Branch-point Energy Research Articles

Branch-point energies and the band-structure lineup at Schottky contacts and heterostrucures

Empirical branch-point energies of Si, the group-III nitrides AlN, GaN, and InN, and the group-II and group-III oxides MgO, ZnO, Al2O3 and In2O3 are determined from experimental valance-band offsets of their heterostructures. For Si, GaN, and MgO, these values agree with the branch-point energies obtained from the barrier heights of their Schottky contacts. The empirical branch-point energies of Si and the group-III nitrides are in very good agreement with results of previously published calculations using quite different approaches such as the empirical tight-binding approximation and modern electronic-structure theory. In contrast, the empirical branch-point energies of the group-II and group-III oxides do not confirm the respective theoretical results. As at Schottky contacts, the band-structure lineup at heterostructures is also made up of a zero-charge-transfer term and an intrinsic electric-dipole contribution. Hence, valence-band offsets are not equal to the difference of the branch-point energies of the two semiconductors forming the heterostructure. The electric-dipole term may be described by the electronegativity difference of the two solids in contact. A detailed analysis of experimental Si Schottky barrier heights and heterostructure valence-band offsets explains and proves these conclusions.

First-principles study of structural and electronic properties of Cd 3P 2

First-principles linear combination of atomic orbitals method within the framework of density functional theory is applied to study structural and electronic properties of tetragonal and cubic phases of Cd 3P 2. The equilibrium lattice constants and bulk moduli deduced from Murnaghan equation of state for the two structures are in good agreement with the experiment. Enthalpy–pressure curves do not show possibility of pressure induced structural phase transitions between the two structures up to 80 GPa. Electronic band structures and Mulliken population analysis for the two structures are presented. It is found that tetragonal Cd 3P 2 has direct band gap 1.38 eV while cubic structure shows indirect band gap of 0.35 eV. The branch point energies for the tetragonal structure lie below the conduction band while for cubic structure it lies in the conduction band. Mulliken population analysis shows that occupancies in 5sp, 6sp and 5d states of Cd and 3sp and 4sp states of P are largely affected on bond formation.

Role of a universal branch-point energy at ZnO interfaces

Contemporary interface state models were tested using the barrier heights of laterally homogeneous ZnO Schottky contacts. A strong correlation was found between barrier height and metal Miedema electronegativity, indicating that interfacial chemical bonding may play an important role in the charge transfer at metal-ZnO interfaces. The charge neutrality level of metal-ZnO interface states was found to lie in the band gap, $0.90\ifmmode\pm\else\textpm\fi{}0.05\text{ }\text{eV}$ below the conduction-band minimum. This is in contrast to the electrical nature of ZnO free surfaces and heterojunctions, and with quasiparticle band-structure calculations which have previously placed the branch-point energy of ZnO in the first conduction band. This large discrepancy indicates that we still lack a comprehensive predictive model for these interfaces.

Band lineup between silicon and transparent conducting oxides

Modern quasiparticle calculations based on hybrid functionals are used to predict natural band discontinuities between silicon and In2O3, ZnO, and SnO2 by two alignment methods, a modified Tersoff method for the branch-point energy and the Shockley–Anderson model via the electron affinity rule. The results of both methods are found to be in good agreement. A tendency for misaligned type-II heterostructures is predicted, indicating efficient electron-hole separation at the Si-oxide interfaces.

Interface-induced gap states and band-structure lineup at TiO2 heterostructures and Schottky contacts

The band-structure lineup at semiconductor interfaces is explained by the continuum of the intrinsic interface-induced gap states (IFIGS) which derive from the complex band structures of the semiconductors. Hence, the valence-band offsets of semiconductor heterostructures and the barrier heights of metal-semiconductor or Schottky contacts are composed of a zero-charge transfer and an electrostatic-dipole term, which are determined by the IFIGS’s branch-point energies and the electronegativity difference of the two materials in contact, respectively. The analysis of experimental valence-band offsets at TiO2 heterostructures yields the p-type branch-point energy of TiO2 as 2.34±0.41 eV. This empirical value also explains the experimental valence-band offsets of TiO2/Si double heterostructures with SiO2, Al2O3, and Si3N4 interlayers and of metal-TiO2 Schottky contacts. The experimental valence-band offsets of Si3N4 heterostructures yield the p-type branch-point energy of this insulator as 1.53±0.11 eV.

Branch-point energies and band discontinuities of III-nitrides and III-/II-oxides from quasiparticle band-structure calculations

Using quasiparticle band structures based on modern electronic-structure theory, we calculate the branch-point energies for zinc blende (GaN, InN), rocksalt (MgO, CdO), wurtzite (AlN, GaN, InN, ZnO), and rhombohedral crystals (In2O3). For InN, CdO, ZnO, and also In2O3 the branch-point energies are located within the lowest conduction band. These predictions are in agreement with observations of surface electron accumulation (InN, CdO) or conducting behavior of the oxides (ZnO, In2O3). The results are used to predict natural band offsets for the materials investigated.

Determination of the branch-point energy of InN: Chemical trends in common-cation and common-anion semiconductors

Bulk and surface electronic properties of Si-doped InN are investigated using high-resolution x-ray photoemission spectroscopy, optical absorption spectroscopy, and quasiparticle corrected density functional theory calculations. The branch point energy in InN is experimentally determined to lie $1.83\ifmmode\pm\else\textpm\fi{}0.10\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the valence-band maximum. This high position relative to the band edges is used to explain the extreme fundamental electronic properties of the material. Far from being anomalous, these properties are reconciled within chemical trends of common-cation and common-anion semiconductors.

On the electric-dipole contribution to the valence-band offsets in semiconductor-oxide heterostructures

The continua of interface-induced gap states (IFIGS) determine the band-structure lineup at semiconductor interfaces. Hence, both barrier heights of Schottky contacts and valence-band offsets in semiconductor heterostructures are composed of a zero-charge-transfer and an electric-dipole term. The analysis of experimental barrier heights and valence-band offsets yields IFIGS branch-point energies of 3.51±0.07eV for SiO2 and 2.98±0.26eV, 2.27±0.14, and 2.87±0.14eV for the high-κ oxides Al2O3, HfO2, and ZrO2, respectively. In the oxide heterostructures, the electric-dipole terms come up to 30% of the valence-band offsets and can thus not be neglected.

Electron depletion at InAs free surfaces: Doping-induced acceptorlike gap states

For almost all $n$-type zinc-blende III-V semiconductor free surfaces a depletion layer is observed. InAs is an exception, since $n$-type InAs free surfaces exhibit electron accumulation, due to donorlike surface states which pin the Fermi level far above the conduction band minimum. High-resolution electron-energy-loss spectroscopy (HREELS) has been used to investigate the free surfaces of slightly degenerate $(n\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ and highly degenerate $(n\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ InAs. From HREEL studies of these InAs samples, an electron accumulation and depletion layer were observed, respectively. The Fermi-level pinning mechanism at free surfaces is discussed in terms of the position of the bulk Fermi level with respect to the branch-point energy $({E}_{B})$. Depending on the location of the bulk Fermi level, amphoteric defects are incorporated into the surface, which if ionized facilitate the band bending that results in the surface Fermi level becoming pinned close to ${E}_{B}$. Occupied cation-on-anion antisite defects and unoccupied anion-on-cation antisite defects at the surface are considered to be the ionized surface states responsible for the depletion and accumulation layer profiles, respectively.

On the band structure lineup of ZnO heterostructures

The interface-induced gap states (IFIGS) are the fundamental mechanism which determines the band structure lineup at semiconductor interfaces. The valence-band offsets of semiconductor heterostructures are given by the difference of the respective IFIGS branch-point energies and electric-dipole terms which may be omitted for elemental group-IV semiconductors, SiC, as well as the III–V, II–VI, and I–III–VI2 compounds and alloys. The branch-point energy of ZnO is determined as 3.04±0.21eV from an analysis of experimental valence-band offsets reported for various ZnO heterostructures.

On the band structure lineup at interfaces of SiO2, Si3N4, and high-κ dielectrics

The interface-induced gap states (IFIGS) are the fundamental mechanism which determines the band structure lineup at semiconductor interfaces. The valence-band offsets of semiconductor heterostructures and the barrier heights of Schottky contacts are given by the branch-point energies of the IFIGS of the semiconductors and respective electric-dipole terms. The branch-point energies of SiO2, Si3N4, and of the high-κ dielectrics Al2O3, HfO2, and ZrO2 are determined as 3.99±0.10, 1.93±0.14, 3.23±0.42, 2.62±0.18, and ≈3.2eV, respectively, from experimental valence-band offsets of heterostructures of these insulators.

Origin of electron accumulation at wurtzite InN surfaces

The origin of electron accumulation at wurtzite InN surfaces is explained in terms of the bulk band structure. Ab initio calculations of the electronic structure of wurtzite InN reveal an unusually low conduction band minimum at the $\ensuremath{\Gamma}$-point. As a result, the branch point energy, ${\mathrm{E}}_{B},$ which is the crossover point from donor-type to acceptor-type surface states, is located in the conduction band at the $\ensuremath{\Gamma}$-point. This allows donor-type surface states to exist in the conduction band. The donor-type surface states emit their electrons into the conduction band, thus giving rise to electron accumulation at the surface. Experimental measurements, probing the conduction band electron plasma, confirm the existence of electron accumulation at InN surfaces, with a surface Fermi level location in agreement with the predictions of the ab initio theory.

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.