Delta layer

T.-C. Shen, T.-Y. Ji, M. A. Zudov, R. R. Du, J. S. Kline and J. R. Tucker, Ultra dense phosphorus delta layers grown in silicon from PH3 molecular precursors, Appl. Phys. Lett. 80, 1580 (2002). 

The intercellular cement or the delta layer is primarily nonkeratinous protein [78-80] that is, it is low in cystine content (about 2%), and its partial amino acid content is summarized in Table 2-8. 

Dowsett, M.G., Kelly, J.H., Rowlands, G., Ormsby, T.X, Guzman, B., Augnstus, R, Beanland, R. (2003) On determining accurate positions, separations, and internal profiles for delta layers. Applied Surface Science, 203-204, 273-276. 

Shard, A.G., Green, F.M., Brewer, P.X, Seah, M.P, Gilmore, I.S. (2008) Qnantitative molecular depth profiling of organic delta-layers by C o ion sputtering and SIMS. 1. Phys. Chem. B, 112,2596-2605. 

Lee, J.L.S., Ninomiya, S., Matsuo, J., Gihnore, I.S., Seah, M.P., Shard, A.G. (2010) Organic depth profiling of a nanostructured delta layer reference material using large argon cluster ions. Anal. Chem., 82, 98-105. 

Figure 5.5 The various means of relaying depth resolution in SIMS depth profile analysis. Note Intensities are plotted on a linear scale. In the inset is the same data with the intensity plotted on a natural logarithmic scale (decay lengths are described using natnral logarithmic arguments). The data is of the sixth Boron delta layer from the Boron delta layer Silicon structure (a structure with atomically abmpt interfaces with the composition following a delta-like function with depth) examined under 0.5 keV Oj primary ion conditions at normal incidence, i.e. from that shown in Figure 5.25.

The derivation of a response function requires the analysis of a solid in which the original location of atoms is known, such that the migration of atoms under well-controlled conditions can be ascertained with a sufficient level of certainty. Such solids generally take the form of delta-layered structures such as that shown in Figure 5.4(a) and 5.4(b). A delta-layered structure is one in which a foreign atom (Boron in Silicon the case of Figure 5.4(a)) is present at a highly specific depth within the matrix of interest, i.e. exists as an atomically abrupt marker layer. 

A marker may be introduced through some carefully controlled atomic or molecular layer deposition process. In such cases, these form what are referred to as a delta layer, so named because of the theoretically defined concentration profile it should exhibit, i.e. abrupt onset and decay with a fiat top. 

Examples of SIMS analysis of elemental and molecular delta layers are shown in Figures 5.25 and 5.4(b), respectively. That shown in Figure 5.25 is accompanied by the cross-sectional TEM image showing the depths of the respective delta layers (TEM is covered in Appendix A. 11.3). Such procedures are particularly useful in defining variable sputter rates such as those evident over the transient region (see Section 3.2.2.2.2). 

Figure 5.25 To the left are overlaid profiles arising from B and SiB" secondary ion anis-sions from a Boron delta layer Silicon stmcture unda 0.5 keV Oj or IkeV Cs impact, respectively. Both profiles, acquired on Quadrupole-based SIMS instruments in separate experiments, are normalized to the depth of the sixth delta and assuming a constant sputter rate. The intensity scale is normalized to unity to allow effective comparison of the two data sets. To the left is shown the TEM cross section of an adjacent section, with the Boron layers depth identified and listed as 1 through 6. The depths of the Boron layers defined in TEM are also signified by the inverted triangles. Note the greater discrepancies at shallower depths. Reproduced with permission from van der Heide et al. (2003) Copyright 2003 Elsevier.

The Back-Propagation Algorithm (BPA) is a supervised learning method for training ANNs, and is one of the most common forms of training techniques. It uses a gradient-descent optimization method, also referred to as the delta rule when applied to feedforward networks. A feedforward network that has employed the delta rule for training, is called a Multi-Layer Perceptron (MLP). 

Henee, using the delta rule, the weight inerements for the hidden layer are... 

The general principle behind most commonly used back-propagation learning methods is the delta rule, by which an objective function involving squares of the output errors from the network is minimized. The delta rule requires that the sigmoidal function used at each neuron be continuously differentiable. This methods identifies an error associated with each neuron for each iteration involving a cause-effect pattern. Therefore, the error for each neuron in the output layer can be represented as ... 

We are now ready to introduce the backpropagation learning rule (also called the generalized delta rule) for multidayercd perceptrons, credited to Rumelhart and McClelland [rumel86a]. Figure 10.12 shows a schematic of the multi-layered per-ceptron s structure. Notice that the design shown, and the only kind we will consider in this chapter, is strictly feed-forward. That is to say, information always flows from the input layer to each hidden layer, in turn, and out into the output layer. There are no feedback loops anywhere in the system. 

Once the wavelength dependence of the molecular form factor F(nqo) is known from the reasonable model of layer organization, the ratios r /ti may be calculated. The value of these ratios (for example, T2/T1, T3/T1) give a good guide to the sharpness of the distribution function f(z) - for an ideal crystal f(z) would be an array of delta-functions and T2 = Ti = = = 1. From the... 

Backpropagation is a generalized version of the delta rule, extended to multiple layers. The central assumption of BP is that when the target output and actual output at a node differ, the responsibility for the error can be divided between ... 

There are a number of ways to introduce dopants into an EC-ALE deposit. For instance, they can be introduced homogeneously throughout the deposit, or delta doped into the structure. For a relatively homogeneous distribution, low concentrations of oxidized precursors can be incorporated into the reactant solutions. By using very low concentrations, the amounts incorporated in each atomic layer will be limited. The dopant can also be incorporated in its own cycle step. Again, a low concentration would be used so that some fraction of an atomic layer is introduced each cycle. Alternatively, a delta doping scheme can be constructed where a fraction of an atomic layer of dopant is deposited every set number of cycles. All these scenarios involve only a simple modification of the EC-ALE program. 

Field studies on the transformation of endrin in the atmosphere were not located in the available literature. Photochemical isomerization of endrin, primarily to the pentacyclic ketone commonly called delta ketoendrin or endrin ketone, was observed after exposure of thin layers of solid endrin on glass to sunlight (Burton and Pollard 1974). Minor amounts of endrin aldehyde were also formed in this reaction. Results of seasonal studies indicated that this isomerization would proceed with a half-life (first-order kinetics) of 5-9 days in intense summer sunlight, with complete conversion to the pentacyclic ketone in 15-19 days. Knoevenagel and Himmelreich (1976) reported that photodegradation of solid endrin in the laboratory... 

The contaminant layer is very thin, such that a Dirac delta pulse is apphcable. 

The optimal distribution of silver catalyst in a-Al203 pellets is investigated experimentally for the ethylene epoxidation reaction network, using a novel single-pellet reactor. Previous theoretical work suggests that a Dirac-delta type distribution of the catalyst is optimal. This distribution is approximated in practice by a step-distribution of narrow width. The effect of the location and width of the active layer on the conversion of ethylene and the selectivity to ethylene oxide, for various ethylene feed concentrations and reaction temperatures, is discussed. The results clearly demonstrate that for optimum selectivity, the silver catalyst should be placed in a thin layer at the external surface of the pellet. 

Most modern weapons use a hollow Pu core or pit with an implosion mechanism for detonation. Also low density Pu or delta-Pu is used due to its high compressibility. Modem pits may be composites of Pu239 and U235. In view of chemical reactivity and toxic nature of Pu, it is a general practice to plate the completed pit with a thin layer of inert material-previously nickel and now gold. 

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