the irreducible representations of the space group. The symmetry labels identifying these irreducible representations at the center of the Brillouin zone Γ are also given in Fig. 2.

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Mattheis⁴⁹ and Coehoorn et al.⁵¹ give a detailed description of the electronic states of group VIb TMDCs close to the energy gap. As an illustration a band structure calculation for WS₂ based on density functional theory using the scalar relativistic, self-consistent augmented sperical wave (ASW) method is shown in Fig. 3,⁵² together with the hexagonal Brillouin zone. Symmetry labels according to electronic states described in Fig. 2 are given for Γ and A. The valence band maximum ${{\rm{\Gamma }}}_{4}^{-}$-state is located at the center of the Brillouin zone and is formed by metal ${d}_{{z}^{2}}$ and chalcogen p_z-states⁵¹ (for more details see below). Unoccupied conduction band states at Γ are 2–3 eV above the valence band maximum and formed only by x⁺ and x⁻-states. The conduction band minimum is located on the line connecting Γ and the Brillouin zone boundary at K. Different metal and chalcogen orbitals contribute to this state. However, the contribution of z-states to the conduction band minimum is rather small.⁵¹

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There is considerable contribution of z-orbitals to conduction band states of layered Mo and W dichalcogenides for wave vectors off the hexagonal symmetry axis (k_∥ > 0). This is because non-hybridized ${d}_{{z}^{2}}$ and p_z-states will disperse upwards in energy,^49,53 when the parallel component of the wave vector k_∥ is increased from zero.

A discussion of the contribution of z-states to the conduction band requires a more detailed consideration of the metal ${d}_{{z}^{2}}$ and chalcogen p_z-states. In Fig. 4 the occupied electronic states at Γ are given in the order of their binding energy. There are two pairs of ${{\rm{\Gamma }}}_{1}^{+}$ and ${{\rm{\Gamma }}}_{4}^{-}$-states, which have intralayer bonding character with respect to the chalcogen p_z-orbitals. These orbital combinations have the same symmetry as the metal ${d}_{{z}^{2}}$-states. As a consequence of identical symmetry, hybridization between p_z and ${d}_{{z}^{2}}$ occurs at ${{\rm{\Gamma }}}_{1}^{+}$ and ${{\rm{\Gamma }}}_{4}^{-}$. The two pairs of states are different with respect to metal-chalcogen bonding. Bonding combination of p_z and ${d}_{{z}^{2}}$ leads to the high binding energy ${{\rm{\Gamma }}}_{1}^{+}$ and ${{\rm{\Gamma }}}_{4}^{-}$-states. The valence band maximum is formed by a metal ${d}_{{z}^{2}}$-chalcogen p_z antibonding ${{\rm{\Gamma }}}_{4}^{-}$-state, which has been pointed out first by Coehoorn et al.⁵¹ Intralayer antibonding p_z-states (${{\rm{\Gamma }}}_{3}^{+}$ and ${{\rm{\Gamma }}}_{2}^{-}$) do not hybridize with metal ${d}_{{z}^{2}}$ because of the missing horizontal mirror plane. Energetically they are situated approximately between the ${d}_{{z}^{2}}$-p_z bonding and antibonding combinations.

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The ionization energies of the chalcogen p_z and the metal ${d}_{{z}^{2}}$-orbitals^c are different, leading to different contributions of metal and chalcogen orbitals to the two pairs of ${{\rm{\Gamma }}}_{1}^{+}$ and ${{\rm{\Gamma }}}_{4}^{-}$-states. The metal-chalcogen bonding combinations at higher binding energies have larger chalcogen p contributions, while the low binding energy states have larger metal d contributions.

As already mentioned above, the z-states should disperse upwards in energy when k_∥ increases from zero.^d This is not readily identified in the band structure (Fig. 3) since hybridization between z and x⁺ (and x⁻) states occurs for ${k}_{\parallel }\ne 0$, which leads to a forbidden crossing of energy bands. This hybrization between (mostly) ${d}_{{z}^{2}}$ and ${d}_{{x}^{2}-{y}^{2}},{d}_{{xy}}$-states is the origin of the energy gap in TMDCs.⁴⁹ Nevertheless z-states have to be expected to contribute to the conduction band. As outlined in the preceeding paragraph, the contribution of chalcogen p-orbitals to the electronic states decreases with lower binding energy and the contribution of metal d-orbitals increases. Upward dispersing z-states should therefore reduce their chalcogen character. Thus, the contribution of z-states to the conduction bands should thus be mostly due to metal ${d}_{{z}^{2}}$-states. This general argument is supported by detailed calculations of orbital contributions to the electronic states of MoSe₂ given by Coehoorn et al.⁵¹ While metal ${d}_{{z}^{2}}$-states contribute to the conduction band minimum and considerably to the slightly higher K₅ conduction band state, no significant contributions of chalcogen p_z-orbitals to the conduction band states are mentioned.

To summarize this section the contribution of z-orbitals to the electronic states of TMDCs close to the energy gap have been identified. At the center of the Brillouin zone all valence band states with binding energies 0–2 eV are derived from chalcogen p_z and metal ${d}_{{z}^{2}}$-orbitals. Contributions of z-orbitals to conduction band states close to the energy gap exist only for k_∥ > 0 and are mainly due to metal ${d}_{{z}^{2}}$-orbitals.

Although the van der Waals-surfaces of the III-VI-compounds InSe and GaSe are also formed by an hexagonal array of close-packed and chemically saturated selenium atoms as in the case of the TMDCs, their electronic structure is significantly different. This is due to the replacement of the transition metal atom by two group III metal atoms. A detailed description of the electronic structure of III-VI-compounds is given in the literature.^55–57 More details will be discussed below. InSe is a direct gap semiconductor with valence band maximum and conduction band minimum located at Γ for the β (2H) polytype, or at Z for the γ (3R) polytype, respectively. The difference in electronic structures of the various polytypes is mainly explained by the different extension of the unit cell along c. The energy bands of the different polytypes can be mapped onto each other by suitable folding procedures. If this is done, almost identical electronic structures are found for the different polytypes.⁵⁷

In the simplest description of the electronic structure of layered III-VI compounds the valence band maximum is derived from chalcogen p_z-orbitals and the conduction band minimum from metal p_z-orbitals (see also Fig. 27). However, as described for the TMDCs, hybridization between chalcogen and metal states is important. More detailed results for InSe are reported by Gomes da Costa et al.⁵⁷ According to them, the valence band maximum is composed of 70% Se p_z and 30% In p_z-orbitals, while the conduction band minimum is composed of Se s (37.5%), Se p_z (25%) and In s-orbitals (37.5%). Significant contributions of chalcogen z-states to both the valence band maximum and the conduction band minimum exist for the III-VI compounds InSe and GaSe. Both band extrema are found at k_∥ = 0.

In summary, the bulk electronic band structure of 2D layered chalcogenides show a small but clearly existing dispersion of the electronic states in the direction perpendicular to the van der Waals surface, which is due to the electronic coupling of the different p_z and ${d}_{{z}^{2}}$ states (see Figs. 2–4). These electronic states are also involved to different degrees, depending on lattice mismatch, in the electronic hybridization across the van der Waals gap when heterostructures are formed.

The weak interaction across the van der Waals-gap is the conceptual basis for the growth of epitaxial layers of one type of layered compound on a layered chalcogenide substrate (2D/2D epitaxy, see Fig. 5). The interactions between two van der Waals-surfaces of different layered compounds is similar to the interlayer interactions in a layered crystal. As a consequence epitaxial films may be grown combining such van der Waals-compounds even when the lattice mismatch is very large. The concept and term van der Waals-epitaxy (vdWe) have been introduced by Koma et al., who first studied the deposition of NbSe₂ on the (0001) van der Waals-surface of MoSe₂ single crystalline substrates.⁴⁸ The prepared interfaces and their electronic properties have been summarized before.⁶

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The growth and nucleation of van der Waals-epitaxy films has been studied with different techniques (see Ref. 6 and references therein). Two examples are shown in Fig. 5. Epitaxial growth and orientation of the overlayer is obvious from low-energy electron diffraction (LEED). The hexagonal diffraction pattern of the growing overlayer is superimposed and aligned to the substrate pattern for intermediate film thicknesses.⁵⁸ Although the epitaxial relation is affected by the substrate only for very large lattice mismatch,⁶ the nucleation might be different as shown by the STM of InSe films deposited on GaSe, MoTe₂ and highly oriented pyrolytic graphite (HOPG) (Fig. 5). These differences are clearly related to the different lattice constants; We attribute the different nucleation behavior to the different strength in the electronic coupling of the overlayer to the various substrates.⁶

The azimuthal orientation of the epitaxial layer to the substrate, which in van der Waals-epitaxy comes along without evidence for an in plane lattice relaxation, is a typical characteristic of the fundamental nature of its orientational interactions. The detailed analysis of the electronic structure of layered compounds proof that there is a small but non-negligible electronic overlap of the electronic states across the van der Waals-gap, which must depend on the orientational arrangement. In the layered chalcogenides the so-called van der Waals gap is formed between the chalcogen layers of two adjacent sandwiches. The chalcogen atoms of the top sandwich unit are situated in threefold hollow sites formed by the chalcogen atoms of the underlying sandwich. In this geometrical arrangement the chalcogen atoms form weak bonding interactions by the overlap of their p_z orbitals with orbitals of the metal atoms of the underlying sandwich unit (see Fig. 4). Due to the lattice mismatch and the specific growth mode in van der Waals-epitaxy it is not possible for all chalcogen atoms to occupy threefold hollow sites. In contrast, some chalcogen atoms of the epilayer film must also sit ontop of substrate chalcogen atoms leading to height modulations. Ohuchi and Parkinson^59,60 observed Moiré-like structures for MoSe₂ on MoS₂ using STM studies, which has been explained by such height undulations. Moiré patterns have also observed for few other material combinations^61,62 and have been analyzed theoretically by Kobayashi.^63,64 Tiefenbacher et al. also observed Moiré like pattern by LEED (Fig. 6) where the I-V analysis also favours a height undulation of the overlayer.⁶⁵ The LEED-pattern associated with the undulation fades out after 2–3 layers and transforms to a standard hexagonal pattern as shown in Fig. 6 with increasing film thickness. Moiré-like LEED-patterns have also been observed for very slowly prepared ultra thin films of InSe deposited by MBE on TiSe₂.⁶⁶ A height undulation should in principle occur for all lattice mismatched vdWe-systems but has, unexpectedly, only been observed in a few substrate/-film combinations. The reason is not clear yet, but can most probably also be related to small differences in the electronic coupling across the vdWe-heterointerface (see also Refs. 63 and 64).

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After the introduction of van der Waals-epitaxy it has been shown that epitaxial layers with large lattice mismatch can also be grown when layered chalcogenides are combined with three-dimensional materials. In Fig. 7 the typical 3D/2D material combinations of interest are schematically sketched. A precondition of such interface growth is in most cases the growth of an hexagonally arranged close packed layer of the 3D material on top of the hexagonally arranged substrate layer surface. For example fcc metals like Cu, Ag, and Au may form epitaxial (111) oriented films on layered chalcogenide (0001) surfaces (2D/3D; used convention: substrate/overlayer).^67,68 Epitaxial layered chalcogenide films may also be grown on hexagonally close packed (111)-surfaces of cubic semiconductor substrates as Si(111):H or GaAs(111) (3D/2D).^69,70 Oriented growth has also been observed for II-VI semiconductors on layered chalcogenide (0001)-surfaces,⁷¹ although strong clustering of the overlayer occurs. These type of heteroepitaxy was named quasi-van der Waals-epitaxy (qvdWe) as the heterointerface was formed between the van der Waals (0001)-surface of the layered compound and a surface plane of a non-layered material, e.g. the (111) plane of fcc compounds, which contains hexagonally close packed atoms.

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Already at the very beginning of quasi-van der Waals-epitaxy research it was considered to use this approach as buffer layer for conventional lattice mismatched semiconductors. Therefore, different 3D materials (metals as well as semiconductors) have been combined with 2D layered chalcogenides as substrates aiming at 3D/2D, 2D/3D and also 3D/2D/3D combinations (see Fig. 7). As first quasi-van der Waals-epitaxy interfaces, metal/semiconductor combinations were prepared and investigated (see Ref. 72 and references therein). For non-reactive interfaces, atomically abrupt metal/semiconductor interfaces are evidently formed.^68,73–77 For noble metals such as e.g. Ag deposited on WSe₂ (0001) the LEED-pattern shows a superposition of undisturbed substrate and overlayer diffraction spots of the Ag film with the 3-fold symmetry of the (111)-plane⁶⁸ (see Fig. 8) As in the case of vdWe interfaces no evident lattice stress or strain is observed for the deposited film. The perfect orientation and high crystallinity of Ag (111) is also evident from the typical Shockley type surface state as identified by angle-resolved valence band spectroscopy.⁷⁵ But, different to vdWe, island growth is usually obtained in qvdWe as for metal films, which is readily identified with STM measurements,^78,79 but also for 3D semiconductor overlayer growth (see below).

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Already in the last century, a lot of different quasi-van der Waals-epitaxy heterointerfaces have been prepared by numerous groups (for a summary see Ref. 6). Also 2D layered chalcogenides were deposited onto 3D substrates, which was also first demonstrated by Koma's group using a lattice mismatched (17%) hetero structure by deposition of MoSe₂ on perfectly F-terminated CaF₂(111).⁸⁰ Also the growth of GaSe on GaAs substrates with different surface orientations have been reported,^81–84 but the structure of the interface has not been identified.⁸⁰ Ohuchi et al. proposed the formation of a GaSe interface layer on GaAs(111)⁸¹ whereas Tatsuyama et al. reported a layer-by-layer growth of GaSe on As or Ga terminated GaAs(111) surfaces.^82,84 Interestingly, it also possible to grow (0001) oriented GaSe films on GaAs(100) surfaces despite the completely different surface symmetry^82–84 assuming the formation of a Ga₂Se₃ interface layer. GaSe layers grow onto slightly misoriented GaAs(100) surfaces with a considerably inclined c-axis.^85,86 As these examples indicate the qvdWe grown heterointerface GaSe/GaAs is not atomically sharp as originally assumed but may contain interface layers depending on the GaAs surface orientation, pretreatment and growth conditions. This is also observed for the growth of GaSe on Si(111) surfaces, which have been investigated in very detail (see below).

Before discussing this important heterostructure, we like to present some other interfaces applying 3D semiconductor growth onto layered chalcogenide (0001) surfaces. Such interfaces are a precondition for the manufacturing of technologically intriguing device structures using 2D buffer layers in lattice mismatched 3D systems. The first reports on 3D/2D/3D systems have been published by Palmer et al.^87–89 showing GaAs growth on a thin GaSe buffer layer on As-terminated Si(111). The 3D GaAs grows as strongly clustered films with large azimuthally oriented islands of approx. 200 nm in diameter. The deposition of 2–6 compounds on layered substrates has also been demonstrated by Löher et al.^71,90–92 On MoTe₂ a (0001)-oriented film of CdS (Wurtzite structure) was deposited (mismatch 17%) (see Fig. 9). Similar results have been obtained for CdTe, ZnSe and CdS deposition on WSe₂, MoTe₂ and InSe (0001).^71,91,92 The crystallites are all azimuthally oriented with respect to the substrate showing their intrinsic lattice constants. In most cases a strong clustering of the growing film is observed (see e.g. a typical STM images obtained for ZnSe/GaSe interfaces as shown Fig. 9).

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Due to the higher surface tension of the 2–6 compound overlayer relative to those of the van der Waals-surfaces of the layered chalcogenides a Vollmer-Weber growth mode is expected and also observed for most cases. Remarkable in this context is the growth of CdS on the layered compound InSe. Löher⁹⁴ achieved oriented epitaxial growth even at room temperature and also initial layer-by-layer growth. But, the CdS film starts to roughen and forms facets of the S-terminated (111) surface toward vacuum for higher coverages. Therefore, additional experiments on the application of InSe buffer layers between Si and CdS or ZnSe have been performed, also showing crystalline orientation^95,96 and photoactivity of the deposited ZnSe layer.⁹⁷ In summary, the growth of highly crystalline qvdWe-heterointerfaces have already been proven for a number of combinations (2D/3D, 3D/2D, 3D/2D/3D). These studies allow to investigate the electronic properties of the formed layers and interfaces in very detail, as will be shown later in this contribution.

Van der Waals-epitaxy therefore offers the possibility to use layered materials as buffer layers in three-dimensional epitaxy between lattice mismatched materials (3D/2D/3D) but also for 2D quantum sized heterostructures. Because of the weak interactions across van der Waals surfaces, this should enable the growth of fully relaxed multilayers of different substrates making use of their intrinsic 2D electronic properties. Therefore, an in depth understanding of the electronic properties of van der Waals-epitaxy interfaces is required, which depends on the crystalline quality of the interface arrangement and the electronic coupling strength. With van der Waals-epitaxy it is, in principle, possible to combine electronically dissimilar materials under defined conditions. In combination with nanofabrication, which has also been shown already at the early times with layered materials using different STM and AFM techniques,^98–107 a large variety of new devices and applications should be within reach. This is a main driver of the recent renewed interest in van der Waals type heterinterfaces. However, more extensive work is needed to optimize growth conditions in order to obtain heterodevices with well-defined interfaces. Therefore, the (q)vdWe 2D heterostructures provide reference data on interfacial coupling across the van der Waals gap.

Silicon is still the most important semiconductor material in microelectronics. Because of its indirect bandgap it can hardly be used for optoelectronic applications. As van der Waals-epitaxy may provide ultrathin buffer layers for lattice mismatched epitaxy, one might dream of growing epitaxial, optoelectronically active semiconductors onto qvdWe buffer layers grown on silicon surfaces, which can integrate the optoelectronic active III-V (or II-VI) materials into the silicon technology. For this approach, the interface Si/layered chalcogenide needs to be investigated. In particular the Si/GaSe interface has so far been one of the most intensively studied interface in quasi-van der Waals-epitaxy because of its outstanding properties (see Ref. 6 and references therein). These studies focus on the Si(111) surface orientation, since rotational symmetry is preserved in van der Waals-epitaxy and therefore best results should be obtained for hexagonal layered materials grown on Si(111).

The peculiar interface structure of Si(111)/GaSe was determined by the group of Eddrief using gracing incidence X-ray diffraction¹⁰⁸ and X-ray standing waves¹⁰⁹ in 1997. The proposed structure has been later also confirmed by photoelectron diffraction.¹¹⁰ The structure of the surface is shown in Fig. 10. The outermost surface is basically identical to a GaSe van der Waals-surface. Each Si surface atom bounds to one Ga atom, while each Ga forms one Si and three Se bonds. Each Se atom binds to three Ga atoms and exposes a doubly occupied lone pair orbital toward vacuum. The three Ga valence electrons are shared with the selenium (2/3 per bond) and Si (1 per bond). Four out of six Se valence electrons are shared with Ga (4/3 per bond). The remaining two Se valence electrons occupy a lone pair orbital. Obviously the electron counting rule¹¹¹ is fulfilled and all chemical bonds are saturated. The Ga–Se surface layer has a structure which is identical to a Se-Ga–Ga–Se unit layer of GaSe single crystals cut across the Ga–Ga bond. A hypothetical cut half-sheet layer of GaSe has an hexagonal array of singly occupied Ga dangling bond orbitals with a lattice constant of 3.74 Å, which matches closely to an unreconstructed Si(111) surface with a surface atom distance of $\sqrt{2}/2\cdot 5.43\,\mathring{\rm A} =3.84\,\mathring{\rm A}$.

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The Si(111)/GaSe interface can be prepared in different ways. The heterojunctions prepared by qvdWe has extensively been studied by many groups.^{70,88,108,109,112–119} In the beginning, most investigations started with H-terminated Si(111) surfaces assuming a quasi-van der Waals-epitaxy ontop of the Si–H surface bonds.^70,114 In the meantime the structure of the interface has been investigated by different techniques and for differently prepared Si(111) substrate surfaces. As starting point either hydrogen terminated Si(111)-1 × 1:H surfaces or Si(111)-7 × 7 surfaces can be used. The latter is stable only in ultrahigh vacuum. GaSe deposition can be either performed by separate evaporation of Ga and Se, or also by direct congruent evaporation of GaSe. All procedures have been applied and lead to the growth of epitaxial GaSe films. For higher substrate temperatures and starting from reconstructed Si surfaces, such as Si(111)-(77), a Si–Ga–Se interlayer as shown in Fig. 11 is evidently formed at first.^108,109 On this interface layer GaSe(0001) grows by homoepitaxy. At lower temperatures, the Si(111):H surface might be preserved. The deposition of GaSe on As terminated Si(111) surfaces was reported by Palmer et al. as an alternative to prepare 3D/2D/3D heterodevices.^87–89

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GaSe surface terminations have also been studied on other Si surfaces.^121–123 A van der Waals surface termination with a distorted GaSe half-sheet resulting in crystalline growth of GaSe(0001) has also been observed for Si(110), while on Si(100) no unique orientation of film growth has been achieved. This behavior can be explained by the respective Si surface structures, which contains one dangling bond per surface atom for (111) and (110) orientation and two dangling bonds per surface atoms for (100) orientation. In the following sections we will concentrate on the electronic properties of the Si(111):GaSe surface. No detailed investigations of the other surface orientations exist so far.

Also InSe was deposited onto Si(111):H as substrate for the subsequent deposition of 3D semiconductors.^95,96 As for the GaSe/GaAs interface, the preparation of quasi-van der Waals-epitaxy InSe/Si heterointerfaces results in more complex interface structures as originally expected and as shown in Fig. 10. Again the pretreatment of the substrate and the deposition conditions seem to play a major role. Additional work is needed for most of the 2D/3D qvdWe-systems investigated so far, to clarify the interface structure, nucleation and growth properties in detail. The chemical composition and structural arrangement across the interface is crucial for the interfacial electronic structure.

The van der Waals-epitaxy of layered metal chalcogenides on graphite substrates leads to films, which are electronically almost decoupled from the substrate. This was first demonstrated for the growth of InSe films on highly oriented pyrolytic graphite (HOPG).¹²⁴ In Fig. 12 both the experimental results and a schematic representation of the observed phenomena are presented. Free-standing single layer films, i.e. films whose electronic states do not couple to those of the substrate, should have a different electronic structure compared to bulk materials, because of the missing interlayer interactions. The topmost valence levels, e.g., which are derived mainly from the p_z-orbitals, can only form a ${{\rm{\Gamma }}}_{1}^{+}$-state in the single layer (see Figs. 2 and 12b). In contrast a double layer film should form an interlayer bonding (${{\rm{\Gamma }}}_{1}^{+}$) and an interlayer antibonding (${{\rm{\Gamma }}}_{4}^{-}$) combination. These two states differ from the ${{\rm{\Gamma }}}_{1}^{+}$ and ${{\rm{\Gamma }}}_{4}^{-}$-states of bulk materials where they form extended Bloch states and are the extremal states of a continuous energy band. By gradually increasing the film thickness from submonolayer coverage the transition from atomic-like single layer states to molecule-like double layer states to bulk energy bands can be observed, if the electronic states are not strongly modified by the substrate. Such a transition has been observed for a number of layered chalcogenides during growth on graphite substrates.^6,52,124,125 Obviously the films are electronically (almost) decoupled from the substrate. However, complete decoupling does not occur. The remaining substrate/film interactions are strong enough to align the layers to the substrate, which is evident from STM (see Fig. 5) and also from LEED when single crystalline graphite substrates are used.⁶

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The possible absence of coupling of electronic states at interfaces determines whether quantized electronic energy levels are formed in the growing layer. Such quantized energy levels are well known for low-dimensional semiconductor structures.^126,127 Energy states are localized within a low-dimensional structure, if the surrounding medium has an energy gap in the corresponding energy range. Electronically decoupled films also lead to the observation of quantized energy levels in thin overlayers with photoemission. Pronounced structures have particularly been reported for Ag on various substrates.^128–132 Surprisingly, for Ag films deposited on Si(111) quantized energy levels are observed, although the substrate has no gap in the given energy range.^128,132 In this case the lattice mismatch between substrate and film remains as the only explanation for the observation of the localized energy levels. Lattice mismatch evidently leads to a partial reflection of the Bloch wave functions at the interface.^e

For van der Waals-epitaxy interfaces, lattice mismatch is also present and in general rather large. One might therefore expect that localized energy levels always show up in the growing films, which would be evident from the thickness dependent changes in electronic structure as described in Fig. 12. But so far such transitions have been found experimentally only, when graphite substrates are used. There are further indications of localized energy levels in GaSe films grown on Si(111),¹²¹ but most van der Waals-epitaxy and quasi-van der Waals-epitaxy interfaces show valence band spectra, which are a superposition of bulk substrate and overlayer valence states (see Ref. 6 and references therein). Therefore another mechanism has been discussed as a precondition of electronically decoupled films in van der Waals-epitaxy¹²⁴: the differences in the electronic structure along z (Γ-A direction of the Brillouin zone, Fig. 3), which is illustrated for InSe, WS₂ and graphite in Fig. 13.

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Any interfacial wave function resulting from a coupling of electronic states of the corresponding contact phases will extend on both sides of the interface and needs to follow the local symmetry restrictions. Therefore only such electronic states can couple, which have the same symmetry in both materials. The symmetry labels are indicated in Fig. 13. Although all three materials belong to the same space group and therefore generally have wave functions of the same symmetry, the respective electronic z-states of graphite have very different binding energies. The z-states, which are responsible for electronic coupling, are the 1⁺, 4⁻, 2⁻, and 3⁺-states (see also Fig. 2). For a large energy difference the electronic overlap will be significantly reduced, which, as a consequence, leads to a decoupling of electronic interlayer interactions. In van der Waals-epitaxy of layered metal chalcogenides the strongest differences in the electronic structures between substrate and layered metal chalcogenide exist for graphite and silicon substrates explaining the observation of electronically decoupled states particularly for these combinations.

The arguments concerning the relative contribution of electronic and structural mismatch are similar to those outlined for the formation of the interface dipole layers at (quasi-) van der Waals-epitaxy interfaces. A final conclusion on the relative importance of these two effects for electronic decoupling cannot be given yet. It is, for example, not clear yet why no indications for electronically decoupled films have so far been observed for the growth of II-VI compounds on van der Waals-surfaces, which also exhibit pronounced electronic structure differences. The reason is probably given by the three-dimensional growth mode of the films, which may lead to too large islands before significant signals of the growing film show up in the photoemission spectra. In addition, the strong valence band emissions of the layered metal chalcogenides make the observation of changes in the electronic structure of growing overlayers more difficult than for graphite substrates, which show no transitions in the corresponding energy regime (see Fig. 12a). It is clearly evident that more detailed experiments are needed with systematic variations of lattice mismatch and electronic structure. But such experiments are difficult and time consuming to perform, as the preparation conditions have to be optimized first for every system.

Getting more detailed insights into the electronic coupling at van der Waals-epitaxy interfaces definitely also requires assistance from theoretical investigations. However, because of the incommensurate interface structures, such calculations are very difficult. Nevertheless, the factors involved in electronic coupling are generally important, since they determine not only the electronic structure of growing overlayers, but most likely also nucleation and initial film growth. The coupling of substrate and overlayer wave functions at the interfaces is also expected to affect charge transport across the interface. These assumptions are indicated by Fig. 5, where different nucleation is observed when InSe is grown under the same conditions on the van der Waals-surfaces of GaSe, MoTe₂ and graphite. However, more systematic investigations of the nucleation in dependence on the differences in electronic structure and lattice mismatch between overlayer and substrate are required to verify the underlying dependencies.

Of further fundamental interest is the development of electronic band alignment in the presence of electronically decoupled films. In the case of InSe films one might expect that the energy of the atomic-like single layer state is approximately intermediate between the molecule-like double layer bonding and anti-bonding states. In contrast, the experiment shows a very similar binding energy of the single layer and double layer ${{\rm{\Gamma }}}_{1}^{+}$-states (see Fig. 12 and Ref. 124). This has tentatively been attributed to thickness dependent changes of the electronic interface dipole.¹²⁴ A in-depth understanding of this phenomenon might probably also offer an intuitive approach to dipole potential drops at semiconductor interfaces.

The electronic decoupling of van der Waals-epitaxy films on graphite substrates offers the unique possibility to study the electronic structure of single layers of layered metal chalcogenides. The transition from single layer to single crystal states is already obvious from the normal emission spectra shown in Fig. 12, which have been taken from InSe films deposited on highly oriented pyrolytic graphite (HOPG). Interlayer interactions of layered metal chalcogenides can be studied in more detail if the complete electronic structure of single layers and single crystals are known. Full k-resolved electronic structure measurements are required for this task. Single crystalline films cannot be prepared on HOPG but only on single crystalline graphite. Unfortunately, LEED pattern taken from InSe and SnS₂ films deposited onto single crystalline graphite substrates show ring-like diffraction patterns.⁶ This corresponds to a lack of azimuthal orientation, which is most likely related to the large lattice mismatch in combination with the weak substrate/film interactions.

Highly azimuthally oriented films of WS₂ have been prepared on single crystalline graphite.^52,125 The films have been deposited using metal-organic van der Waals-epitaxy (MOvdWE) using W(CO)₆ and S₂ as precursors.^134,135 The latter can be obtained by thermal decomposition of pyrite FeS₂. Although some residual ring-like diffraction intensity remains in LEED, it has been possible to determine k-resolved valence band spectra for the ΓM and ΓK directions of the Brillouin zone.^52,125 Linearly polarized synchrotron light has been further employed to investigate the polarization dependence of the photoionization selection rules, which was used to identify the symmetry of experimentally observed transitions for a comparison with theoretical band structure calculations.

Angle-resolved band structures for single layer WS₂ along ΓM and ΓK are shown in Fig. 14. The data are compared to an experimental band structure of a WS₂ single crystal in (a) and (b). The experimental single layer and single crystal band structures are almost identical. Remaining differences, as the missing splitting of topmost band near Γ, are explained by the absence of interlayer interactions and by photoionization cross-sections.⁵² In contrast to the single crystal, the valence band maximum of the single layer is located at the K point of the Brillouin zone as the single crystal (${{\rm{\Gamma }}}_{4}^{-}$) valence band maximum state is absent because of missing interlayer interactions. With this change, a direct optical transition of a single layer of WS₂ results as the conduction band minimum of the semiconducting transition metal dichalcogenides is also located at the K point of the Brillouin zone.^50,51 It is noted that the electronic states at the conduction band minimum are not affected by the missing interlayer interactions, as the corresponding states are formed by transition metal d_xy and ${d}_{{x}^{2}-{y}^{2}}$ states, which do not overlap across the van der Waals gap. The transition from a direct to an indirect gap has been observed nearly 20 years later for MoS₂ by photoluminescence.¹³⁶

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Figures 14c and 14d shows a comparison of experimental single layer and single crystal band structures with theoretical band structures along ΓK. The theoretical bands are calculated using density functional theory in the local density approximation (LDA) and the scalar relativistic augmented spherical wave (ASW) method with linear muffin tin orbitals (LMTO) (for more details see Ref. 52). The agreement between experimental and theoretical band structure is very good for single crystalline WS₂ as shown in Fig. 14c. In contrast, there is less good agreement for the single layer (Fig. 14d). Obviously the calculated band structures show differences between single layer and single crystal, which are not observed in the experiment. This has been attributed to the atomic positions used in the calculation.⁵² As no structural data exist for the single layer, atomic positions identical to those of the single crystal have been assumed. But smal structural relaxations of the atoms in the absence of interlayer interactions might account for the observed differences between experiment and theory.

To check if relaxation occurs, band structure calculations of single crystal and single layer WS₂ including optimization of atomic positions have been performed.¹³⁷ In this case band structures are calculated using the CASTEP program, which employs pseudopotentials and a plane wave basis set. No evidence for relaxation is deduced from these calculations. Furthermore, the band structures calculated for single layer and single crystal are very similar and also agree with experiments as shown in Fig. 15. Therefore, it is assumed that the differences observed for the ASW calculations are most likely related to the calculational technique. This is supported by a calculation of MoS₂ and MoSe₂ band structures,⁶⁴ which also reveal differences depending on the calculation method.

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This section describes the energy band alignment at interfaces between different semiconducting layered chalcogenides. The electronic properties of vdWe-heterointerfaces are always deduced in our studies from step-by-step deposited epilayer films analyzed by photoelectron spectroscopy after transfer in integrated cluster tools without breaking vacuum.^138,139 With this technique it is possible to follow changes in interface chemistry and surface potentials as a function of film thickness. The investigated interfaces show no indication of chemical interface reactions or adsorbates,⁶ which would modify the band alignment.^140–142

Because of their chemically saturated surfaces, a different interface behavior compared to three-dimensional semiconductors can be expected for layered materials. First studies of band alignment at van der Waals-epitaxy interfaces by photoelectron spectroscopy yield only very small interface dipole potentials, which are within the error limit of the experiment.^143,144 This suggests that the band alignment is governed by the electron affinity rule, as it is also observed for interfaces between organic compounds,^145,146 which are also characterized by weak chemical interactions.

As typical examples we present in Fig. 16 the semiconductor (quantum) well structures GaSe/InSe/GaSe¹⁴⁴ and SnS₂/SnSe₂/SnS₂.¹⁴⁷ In the first experiment we have used a single crystal of GaSe with the (0001) surface cleaved in UHV as the substrate and an InSe overlayer has been epitaxially grown in several steps, before GaSe has subsequently been deposited onto the InSe/GaSe layer sequence. The same approach was followed in the case of SnS₂/SnSe₂/SnS₂.

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For the GaSe/InSe/GaSe quantum well structure hexagonal LEED-patterns indicate epitaxial growth of the lattice mismatched systems during the whole experiment.¹⁴⁴ Very sharp SXPS core level spectra comparable to cleaved single crystals measured with synchrotron radiation further indicate the crystallinity of the grown films. The electronic properties of such interfaces are evidently not affected by large contributions of interfacial defects either related to non-stoichiometry or edge planes nor chemical adsorbates. Therefore, our experiments provide references data compared to interfaces prepared under ambient conditions or with defective van der Waals interfaces.

The band alignment is derived from the experimentally determined core level binding energies.^138,139 The resulting valence band offsets are identical for both quantum structures prepared (InSe/GaSe/InSe and GaSe/InSe/GaSe). Both interfaces follow the commutativity rule, which is established by the independence of band offsets on deposition sequence. The values of the conduction band offsets are calculated with the known band gaps. The magnitude of the interface dipole potential is only very small and thus the experimentally determined band alignment follows the electron affinity rule (EAR) within the experimental uncertainty.

A quantum well structure with an inverted ratio of valence band and conduction band offsets is obtained for the SnS₂/SnSe₂/SnS₂ vdWe-system.¹⁴⁷ Again we consider an isoelectronic and isostructural combination of materials. In this case also band bending and doping effects can be considered because of the larger thickness of the deposited layers. Again an experimentally determined energy band diagram can be constructed being close to the ideal expectations of 2D van der Waals heterointerfaces. The interface dipole potentials are also close to the expectation of the EAR. In contrast to the GaSe/InSe/GaSe system, where the different energy gaps result in different conduction band energies, a similar difference of the energy gaps of SnS₂ and SnSe₂ is mostly accommodated by a discontinuity in the valence band. This can be related to the fact that SnS₂ and SnSe₂ form a common cation (Sn) system, rather than a common anion (Se) system as in the case of the InSe/GaSe heterojunction. Apparently, the common anion (cation) rule for semiconductor band alignment^139,148 is also fulfilled for layered chalcogenides, at least for isostructural and isoelectronic systems.

In an extensive evaluation of band alignments at interfaces between semiconducting two-dimensional layered chalcogenides, Schlaf et al. could observe a small but systematic deviation of the band alignment from the electron affinity rule.^{6,58,149–151} The experimentally determined valence band offsets of a number of vdWe-interfaces is plotted in Fig. 17 vs the offsets expected using a vacuum level alignment and experimentally determined ionization potentials. It is evident that the band offsets show a small but systematic deviation from the electron affinity rule.

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The deviation has been qualitatively related to an electronic dipole potential formed in relation to the model of Ruan and Ching.¹⁵² In this model, an interface dipole is formed by tunneling of electrons from the valence bands into the conduction band of the contacting semiconductor. Therefore, its magnitude should depends on the deviation from a symmetric lineup, which is given by valence and conduction band offsets of the same magnitude. The interface dipole δ is then proportional to the deviation from symmetric lineup and given by:

$$\begin{eqnarray}&&\delta =K\cdot \left[{\rm{\Delta }}{E}_{{VB}}(\mathrm{EAR})-{\rm{\Delta }}{E}_{{CB}}(\mathrm{EAR})\right]\end{eqnarray} \tag{ 1 }$$

The proportionality constant is determined by fitting the experimental data to Eq. 1, revealing K = 0.09.^6,58,149,150 Equation 1 can also be fitted to experimental data of three-dimensional semiconductors, which results in a proportionality constant of approximately twice the value for the layered semiconductors. This difference can qualitatively be understood because the interlayer interactions (electronic coupling) at van der Waals-epitaxy interfaces is small compared to three-dimensional semiconductors, leading to less charge transfer and consequently to smaller double layer potentials. However, the results of Schlaf et al. also show that small electronic interface dipole potentials are also present at van der Waals-epitaxy interfaces. This is a clear proof of the general validity of the induced gap states concept. The smaller magnitude of the charge transfer at van der Waals-epitaxy interfaces is easily understood as a manifestation of the weaker overlap of the substrate and overlayer wave functions as discussed above.

Metals deposited onto layered semiconductors may exhibit different properties. Alkali metals generally intercalate into the van der Waals-gap of the layered materials if deposited at room temperature.^153–155 Transition metals generally lead to interface reactions because of their large heat of adsorption (see Ref. 156 and references therein). The sp-metals, i.e. metals without d valence electrons, often form non-reactive and atomically sharp interfaces with a varying tendency to three-dimensional island growth.^{67,68,72,74,78,156} It has been stated that the barrier heights for such metals on semiconducting layered chalcogenides follow the Schottky-limit, indicating a validity of the electron affinity rule.^68,72,74,157

Schottky barrier heights of In, Cu, Au, Pt, on p-type and n-type WSe₂ single crystals are shown in Fig. 18. In general a high work function metal gives a larger barrier height on n-type WSe₂ as expected. The barrier height of In on p-WSe₂ is given by Φ_{B, p} = 1.03 eV,^74,156 which agrees with the difference of the semiconductor ionization potential (I_P(WSe₂) = 5.2 eV) and the metal electron affinity (χ (In) = 4.2 eV). However, the other metals form p-type barrier heights, which are approximately 0.7 eV higher than the corresponding difference as indicated by the dotted lines in Fig. 18.

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This result is difficult to understand in terms of the interface dipole potentials discussed in terms of the induced gap states model.^158–160 Any of the described dipoles would lead to lower barrier heights compared to the electron affinity rule as a part of the contact potential difference is compensated by the dipole potentials induced by the formed interface states. In contrast, the barrier heights would follow the Schottky limit if the work function of WSe₂ is taken 0.7 eV larger than measured values (or the metal work function is 0.7 eV lower than the measured values).

This modification of barrier heights might be attributed to a lowering of the surface dipoles of the metals, which considerably contributes to the work function¹⁶¹: If the spill-out of wave functions at the interface is considerably reduced compared to the free surface, this would lead to a lower metal work function. To finalize this explanation of the data in Fig. 18 more systematic studies on Schottky barrier heights on layered semiconductors and, even more important, theoretical investigations would be required.

The large interface dipole potential is not the only surprising result obtained for Schottky barriers on layered materials. Schottky barrier heights of different semiconductors with the same metal (mainly Au or Al) are sometimes used to predict the band alignment at semiconductor heterojunctions.^162,163 This procedure is based on the transitivity of band alignments and related to the fact that band offsets and Schottky barriers are governed essentially by the same alignment of charge neutrality levels.^158,160,164 The p-type Schottky barrier height of Au on WSe₂ amounts to 0.76 eV.^75,156 Measurements of InSe/Au Schottky barrier formation give values ranging from 0.2–0.7 eV (see compilation of data in Ref. 6). Together with the valence band offset between InSe and WSe₂ of ΔE_VB = 0.4 eV¹⁶⁵ (see also Fig. 17) this corresponds to a deviation from transitivity of at least 0.45 eV. The barrier heights of the sequence Au/WSe₂/InSe/Au are illustrated in Fig. 19.

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There has been an attempt by Mönch to attribute the Schottky barrier heights of layered semiconductors to metal induced gap states using an electronegativity approach.¹⁶³ The results presented in Figs. 18 and 19 disagree with the suggestion by Mönch. His concept, that charge transfer at interfaces is strongly related to the difference in electronegativities, can be successfully applied to three-dimensional materials. But this approach is not appropriate for interfaces including the chemically saturated van der Waals-surfaces of layered materials, since no (strong) covalent chemical bonds can form at these interfaces.

Experimental results

The growth of II-VI semiconductors on layered metal dichalcogenides is characterized by a strong tendency of three-dimensional island growth, which is due to the strong chemical bonds within the II-VI compounds and the small adhesive energy on the van der Waals-surface. A lowering of the surface energy is hence achieved by island formation. For the use of layered materials as buffer layers in in 3D/2d/3D systems, preferentially single crystalline layers should be formed. This is generally not possible with island growth, since the formation grain boundaries has to be expected during island coalescence with increasing film thickness. There are also two different growth domains found on the surfaces, which are rotated by 180° (see Fig. 9). Although single crystalline growth of three-dimensional materials on the van der Waals-surface has not yet been achieved by using qvdWe approaches, it has been possible to investigate the electronic properties of these interfaces.

The band alignment at interfaces between layered semiconductors and II-VI compounds has been studied by Löher et al.,^{90,94,151,166} and by Wisotzki et al.¹⁶⁷ On transition metal dichalcogenides like MoTe₂ and WSe₂ large interface dipoles of the order of ∼1.1 eV for CdS and of ∼0.8 eV for CdTe are observed.¹⁶⁶ In addition to the interfaces studied by Löher et al., an interface dipole of 0.6–0.7 eV has been determined at the WSe₂/ZnSe interface. Energy band diagrams of the investigated interfaces are given in Fig. 20a. In contrast only small interface dipoles of <0.3 eV have been determined for CdS and CdTe on InSe⁹⁴ and for ZnSe on InSe and GaSe,¹⁶⁷ as shown in Fig. 20b.

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As a consequence, a fundamental difference between quasi van der Waals-epitaxy interfaces of the layered transition metal dichalcogenides (TMDC: WSe₂, MoTe₂) and of the III-VI compounds (InSe, GaSe) is suggested. Larger interface dipole potentials are observed for the transition metal dichalcogenides, for both metallic and II-VI contact partners. The different interface dipole potentials for II-VI films, comparable to the non-transitivity observed for metal contacts shown in Fig. 19.

The structural dipole model

The origin of the large interface dipole potentials at TMDC/II-VI interfaces has been related to the orientation of the growing overlayer. Although strong clustering of the II-VI films occurs, the overlayers grow with their three-fold $\langle 111\rangle$ (for zincblende) or six-fold $\langle 0001\rangle$ (for wurtzite) symmetry axis perpendicular to the van der Waals-surface.^71,92,94,167 These directions are polar directions with alternating layers of positively and negatively charged atomic planes, which induce an alternating electrostatic potential and result in different electron affinities of the cation and anion terminated (111) surfaces.^168–170 A sketch of the band alignment at interfaces between II-VI compounds and layered semiconductors including these structural dipoles is given in Fig. 21.

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The large interface dipole potentials at the TMDC/II-VI interfaces correspond to a particular orientation of the II-VI layer, where the (low electron affinity) cation terminated surface is adjacent to the substrate and the (high electron affinity) anion terminated surface forms the growth front. This assumption is confirmed by (i) the large ionization potentials measured for the surfaces of the II-VI films and (ii) the observation of facets on the film surface.^94,166 The first observation is clearly connected to the anion terminated surface with the negatively charged planes on top. In addition, facetting is reported for the anion terminated $(\bar{1}\bar{1}\bar{1})$ or $(000\bar{1})$ surfaces.¹⁷¹

The magnitude of the internal structural dipole for CdS and CdTe can be estimated based on the differences of the electron affinities for GaAs(111) and GaAs $(\bar{1}\bar{1}\bar{1})$, which has been measured by Ranke.¹⁶⁸ The experimental value for GaAs of Δχ₁₁₁ = 0.4 eV has been scaled by using material specific ionicities (from Ref. 172) and lattice parameters resulting in Δχ₁₁₁ = 0.6, 0.8 eV and 0.75 eV for CdTe, CdS and ZnSe, respectively.¹⁶⁶ For CdTe and CdS the experimental values are 0.2–0.3 eV larger (Fig. 20a), which could possibly be explained by an additional electronic interface dipole as indicated by "eD_e" in Fig. 21. This electronic interface dipole is then of the same order of magnitude as the dipoles observed at interfaces between two layered compounds.

The structural dipole model for the band alignment at interfaces between II-VI semiconductors and layered metal chalcogenides is basically a modification of the electron affinity rule, which considers two additional contributions to the lineup: electronic dipole potentials, which are always present but are considered to be small at (quasi-) van der Waals-epitaxy interfaces, and the structural dipole, which results from the alternatingly charged atomic planes in the $\langle 111\rangle$ or $\langle 0001\rangle$ growth direction of the II-VI semiconductors. As long as the interface is atomically abrupt (as assumed in Fig. 21b), the structural dipole should not form on the van der Waals-surface of layered substrate but only in the II-VI overlayer. This seems to be true for different TMDC substrates, but evidently not for all layered semiconductors (see Fig. 20b). A first explanation for the smaller dipoles at III-VI/II-VI interfaces is based on structural arguments⁹⁴: The lattice constants of InSe and CdS are very close. A different interface structure, where the first Cd plane can penetrate into the Se surface plane, is therefore possible. In this case a partial screening of the positive charge of the Cd can occur, resulting in a smaller interface dipole. However, this explanation cannot account for all of the investigated interfaces, since the InSe/CdTe and GaSe/ZnSe interface exhibit a large lattice mismatch but also show only small interface dipoles. Consequently the structural dipole model proposed by Löher et al. cannot consistently explain the interface dipole potentials at layered semiconductor/II-VI interfaces.

An electronic dipole model

In this section a alternative model to describe the band alignment at quasi-van der Waals-epitaxy interfaces is presented. The model does not take structural dipoles into account, but rather considers electronic interface dipoles. Electronic interface dipoles are related to the local interactions at the interface.^158–160 Charge transfer across an interface, which is the origin of this dipole, occurs from occupied orbitals on one side of the interface to unoccupied orbitals on the other. Significant charge transfer occurs only if the respective orbitals exhibit small energy differences and large spatial overlap. The smallest energy differences between occupied and unoccupied energy levels in solids is possible for electronic states close to the Fermi energy, which correspond to states close the energy gap in semiconductors. Understanding the dipoles at quasi-van der Waals-epitaxy interfaces therefore requires a detailed description of the symmetry, energy levels and orientation of the respective orbitals. In the following we will discuss the involved charge transfer for the layered dichalcogenides of group VIb transition metals (WSe₂ and others), the layered III-VI compounds (InSe,GaSe) and the (111) surfaces of zincblende compounds.

The electronic structures of the layered materials as described below are strictly valid only for bulk materials. At quasi-van der Waals epitaxy heterointerfaces the interactions may be different from those across the van der Waals-gap in bulk material, but it is assumed that the structure of the van der Waals-surface does not change during interface formation. Basically, the interlayer interactions are absent at the surface, which should lead to a modification of the respective electronic states as discussed in Ref. 52. The energy levels of the involved states are expected to be situated within the range of the interlayer energy splitting, which corresponds to the energy dispersion along the ΓA direction of the hexagonal Brillouin zone.^52,124 As the dispersion along ΓA is generally small, the electronic states interacting at an interface should have energies close to the bulk p_z and/or ${d}_{{z}^{2}}$-states.

The (111) surfaces of compound semiconductors.—The surface electronic structure of the (111) surfaces of II-VI compound semiconductors is influenced by the surface reconstruction. Reconstructions of polar surfaces are a consequence of the surface charge of ideally bulk terminated surfaces, which are electrostatically unstable¹⁷⁰ in analogy to polar interfaces between heterovalent semiconductors.^173,174 For the hexagonal symmetry of the van der Waals-surfaces and the experimentally observed (111) or (0001) orientation of the growing overlayers, one has to distinguish between the cation terminated (111) (or (0001)) and the anion terminated $(\bar{1}\bar{1}\bar{1})$ (or ($000\bar{1})$) surfaces of the zincblende (or wurtzite) crystal structures. The cation and anion terminated surfaces are not equivalent because of the alternating distance of the cation and anion (111) planes.

In Fig. 22a the structure of the ideal bulk terminated zincblende (111) surface is shown. The (111) surfaces of III-V semiconductors usually show a 2 × 2 reconstruction.¹⁷¹ A cation vacancy model (or vacancy buckling model) as sketched in Fig. 22b, is the accepted structural model for the 2 × 2 reconstruction of III-V (111) surfaces (for example for GaAs).^175–177 The model is consistent with STM images¹⁷⁸ and gives the lowest surface energy as long as the chemical potential of the anion (As) is not too high.¹⁷⁷ In the cation vacancy model one of four surface Ga atoms is removed, resulting in three Ga and three As dangling bonds per 2 × 2 unit cell. The Ga dangling bonds are directed toward the surface while the dangling bonds of the As atoms adjacent to the vacancy are oriented parallel to the surface toward the Ga vacancy.

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A relaxation of the Gallium atoms toward the As plane and of the As atoms toward the Ga vacancy is decuded from total energy minimized surface energy calculations.^176,177 This relaxation leads to an approximate sp² configuration of the Ga atoms and an approximate pyramidal coordination of As. Corresponding surface relaxations leading to a comparable electronic configuration are observed for all (110) surfaces of III-V and II-VI compounds.^160,171 This relaxation leads to an upward shift of the Ga dangling bond energy and a downward shift of the As dangling bond energy and consequently to transfer of electrons from the Ga to the As dangling bonds. Roughly speaking all cation dangling bond states are empty and all As dangling bonds are doubly occupied. This general behavior has been condensed in the so-called electron counting rule,¹¹¹ which is an easy rule for determining possible surface structures at semiconductor surfaces and which guarantees that the surfaces are not charged and therefore are electrostatically stable.

A 2 × 2 reconstruction is also observed for the As terminated $(\bar{1}\bar{1}\bar{1})$ surfaces of GaAs.¹⁷¹ In analogy to the (111)—2 × 2 surface an uncharged surface would be consistent with an anion vacancy reconstruction. However, for a large range of the As chemical potential an adsorbed trimer structure as shown in Fig. 22c is thermodynamically more stable.¹⁷⁷ An As trimer model is also consistent with STM measurements of MBE grown GaAs $(\bar{1}\bar{1}\bar{1})\unicode{x02014}2\,\times \,2$ surfaces.¹⁷⁹ The 2 × 2 surface transforms with heating into a $\sqrt{19}\times \sqrt{19}$ reconstruction before Ga precipitation occurs. For other III-V compounds other surface reconstructions are observed in addition, which are, however, less well understood than those of GaAs.

Only very few data are available on surface reconstructions of II-VI semiconductors.¹⁷¹ CdTe, ZnSe and ZnTe (111) surfaces also show 2 × 2 reconstructions in LEED.¹⁸⁰ Although not explicitly stated in the literature, a cation vacancy structure is also likely for those materials, as the electron counting rule is satisfied by such a structure. Further evidence for this assumption is given by the similarity between the reconstructions of the II-VI and the III-V (110) surfaces.¹⁷¹ The $(\bar{1}\bar{1}\bar{1})$ surfaces of II-VI semiconductors are distinct from those of the III-V compounds. 1 × 1 reconstructions with {110} and {331} facets are reported for CdTe, ZnSe and ZnTe.¹⁸⁰ Facetted surfaces are also observed with LEED during growth of II-VI compounds on layered semiconductors.¹⁸¹ However, in the presence of facetting, reconstructions might be difficult to identify. It is not clear if the differences between the III-V and II-VI $(\bar{1}\bar{1}\bar{1})$ surfaces are due to different surface preparation conditions. The II-VI surfaces investigated in Ref. 180 have been prepared by sputtering and annealing, while the III-V surfaces are often prepared by molecular beam epitaxy.

A detailed electronic band structure calculation for a (111) surface is given for GaAs(111) by Henk and Schattke.¹⁸² As a result of the reconstruction the Ga dangling bonds are shifted upwards in energy to 1.7 eV above the valence band maximum. Several filled surface state energy bands are identified, which basically agree with angle-resolved photoemission data.¹⁸³ For binding energies between 0–2 eV with respect to the valence band maximum there are four occupied surface state bands. These are dominated by As p_x and p_y-orbitals, since the dangling bond states point toward the Ga vacancy. However, also contributions from As p_z-orbitals to these surface states are found.¹⁸² According to Henk and Schattke the largest contribution of z-states results from the As atom, which is not in the neighborhood of a vacancy. Other surfaces states with higher binding energies have large contributions from atoms of the 3rd and 4th atomic planes and will therefore not contribute to the charge transfer at the quasi-van der Waals-epitaxy interfaces.

The charge transfer.—At an interface charge transfer in both directions is in principle possible (bonding and back bonding) if the corresponding electronic states exist. For the argumentation given below, it is assumed that the electronic structure of the (111) or (0001) surfaces of II-VI compounds adjacent to the van der Waals-surfaces corresponds to those of the GaAs(111) − 2 × 2 surface, because of the lack of other data.

At interfaces between the van der Waals-surfaces of group VIb transition metal dichalcogenides with the hexagonal surfaces of II-VI compounds, electron transfer from the TMDC to the II-VI semiconductor is easily accomplished from the occupied ${d}_{{z}^{2}}$ and p_z-states at the valence band maximum of the TMDC to the unoccupied cation (Cd, Zn) dangling bond states. The latter have energies close to the conduction band minimum of the II-VI semiconductor. Back bonding is much less probable at these interfaces since (i) the occupied surface states of the II-VI's are dominated by p_x and p_y-states and (ii) the conduction band states of the TMDCs are also dominated by x, y-states. Overlap between orbitals, which are directed parallel to the interface can be expected to be very low.

It has been discussed above that there are also small contributions of metal ${d}_{{z}^{2}}$-states to the TMDC conduction band. It is expected that these states do not lead to a significant charge transfer across the interface, since these atoms are located in the second atomic layer and shielded by the chalcogen atoms. Therefore overlap of occupied II-VI-states with unoccupied TMDC-states will be small. The (bonding) charge transfer $\mathrm{TMDC}\to \mathrm{II}-\mathrm{VI}$ is therefore expected to be considerably larger than the (back bonding) charge transfer $\mathrm{II}-\mathrm{VI}\to \mathrm{TMDC}$. Orbital symmetries and expected magnitude of charge transfer at TMDC/II-VI semiconductor interfaces is sketched in Fig. 23a.

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Interactions are different at interfaces between II-VI semiconductors and III-VI layered chalcogenides InSe and GaSe. As for the TMDCs charge transfer $\mathrm{III}-\mathrm{VI}\to \mathrm{II}-\mathrm{VI}$ is easily accomplished from the chalcogen p_z-orbitals to the cation dangling bond states. In contrast to the TMDCs the conduction band minimum of InSe and GaSe has also large contributions from chalcogen p_z-orbitals and electron transfer $\mathrm{II}-\mathrm{VI}\to \mathrm{III}-\mathrm{VI}$ is consequently not forbidden by symmetry. However, the symmetries of the occupied II-VI surface states would still allow only for a reduced overlap, resulting in a smaller back bonding charge transfer. Although there is still a net charge transfer from the layered semiconductor to the II-VI compound, a smaller overall interface dipole can be expected compared to the interfaces between TMDCs and II-VI semiconductors. A schematic representation of the interfaces between layered III-VI compounds and II-VI semiconductors together with the resulting charge transfer is summarized in Fig. 23b.

By considering the electronic structures of layered chalcogenides and of II-VI surfaces it is now possible to qualitatively explain (i) the large magnitude of the interface dipole potentials for the layered group VIb transition metal dichalcogenides and (ii) the difference of interface dipole potentials between the TMDCs and the III-VI compounds. For both materials transfer of electrons from occupied valence states into unoccupied states of the II-VI semiconductor surface is easily accomplished, while the reverse transfer is strongly hindered for the TMDCs and at least less probable for the III-VI compounds. In both cases a net interface dipole with its negative end at the II-VI compound is induced. It is larger for TMDCs, which agrees with the experimental observations.

Structural vs electronic dipoles

Chemical passivation of semiconductor surfaces is an important research topic in materials science and technology. Hydrogen termination of silicon is widely used to prevent surface oxidation of Si by a saturation of the surface dangling bonds via the formation of Si–H bonds. Mostly electrochemical preparation routes are applied. The most simple procedure is dipping a Si wafer into hydrofluoric acid, which also removes oxides from the surface, but improved passivation can be achieved with more elaborate processes as described in Ref. 189. Hydrogen terminated silicon wafers can be handled in air for several minutes only, before oxidation sets in. In contrast, it has been shown that GaSe covered Si(111) surfaces show almost no oxidation even after 30 days storage in air.¹⁹⁰ The GaSe termination layer is stable up to temperatures above 500 °C.^110,119 When a Si:H surface is exposed to a GaSe flux at elevated temperature below the desorption temperature of monohydrides (Si–H), the Si–H bonds are replaced by the Si–Ga–Se bonds. These results indicate that the Si:GaSe surface forms a thermodynamically very stable surface termination layer.

Also electronic passivation of the Si(111):GaSe surface has been proven by photoemission.¹⁹¹ In these experiments, the GaSe half-sheet termination layer was prepared by a stepwise deposition of Ga and Se onto a Si(111)-7 × 7 surface. This procedure for preparation of the Si(111)-GaSe van der Waals surface termination is not ideal, as it is accompanied by several structural rearrangements of the Si and Ga atoms at the surface, most likely leading to an incomplete coverage.¹⁹² However, it allows to follow the evolution of the surface potentials during deposition as shown in Fig. 24, giving more insight into the chemical bonds at the surface.

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Compared to other silicon surface terminations by hydrogen¹⁹³ or arsenic,¹⁹⁴ the GaSe surface termination shows no evident surface core-level shift of the Si 2p level indicating the formation of a non-polar Si–Ga chemical bond despite the electronegativity difference of Si and Ga. This can be rationalized in the following way: Deposition of only Ga leads at first to a decrease of the electron affinity as shown in Fig. 24b. This corresponds to a surface dipole with its positive end toward vacuum or a charge transfer from Ga to Si, in agreement with the larger electronegativity of Si. But selenization of the Si(111):Ga surface leads to a strong increase of the electron affinity. The reversal of the surface dipole is explained by charge transfer from Ga to Se, which is even more electronegative than Si. As the polarity of the Ga–Se bond leads to a strong charge transfer from Ga to Se, the positive charge at the Ga atom is lowered and eliminates the polarity of the Si–Ga bond.

The Si(111):GaSe surface shows nearly flatband conditions as no band bending remains at the Si(111):GaSe surface.¹⁹¹ The Si dangling bond states situated close to midgap on the (111) surface are electronically saturated by forming the Si–Ga–Se surface bonds and lead to a low density of electronic surface states in the bandgap. Although it cannot be directly quantified from the PES measurements, the flatband condition indicates a surface state density of the order of those observed at Si(111):H surfaces (<3 × 10¹⁰ cm⁻³).^189,195

The electronic valence band structure of the surface, which is discussed in the following section, can thus be described by an almost undisturbed GaSe band structure, where the Ga–Ga bond is replaced by the Si–Ga bond leading to an almost one-to-one replacement of the corresponding energy levels. This further establishes the non-polarity of the Si–Ga bond in the Si(111):GaSe half-sheet van der Waals surface termination. In combination with the chemical inertness and temperature stability of the surface, which is superior to any other Si surface terminations, the GaSe termination layer generates an exceptional Si(111) substrate to be used for Si based heterostructure devices.

The electronic band structure of Si(111):GaSe has been determined by angle-resolved and energy dependent valence band photoelectron spectroscopy (ARPES) using synchrotron radiation. Measurements have been performed in our group¹²¹ and by the group of M. Olmstead at University of Washington, Seattle (USA).¹⁹⁶ Details of the ARPES technique can be found in Ref. 197. A complete interpretation of the spectra is presented here for the first time.

Normal emission spectra probe the electronic structure perpendicular to the surface. This corresponds to the ΓL direction of the silicon Brillouin zone¹⁹⁷ and to the ΓA direction of the hexagonal GaSe Brillouin zone. The latter is identical to those of WS₂, which has been displayed in Fig. 3. In Fig. 25a normal emission valence band spectra, as obtained using excitation energies hν = 14–30 eV, are presented. The observed electronic transitions (peaks and shoulders) can be plotted vs wave vector as done in Fig. 25b, where the perpendicular component k_⊥ of k has been determined assuming direct transitions to free electron final states with an inner potential of 12.5 eV. Values of k_⊥ are further reduced to the first Si Brillouin zone.

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The binding energy of most of the transitions deduced from normal emission photoemission do not depend on k. Such dispersion-less states are expected for surface state emissions. Only some reminiscences of Si bulk states are observed. The fact that surface state emissions dominate the spectra is not surprising as the GaSe half-sheet is almost as thick as the minimum of the photoelectron escape depth, which is attained at ∼50 eV electron kinetic energy.¹⁹⁹

In Fig. 26 binding energies of electronic transitions obtained from angular dependent valence band spectra taken with hν = 21 and 72 eV are shown along the ΓM symmetry direction.^121,196,198 An experimentally determined band structure obtained from a vacuum cleaved GaSe single crystal is shown for comparison.¹²¹ There is a striking similarity between the GaSe and the Si(111):GaSe band structures, which will be explained in more dtail in the following discussion by considering the molecular orbital contributions to the states involved in the respective transitions for GaSe and the changes expected at the half-sheet layer. The theoretical band structure given by the semiempirical tight binding calculation of Doni et al.⁵⁶ will be used for comparison. Their calculation shows no systematic deviation to a more recent band structure calculation by Gomes da Costa et al.,⁵⁷ but provides more details about the origin of the electronic states. The calculated GaSe band structure is presented in Fig. 27.

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In normal emission ultraviolet photoelectron spectra of III-VI compounds, emission features involving four groups of bands are observed, which are labelled A to D (see Fig. 26 and Refs. 124, 200, and 201). In normal emission from van der Waals-surfaces, the observed transitions involve only electronic states with k vectors along ΓA. Groups of bands (A-D) are also indicated on the left of Fig. 27a. The molecular orbital character of the corresponding states at Γ and A is given as Se p_z (A), p_x and p_y (B), and Ga s (C, D).^55,56 The Ga s-orbitals form bonding (D) and antibonding (C) combinations with respect to the Ga–Ga bond.

Because of hybridization the energy levels derived from certain orbital combinations do not directly correspond to the calculated energy bands. In terms of energy band structure a crossing of bands is only allowed, if they have different symmetry, i.e. they do not interact (hybridize). In contrast, the hybridization of energy bands leads to an energy gap. With the help of tabulated symmetrized combinations of atomic orbitals and critical point symmetry labels,⁵⁶ hypothetical energy bands without hybridization can be drawn for bulk GaSe. The result is shown in Fig. 27b. The construction of non-hybridized energy bands is easily accomplished for the ΓM direction, which corresponds to the crystallographic y-axis (see Fig. 27d).^f The given hypothetical energy bands show the dispersions expected from simple tight binding considerations.⁵³

Of interest in the present context are those electronic states, which are expected to persist for an isolated half-sheet layer. These can, at least partly, be a priori identified. First of all, interlayer interactions, which are indicated in Fig. 27 by the shaded grouping of bands, have to be omitted (see the Section on the electronic structure of layered chalcogenides and Ref. 52). In addition, cutting the layer between the two Ga atoms will also modify the intralayer interactions mainly affecting the z-states and removing the (small) splitting between the x⁺ and x⁻-states (see Fig. 2). No strong changes of the energy dispersion of Se p_x and p_y-bands are expected on the other hand, since the distance between the two Se sheets within a single layer are rather large and hybridization of the chalcogen p_x and p_y-states with the Ga p_x and p_y-states is still possible and not strongly modified, because of the almost unchanged Ga–Se bond length and geometry.

Based on these considerations, tentative energy bands for a hypothetical isolated GaSe half-sheet layer are drawn in Fig. 27c. As argued above, the p_x and p_y-bands are not modified (bands III and IV). The Ga–Ga bonding and antibonding states (groups C and D at Γ) are represented by dashed lines in Fig. 27c. As there are no Ga–Ga bonds the splitting should be absent for an isolated half-sheet layer and the two bands are replaced by a single band approximately half-way between the dashed bands, as indicated by a solid line dispersing upwards along ΓM. The situation is more complicated for the p_z-state, which forms the valence band maximum, as the Ga–Se p_z intralayer overlap is still existent (compare Fig. 27d). It is remembered that the experimentally observed energy bands should follow the dispersion of hybridized bands. The construction of non-hybridized bands is just meant to more easily identify those parts of the GaSe band structure, which can be expected to persist at the half-sheet layer.

The p_x and p_y-states give rise to strong emission from the Si(111):GaSe surface at a binding energy of BE ≈ 3 eV at Γ (see Figs. 26b and 26c). Around BE = 8 eV at M the p_y-states are also clearly present. The p_x-states at M contribute to the number of transitions observed at the expected binding energies. Furthermore the Si(111):GaSe surface also shows emissions both at Γ as well as at M at binding energies, which agree to those of the single crystal Ga–Ga bonding and antibonding states. These emissions are therefore most likely attributed to the replacement of the Ga–Ga bond with the Ga-Si bond. Hence, the binding energies of the bonding and antibonding Ga-Si states of Si(111):GaSe agree with those of the Ga–Ga states measured at GaSe single crystals. This confirms the non-polarity of the Ga-Si bond at this surface, as also deduced from the absence of a Si surface core-level shift.¹⁹¹

Transitions with lowest binding energies emerge from the topmost valence band, which is the ${{\rm{\Gamma }}}_{4}^{-}$ state at GaSe single crystals. Respective emissions are also clearly observed from Si(111):GaSe with the only difference of missing interlayer splitting. Hence, also these states are only little affected by putting a half-sheet of GaSe on top of the Si surface. The expected upward dispersion of unhybridized p_z-states with increasing k_∥ is not observed. The missing upward dispersion of the valence band maximum state for k_∥ > 0 at GaSe single crystals, which is a consequence of hybridization between p_z and p_x, p_y,^g is therefore also missing at Si(111):GaSe. This could have been expected from the minor changes of the symmetry of the layer. It has an important consequence, as it produces a surface without electronic states within the Si bandgap, leading to an electronically passivated surface.