Virtual Gap States Research Articles

Charge density waves and Fermi level pinning in monolayer and bilayer SnSe2

Materials with reduced dimensionality often exhibit exceptional properties that are different from their bulk counterparts. Here, we report the emergence of a commensurate $2\ifmmode\times\else\texttimes\fi{}2$ charge density wave (CDW) in monolayer and bilayer ${\mathrm{SnSe}}_{2}$ films by scanning tunneling microscopy. The visualized spatial modulation of the CDW phase becomes prominent near the Fermi level, which is pinned inside the semiconductor band gap of ${\mathrm{SnSe}}_{2}$. We show that both CDW and Fermi level pinning are intimately correlated with band bending and virtual induced gap states at the semiconductor heterointerface. Through interface engineering, the electron-density-dependent phase diagram is established in ${\mathrm{SnSe}}_{2}$. Fermi surface nesting between symmetry inequivalent electron pockets is revealed to drive the CDW formation and to provide an alternative CDW mechanism that might work in other compounds.

Valence-band offsets of InGaZnO4, LaAlO3, and SrTiO3 heterostructures explained by interface-induced gap states

The intrinsic interface-induced gap states (IFIGS) which derive from the virtual gap states of the complex band structure are the fundamental mechanism that determines the band-structure lineup at semiconductor interfaces. The valence-band offsets of heterostructures are composed of a zero-charge-transfer term and an electrostatic-dipole contribution which are given by the difference of the p-type branch-point energies of the IFIGS and of the electronegativities, respectively, of the two semiconductors involved. The valence-band offsets of InGaZnO4, LaAlO3, and SrTiO3 heterostructures are quantitatively and consistently explained by the IFIGS-and-electronegativity concept. The analysis of the experimental InGaZnO4, LaAlO3, and SrTiO3 data yields the p-type branch-point energies as 2.37 ± 0.18 eV, 2.59 ± 0.13 eV, and 2.86 ± 0.14 eV, respectively.

Virtual gap states induced modifications in charge neutrality level in cadmium oxide thin films

Present manuscript reports on the creation of virtual gap states (ViGS) in sol–gel spin coated cadmium oxide thin films by tin doping and irradiation at different density of electronic excitations (EEs) induced by energetic ions. Effects of ViGS on charge neutrality level (CNL), which affects the modifications in band gap (BG) of such oxide semiconductors are investigated. Studies reveal that there were insignificant changes in the structural and morphological properties of the films. Interestingly, the transmittance spectrum shows insignificant changes in the films irradiated by low density EEs but an overall decrease in transmittance for high density EEs. However, Raman spectroscopy reveals a significant change in longitudinal optical (LO) modes with tin doping which get intensified and they exhibit an insignificant influence upon irradiation. The BG with respect to bulk is observed to be increased by 0.57 eV and 0.83 eV upon tin doping and irradiation, respectively. These variations are attributed to the combined effect of Burstein–Moss shift (BMS) and ViGS, which were created by tin doping and EEs. It is observed that density of ViGS strongly depends on the density of EEs. A schematic band diagram is also developed for demonstrating the observed influence of ViGS on band gap modifications. Thus the reported investigations are very interesting for the in-depth understanding of fundamental interactions and besides their possible potential applications in the development of optoelectronic devices.

Correlations of charge neutrality level with electronic structure and p-d hybridization

The formation of charge neutrality level (CNL) in highly conducting Cadmium oxide (CdO) thin films is demonstarted by the observed variation in the band gap upon annealing and doping. It may be explained by the observation that Tin (Sn) doping breaks the perfect periodicity of CdO cubic crystal structure and creates virtual gap states (ViGS). The level of local CNL resides at the branch point of ViGS, making the energy at which native defect’s character changes from predominantly donor-like below CNL to predominantly acceptor-like above the CNL and a schematic band diagram is developed to substantiate the same. Further investigations using soft x-ray absorption spectroscopy (SXAS) at Oxygen and Cadmium edges show the reduction of Sn4+ to Sn2+. The analysis of the spectral features has revealed an evidence of p-d interaction between O 2p and Cd 4d orbitals that pushes the valence band minima at higher energies which is symmetry forbidden at г point and causing a positive valance band dispersion away from the zone centre in the г ~ L, K direction. Thus, origin of the CNL is attributed to the high density of the Oxygen vacancies as confirmed by the change in the local electronic structure and p-d hybridization of orbitals.

Unification of the electrical behavior of defects, impurities, and surface states in semiconductors: Virtual gap states in CdO

In contrast to conventional semiconductors, native defects, hydrogen impurities, and surface states are all found to be donors in $n$-type CdO. Using this as a model system, the electrical behaviors of defects, dopants, and surface states in semiconductors are unified by a single energy level, the charge neutrality level, giving much insight into current materials and allowing a band-structure engineering scheme for obtaining desired custom electronic properties in new compound semiconductors.

Variation of band bending at the surface of Mg-doped InGaN: Evidence ofp-type conductivity across the composition range

The variation of band bending as a function of composition at oxidized (0001) surfaces of Mg-doped ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ is investigated using x-ray photoelectron spectroscopy. Distinctly different trends in barrier height are seen for the Mg-doped compared to undoped alloys, which is explained in terms of Fermi-level pinning at the surface and virtual gap states. Solutions of Poisson's equation within the modified Thomas-Fermi approximation are used to model the band bending and corresponding variation of carrier concentration with depth below the surface. A transition from a surface inversion layer for In-rich alloys to a surface hole depletion layer for Ga-rich alloys occurs at $x\ensuremath{\approx}0.49$. The trend in barrier height, calculated space-charge profiles, and difference of barrier height for undoped and Mg-doped InN indicate that Mg doping induces bulk $p$-type conductivity across the entire composition range.

Elementary calculation of the branch-point energy in the continuum of interface-induced gap states

The band alignment at ideal semiconductor interfaces may be described by the continuum of interface-induced gap states. These intrinsic interface states derive from the virtual gap states (ViGS) of the complex semiconductor band structure. The energy at which their character changes from predominantly donorlike to acceptor-like is defined as their branch point. This branch point is located slightly below the middle of its band gap at the mean-value point in the Brillouin zone. By comparison with GW band-structure data it is demonstrated that, first, the width of the band gap at the mean-value point equals the dielectric band gap and that, second, the empirical tight-binding approximation reproduces the dispersion of the GW valence bands from the middle to the mean-value point of the Brillouin zone. Branch points computed by Tersoff for 15 semiconductors are found slightly below the middle of the respective dielectric band gaps at the mean-value point of the Brillouin zone. These results make possible simple calculations of branch points for other zincblende-structure semiconductors.

Empirical tight-binding calculation of the branch-point energy of the continuum of interface-induced gap states

The band lineup at metal–semiconductor contacts as well as at semiconductor heterostructures may be described by one and the same physical concept, the continuum of interface-induced gap states. These intrinsic interface states derive from the virtual gap states (ViGS) of the complex semiconductor band structure and their character varies from predominantly donorlike closer to the valence band to mostly acceptorlike nearer to the conduction band. Calculations are presented of the respective branch points for elemental and binary as well as ternary compound semiconductors which make use of Baldereschi’s concept of mean-value points in the Brillouin zone [Phys. Rev. B 7, 5212 (1973)], Penn’s idea of dielectric band gaps [Phys. Rev. 128, 2093 (1962)], and the empirical tight-binding approximation (ETB). The results are as follows. First, at the mean-value point the band gaps calculated in the GW approximation have the same widths as the dielectric band gaps. Second, the ETB approximation reproduces the GW valence-band energies at the mean-value point. Third, the branch points of the ViGS are slightly below midgap at the mean-value point. The ETB branch-point energies excellently reproduce the barrier heights of gold Schottky contacts on 19 semiconductors and the valence-band offsets of Al1−xGaxAs/GaAs heterostructures.

Chemical interactions and Schottky barrier determinations at the Mg/Si(100) interface studied using X-ray photoelectron spectroscopy

Low work function metal-on-semiconductor systems have technological importance as efficient photocathodes or as thermionic energy converters. Mg-on-Si provides one such system that we have studied here. When the metal is deposited onto Si(100) at room temperature, it reacts to form a thin (approximately two monolayers) layer of Mg 2Si. Upon further deposition, the silicide behaves as a reaction barrier preventing the reactants coming into contact. Mg metal therefore grows on top of the silicide. Furthermore, it adopts a layer-by-layer growth mode. The Schottky barrier formed at this interface is very close in value to that quoted by Mönch [Phys. Rev. Lett. 58 (1987) 1260], i.e. approximately 0.5 eV. This close agreement suggests that the final pinning position may be a consequence of metal-induced virtual gap states.

Metal-semiconductor contacts: electronic properties

Rectification in metal-semiconductor contacts was first described by Braun in 1874. We owe the explanation of this observation to Schottky. He demonstrated that depletion layers exist on the semiconductor side of such interfaces. The current transport across such contacts is determined by their barrier heights, i.e., the respective energy difference between the Fermi level and the edge of the majority-carrier band. Since Schottky had published his pioneering work in 1938 the mechanisms, which determine the barrier heights of metal-semiconductor contacts, have remained under discussion. In 1947, Bardeen attributed the failure of the early Schottky-Mott rule to the neglect of electronic interface states. The foundations for a microscopic description of interface states in ideal Schottky contacts was laid by Heine in 1965. He demonstrated that a continuum of metal-induced gap states (MIGS), as they were called later, derives from the virtual gap states of the complex semiconductor band-structure. Neither this MIGS model nor any of the many other monocausal approaches, the most prominent is Spicer's Unified Defect Model, can explain the experimental data. In 1987, Mönch concluded that the continuum of MIG states represents the primary mechanism, which determines the barrier heights in ideal, i.e., intimate, abrupt, and homogeneous metal-semiconductor contacts. He attributed deviations from what is predicted by the MIGS model to other and then secondary mechanisms. In this respect, interface defects, structure-related interface dipoles. interface strain, interface compound formation, and interface intermixing, to name a few examples, were considered.

Atomic nitrogen on InAs(110) surfaces at room temperature

The interaction of atomic nitrogen with cleaved InAs(110) surfaces at room temperature was investigated by using a Kelvin probe and photoemission spectroscopy excited with Mg(Kα), Zr(Mζ) as well as monochromatic He I and He II radiation. The increase of the N(1s) signal by a simultaneous decrease of the As(3s) intensity accompanied by a constant In(3d 5/2) signal indicates an anion exchange. An N-induced build-up of inversion layers was found on samples doped p-type and of accumulation layers on those doped n-type. For larger exposures the Fermi level becomes pinned at 0.58 eV above the top of the valence band at the surface irrespective of the type of doping. This energy position of the Fermi level agrees very well with the charge-neutrality level of the virtual gap states. With increasing nitrogen exposure two new components to the In(4d) core-level spectra were observed which are chemically shifted by 0.23 and 0.64 eV to larger binding energies with respect to the bulk component. With the As(3d) level a component shifted by 2.1 eV to larger binding energies was detected. All shifts are caused by bonds with nitrogen. The ionization energy initially decreases but increases for larger exposures. The minimum occurs at an N-coverage of one monolayer. It is explained by the removal of the relaxation and a build-up of two additional surface dipoles.

Increase in Schottky Barrier Height in the CoSi2/Si (100) Interface Caused by Hydrogen

ABSTRACTIt is shown that the presence of 8 × 1015 hydrogen atoms/cm2 in the CoSi2/Si (100) interface causes an increase in the Schottky barrier height of 120 meV, and that passivation of dopants in the substrate is not the cause of this change. The data is evidence that the position of the Fermi level in this interface is controlled by defect-related interface states. After hydrogenation the Schottky barrier height agrees with that predicted by theory for Fermi level pinning by virtual gap states of the silicon.

Adsorbate-induced surface states and Fermi-level pinning at semiconductor surfaces

Adatoms on semiconductors are inducing surface states and surface dipoles. These adatom-induced surface states are responsible for the pinning of the Fermi level at adsorbate-covered semiconductor surfaces. Adatom-induced surface dipoles, on the other hand, are changing the ionization energy of the surface. Metal atoms evaporated on, for example, GaAs(110) surfaces held at low temperatures were observed to induce surface states of donor character while with nonmetal adatoms such as chlorine, sulfur, and oxygen, on the other hand, adatom-induced surface acceptors were observed. The energy levels of the metal-induced surface donors were found to be linearly correlated with the first ionization energies of the metal atoms. For metal adatoms with one outer s electron, this chemical trend is explained in a surface–molecule or bond picture by using a simple tight-binding approach. In the band picture, on the other hand, adatom-induced surface dipoles are described by the tails of the electron wave functions of the adatoms into the semiconductor. These tails are derived from the virtual gap states of the complex band structure of the semiconductor.

Mechanisms of band bending at CsOx/GaAs(110) interfaces: Influence of overlayer stoichiometry and interfacial reactivity

The band-bending behavior at interfaces between thin Cs–oxide films and GaAs(110) is studied by photoemission as a function of overlayer stoichiometry and interfacial reactivity. For a substrate temperature of 140 K, nonreactive Cs–oxide/GaAs(110) interfaces with various Cs–oxide stoichiometries were prepared either by successive Cs and oxygen exposure or by codeposition of Cs and oxygen. A remarkable correlation between overlayer stoichiometry and band bending is observed: For both n- and p-type substrates, oxygen-rich overlayers result in almost flat-band conditions, while Cs-rich overlayers lead to Fermi-level positions close to midgap. This behavior is interpreted as a manifestation of a negligible influence of defect states to band bending in the case of these nonreactive interfaces, strongly supporting a mechanism based on virtual gap states. Thermal annealing of the interfaces causes strong interfacial chemical reactions and an increase in band bending for both n- and p-type substrates, signaling non-negligible contributions of reaction-induced defect states in this case.

Adsorption of chlorine and oxygen on cleaved InAs(110) surfaces: Raman spectroscopy, photoemission spectroscopy, and Kelvin probe measurements

The interaction of Cl2 and of O2 molecules with cleaved InAs(110) surfaces was investigated at room temperature. Ultraviolet photoemission spectroscopy, a Kelvin probe, and electric-field-induced Raman spectroscopy were used to determine both the changes of surface band bending and of the ionization energy as a function of exposure to the molecules mentioned. Chlorine as well as oxygen are inducing depletion (inversion) and accumulation layers on samples doped p- and n-type, respectively. The Fermi level becomes finally pinned at 0.52 eV above the valence-band top for both adsorbates. This behavior indicates the presence of adsorbate-induced surface states of donor type at this energy position. With chlorine, an intermediate pinning position at 0.48 eV above the valence-band maximum, which is below the branch point of the virtual gap states of the complex InAs band structure, is observed. This result suggests that chlorine induces surface states of acceptor character on InAs(110) surfaces as is observed with GaAs(110) as well as InP(110) surfaces. Electric-field-induced Raman scattering has proven to be a very valuable tool for studies of accumulation layers.

Electronic properties of sulfur adsorbed on cleaved GaAs surfaces

The interaction of molecular S2 with cleaved GaAs(110) surfaces was followed by using a Kelvin probe and ultraviolet photoemission spectroscopy. The adsorption of sulfur increases the ionization energy of the cleaved surfaces by up to 0.92 eV and causes a Fermi-level pinning at 0.34 eV above the valence-band top for both types of doping. The sign of the change of the ionization energy can be explained by a chemical charge transfer between the adsorbed sulfur and adsorbate-induced gap states, since sulfur is more electronegative than GaAs. The sulfur-related pinning position of the Fermi level is located below the charge-neutrality level of the virtual gap states (ViGS) of the complex GaAs band structure, where the ViGS predominantly possess donor character. This result confirms the predictions from the ViGS model of adsorbate-induced gap states. The energy of the sulfur as well as the oxygen- and chlorine-related surface states, which are of the acceptor type, correlate with the respective atomic electron affinities.

Mechanisms of Schottky-barrier formation in metal–semiconductor contacts

During the formation of metal–semiconductor contacts two principally different types of electronic states are effective in determining the surface position of the Fermi level within the semiconductor band gap. These are, first, adatom-related surface states of donor character and, second, the continuum of adsorbate-induced interface states which result from the tailing of the metal wave functions into the virtual gap states of the semiconductor band structure. The first type of state is observed at submonolayer coverages either after depositions at low temperatures or even at room temperature when a cation exchange occurs. Each metal adatom contributes one of those surface donors and their energy levels are linearly correlated with the first ionization energies of the metal atoms. The second type of state exists at interfaces under metallic islands and continuous metallic films. The charge transferred across the interface by these tails of the metal wave functions is explained by the difference in electronegativities of metal and semiconductor in analogy to the concept of the partial ionic character of covalent bonds.

Chemical trends in Schottky barriers: Charge transfer into adsorbate-induced gap states and defects.

The chemical trends reported for barrier heights in metal-GaAs contacts are explained by a charge transfer between the metal and adsorbate-induced gap states, which are identified as the virtual gap states of the complex band structure of GaAs, as well as fabrication-induced defects of donor type. Following the concept of the ionicity of chemical bonds, the charge transfer is described by the difference in the electronegativities of overlayer and substrate atoms. The density of fabrication-induced defects varies considerably.

Pinning of the Fermi level close to the valence-band top by chlorine adsorbed on cleaved GaAs(110) surfaces

The adsorption of chlorine on cleaved GaAs(110) surfaces was found to increase their ionization energy by up to 1.4 eV and to pin the Fermi level at 0.1 and 0.2 eV above the valence-band top on samples doped p and n type, respectively. These experimental findings are explained by a charge transfer between adsorbate-induced surface states of the semiconductor and the adatoms, which are charged negatively, since chlorine is much more electronegative than GaAs. The adsorbate-induced surface states are identified as virtual gap states (ViGS) of the complex band structure of GaAs. The chemical trends in Fermi-level pinning observed with Cs, Cu, Ag, and Au adsorbed on GaAs are also described by this ViGS model of adsorbate-induced surface states. At larger exposures to Cl2, the Fermi level assumes a second pinning position at 0.55 above the valence-band top for both types of doping. This change of pinning positions is attributed to the formation of adsorbate-induced defects.

Inverse photoemission from surface and interface states of III–V semiconductors

We have measured unoccupied surface and interface states on Ga‐ and In‐derived III–V semiconductors with momentum‐resolved inverse photoemission. The position of the surface states is found to be unrelated to the fundamental band gap. Instead, a connection with the gap of p‐like states can be made. This finding is discussed in the context of theories of Fermi level pinning and band lineup, which use (virtual) gap states as a reference energy. Unoccupied metal‐induced gap states are found for transition metals (Y, Ti, V, Mn, Pd) on GaAs(110) and InP(110). Their energy tracks the Fermi level pinning position, suggesting that these states are connected with the pinning process. A tentative assignment in terms of nonbonding metal d states is given.