The ${E}_{0}$, ${E}_{0}+{\ensuremath{\Delta}}_{0}$, ${E}_{1}$, ${E}_{1}+{\ensuremath{\Delta}}_{1}$, ${E}_{0}^{\ensuremath{'}}$, and ${E}_{2}$ optical transitions have been measured in ${\mathrm{Ge}}_{1\ensuremath{-}y}{\mathrm{Sn}}_{y}$ alloys $(yl0.2)$ using spectroscopic ellipsometry and photoreflectance. The results indicate a strong nonlinearity (bowing) in the compositional dependence of these quantities. Such behavior is not predicted by electronic structure calculations within the virtual crystal approximation. The bowing parameters for ${\mathrm{Ge}}_{1\ensuremath{-}y}{\mathrm{Sn}}_{y}$ alloys show an intriguing correlation with the corresponding bowing parameters in the ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Si}}_{x}$ system, suggesting a scaling behavior for the electronic properties that is the analog of the scaling behavior found earlier for the vibrational properties. A direct consequence of this scaling behavior is a significant reduction (relative to prior theoretical estimates within the virtual crystal approximation) of the concentration ${y}_{c}$ for a crossover from an indirect- to a direct-gap system.

Optical critical points of thin-film Ge 1-y Sn y alloys: A comparative Ge 1-y Sn y /Ge 1-x Si x study

▪ Abstract New classes of Sn-containing group IV semiconductors are described. Novel CVD routes lead to growth of a broad range of Ge1−ySny alloys and compounds directly on Si substrates. The direct bandgap (E0) and optical transitions E0+Δ0, E1, E1+Δ1, E0′, and E2 of Ge1−ySny exhibit strong nonlinearities in the compositional dependence, and their bowing parameters correlate with those in Ge1 −xSix, suggesting a scaling behavior for the electronic properties. The Ge1−ySny films can be used as “virtual substrates” for the subsequent growth of Ge1−x−ySixSny ternaries. These are created for the first time and exhibit unprecedented thermal stability, superior crystallinity and unique optical and strain properties such as adjustable bandgaps, and controllable strain states (compressive, relaxed, and tensile). The synthesis of Ge1−x−ySixSny makes it possible to decouple strain and bandgap and adds new levels of flexibility to the design of group IV devices. The Ge-Si-Sn system also represents a new class of “d...

TIN-BASED GROUP IV SEMICONDUCTORS: New Platforms for Opto- and Microelectronics on Silicon

This paper is based on a comprehensive review of the literature and our own studies. We present a summary of the theoretical models and related empirical expressions to evaluate parameters related to the carrier transport within Si/SiGe heterostructures. The models and expressions include the effects of alloy composition and mechanical strain on the band structure of Si/SiGe alloys and the corresponding interfaces. They are presented in a form suitable for implementation in various types of device simulators. Important parameters, such as the band structure of strained or relaxed SiGe, the conduction and valence band offsets in the Si1−xGex/Si1−yGey heterostructures, the effective transport masses and the densities of states, have been calculated and shown to be in good agreement with existing experimental and theoretical results. Analytical expressions of those parameters as a function of Ge composition of the SiGe alloy have been given for strained Si on relaxed Si1−yGey substrate and strained Si1−xGex on Si substrate.

https://iopscience.iop.org/article/10.1088/0268-1242/19/10/002/pdf

Si/SiGe heterostructure parameters for device simulations

We discuss a model for the onsite matrix elements of the $s{p}^{3}{d}^{5}{s}^{\ensuremath{\ast}}$ tight-binding Hamiltonian of a strained diamond or zinc-blende crystal or nanostructure. This model features onsite, off-diagonal couplings among the $s$, $p$, and $d$ orbitals and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full Brillouin zone. It introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions. We apply this model to silicon, germanium, and their alloys as an illustration. In particular, we make a detailed comparison of tight-binding and ab initio data on strained Si, Ge, and SiGe.

Onsite matrix elements of the tight-binding Hamiltonian of a strained crystal: Application to silicon, germanium, and their alloys

This feature article presents an overview of a study of several different aromatic-functionalized amphiphilesfatty acid and phospholipid derivatives. These amphiphiles form organized assemblies when the fatty acids are spread as monolayers at the air−water interface or when the phospholipids are dispersed in aqueous solutions. For a wide range of aromatic chromophorestrans-stilbene derivatives and a series of “vinylogues” (1,4-diphenyl-1,3-butadiene and 1,6-diphenyl-1,3,5-hexatriene), diphenylacetylenes, and azobenzenes such as phenyl, biphenyl, and terphenyl derivatives and modified stilbenes (styryl thiophenes and styryl naphthalenes)assembly formation is accompanied by formation of aggregates of the aromatic groups. Results of experimental studies and simulations indicate that in many cases the aromatics form a small, stable “unit aggregate” characterized by strong “noncovalent” edge-to-face interactions among adjacent aromatics. Although the unit aggregates exhibit characteristic spectral shifts and s...

Self-Assembly of Aromatic-Functionalized Amphiphiles: The Role and Consequences of Aromatic−Aromatic Noncovalent Interactions in Building Supramolecular Aggregates and Novel Assemblies

The systematic study of band‐edge luminescence in pseudomorphic Si/Si1−xGex/Si double‐heterostructure layers is reported for a wide composition range, 0.12<x<0.24, for the first time. An analytical expression for the exciton energy gap at 4.2 K valid for x<0.24 is derived from the no‐phonon line energies: ESX(x) = 1.155−0.874x+0.376x2 eV. Addition of an expression for the exciton binding energy provides an approximation for the energy difference between the alloy valence band and the lowest conduction‐band edge at low temperature. An exciton upshift of 16.9 meV due to quantum confinement is observed in a 6.3‐nm Si0.83Ge0.17 alloy well. This is consistent with either type‐I or type‐II band alignment for which the conduction‐band offset has a magnitude ‖ΔEc‖ ≤ 10 meV. The excitonic hole is closely confined in the alloy but the spectra suggest that the electron density in the silicon barriers is increased for the thin layer.

Near‐band‐gap photoluminescence from pseudomorphic Si1−xGex single layers on silicon

Spectroscopic ellipsometry has been used to study thick, relaxed and thin, strained epilayers of Si1−xGex on Si in the range 0.1<x<0.25. Dielectric functions of relaxed Si0.87Ge0.13 and Si0.8Ge0.2 have been obtained and long‐wavelength absorption coefficient values, required for interference fringe fitting, shown to be higher than measured previously. The dielectric function of strained Si0.78Ge0.22 has been measured for the first time and the effects of strain on the critical points shown to be consistent with deformation potential theory. An interpolation procedure has been developed for the fitting of layer composition and thickness, and excellent agreement with conventional techniques obtained for a series of uncapped single epilayers. The surface roughness of Si1−xGex epilayers has been studied as a function of time and deposition temperature and shown to play an important role in the modeling. The application of the technique to the characterization of buried strained layers is discussed.

Spectroscopic ellipsometry characterization of strained and relaxed Si1-xGex epitaxial layers

Critical point (CP) transition energies have been calculated for strained Si1−xGex (0≤x≤0.255) between 2.5 and 3.5 eV from Lorentzian fits to the second differential of reference dielectric function spectra. E1 and E’0 transition energies are similar to those of the relaxed alloy. Comparison with deformation potential theory shows E1+Δ1 to be coincident with E’0 due to a strain‐induced up shift in the former’s transition energy. The reference spectra and CP transition energies are used in an interpolation procedure to analyze spectroscopic ellipsometry spectra of both uncapped and buried layers of strained Si1−xGex. Compositions and thicknesses are obtained in good agreement with alternative techniques.

A. D. Pitt

Papers

Near‐band‐gap photoluminescence from pseudomorphic Si1−xGex single layers on silicon

Spectroscopic ellipsometry characterization of strained and relaxed Si1-xGex epitaxial layers

Spectroscopic ellipsometry of Si1−xGex epilayers of arbitrary composition 0≤x≤0.255

Spectroscopic ellipsometry of Si1-xGex multi-quantum wells