Layer Charge Distribution Research Articles

Donor ordering and the statistics of quantum dot level spacings and widths from full 3D self-consistent electronic structure

Using full 3D self-consistent electronic structure calculations of small (electron numberN∼ 100) lateral quantum dots formed on GaAs–AlGaAs HEMT devices we calculate the statistics of level spacings Δϵpand tunneling coefficients Γpbetween leads and confined states of the dot. We employ random and ordered donor layer charge distributions, the latter generated through Monte Carlo variable range hopping simulations, as well as a homogeneous (jellium) ionic charge distribution, and examine the effects on these statistics.It has recently been argued that the statistics of the level spacings and widths follow from random matrix theory when the Hamiltonian is described by the Gaussian orthogonal ensemble (GOE) for zero magnetic fieldB, and by the Gaussian unitary ensemble (GUE) forBsufficiently large to break time reversal symmetry. Specifically it is argued that when the dot wave functions are expanded in an arbitrary basis the expansion coefficients, according to the postulate of Porter and Thomas, are uniformly distributed in Hilbert space.In our calculation we obtain statistics of level spacings and widths by generating many configurations of disordered and ordered donor charge. This corresponds to the experimental situation of thermal cycling of the device. We find that a pronounced transition occurs in the level spacing statistics between the completely disordered donor layer ensemble, which seems to be well described by random matrix theory, and the ordered ensemble which is dominated by secular variations in the coefficients. In particular, a shell structure in the levels, which results from approximate parabolicity in the self-consistent confining potential, is observed. This, and the effects of symmetry under inversion and azimuthal symmetry, are speculated to undermine level repulsion and result in Poisson statistics for the levels here at the band edge.Finally we find that distortions in the dot shape are markedly less significant in varying the widths (and level spacings) than calculations based on a hard wall potential for the dot predict. This suggests that the notion of invariant atomic structure for sufficiently small dots is not invalidated by the randomness inherent in donor positions and shape distortion but, on the contrary, a systematic study of dot structure is possible.

Saponite and Vermiculite in Amygdales of the Granby Basaltic Tuff, Connecticut Valley

AbstractClay of apparent hydrothermal origin that fills amygdales in the Granby Basaltic Tuff (Lower Jurassic) of the Connecticut Valley was analyzed and found to consist of two exceptionally well-crystallized Fe-rich, trioctahedral 2:1 layer expandable phyllosilicates. Based on chemical and XRD analyses, the minerals were tentatively identified as saponite and vermiculite. The saponite exists predominately in the two-water hydration state, but also displays one- and three-water layer hydration states, which suggests heterogeneous layer charge distribution—a phenomenon not uncommon in smectites. The identity of the second clay remains equivocal, but XRD analyses, especially with regard to the swelling properties of the clay, indicate that it is a vermiculite. The well-crystallized nature of the Granby clay and the large size of the clay flakes (up to 1 mm) allowed us to use SEM/EDS X-ray imaging and spot analysis techniques in an attempt to detect chemical differences between the saponite and vermiculite. Results showed that the chemistry of individual crystals, within and among amygdales, was essentially uniform. This suggests that the saponite and vermiculite are chemically similar and that variations in their swelling properties result from other factors, such as crystal size, layer charge density, or charge localization within the unit layers. Crystal size differences in the Granby clay were observed with both the petrographic and scanning electron microscope. Changes in layer charge density or charge localization within unit layers could have been affected by the oxidation of Fe2+ to Fe3+, a transformation inferred from the green-to-brown color changes observed in the larger amygdales. The Granby clay is of special importance, because it is one of the few examples of a naturally occurring mixture of two well-crystallized, Fe-rich trioctahedral 2:1 layer expandable phyllosilicates with crystallochemical and swelling properties that appear to bridge the operational definitions for the smectite and vermiculite groups.

CLAYFORM: a FORTRAN 77 computer program apportioning the constituents in the chemical analysis of a clay or other silicate mineral into a structural formula

The FORTRAN 77 computer program CLAYFORM apportions the constituents of a conventional chemical analysis of a silicate mineral into a user-selected structure formula. If requested, such as for a clay mineral or other phyllosilicate, the program distributes the structural formula components into appropriate default or user-specified structural sites (tetrahedral, octahedral, interlayer, hydroxyl, and molecular water sites), and for phyllosilicates calculates the layer (tetrahedral, octahedral, and interlayer) charge distribution. The program also creates data files of entered analyses for subsequent reuse.

Expanding behaviour, structural disorder, regular and random irregular interstratification of 2:1 layer-silicates studied by high-resolution images of transmission electron microscopy

AbstractExpanding and non-expanding layers of interstratified clay minerals have been examined by high-resolution transmission electron microscopy. Permanent expansion of swelling layers under the electron beam was achieved by intercalation ofn-alkylammonium ions, especially the octadecylammonium ion. Oriented flakes of clay minerals were prepared by embedding the expanded or non-expanded clay minerals in epoxy resin, followed by centrifugation before hardening of the resin. The minerals were then cut perpendicular to 001 using an ultramicrotome. Crystals ofmacroscopic trioctahedral vermiculitesshow homogeneous interplanar distances of 24 Å after intercalation of octadecylammonium ions. Crystals ofdioctahedral soil vermiculitesoften show a central zone with non-expanding 10 Å layers; the outer zone shows a disturbed layer sequence extensively expanded byn-alkylammonium ions. After embedding in epoxy resin, vermiculites show stable 9·2 Å interplanar spacings but smectites expand to 13 Å.Montmorillonitesof theWyoming typeshow curved stacks of layers. Most of the layer stacks ofmontmorillonitesof theCheto typeare split and disordered aggregates of single layers are formed. Crystals ofillitesandglauconitesare built up of aggregated small stacks of 10 Å layers, the layer stacks consisting of 10 layers. Mostly the boundaries of the layer stacks are parallel to their 001 planes; sometimes low-angle boundaries are found. The dimensions of the layer stacks, ∼ 100 Å thick and some hundreds of Å in plane, are equal to the dimensions of the domains of coherent scattering of X-rays. The border layers between the layer stacks are identical with those 5 to 10% of layers which swell with glycerol or ethylene glycol during X-ray analysis. Some of the layer stacks of illite and glauconite crystals are expanded by octadecylammonium ions within a fortnight. The other stacks show unchanged 10 Å spacings. The different expanding behaviour of different layer stacks reflects the heterogeneity of the layer-charge distribution in the mica clay minerals.K-bentonitesshow the same expanding behaviour as illites and glauconites but the number of layers expanding with octadecylammonium ions is greater in K-bentonites than in illite crystals. Expanded mixed-layered minerals of the illite-smectite type show a different layer stacking sequence from illites. Random irregular stacking of mica layers with expanded layers are recognized rather than coherent stacks of mica layers. The crystals have a stepped morphology, perhaps effected by translations along the 001 plane. After reaction of therectoritefromGarland Countywith octadecylammonium ions, the non-expanded mica layers and the expanded smectite-like layers can be distinguished. The heterogeneity of the interlayer charges of the smectite layers is documented by the formation of alkyl double-layers with 17 Å spacings and alkyl triple-layers with 21 Å spaces in irregular sequence. The ‘rectorite’ from theGoto Mineexpands nearly homogeneously in comparison with the rectorite from Garland County. After reaction with octadecylammonium ions, interplanar spacings of mostly 31 Å are observed but rarely spacings of 27 Å. The smectite layers of thecorrensitefromKaubenheimare expanded by tetradecyl-ammonium ions to 18 Å spacings by formation of alkyl double-layers. A regular 1 : 1 layer structure of 14 Å chlorite layers and expanded 18 Å smectite layers with total spacing of 32 Å can be observed.Muscoviteandpyrophylliteare not expandable byn-alkyl-ammonium ions within a fortnight. However, sporadic layers ofceladonitecrystals are expanded. Generally the 10 Å or 9·2 Å layers extend over the whole crystals of the three minerals. In celadonite crystals, disorder is caused sporadically by interrupted layers or slightly enlarged layer spacings.

Expansion of Smectites as a Function of Vapor Pressure of Ethylene Glycol

AbstractMagnesium‐saturated, 0.2‐ to 1‐µm fraction of six references smectites and two smectite‐rich soil clays were solvated with ethylene glycol vapor at 65°C under graded relative vapor pressures from 3 to 100%. Each smectite expanded over a range of relative vapor pressure. This observation implied that heterogeneity in layer charge distribution of the smectites was common in the specimens. Relatively, Wards 25 and Wards 27 were least heterogeneous, and Wards 31 and Wards 23 were most heterogeneous among the specimens. The relative expandability of smectites under solvation of ethylene glycol vapor followed the sequence of: SHe‐1>Wards 25 = Wards 27≥SWy‐1> Wards 23>Bowdoin C>LC> Wards 31. The sequence corresponded approximately with that of total layer charge of the specimens. Six of the eight smectites exhibited heterogeneity in a random interstratification manner, two exhibited heterogeneity in a zoned interstratification manner. The moisture‐ethylene glycol interaction enhanced the expansion of smectites when they were partially solvated with ethylene glycol.

Silicon and aluminium site distributions in 2:1 layered silicate clays

Although the layer charge in 2:1 phyllosilicate minerals is known to result from the replacement of tetrahedral Si or octahedral Al, Fe and Mg by ions of lower charge, there is only limited information concerning the distribution of layer charge from X-ray crystallographic data1–3. Here we use 29Si and 27Al magic angle spinning (MAS) NMR spectroscopy to examine the site distribution of tetrahedral Si and Al in a series of synthetic trioctahedral clays with (Si/Al)tetr values in the range 2.74–7.69. Analysis of the 29Si spectra shows that Loewenstein's rule for Al occupancy of the tetrahedral sheet is obeyed and that there is some short-range ordering for Al sites. The nature of the ordering is explained in part by the results of electrostatic potential energy calculations. In general, strong 27Al resonances are observed for Al in tetrahedral sites, but the resonances due to Al in octahedral sites are considerably weaker than would be expected on the basis of chemical analysis. Consequently, no quantitative analysis of the 27Al spectra is possible.

Potassium- and Ammonium-Treated Montmorillonites. I. Interstratified Structures with Ethylene Glycol and Water

AbstractMonoionic K- and NH4-smectites saturated with ethylene glycol form mixed-layer structures which usually consist of three kinds of layers: a 10-Å, non-expanded layer; a 14-Å, partly expanded layer; and a 16.8-Å, completely expanded layer. In some samples, the 14-Å layers formed 60–70% of all layers present. When saturated with water vapor the smectites commonly consisted of three kinds of layers (10-, 12.6-, and 15.5-Å). Generally these samples contained fewer expanded layers than those saturated with ethylene glycol. This result is attributed to the smaller dipole moment of water compared with that of ethylene glycol. The greater solvation energy of NH4+ in comparison with that of K+ causes the expansion of a part of layers which did not expand in the K forms. This result indicates that there is an inhomogeneous distribution of layer charge in the smectite structure. The prevalent type of mixed layering in the studied samples is that of random distribution of layers.

A charge-sheet model of the MOSFET

Intuition, device evolution, and even efficient computation require simple MOSFET (metal-oxide-semiconductor field-effect transistor) models. Among these simple models are charge-sheet models which compress the inversion layer into a conducting plane of zero thickness. It is the purpose of this paper to test one such charge sheet model to see whether this approximation is too severe. This particular model includes diffusion which is expected to be important in the subthreshold and saturation regions. As a test the charge sheet model is applied to long-channel devices. Long-channel MOSFET behavior has been thoroughly studied, and is very well explained by the Pao-Sah double-integral formula for the current. Hence, a clear-cut test is a comparison of the charge sheet model with the Pao-Sah model. We find the charge sheet model has two advantages over the Pao-Sah model. (1) It leads to a very simple algebraic formula for the current of long-channel devices. The same formula applies in all regimes from subthreshold to saturation. Neither splicing nor parameter changes are needed. No discontinuities occur in either the current or the small-signal parameters, or in the derivatives of the small-signal parameters. (2) It is simpler to extend the charge sheet model to two or three dimensions than the Pao-Sah model. This simplification is a result of dropping the details of the inversion layer charge distribution. An important aspect of the gradual channel approximation is brought out by the analysis. Suppose the boundary condition relating the quasi-fermi level at the drain, φ fL , to that at the source, φ fo , namely φ ƒL=φ ƒ0+V D where V D is the drain voltage, is applied in all bias regimes. Then it is shown that this means the potential at the drain end of the channel, φ sL is not related to the potential at the source end of the channel, φ so , by φ sL=φ s0+V D Instead, φ sL is computed, not imposed as a boundary condition. It is suggested that this failure of the potential to satisfy the boundary condition at the drain is justifiable. That is, φ sL should be reinterpreted as the potential at the point in the channel where the gradual channel approximation fails. Hence, (2) may be relaxed. However, the “channel length” in the gradual-channel approximation now becomes a fitting parameter and is not the metallurgical source-to-drain separation. In addition several aspects of the long-channel MOSFET are brought out: (1) Pinch-off is achieved only asymptotically as the drain voltage tends to infinity. This is in marked contrast to the often-stated, textbook view that pinch-off is achieved for some finite drain voltage, the saturation voltage. (2) The channel or drain conductance approaches zero only asymptotically. (3) The transconductance saturates only asymptotically. Figures comparing the simple charge-sheet model formulas with the usual textbook formulas are included for direct-current vs drain voltage, channel conductance vs drain voltage, and transconductance vs drain voltage. The charge-sheet model agrees with the original Pao-Sah double-integral formula for the current at all gate and drain voltages, and possesses the correct subthreshold behavior. The textbook formulas do not.

IONIC EQUILIBRIUM AND THE ELECTRICAL CONDUCTIVITY IN THUNDERCLOUDS

The electrical conductivity existing in electrified clouds is computed under the assumption that a primary positive dipole charge distribution exists within the cloud and that the small ion concentrations are controlled by the rate of ion production from cosmic ray ionization, and by the rates of ion loss from the separate processes of ion recombination, diffusion, and conduction. The results show that the cloud is nearly non-conducting by the small ion conduction mechanism when electric fields are present. The charge transfer mechanisms in the cloud boundary regions and in the cloud updraft are examined, and the thickness of the sheathing layer charge distribution in quasi-static cloud boundaries is estimated.

Interstratification in Montmorillonite

Abstract Direct analysis by Fourier transform methods revealed interstratification of three components for a homogeneous, potassium-treated and organic-solvated montmorillon-ite. An initial simple interpretation based on random mixing of two components was shown to be incorrect. Ethylene glycol solvation showed enhanced expansion in agreement with earlier investigations. Glycerol solvation produced a noteworthy contribution from a 14 Å component. An interpretation of the 14 Å component is suggested, based on an asymmetric distribution of layer charge. Regular interstratification, bending or curling of clay layers and anomalous dehydroxylation temperatures may be a consequence of asymmetric layer charge distribution in montmorillonites.

The application of the verwey and overbeek theory to the stability of kaolinite-water systems

A general method for measuring the adsorption of various anions on kaolinite has been presented. Using this method, the adsorption of citrate ions and hydroxyl ions on kaolinite has been described over the alkaline pH range. It has also been shown that the adsorption of these ions does not occur primarily on either the edges or faces of the kaolinite crystal, but probably occurs uniformly over the surface of the particle. The adsorption measurements permitted the calculation of all quantities pertinent to the Verwey and Overbeek theory. This, in turn, permitted a quantitative test of the applicability of this theory to the stability of kaolinite-water systems. It was found, with no overt contradictions, that a great deal of the viscous behavior of aqueous kaolinite suspensions could be explained on the basis of this theory. The results also permitted the formulation of a mechanism for the flocculation and deflocculation of aqueous kaolinite suspensions. It has been shown that three circumstances control the repulsion between particles. These are the extent to which the diffuse parts of the double layers of the particles interact, the total charge of the particles and the potential existing between the surface of the particles and the intermicellar solution, and the distribution of charges in the diffuse part of each double layer. It has also been shown that, in most cases, the effects of charge and potential are of minor importance and that the dispersion and flocculation of aqueous kaolinite suspensions depend only on the effects of diffuse layer interaction and charge distribution in the diffuse layer.