[en] The form of the density of states for a tight-binding model with the first and the next-nearest neighbour hoppings for a rectangular planar lattice and a shift of the chemical potential are calculated. This is newly and comprehensively formulated integral form illustrated numerically, helpful in approach to two-dimensional superconducting models. In some particular cases the complete analytical forms of the density of states are obtained. It is shown for all cases the density of states has a single van Hove singularity of the logarithmic type at the identically defined point. the proper approximate analytical representations are found. The difference between the exact numerical and approximate analytical forms is evaluated and illustrated. (author)

[en] The s-paired BCS superconductor with the electron density of states depending on energy in the vicinity of Fermi level is considered. The existence of such fluctuations of electron density of states may be referred to Van Hove singularities widely discussed in literature. In the paper three types of small fluctuations of the electron density of states introduced about its average background's value are analysed: Lorentzian, triangle, and logarithmic ones. In order to calculate numerically the energy gap and critical temperature, the formalism of parametric BCS gap equations is applied. The positive fluctuations (peaks) correspond to the increase in occupied states number including a higher critical temperature. On the other hand, negative fluctuations, which decrease the number of occupied states, lead to the lower critical temperature. Such decrease in critical temperature can lead, at a specific choice of parameters, to the decrease in superconductivity. The presence of fluctuations finds reflection in the shape of the energy gap as a function of temperature. In the vicinity of T = 0 an abrupt decrease or increase in the energy gap to the original BCS value, according to the sign of the fluctuation, is observed. In turn the fluctuations do not change the behaviour of the energy gap near T_c. (author)

[en] Broadening of interband transitions was calculated for inhomogeneous InGaN quantum wells (QWs) dedicated for emitters operating in green spectral range. In order to simulate inhomogeneities for InGaN QW system, it was assumed that the QW width, barrier widths and indium concentration vary with a Gaussian distribution where the nominal QW width, barrier widths and indium concentration correspond to the mean value in this distribution and their fluctuations correspond to the deviation from the main value. Calculations of QW transitions were performed within the electron effective mass approximation for a thousand of randomly generated InGaN QWs and next a histogram of the intensity of optical transitions was built from the result of these calculations. In this way the influence of the each parameter (QW width, barrier width, and indium concentration) on the broadening of interband transitions was considered independently and, finally, all the parameters were taken into account at the same time. The obtained spectrum of interband transitions was compared with experimental data for InGaN QWs (i.e., photoluminescence and contactless electroreflectance measurements). It was found that the large broadening of interband transitions in InGaN QWs results from the inhomogeneous distribution of QW sizes and indium concentration. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

[en] It is shown that in polar InGaN QWs emitting in the blue-green spectral region a Stokes shift between spontaneous emission (SE) and optical transition observed in contactless electroreflectance (CER) spectrum (absorption-like technique) can be observed even at room temperature, despite the fact that the SE is not associated with localized states. Time resolved photoluminescence measurements clearly confirm that the SE is strongly localized at low temperatures whereas at room temperature the carrier localization disappears and the SE can be attributed to the fundamental transition in this QW. The Stokes shift is observed in this QW system because of the large built-in electric field, i.e., the CER transition is a superposition of all optical transitions with non-zero electron-hole overlap integrals and, therefore, the energy of this transition does not correspond to the fundamental transition of InGaN QW. Lasing from this QW has been observed at the wavelength of 475 nm, whereas the SE was observed at 500 nm. The 25 nm shift between the lasing and SE is observed because of a screening of the built-in electric field by photogenerated carriers. However, our analysis shows that the built-in electric field inside the InGaN QW region is not fully screened under the lasing conditions. (orig.)

[en] The radiative recombination time (τ_r) was calculated for inhomogeneous polar InGaN QWs emitting in the green spectral range. These calculations were performed in the framework of a model where the τ_r is inversely proportional to the electron-hole overlap integral. In order to simulate inhomogeneities in this model, it was assumed that the QW width, barrier widths and indium concentration vary with a Gaussian distribution where the nominal QW width, barrier widths and indium concentration correspond to the mean value in this distribution and their fluctuations correspond to the deviation from the main value. The τ_r was calculated for five thousands of randomly generated InGaN QWs and next the spectral map of PL decay was generated for the calculated τ_r which correspond to various QW regions. The obtained maps were compared with the measured maps of PL decay for InGaN QWs emitting in the green spectral range. It has been clearly shown that QW inhomogenities (i.e., QW width fluctuations and indium concentration fluctuations) lead to a spectral dispersion of the τ_r and the non-exponential behavior of PL decay curves. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

[en] Polarization engineering of GaN-based heterostructures opens a way to develop advanced transistor heterostructures, although measurement of the electric field in such heterostructures is not a simple task. In this work, contactless electroreflectance (CER) spectroscopy has been applied to measure the electric field in GaN-based heterostructures. For a set of GaN( d   =  0, 5, 15, and 30 nm)/AlGaN(20 nm)/GaN(buffer) heterostructures a decrease of electric field in the GaN(cap) layer from 0.66 MV cm⁻¹ to 0.27 MV cm⁻¹ and an increase of the electric field in the AlGaN layer from 0.57 MV cm⁻¹ to 0.99 MV cm⁻¹ have been observed with the increase in the GaN(cap) thickness from 5–30 nm. For a set of GaN(20 nm)/AlGaN( d   =  10, 20, 30, and 40 nm)/GaN(buffer) heterostructures a decrease of the electric field in the AlGaN layer from 1.77 MV cm⁻¹ to 0.64 MV cm⁻¹ and an increase of the electric field in the GaN layer from 0.57 MV cm⁻¹ to 0.99 MV cm⁻¹ were observed with the increase in the AlGaN thickness from 10–40 nm. To determine the distribution of the electric field in these heterostructures the Schrödinger and Poisson equations are solved in a self-consistent manner and matched with experimental data. It is shown that the built-in electric field in the GaN(cap) and AlGaN layers obtained from measurements does not reach values of electric field resulting only from polarization effects. The measured electric fields are smaller due to a screening of polarization effects by free carriers, which are inhomogeneously distributed across the heterostructure and accumulate at interfaces. The results clearly demonstrate that CER measurements supported by theoretical calculations are able to determine the electric field distribution in GaN-based heterostructures quantitatively, which is very important for polarization engineering in this material system. (paper)

[en] The authors have applied modulation spectroscopy to study the intersubband (IS) and the interband (IB) transitions in InGaN/AlInN multi-quantum well (QW) structures with the QW width varying from 1.3 to 1.8 nm, and proposed a simple method to analyse the broadening of IS and IB transitions. With this method the measured broadenings of IS and IB transitions have been compared with theoretical calculations performed within the effective mass approximation for a QW system with various QW width fluctuations. Within the framework of this comparison it has been found that the QW width fluctuation in the investigated InGaN/AlInN QW system is close to 2 monolayers.

[en] In order to describe theoretically the tuning of the optical gain by hydrostatic pressure in GaInNAs/GaAs quantum wells (QWs), the optical gain calculations within kp approach were developed and applied for N-containing and N-free QWs. The electronic band structure and the optical gain for GaInNAs/GaAs QW were calculated within the 10-band kp model which takes into account the interaction of electron levels in the QW with the nitrogen resonant level in GaInNAs. It has been shown that this interaction increases with the hydrostatic pressure and as a result the optical gain for GaInNAs/GaAs QW decreases by about 40% and 80% for transverse electric and transverse magnetic modes, respectively, for the hydrostatic pressure change from 0 to 40 kilobars. Such an effect is not observed for N-free QWs where the dispersion of electron and hole energies remains unchanged with the hydrostatic pressure. This is due to the fact that the conduction and valence band potentials in GaInAs/GaAs QW scale linearly with the hydrostatic pressure

[en] The electronic band structure and material gain have been calculated for GaAsBi/GaAs quantum wells (QWs) with various bismuth concentrations (Bi ≤ 15%) within the 8-band and 14-band kp models. The 14-band kp model was obtained by extending the standard 8-band kp Hamiltonian by the valence band anticrossing (VBAC) Hamiltonian, which is widely used to describe Bi-related changes in the electronic band structure of dilute bismides. It has been shown that in the range of low carrier concentrations n < 5 × 10"1"8" cm"−"3, material gain spectra calculated within 8- and 14-band kp Hamiltonians are similar. It means that the 8-band kp model can be used to calculate material gain in dilute bismides QWs. Therefore, it can be applied to analyze QWs containing new dilute bismides for which the VBAC parameters are unknown. Thus, the energy gap and electron effective mass for Bi-containing materials are used instead of VBAC parameters. The electronic band structure and material gain have been calculated for 8 nm wide GaInAsBi QWs on GaAs and InP substrates with various compositions. In these QWs, Bi concentration was varied from 0% to 5% and indium concentration was tuned in order to keep the same compressive strain (ε = 2%) in QW region. For GaInAsBi/GaAs QW with 5% Bi, gain peak was determined to be at about 1.5 μm. It means that it can be possible to achieve emission at telecommunication windows (i.e., 1.3 μm and 1.55 μm) for GaAs-based lasers containing GaInAsBi/GaAs QWs. For GaInAsBi/Ga_0_._4_7In_0_._5_3As/InP QWs with 5% Bi, gain peak is predicted to be at about 4.0 μm, i.e., at the wavelengths that are not available in current InP-based lasers

[en] Contactless electroreflectance is applied to study direct optical transitions from the heavy hole, light hole, and spin-orbit split-off band to the conduction band in compressively strained Ge_1−xSn_x layers of various Sn concentrations at room temperature. It is shown that the energies of these transitions are in very good agreement with theoretical predictions, which take into account non-linear variation of bandgap and spin-orbit splitting plus the strain-related shifts obtained from the Bir-Pikus theory. The bowing parameter for the direct bandgap has been determined to be 1.8 ± 0.2 eV and agree with this one obtained within ab initio calculations, which is 1.97 eV (for indirect bandgap the bowing parameter is 0.26 eV)