Band Anticrossing Research Articles

Theory of electronic structure of BGaAs and related alloys

AbstractPrevious experiments on Bx Ga1–x As containing a few percent boron show a dramatic increase in electron effective mass, m*e , similar to that observed in many GaNx As1–x samples. By contrast, there is a near‐linear blue‐shift of the energy gap, which can be conventionally described using the virtual crystal approximation. We use a tight‐binding model to show that isolated B atoms have little effect either on the band gap or lowest conduction band dispersion in Bx Ga1–x As. By contrast, B pairs and clusters introduce defect levels close to the conduction band edge (CBE) which, through a weak band‐anticrossing (BAC) interaction, significantly reduce the band dispersion in and around the Γ ‐point, thus accounting for the strong increase in m*e and reduction in mobility observed in these alloys. Calculations show that replacing gallium by aluminium shifts the CBE upwards, leading to a large density of B‐related states in the energy gap. By contrast, indium shifts the band edge downwards, leading eventually to a band edge m*e close to that predicted by the virtual crystal approximation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical analysis of [formula omitted] emitting GaInNAs QD's on different substrates

We present a theoretical study which compares the electronic and optical properties of dilute nitrogen GaInNAs quantum dots (QD) on two different substrates, GaAs and InP. The calculations are based on a 10 band k ⋅ p band-anti-crossing (BAC) Hamiltonian, incorporating valence, conduction and nitrogen-induced bands. We show that 1.55 μ m emission can be achieved on both substrates through appropriate tailoring of the QD size. On GaAs, the dominant dipole matrix element is the e ^ x and e ^ y light polarization, whereas on InP substrate, the dominant component is the e ^ z light polarization. Our results also identifiy the different In and N QD compositions required for long-wavelength emission on both substrates.

Photoluminescence of InNAs alloys: S-shaped temperature dependence and conduction-band nonparabolicity

Photoluminescence (PL) has been used as a means of unambiguously observing band gap reduction in InNAs epilayers grown by molecular beam epitaxy. The observed redshift in room temperature emission as a function of nitrogen concentration is in agreement with the predictions of the band anticrossing (BAC) model, as implemented with model parameters derived from tight-binding calculations. The temperature dependence of the emission from certain samples exhibits a signature non-Varshni-like behavior indicative of electron trapping in nitrogen-related localized states below the conduction-band edge, as predicted by the linear combination of isolated nitrogen states (LCINS) model. This non-Varshni-like behavior tends to grow more pronounced with increasing nitrogen content, but for the highest nitrogen concentration studied, the more familiar Varshni-like behavior is recovered. Although unexpected, this observation is found to be consistent with the BAC and LCINS models. With consideration given to the effects of conduction-band nonparabolicity on the emission line shapes, the BAC model parameters extracted from the measured PL transition energies are found to be in excellent agreement with the predictions of the aforementioned tight-binding calculations.

Effect of non‐parabolicity on the density of states for high‐field mobility calculations in dilute nitrides

AbstractUsing the 2‐level band anticrossing (BAC) model or its generalisation to n ‐bands, the essential features of the non‐parabolicity of the band structure in dilute nitride materials can be captured using a k·p – like formulation. However, the derived densities of states in both 3D and 2D are then badly behaved near the nitrogen impurity levels with unrealistic consequences. Densities of states in the general n ‐band case are derived using a Green's function approach, which are well‐behaved and conserve the number of states in the crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Alloying of GaNxAs1−x with InNxAs1−x: A simple formula for the band gap parametrization of Ga1−yInyNxAs1−x alloys

It has been shown that the band gap energy of dilute nitride ternary alloys (Ga1−yInyNxAs1−x in this case) can be predicted by knowing the band gap energy for dilute nitride binary alloys (GaNxAs1−x and InNxAs1−x alloys in this case) and a bowing parameter. The band gap energy for GaNxAs1−x and InNxAs1−x can be calculated after the band anticrossing (BAC) model [W. Shan et al., Phys. Rev. Lett. 82, 1221 (1999)] or other formula, whereas the bowing parameter can be assumed to be the same as for the GaInAs alloy. This approach does not require the BAC parameters related to Ga1−yInyNxAs1−x and can be applied for other dilute nitride ternary alloys. The obtained band gap predictions are in good agreement with available experimental data for as-grown GaInNAs materials. It means that the proposed energy gap parametrization corresponds to the random environment of N atoms by Ga and In atoms since alloying of GaNxAs1−x with InNxAs1−x also corresponds to alloying of Ga-rich environment of N atoms (which is expected for the as-grown GaInNAs material with low indium content) with In-rich environment of N atoms (which is expected for the as-grown GaInNAs material with high indium content).

Band alignments of InGaPN/GaPN quantum well structures on GaP and Si

We proposed a calculation method for the band alignment of a novel InGaPN/GaPN single-quantum well (SQW) on GaP and Si substrates. The calculation method composed the model-solid theory (MST) for the band edge shifts due to strain and the band anticrossing (BAC) model for a large band bowing of an InGaPN alloy due to N incorporation. The band alignments of the InGaPN/GaPN SQW with In compositions larger than 27% on GaP and Si substrates were investigated by the calculation method, whose QW could have a direct bandgap. The 18-K experimental photoluminescence (PL) peak energy of the InGaPN/GaPN SQW on a GaP substrate, which was grown by radiofrequency plasma-assisted molecular-beam epitaxy (RF-MBE), was in good agreement with the calculated transition energy between the first electron quantum level and the first heavy-hole quantum level. The conduction band offsets of the InGaPN/GaPN SQW with N compositions of 1–2% into the InGaPN well grown on GaP substrates were several dozens meV at the most, while the valence band offsets were 200–300 meV due to compressive strain increased by increasing In compositions. Therefore, larger N compositions of the InGaPN well were required to increase the conduction band offsets of the InGaPN/GaPN SQW for light-emitting devices. It was demonstrated that the type-I InGaPN/GaPN SQW with a direct bandgap could be obtained on Si substrates. Our calculation results showed that the appropriate In composition of the InGaPN well were 30–45% and N composition of the GaPN barrier 1–2%. The differences of N compositions around 3% between the InGaPN well and the GaPN barrier were required for realizing a conduction band offset of 300 meV.

Hydrostatic pressure experiments on dilute nitride alloys

AbstractGaNx As1–x and Ga1–y Iny Nx As1–x are the most prominent members of a novel class of non‐amalgamation type semiconductor alloys where a fraction x of the anions of the host (e.g., GaAs or Ga1–y Iny As) is replaced by N isovalent impurity atoms. The localized N‐states in GaNx As1–x and Ga1–y Iny Nx As1–x form a series of discrete energy levels (e.g., isolated N‐state, N‐pairs and higher order N‐cluster states) resonant with the conduction band of the host. The effect of the alloying with nitrogen on the bandstructure of GaNx As1–x and Ga1–y Iny Nx As1–x can be well parameterized using a band‐anticrossing (BAC) model, namely, assuming a level repulsion between an effective N‐state and the conduction band‐edge state. The dependence of several physical properties on nitrogen incorporation can be predicted qualitatively in the framework of this model, e.g., a tremendous increase of the electron effective mass in GaNx Asx with increasing x, a huge cross section for scattering of electrons by N impurities in electronic transport, etc. Most of these predictions can be tested and verified by performing hydrostatic pressure experiments which, within the picture of the BAC model, allow one to tune continuously the energy difference between the host‐like conduction band edge and the effective N‐level within one and the same specimen. Several examples of this kind will be discussed. Furthermore, we will demonstrate the limitations of the BAC model in the case of GaNx P1–x and also of GaNx As1–x . In particular, we will show several examples where the description by a single effective N‐state fails and that the multiplicity of the N‐states needs to be taken into account. Again hydrostatic pressure experiments prove to be a useful and suitable tool for revealing the effects due to N‐cluster states. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental and theoretical investigation of the conduction band edge ofGaNxP1−x

We show that a two-level band-anticrossing (BAC) model fails to describe the evolution of N-related states in $\mathrm{Ga}{\mathrm{N}}_{x}{\mathrm{P}}_{1\ensuremath{-}x}$. Band structure calculations prove that a two-level model describes these states in ordered GaNP supercells. Photocurrent measurements support a BAC-related blueshift of the GaP-like direct band gap in disordered GaNP, but calculations and electromodulated absorption and pressure studies show that the wide energy distribution of the lower-lying N-related states leads to the anticrossing interaction involving many N levels in disordered GaNP.

Band anticrossing in InGaPN alloys induced by N-related localized states

Temperature-dependent photoreflectance measurements are employed to characterize the electronic band structure of InGaPN grown on GaAs substrates. In addition to the fundamental band gap, the upper subband E+ is observed as predicted by the band anticrossing (BAC) model. By eliminating the contributions of the epitaxial-strain and atomic-ordering effects in InGaPN and also assigning the localized state energy EN introduced by an isolated N to be 2.040eV at 293K, the interaction potential V is determined as 1.449±0.170eV. The incorporation of a temperature-dependent EN level into the BAC model fits the experimental data better than assuming EN to be a constant. This contrasts with previously published results and so provides a different view of the temperature dependence of the EN level in InGaPN.

Influence of N cluster states on band dispersion in GaInNAs quantum wells

We use a modified band-anticrossing (BAC) model to investigate the band dispersion in a GaN x As 1 - x / AlGaAs quantum well (QW) as a function of hydrostatic pressure. The band edge mass increases considerably more quickly with pressure than in the case of a GaAs/AlGaAs QW, and the subband separation also decreases significantly. We predict that the strong anticrossing interaction between the GaAs host conduction band and isolated N levels will inhibit tunnelling through the QW for a range of energy above the isolated N levels. The energy of N resonant states depends strongly on details of the local environment, giving a broader calculated distribution of N states in GaInNAs compared to GaNAs.

Modeling of band gap properties of GaInNP alloys lattice matched to GaAs

Compositional and temperature dependences of the band gap energies of GaInNP alloys, which are lattice matched to GaAs, are determined and modeled by a band anticrossing (BAC) interaction between the localized state of the isolated NP and extended host states. The BAC parameters are deduced as EN=2.1±0.1eV and CMN=1.7±0.2eV. The low value of the coupling parameter CMN implies weaker coupling of the N level with the host matrix, presumably due to short range ordering effects, similar to the case of GaInNAs alloys with a high In content. The obtained information is important for future modeling of the electronic structure of the alloys.

Influence of composition diffusion on the band structures of InGaNAs∕GaAs quantum wells investigated by the band-anticrossing model

We investigate the influence of quantum-well intermixing (QWI) on the electronic band structure of GaInNAs∕GaAs multiquantum wells. The band structures and optical transitions have been calculated based on the band-anticrossing (BAC) model and Fick’s interdiffusion law for both intermixed and nonintermixed samples, respectively. The calculated results are consistent with the true optical transitions observed by photoluminescence excitation spectroscopy and secondary ion mass spectroscopy. Our investigation indicates that BAC model is valid for interdiffused quantum wells and verifies that the QWI process in GaInNAs∕GaAs multiquantum wells is induced mainly by the interdiffusion of In–Ga between the quantum wells and barriers.

Composition and carrier-concentration dependence of the electronic structure of InyGa1−yAs1−xNx films with nitrogen mole fraction of less than 0.012

The electronic structure of Si-doped InyGa1−yAs1−xNx films on GaAs substrates, grown by nitrogen-plasma-assisted molecular-beam epitaxy, was examined by photoreflectance (PR) spectroscopy at temperatures between 20 and 300K. The films were approximately 0.5μm thick and had nitrogen mole fraction between x=0.0014 and x=0.012, measured indirectly by a secondary-ion-mass spectrometry calibration; indium mole fraction between y=0.052 and y=0.075, measured by electron-dispersive x-ray spectroscopy; and carrier concentration between 2×1016 and 1.1×1018cm−3, measured by Hall effect. Three critical-point transitions were identified by PR: the fundamental band gap (highest valence band to the lowest conduction band); the spin-orbit split valence band to the lowest conduction band; and the highest valence band to a nitrogen impurity band (above the lowest conduction band). The measured critical-point energies were described by a band anticrossing (BAC) model with the addition of a Burstein-Moss band-filling term. The fitted BAC parameters were similar to previously reported values. The N impurity level was located 0.3004±0.0101eV above the conduction-band edge at 20K and 0.3286±0.0089eV above the conduction-band edge at 295K. The BAC interaction parameter was 2.588±0.071eV. From the small magnitude of the Burstein-Moss energy shift with increasing carrier concentration, it was inferred that the carrier concentration probed by PR is reduced from the bulk (Hall-effect) carrier concentration by a reduction factor of 0.266±0.145. The PR lines broadened with increasing carrier concentration; the line broadening tracked the predicted Burstein-Moss energy shift for the bulk carrier concentration. The surface-normal lattice constants of the films were measured by x-ray diffraction. Comparison of the measured lattice constants with Vegard’s law showed the presence of tensile strain (in the surface-normal direction) with magnitude between 1.5×10−3 and 3.0×10−3. The effect of strain on the PR energies was too small to observe.

Generalized band anticrossing model for highly mismatched semiconductors applied toBeSexTe1−x

We report a new model for highly mismatched semiconductor (HMS) alloys. Based on the Anderson impurity Hamiltonian, the model generalizes the recent band anti-crossing (BAC) model, which successfully explains the band bowing in highly mismatched semiconductors. Our model is formulated in empirical tight-binding (ETB) theory and uses the so called sp$^{3}$s* parameterization. It does not need extra parameters other than bulk ones. The model has been applied to BeSe$_{x}$Te$_{1 - x}$ alloy. BeTe and BeSe are wide-band gap and highly mismatched semiconductors. Calculations show large band bowing, larger on the Se rich side than on the Te rich side. Linear interpolation is used for an arbitrary concentration $x$. The results are applied to calculation of electronic and optical properties of BeSe$_{0.41}$Te$_{0.59}$ lattice matched to Si in a superlattice configuration.

Photoreflectance study of the electronic structure of Si‐doped In y Ga 1− y As 1− x N x films with x < 0.012

The electronic structure of Si-doped InyGa1−yAs1−xNx films on GaAs substrates, grown by nitrogen-plasma-assisted MBE, was examined by photoreflectance (PR) spectroscopy at temperatures between 20 K and 300 K. The measured critical-point energies were described by a band anti-crossing (BAC) model with the addition of a Burstein-Moss band-filling term. The energy difference between the nitrogen impurity level and conduction band edge was (0.3004 ± 0.0101) eV at 20 K, and (0.3286 ± 0.0089) eV at 295 K; the BAC interaction parameter was (2.588 ± 0.071) eV. It was inferred from the magnitude of the Burstein-Moss shift that the near-surface carrier concentration, probed by PR, is reduced from the bulk (Hall effect) carrier concentration by a reduction factor of 0.266 ± 0.145. The effect of strain on the PR energies was too small to observe. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Highly Mismatched Alloys for Intermediate Band Solar Cells

AbstractIt has long been recognized that the introduction of a narrow band of states in a semiconductor band gap could be used to achieve improved power conversion efficiency in semiconductor-based solar cells. The intermediate band would serve as a “stepping stone” for photons of different energy to excite electrons from the valence to the conduction band. An important advantage of this design is that it requires formation of only a single p-n junction, which is a crucial simplification in comparison to multijunction solar cells. A detailed balance analysis predicts a limiting efficiency of more than 50% for an optimized, single intermediate band solar cell. This is higher than the efficiency of an optimized two junction solar cell. Using ion beam implantation and pulsed laser melting we have synthesized Zn1-yMnyOxTe1-x alloys with x<0.03. These highly mismatched alloys have a unique electronic structure with a narrow oxygen-derived intermediate band. The width and the location of the band is described by the Band Anticrossing model and can be varied by controlling the oxygen content. This provides a unique opportunity to optimize the absorption of solar photons for best solar cell performance. We have carried out systematic studies of the effects of the intermediate band on the optical and electrical properties of Zn1-yMnyOxTe1-x alloys. We observe an extension of the photovoltaic response towards lower photon energies, which is a clear indication of optical transitions from the valence to the intermediate band.

Unification of the Band Anticrossing and Cluster-State Models of Dilute Nitride Semiconductor Alloys

We show that a quantitative description of the conduction band in Ga(In)NAs is obtained by combining the experimentally motivated band anticrossing model with detailed calculations of nitrogen cluster states. The unexpectedly large electron effective mass values observed in many GaNAs samples are due to hybridization between the conduction band edge E- and nitrogen cluster states close to the band edge. Similar effects explain the difficulty in observing the higher-lying E+ level at low N composition. We predict a decrease of effective mass with hydrostatic pressure in many GaNAs samples.

Theory of electron confinement and electron effective mass in dilute nitride alloys and heterostructures

AbstractThe band‐anti‐crossing (BAC) model describes the strong band‐gap bowing at low N composition x in Ga(In)NxAs1–x in terms of an interaction between the conduction band edge and a higher‐lying band of localized nitrogen resonant states. We first present an analytical technique based on the BAC model to calculate electron energies in Ga(In)NAs square quantum well (QW) structures. We then show through detailed comparison with photoreflectance measurements that the BAC model successfully describes ground and excited state interband transition energies in bulk and QW GaNAs samples, both at ambient pressure and as a function of hydrostatic pressure. Turning to the conduction band dispersion, we find that the two‐level BAC model is insufficient, and must be modified to give a quantitative understanding of the unexpectedly large electron effective mass values observed in some GaNAs samples, which we attribute to hybridisation between the conduction band edge and nitrogen states close to the band edge. We predict a non‐monotonic variation of electron mass with hydrostatic pressure in many GaNAs samples. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of cluster states on band dispersion in bulk and quantum well (ultra-)dilute nitride semiconductors

The band-anti-crossing (BAC) model successfully describes many of the electronic properties of GaNxAs1−x. Experimental and theoretical studies show a range of resonant defect levels close to the conduction band edge in GaNxAs1−x, due to the formation of N complexes which are ignored in the conventional BAC model. The consequences of these resonant levels for the band dispersion are investigated. The rapid increase in N–N pairs with N composition (∝x2) is shown to have little effect on the calculated room-temperature band-edge dispersion, but modifies the low-temperature band dispersion with increasing x. For low temperatures, it is shown that at low N composition (0.001≤x≤0.01) the band dispersion is best described using a modified BAC model, which explicitly includes the effects of N–N pairs, while at higher compositions (x>0.01) the effects of longer-range N–N interactions need also to be considered. The consequences of this are analysed for the predicted evolution of band dispersion with x in magneto-tunnelling experiments.

Intrinsic limits on electron mobility in disordered dilute nitride semiconductor alloys

The authors have previously shown that there is a fundamental connection between the composition-dependence of the conduction-band-edge energy and the n-type carrier scattering cross-section in dilute alloys, imposing general limits on the electron mobility in Ga(In)NAs alloys and heterostructures. A simple general expression is derived for scattering in the ultra-dilute regime, showing that the scattering rate is proportional to |dEc/dx|2, the square of the initial variation of the conduction-band-edge energy with alloy composition x. The mobility estimated in GaNxAs1−x using the two-level band-anti-crossing (BAC) model is of the right magnitude (∼1000 cm2/Vs), but still larger than typical experimental values. The effects of N clusters and inhomogeneous broadening of energy levels are considered, including the formation of N–N pairs (where a single Ga atom has two N neighbours) and more complex clusters. It is shown that such complexes play a major role in further limiting the mobility, giving values of 200–400 cm2/Vs, in close agreement with experiment. It is concluded that random alloy scattering, rather than film quality or other factors, dominates the carrier mobility in these materials.