The optical constants of amorphous Ge are determined for the photon energies from 0.08 to 1.6 eV. From 0.08 to 0.5 eV, the absorption is due to k-conserving transitions of holes between the valence bands as in p-type crystals; the spin-orbit splitting is found to be 0.20 and 0.21 eV in non-annealed, and annealed samples respectively. The effective masses of the holes in the three bands are 0.49 m (respectively 0.43 m); 0.04 m, and 0.08 m. An absorption band is observed below the main absorption edge (at 300 °K the maximum of this band is at 0.86 eV); the absorption in this band increases with increasing temperature. This band is considered to be due to excitons bound to neutral acceptors, and these are presumably the same ones that play a decisive role in the transport properties and which are considered to be associated with vacancies. The absorption edge has the form: ω2ϵ2∼(hω−Eg)2 (Eg = 0.88 eV at 300 °K). This suggests that the optical transitions conserve energy but not k vector, and that the densities of states near the band extrema have the same energy-dependence as in crystalline Ge. A simple theory describing this situation is proposed, and comparison of it with the experimental results leads to an estimate of the localization of the conduction-band wavefunctions.

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Optical Properties and Electronic Structure of Amorphous Germanium

Band structure of indium antimonide

A set of 61 ion polarizabilities has been derived from the dielectric constants of 129 oxides and 25 fluorides using a least squares refinement technique in conjunction with the Clausius–Mosotti equation. These polarizabilities can be used to estimate mean dielectric constants of ‘‘well‐behaved’’ compounds. They should be particularly useful in calculation of mean dielectric constants of compounds whose dielectric constants have not been determined. They can also be used as a framework for distinguishing unusual dielectric behavior from normal dielectric behavior where deviations can frequently be attributed to piezo‐ or ferroelectricity, conductivity (ionic or electronic), ‘‘rattling’’ or ‘‘compressed’’ cations with correspondingly high or low polarizabilities, or the presence of dipolar impurities. Deviations observed from calculated dielectric constants can be used to search for unusual physical behavior.

Dielectric polarizabilities of ions in oxides and fluorides

Starting from known properties of non-specific salt effects on the surface tension at an air–water interface, we propose the first general, detailed qualitative molecular mechanism for the origins of ion-specific (Hofmeister) effects on the surface potential difference at an air–water interface; this mechanism suggests a simple model for the behaviour of water at all interfaces (including water–solute interfaces), regardless of whether the non-aqueous component is neutral or charged, polar or non-polar Specifically, water near an isolated interface is conceptually divided into three layers, each layer being 1 water-molecule thick We propose that the solute determines the behaviour of the adjacent first interfacial water layer ( I 1 ); that the bulk solution determines the behaviour of the third interfacial water layer ( I 3 ), and that both I 1 and I 3 compete for hydrogen-bonding interactions with the intervening water layer ( I 2 ), which can be thought of as a transition layer The model requires that a polar kosmotrope (polar water-structure maker) interact with I 1 more strongly than would bulk water in its place; that a chaotrope (water-structure breaker) interact with I 1 somewhat less strongly than would bulk water in its place; and that a non-polar kosmotrope (non-polar water-structure maker) interact with I 1 much less strongly than would bulk water in its place We introduce two simple new postulates to describe the behaviour of I 1 water molecules in aqueous solution The first, the ‘relative competition’ postulate, states that an I 1 water molecule, in maximizing its free energy (—δG), will favour those of its highly directional polar (hydrogen-bonding) interactions with its immediate neighbours for which the maximum pairwise enthalpy of interaction (—δ H ) is greatest; that is, it will favour the strongest interactions We describe such behaviour as ‘compliant’, since an I 1 water molecule will continually adjust its position to maximize these strong interactions Its behaviour towards its remaining immediate neighbours, with whom it interacts relatively weakly (but still favourably), we describe as ‘recalcitrant’, since it will be unable to adjust its position to maximize simultaneously these interactions The second, the ‘charge transfer’ postulate, states that the strong polar kosmotrope–water interaction has at least a small amount of covalent character, resulting in significant transfer of charge from polar kosmotropes to water–especially of negative charge from Lewis bases (both neutral and anionic); and that the water-structuring effect of polar kosmotropes is caused not only by the tight binding (partial immobilization) of the immediately adjacent ( I 1 ) water molecules, but also by an attempt to distribute among several water molecules the charge transferred from the solute When extensive, cumulative charge transfer to solvent occurs, as with macromolecular polyphosphates, the solvation layer (the layer of solvent whose behaviour is determined by the solute) can become up to 5- or 6-water-molecules thick We then use the ‘relative competition’ postulate, which lends itself to simple diagramming, in conjunction with the ‘charge transfer’ postulate to provide a new, startlingly simple and direct qualitative explanation for the heat of dilution of neutral polar solutes and the temperature dependence of relative viscosity of neutral polar solutes in aqueous solution This explanation also requires the new and intriguing general conclusion that as the temperature of aqueous solutions is lowered towards o °C, solutes tend to acquire a non-uniform distribution in the solution, becoming increasingly likely to cluster 2 water molecules away from other solutes and surfaces (the driving force for this process being the conversion of transition layer water to bulk water) The implications of these conclusions for understanding the mechanism of action of general (gaseous) anaesthetics and other important interfacial phenomena are then addressed

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033583500005369

The Hofmeister effect and the behaviour of water at interfaces.

Publisher Summary A refractive index can be increased by ion implantation by changes in density and structure, by the addition of high-polarizability impurity ions, by a reduction of the plasma effect that increases the index and that is most important in the wavelength region far from the energy gap, and by absorption changing in the index in the region of the gap, that is, via the Kramers–Kronig relation. This chapter discusses the optical properties of implanted semiconductors, electrooptic components formed by ion implantation, general principles that determine most luminescent systems, effects of implantation temperature, luminescence centers in LiF-Mg-Ti radiation dosimeters, and use of line spectra in defect studies. In the LiF system, the luminescence bands are broad, and if alternative versions of the same complex exist, they cannot be resolved from the spectra. The addition, by implantation, of ions with incomplete inner electron shells opens up new possibilities as the lattice distortions of the free-ion energy levels are strongly perturbed by the defects in the neighborhood of the ion.

Optical Effects of Ion Implantation

A set of electronic polarizabilities has been obtained from a least-squares fit of experimental refraction data using simple additivity and a Lorentz factor of $\frac{4\ensuremath{\pi}}{3}$. Except for the fluorides, the electronic polarizability values of the alkali-halide crystals calculated from this set agree with the experimental data within 3 percent. Similar least-squares fits were attempted with various values of the Lorentz factor, the best fit being obtained for $\frac{4\ensuremath{\pi}}{3}$. On the basis of $\frac{4\ensuremath{\pi}}{3}$, the additivity assumption and the alkali-halide set, polarizabilities have been obtained for other ions. The best values for the sodium $D$ line in ${\mathrm{A}}^{3}$ are ${\mathrm{Li}}^{+}$ 0.03, ${\mathrm{Na}}^{+}$ 0.41, ${\mathrm{K}}^{+}$ 1.33, ${\mathrm{Rb}}^{+}$ 1.98, ${\mathrm{Cs}}^{+}$ 3.34, ${\mathrm{F}}^{\ensuremath{-}}$ 0.64, ${\mathrm{Cl}}^{\ensuremath{-}}$ 2.96, ${\mathrm{Br}}^{\ensuremath{-}}$ 4.16, ${\mathrm{I}}^{\ensuremath{-}}$ 6.43, ${\mathrm{Ca}}^{++}$ 1.1, ${\mathrm{Sr}}^{++}$ 1.6, ${\mathrm{Ba}}^{++}$ 2.5, ${\mathrm{O}}^{\ensuremath{-}\ensuremath{-}}$ 0.5-3.2, ${\mathrm{S}}^{\ensuremath{-}\ensuremath{-}}$ 4.8-5.9, ${\mathrm{Se}}^{\ensuremath{-}\ensuremath{-}}$ 6.0-7.5, ${\mathrm{Te}}^{\ensuremath{-}\ensuremath{-}}$ 8.3-10.2, ${\mathrm{Ag}}^{+}$ 2.4, ${\mathrm{Cu}}^{+}$ 1.6, ${\mathrm{Cu}}^{++}$ 0.2, ${\mathrm{Zn}}^{++}$ 0.8, ${\mathrm{Cd}}^{++}$ 1.8, ${\mathrm{Ge}}^{4+}$ 1, ${\mathrm{Sn}}^{4+}$ 3.4, ${\mathrm{Pb}}^{++}$ 4.9. Values represented by a spread indicate ions that cannot be treated additively.

Electronic Polarizabilities of Ions in Crystals

The Drude-Zener theory of optical absorption by free carriers is applied to the infrared absorption of $n$-type germanium and $p$-type silicon. Average effective masses so determined are: for electrons in germanium ${〈(\frac{{m}^{*}}{m})〉}_{\mathrm{Av}}$ ranges from 0.11 to 0.22; for holes in silicon ${〈(\frac{{m}^{*}}{m})〉}_{\mathrm{Av}}$ ranges from 0.19 to 0.55. The average effective mass values of electrons in germanium are in good agreement with those measured by cyclotron resonance. The infrared absorption bands of $p$-type germanium are explained on the basis of transitions of holes between three energy bands lying near the top of the valence band. This band structure is suggested by cyclotron resonance experiments. Application of the theory to $p$-type silicon leads to the prediction of an absorption peak near $25\ensuremath{\mu}$ and two lesser ones near $33\ensuremath{\mu}$.

Theory of the Infrared Absorption of Carriers in Germanium and Silicon

F-Center Wave Functions and Electronic g-Values in KCl Crystals

Electrical conductivity in a strong magnetic field was calculated for the case of scattering by delta-function impurities. The impurity concentration was taken as being so sufficiently weak that collision broadening could be neglected. The scattering by an individual center was solved exactly, rather than by perturbation theory. As a result transition probabilities for an electron at the bcttom of a Landau level vanished, rather than diverged. Expressions were given for the longitudinal and transverse conductivities in the oscillatory range and in the quantum limit range for degenerate and nondegenerate statistics. The relation of-this theory to those employing collision broadening was discussed. (auth)

Arnold H. Kahn

Papers

Electronic Polarizabilities of Ions in Crystals

Theory of the Infrared Absorption of Carriers in Germanium and Silicon

F-Center Wave Functions and Electronic g-Values in KCl Crystals

Electron scattering in high magnetic field