Critical Point Energies Research Articles

Engel-Vosko GGA Approach Within DFT Investigations of the Optoelectronic Structure of the Metal Chalcogenide Semiconductor CsAgGa2Se4

Metal chalcogenide semiconductors have a significant role in the development of materials for energy and nanotechnology applications. First principle calculations were applied on CsAgGa2Se4 to investigate its optoelectronic structure and bonding characteristics, using the full-potential linear augmented plane wave method within the framework of generalized gradient approximations (GGA) and Engel-Vosko GGA functionals (EV-GGA). The band structure from EV-GGA shows that the valence band maximum and conduction band minimum are situated at Γ with a band gap value of 2.15 eV. A mixture of orbitals from Ag 4p 6/4d 10, Se 3d 10, Ga 4p 1, Se 4p 4 , and Ga 4s 2 states have a primary role to lead to a semiconducting character of the present chalcogenide. The charge density iso-surface shows a strong covalent bonding between Ag-Se and Ga-Se atoms. The imaginary part of dielectric constant reveals that the threshold (first optical critical point) energy of dielectric function occurs 2.15 eV. It is obvious that with a direct large band gap and large absorption coefficient, CsAgGa2Se4 might be considered a potential material for photovoltaic applications.

Probing Critical Point Energies of Transition Metal Dichalcogenides: Surprising Indirect Gap of Single Layer WSe2.

By using a comprehensive form of scanning tunneling spectroscopy, we have revealed detailed quasi-particle electronic structures in transition metal dichalcogenides, including the quasi-particle gaps, critical point energy locations, and their origins in the Brillouin zones. We show that single layer WSe2 surprisingly has an indirect quasi-particle gap with the conduction band minimum located at the Q-point (instead of K), albeit the two states are nearly degenerate. We have further observed rich quasi-particle electronic structures of transition metal dichalcogenides as a function of atomic structures and spin-orbit couplings. Such a local probe for detailed electronic structures in conduction and valence bands will be ideal to investigate how electronic structures of transition metal dichalcogenides are influenced by variations of local environment.

Optical constants of Cu(In, Ga)Se2 for arbitrary Cu and Ga compositions

The optical constants of Cu(In, Ga)Se2 (CIGS)-based polycrystalline layers with different Cu and Ga compositions are parameterized completely up to a photon energy of 6.5 eV assuming several Tauc-Lorentz transition peaks. Based on the modeled optical constants, we establish the calculation procedure for the CIGS optical constants in a two-dimensional compositional space of (Cu, Ga) by taking the composition-induced shift of the critical point energies into account. In particular, we find that the variation of the CIGS optical constants with the Cu composition can be modeled quite simply by a spectral-averaging method in which the dielectric function of the target Cu composition is estimated as a weighted average of the dielectric functions with higher and lower Cu compositions. To express the effect of the Ga composition, on the other hand, an energy shift model reported earlier is adopted. Our model is appropriate for a wide variety of CIGS-based materials having different Cu and Ga compositions, although the modeling error increases slightly at lower Cu compositions [Cu/(In + Ga) < 0.69]. From our model, the dielectric function, refractive index, extinction coefficient, and absorption coefficient for the arbitrary CIGS composition can readily be obtained. The optical database developed in this study is applied further for spectroscopic ellipsometry analyses of CIGS layers fabricated by single and multi-stage coevaporation processes. We demonstrate that the compositional and structural characterizations of the CIGS-based layers can be performed from established analysis methods.

Ellipsometry as Testing Method of Properties of Nano-Scale Films

Ellipsometry is power instrument for testing several properties of thin films. Advantage and attractiveness of these optical studies consist in that they are non-destructive and non-disturbing. High sensitivity to surface state allows us to monitoring properties of films beginning from atomic scale as in-situ and as ex situ. Ellipsometry give us information about film thickness, and film composition, and its surface morphology. From analysis of ellipsometric spectra it is possible get data about zone structure of semiconductor materials, such as energy of critical points, absorption edge location, and crystallinity. Speed of data acquisition is sufficient high to test dynamic of film growth. Ellipsometric measurements are quite simple but its interpretation requires special software. In this paper some possibilities of ellipsometric method are demonstrated in examples film polymorphism.

Compositional dependence of optical interband transition energies in GeSn and GeSiSn alloys

The dielectric functions of GeSn and GeSiSn alloys were measured in the 1–6eV energy range using spectroscopic ellipsometry. The contributions from the E1, E1+Δ1, E0′, E2, and E1′ critical points in the joint density of electronic states were enhanced by computing numerical second derivatives of the measured dielectric function, and the resulting lineshapes were fitted with model expressions from which the critical point energies, amplitudes, broadenings, and phases were determined. A detailed analysis of the compositional dependence of the different transition energies is presented. By describing this dependence in terms of quadratic polynomials, the bowing parameter (quadratic coefficient) for each transition is determined. It is shown that the bowing parameters in the ternary alloy follow a distinct chemical trend, in which the ternary is well described in terms of bowing parameters for the underlying binary alloys, and these bowing parameters increase as a function of the size and electronegativity mismatch of the alloy constituents.

Dielectric functions of Cu2ZnSnSe4 and Cu2SnSe3 semiconductors

The dielectric functions of co-evaporated Cu2ZnSnSe4 (CZTSe) and Cu2SnSe3 (CTSe) polycrystalline layers are determined accurately from self-consistent spectroscopic ellipsometry analyses. To minimize the effects of the compositional modulation and light scattering induced by rough surfaces, quite thin CZTSe and CTSe layers (<50 nm) having the single-phase stoichiometric compositions are characterized. The dielectric functions of CZTSe and CTSe show rather similar spectral features with almost identical critical point energies for the transition peaks at 2.4 and 3.9 eV. The CTSe dielectric function, however, indicates strong free carrier absorption, expressed by the Drude model, due to high p-type conductivity in the layer. We find that CZTSe and CTSe show quite large absorption coefficients exceeding 105 cm−1 at 2.0 eV with band gap values of 0.91 ± 0.02 eV and 0.68 ± 0.05 eV, respectively. To characterize the optical transition in CZTSe in more detail, the dielectric response of each interband transition is calculated by applying density functional theory. The calculation result reveals that the strong visible light absorption in CZTSe is induced by the high joint density of states at the P point in the Brillouin zone. The optical constants of CZTSe and CTSe deduced in this study are further parameterized in an energy range up to 6.0 eV by expressing the transition peaks using the Tauc-Lorentz model. From the above results, we discuss the fundamental optical properties of (Cu,Se)-based compound semiconductors.

Optical properties of large-area ultrathin MoS2 films: Evolution from a single layer to multilayers

We investigated the optical properties of ultrathin MoS2 films (number of layers: N = 1, 2, 4, and 12) using Raman spectroscopy, photoluminescence (PL) spectroscopy, and spectroscopic ellipsometry. We estimated the layer thicknesses based on Raman spectra. We characterized the microstructural properties of a single-layer MoS2 film using atomic force microscopy. We measured the lowest-energy A and B excitons using PL spectroscopy. We measured the ellipsometric angles (Ψ and Δ) of MoS2 thin films using spectroscopic ellipsometry, and obtained the dielectric functions as the films' thickness changed from a single layer to multi-layers. We determined the films' optical gap energies from the absorption coefficients. Applying the standard critical point model to the second derivative of the dielectric function (d2ε(E)/dE2), we determined several critical point energies. The d2ε(E)/dE2 spectra showed doublet peaks around 3 eV corresponding to the C and D transitions, as well as doublet peaks around 2 eV corresponding to the A and B transitions. These doublet structures at 3 eV are attributed to the transitions in the Brillouin zone between the Γ and K points.

Optical properties of pseudomorphic Ge1−xSnx (x = 0 to 0.11) alloys on Ge(001)

The characterization of the optical properties of pseudomorphic Ge1−xSnx/Ge/Si (x = 0 to 0.11) alloys from the IR to UV is presented. The Ge1−xSnx alloys were epitaxially grown on relaxed Ge grown on Si. Rutherford backscattering (RBS) and RBS ion channeling methods were used to confirm the Sn composition and substitutional nature of the Sn into the Ge lattice. The pseudomorphic nature of the Ge1−xSnx on Ge is confirmed using high resolution x-ray diffraction (HRXRD) and transmission electron microscopy. Although HRXRD reciprocal space maps indicated that the Ge1−xSnx was pseudomorphic to Ge, the shape of the Bragg peaks indicated that the sample surface was rough. The rough surface morphology is confirmed using atomic force microscopy. The complex dielectric function is reported in the IR, visible, and UV spectrum in the wavelength range of 0.2–5.06 eV. The E1, E1 + Δ1, E2, and E0 critical points are extracted using second and third derivative line shape fitting and are compared with the elastic theory calculations of strained Ge1−xSnx (x = 0 to 0.11) alloys and fully relaxed Ge1−xSnx (x = 0 to 0.11) alloys. The E0 critical point energies are observed to have slightly larger values than those calculated for completely relaxed Ge1−xSnx alloys due to the presence of compressive strain.

Ellipsometric study of the temperature dependences of the dielectric function and the critical points of AlSb at temperatures from 300 to 803 K

We report the complex pseudodielectric function = + i of an oxide-free AlSb film for energies from 0.7 to 5.0 eV and temperatures from 300 to 803 K. The 1.5-μm-thick film was grown on a (001) GaAs substrate by using molecular beam epitaxy. We maintained the film in an ultrahigh vacuum to prevent oxidation artifacts and used a rotating-compensator ellipsometer to obtain the optical properties. Critical-point (CP) energies were obtained by numerically calculating second energy derivatives of the data. Blue shifts of the CP energies and sharper structures were observed with decreasing temperature. The calculated CP energies were fit to a linear equation.

Dielectric functions and interband transitions of InxAl1 − xP alloys

We report pseudodielectric functions <ε> from 1.5 to 6.0 eV of InxAl1 − xP ternary alloy films. Data were obtained by spectroscopic ellipsometry on 1.2 μm thick films grown on (001) GaAs substrates by molecular beam epitaxy. Artifacts were minimized by real-time assessment of overlayer removal, leading to accurate representations of the bulk dielectric responses of these materials. Critical-point (CP) energies were obtained from numerically calculated second energy derivatives, and their Brillouin-zone origins identified by band-structure calculations using the linear augmented Slater-type orbital method.

Optical constants and electronic energy-band structure of AgGaSe2

The complex dielectric-function spectra, ε(E) = ε1(E) + iε2(E), of the AgGaSe2 chalcopyrite semiconductor have been measured by spectroscopic ellipsometry (SE) for light polarizations perpendicular (E ⊥ c) and parallel to the c-axis (E ∥ c) in the 1.6–5.3 eV photon-energy range at room temperature. The measured ε(E) spectra reveal distinct structures of critical points in the Brillouin zone. Analysis of the numerically derived ε(E) spectra facilitates the precise determination of critical-point energies. By performing the band-structure and dielectric-function calculations, these critical points are successfully assigned to specific points in the Brillouin zone. The dielectric-related optical constants of AgGaSe2, such as the complex refractive index n* = n + ik, the absorption coefficient α, and the normal-incidence reflectivity R, are presented.

Optical properties of TlGaxIn1-xSe2-layered mixed crystals (0.5 ≤ x ≤ 1) by spectroscopic ellipsometry, transmission, and reflection measurements

The layered semiconducting TlGaxIn1-xSe2-mixed crystals (0.5 ≤ x ≤ 1) were studied for the first time by spectroscopic ellipsometry measurements in the 1.2–6.2 eV spectral range at room temperature. The spectral dependence of the components of the complex dielectric function, refractive index, and extinction coefficient were revealed using an optical model. The interband transition energies in the studied samples were found from the analysis of the second-energy derivative spectra of the complex dielectric function. The effect of the isomorphic cation substitution (indium for gallium) on critical point energies in TlGaxIn1-xSe2 crystals was established. Moreover, the absorption edge of TlGaxIn1-xSe2 crystals have been studied through the transmission and reflection measurements in the wavelength range of 500–1100 nm. The analysis of absorption data revealed the presence of both optical indirect and direct transitions. It was found that the energy band gaps decrease with the increase of indium content in the studied crystals.

Interplay between strain, quantum confinement, and ferromagnetism in strained ferromagnetic semiconductor (In,Fe)As thin films

We systematically investigated the influence of strain on the electronic structure and ferromagnetism of (In,Fe)As thin films. It is found that while the shift of the critical point energies of compressive-strained (In,Fe)As layers grown on (In1−y,Gay)As (y = 0.05, 0.1) buffer layers can be explained by the hydrostatic deformation effect (HDE) alone, those of tensile-strained (In,Fe)As layers grown on (Ga1−z,Alz)Sb (z = 0, 0.5, 1) buffer layers can be explained by the combination of HDE and the quantum confinement effect (QCE). The Curie temperature TC of the (In,Fe)As layers strongly depends on the strain, and shows a maximum for the (In,Fe)As layer grown on a GaSb buffer layer. The strain dependence of TC can be explained by the s-d exchange mechanism taking into account HDE and QCE.

Electronic transitions and dielectric functions of relaxor ferroelectric Pb(In1∕2Nb1∕2)O3-Pb(Mg1∕3Nb2∕3)O3-PbTiO3 single crystals: Temperature dependent spectroscopic study

Optical properties and phase transitions of Pb(In1∕2Nb1∕2)O3-Pb(Mg1∕3Nb2∕3)O3-PbTiO3 (PIN-PMN-PT) crystals near morphotropic phase boundary (MPB) have been investigated by temperature dependent transmittance and reflectance spectra. Three critical point energies Eg = 3.17–3.18 eV, Ea = 3.41–3.61 eV, and Eb = 4.74–4.81 eV can be assigned to the transitions from oxygen 2p to titanium d, niobium d, and lead 6p states, respectively. They show narrowing trends with increasing temperature, which can be caused by thermal expansion of the lattice and electron-phonon interaction. Deviation from the linear behaviors can be observed from Ea and Eb versus PT concentration, indicating a complex multiphase structure near MPB region.

Parameterization of the dielectric function of semiconductor nanocrystals

Optical methods like spectroscopic ellipsometry are sensitive to the structural properties of semiconductor films such as crystallinity or grain size. The imaginary part of the dielectric function is proportional to the joint density of electronic states. Consequently, the analysis of the dielectric function around the critical point energies provides useful information about the electron band structure and all related parameters like the grain structure, band gap, temperature, composition, phase structure, and carrier mobility. In this work an attempt is made to present a selection of the approaches to parameterize and analyze the dielectric function of semiconductors, as well as some applications.

Optical analysis of TlInS2xSe2(1−x) mixed crystals

The ellipsometry measurements were carried out on TlInS2xSe2(1−x) mixed crystals in the spectral range of 1.5–6.0 eV at room temperature. The refractive index, extinction coefficient, real and imaginary parts of dielectric function were found as a result of ellipsometric measurements. The energies of interband transitions (critical point energies) of the TlInS2xSe2(1−x) mixed crystals were obtained by means of the second derivative of the real and imaginary parts of dielectric function. The variation of the critical point energies with the isomorphic anion substitution that is sulfur for selenium atoms was established.

Critical Points in the Band Structure of Absorber and Buffer Layers of CuIn $_{{\bm 1}-{\bm x}}$Ga$_{\bm x}$ Se$_{\bf 2}$ Solar Cells by Electroreflectance Spectroscopy

We explore the use of electroreflectance (ER) spectroscopy at room temperature to characterize simultaneously Cu(In,Ga)Se2 (CIGS) absorber and CdS/i-ZnO buffer layers of thin-film solar cells. Absorber layers are coevaporated from elemental sources. The CdS buffer layers are deposited by chemical bath deposition. We apply ER at different incidence angles to distinguish ER signals from interference fringes. Bandgaps, critical point energies, and broadening parameters that describe the band structure of absorber and buffer films are determined by fitting the ER spectra with a third-derivative functional form. Absorbers grown with a vertical gradient in the Ga/(Ga+In) (GGI) ratio are compared with cells without a GGI gradient but the same integral GGI compositions. We also measure samples with no gradient but different integral GGI ratios of 0 (CuInSe2), 0.3, 0.6, and 1 (CuGaSe2). The ER signal of CdS yields three excitonic transitions, consistent with theory.

Dielectric function and critical points of AlP determined by spectroscopic ellipsometry

Abstract We report the room-temperature dielectric function e of AlP from 0.74 to 6.54 eV obtained by in situ spectroscopic ellipsometry. Measurements were done on a 1.2 μm thick film grown on (0 0 1) GaAs by molecular beam epitaxy, with e extracted using a multilayer parametric model. Critical point energies of features in the e spectra were obtained from numerically calculated second-energy-derivatives, and their Brillouin-zone origins identified by band-structure calculations done using the linear augmented Slater-type orbital method.

Temperature dependence of the dielectric functions and the critical points of InSb by spectroscopic ellipsometry from 31 to 675 K

We report the complex dielectric function of InSb for temperatures from 31 to 675 K and energies from 0.74 to 6.42 eV. The spectra were obtained by rotating-compensator spectroscopic ellipsometry on bulk InSb. The critical point (CP) energies were determined using numerically calculated second energy derivatives of the data. At low temperature, the CP structures are blue-shifted and significantly sharpened relative to those seen at high temperature. The temperature dependence of the E1, E1+Δ1, E0′, Δ5cu-Δ5vu (0.35, 0, 0), E0′+Δ0′, Δ5cl-Δ5vu (0.35, 0, 0), E2, E2′, E2+Δ2, E2′+Δ2, E1′, E1′+Δ1′, and E1′+Δ1′+Δ1 CPs was determined by fitting to a phenomenological expression that contains the Bose-Einstein statistical factor or to a linear equation. In particular, temperature dependences of CPs below 100 K and those of the E0′, E0′+Δ0′, E2′, E2+Δ2, E2′+Δ2, E1′+Δ1′, and E1′+Δ1′+Δ1 transitions have not previously been reported.

In-plane optical anisotropy of InAs/GaSb superlattices with alternate interfaces

The in-plane optical anisotropy (IPOA) in InAs/GaSb superlattices has been studied by reflectance difference spectroscopy (RDS) at different temperatures ranging from 80 to 300 K. We introduce alternate GaAs- and InSb-like interfaces (IFs), which cause the symmetry reduced from D2d to C2v. IPOA has been observed in the (001) plane along [110] and [11¯0] axes. RDS measurement results show strong anisotropy resonance near critical point (CP) energies of InAs and GaSb. The energy positions show red shift and RDS intensity decreases with the increasing temperature. For the superlattice sample with the thicker InSb-like IFs, energy positions show red shift, and the spectra exhibit stronger IPOA. The excitonic effect is clearly observed by RDS at low temperatures. It demonstrates that biaxial strain results in the shift of the CP energies and IPOA is enhanced by the further localization of the carriers in InSb-like IFs.