Many physical phenomena are described by first-order differential equations whose solution is an exponential decay. Determining the time constants and amplitudes of exponential decays from the experimental data is a common task in semiconductor physics (deep level transient spectroscopy), biophysics (fluorescence decay analysis), nuclear physics and chemistry (radioactive decays, nuclear magnetic resonance), chemistry and electrochemistry (reaction kinetics) and medical imaging. This review article discusses the fundamental mathematical limitations of exponential analysis, outlines the critical aspects of acquisition of exponential transients for subsequent analysis, and gives a comprehensive overview of numerical algorithms used in exponential analysis. In the first part of the article the resolution of exponential analysis as a function of noise in input decays is discussed. It is shown that two exponential decays can be resolved in a transient only if the ratio of their time constants is greater than t...

Exponential analysis in physical phenomena

We calculate the double resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes, and two-phonons ones. Phonon and electronic dispersions reproduce calculations based on density functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kind of idealized defects. For an excitation energy of $\epsilon_L=2.4$ eV, the agreement with measurements is very good and calculations reproduce: the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the D, $D'$, 2D and $2D'$ lines; the line shapes; the presence of small intensity lines in the 1800, 2000 cm$^{-1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. According to the present findings, the intensity ratio between the $2D'$ and 2D lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and $D'$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal.

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Theory of double-resonant Raman spectra in graphene: intensity and line shape of defect-induced and two-phonon bands

Since its discovery1, early in 1928, the scattering of light with altered frequency has been investigated in many crystals, and much valuable information has been accumulated. The significance of the results and their relation to theories of solid state are clearly matters of great interest.

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Scattering of light in crystals

We present a comprehensive review of implementation and application of Laplace deep-leve1 transient spectroscopy (LDLTS). The various approaches that have been used previously for high-resolution DLTS are outlined and a detailed description is given of the preferred LDLTS method using Tikhonov regularization. The fundamental limitations are considered in relation to signal-to-noise ratios associated with the measurement and compared with what can be achieved in practice. The experimental requirements are discussed and state of the art performance quantified. The review then considers what has been achieved in terms of measurement and understanding of deep states in semiconductors through the use of LDLTS. Examples are given of the characterization of deep levels with very similar energies and emission rates and the extent to which LDLTS can be used to separate their properties. Within this context the factors causing inhomogeneous broadening of the carrier emission rate are considered. The higher resolution achievable with LDLTS enables the technique to be used in conjunction with uniaxial stress to lift the orientational degeneracy of deep states and so reveal the symmetry and in some cases the structural identification of defects. These issues are discussed at length and a range of defect states are considered as examples of what can be achieved in terms of the study of stress alignment and splitting. Finally the application of LDLTS to alloy systems is considered and ways shown in which the local environment of defects can be quantified.

Laplace-transform deep-level spectroscopy: the technique and its applications to the study of point defects in semiconductors

Series Preface. Preface. Acknowledgements. 1 Structural Properties. 1.1 Ionicity. 1.2 Elemental Isotopic Abundance and Molecular Weight. 1.3 Crystal Structure and Space Group. 1.4 Lattice Constant and Its Related Parameters. 1.5 Structural Phase Transition. 1.6 Cleavage Plane. 2 Thermal Properties. 2.1 Melting Point and Its Related Parameters. 2.2 Specific Heat. 2.3 Debye Temperature. 2.4 Thermal Expansion Coefficient. 2.5 Thermal Conductivity and Diffusivity. 3 Elastic Properties. 3.1 Elastic Constant. 3.2 Third-Order Elastic Constant. 3.3 Young's Modulus, Poisson's Ratio and Similar. 3.4 Microhardness. 3.5 Sound Velocity. 4 Lattice Dynamic Properties. 4.1 Phonon Dispersion Relation. 4.2 Phonon Frequency. 4.3 Mode Gruneisen Parameter. 4.4 Phonon Deformation Potential. 5 Collective Effects and Some Response Characteristics. 5.1 Piezoelectric and Electromechanical Constants. 5.2 Frohlich Coupling Constant. 6 Energy-Band Structure: Energy-Band Gaps. 6.1 Basic Properties. 6.2 E0-Gap Region. 6.3 Higher-Lying Direct Gap. 6.4 Lowest Indirect Gap. 6.5 Conduction-Valley Energy Separation. 6.6 Direct-Indirect-Gap Transition Pressure. 7 Energy-Band Structure: Effective Masses. 7.1 Electron Effective Mass: G Valley. 7.2 Electron Effective Mass: Satellite Valley. 7.3 Hole Effective Mass. 8 Deformation Potentials. 8.1 Intravalley Deformation Potential: G Point. 8.2 Intravalley Deformation Potential: High-Symmetry Points. 8.3 Intervalley Deformation Potential. 9 Electron Affinity and Schottky Barrier Height. 9.1 Electron Affinity. 9.2 Schottky Barrier Height. 10 Optical Properties. 10.1 Summary of Optical Dispersion Relations. 10.2 The Reststrahlen Region. 10.3 At or Near The Fundamental Absorption Edge. 10.4 The Interband Transition Region. 10.5 Free-Carrier Absorption and Related Phenomena. 11 Elastooptic, Electrooptic and Nonlinear Optical Properties 11.1 Elastooptic Effect. 11.2 Linear Electrooptic Constant. 11.3 Quadratic Electrooptic Constant. 11.4 Franz-Keldysh Effect. 11.5 Nonlinear Optical Constant. 12 Carrier Transport Properties. 12.1 Low-Field Mobility: Electrons. 12.2 Low-Field Mobility: Holes. 12.3 High-Field Transport: Electrons. 12.4 High-Field Transport: Holes. 12.5 Minority-Carrier Transport: Electrons in p-Type Materials. 12.6 Minority-Carrier Transport: Holes in n-Type Materials. 12.7 Impact Ionization Coefficient. Index.

Properties of group-IV, III-V and II-VI semiconductors

An arrangement of self-assembled GaN nanowires (NWs) grown by plasma-assisted molecular beam epitaxy on a Si(111) substrate is studied as a function of the temperature at which the substrate is nitridized before GaN growth. We show that the NWs grow with the c-axis perpendicular to the substrate surface independently of nitridation temperature with only a slight improvement in tilt coherency for high nitridation temperatures. A much larger influence of the substrate nitridation process on the in-plane arrangement of NWs is found. For high (850 °C) and medium (450 °C) nitridation temperatures angular twist distributions are relatively narrow and NWs are epitaxially aligned to the substrate in the same way as commonly observed in GaN on Si(111) planar layers with an AlN buffer. However, if the substrate is nitridized at low temperature (~150 °C) the epitaxial relationship with the substrate is lost and an almost random in-plane orientation of GaN NWs is observed. These results are correlated with a microstructure of silicon nitride film created on the substrate as the result of the nitridation procedure.

https://iopscience.iop.org/article/10.1088/0957-4484/24/3/035703/pdf

Influence of substrate nitridation temperature on epitaxial alignment of GaN nanowires to Si(111) substrate.

Laterally Overgrown Structures as Substrates for Lattice Mismatched Epitaxy

The results on growth mechanism of GaAs layers by epitaxial lateral overgrowth (ELO) technique from the liquid phase are reviewed. In particular, effects of melt supersaturation, seed orientation, density of surface steps and growth temperature on properties of ELO layers are discussed. It is shown that the results obtained are not a specific attribute of LPE ELO growth of GaAs layers on GaAs substrates but represent a more general phenomena encountered during the ELO growth of other epitaxial systems.

Epitaxial lateral overgrowth of GaAs: Principle and growth mechanism

Contactless electroreflectance studies of the Fermi level position at the air/GaN interface: Bistable nature of the Ga-polar surface

The growth mode and structural and optical properties of novel type of inclined GaN nanowires (NWs) grown by plasma-assisted MBE on Si(001) substrate were investigated. We show that due to a specific nucleation mechanism the NWs grow epitaxially on the Si substrate without any SixNy interlayer, first in the form of zinc-blende islands and then as double wurtzite GaN nanorods with Ga-polarity. X-ray measurements show that orientation of these nanowires is epitaxially linked to the symmetry of the substrate so that [0001] axis of w-GaN nanowire is directed along the [111]Si axis. This is different from commonly observed behavior of self-induced GaN NWs that are N-polar and grow perpendicularly to the surface of nitridized silicon substrate independently on its orientation. The inclined NWs exhibit bright luminescence of bulk donor-bound excitons (D0X) at 3.472 eV and exciton-related peak at 3.46 eV having a long lifetime (0.7 ns at 4 K) and observable up to 50 K.

https://iopscience.iop.org/article/10.1088/0957-4484/25/13/135610/pdf

Zbigniew R. Zytkiewicz

Papers

Influence of substrate nitridation temperature on epitaxial alignment of GaN nanowires to Si(111) substrate.

Laterally Overgrown Structures as Substrates for Lattice Mismatched Epitaxy

Epitaxial lateral overgrowth of GaAs: Principle and growth mechanism

Contactless electroreflectance studies of the Fermi level position at the air/GaN interface: Bistable nature of the Ga-polar surface

Growth by molecular beam epitaxy and properties of inclined GaN nanowires on Si(001) substrate