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12.1 THE SUPERLATTICE UNIT CELL The large-basis approach to a pseudopotential calculation can be applied to semiconductor heterostructures, where in particular, the short-period nature of the repeating unit cell in a superlattice is an ideal example. In order to proceed with such a calculation, it is necessary only to deduce the Bravais lattice vectors describing the crystal symmetry of the superlattice and from these derive the reciprocal lattice vectors. Fig. 12.1 displays the now familiar zinc blende crystal lattice along one of the (100) directions. The crystal can be thought of as being composed of a series of 'one-dimensional' spirals which project into the plane of the paper. Such a spiral begins on an atom (in this case a cation) labelled ' 1' and then proceeds anticlockwise through atoms '2', '3' and '4', with the fifth atom in the spiral being exactly one lattice constant behind the first. This is illustrated more clearly in Fig. 12.2. Choosing the z-axis along the length of the spiral, then the atomic positions, in units of AQ, follow

Using a tt extension would automatically cause the le to be associated with the TextTemplatingFileGenerator, which will be executed every time the Transform All Templates button is used in the authoring solution Using the tt le extension avoids this

Figure 12.2 A single spiral of zinc blende: (left) Looking along one of the (100) directions; (centre) slightly off axis; (right) side view

In QuickBooks, the steps in the customer transaction cycle are approximated on the Customer Navigator screen, shown in Figure 14-1. Icons on the screen represent signi cant accounting events in each customer transaction, such as providing customers with estimates, creating invoices, and receiving payments.

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This provides the text of the new le to be created alongside the model le $safeitemname$ will be substituted for the item name entered in the Add New Item dialog on item template expansion Now we need to reference this le from the item template de nition Open CSharptt in the same folder and edit it to add an entry in the <TemplateContent> section, as follows (the entry is shown in bold italics):

This is easily generalised to a superlattice by simply defining the atomic positions with the appropriate choice of species. Fig. 12.3 illustrates this for a diamond (just to keep the illustration simple) heterostructure. Again, the atomic positions within the unit cell are repetitions of the four primitive vectors r1 to r4 given in equations (12.1) to (12.4) above. Thus for a superlattice of period n z A 0 , the position vectors of the atoms within this larger basis are given by:

Figure 14-1: The Customer Navigator screen icons represent events in the customer transaction cycle.

The Bravais lattice vector describing the periodicity of the superlattice along the axis of symmetry (usually defined as the z-axis) is therefore clearly just nzA0k^. Referring back to Fig. 12.1, then the Bravais lattice vectors describing the in-plane (x-y) periodicity are those linking the atoms labelled ' 1', i.e. in units of A0, (1/2,1/2,0) and (1/2, 1/2,0). In summary, the Bravais lattice vectors for a superlattice are:

<#@ template inherits="MicrosoftVisualStudioTextTemplatingVSHostModelingTextTransformation" debug="true"#> <#@ output extension="vstemplate" #> <#@ Dsl processor="DslDirectiveProcessor" requires="fileName='\\Dsl\DslDefinitiondsl'" #> <!--DSL Tools Language Template--> <VSTemplate Version="200" Type="Item" xmlns="http://schemasmicrosoftcom/developer/vstemplate/2005" xmlns:xsi="http://wwww3org/2001/XMLSchema-instance"> <TemplateData> <Name Package="{<#= thisDslPackageGuid #>}" ID="103"/> <Description Package="{<#= thisDslPackageGuid #>}" ID="102"/> <Icon Package="{<#= thisDslPackageGuid #>}" ID="201" /> <ProjectType>CSharp</ProjectType> <SortOrder>360</SortOrder> <DefaultName> <#=thisDslName#><#=thisDslEditorFileExtension#> </DefaultName> <AppendDefaultFileExtension>true</AppendDefaultFileExtension> </TemplateData> <TemplateContent> <ProjectItem TargetFileName=" $fileinputname$<#=thisDslEditorFileExtension#>"> <#=thisDslEditorFileExtension#><#=thisDslEditorFileExtension#> </ProjectItem> <ProjectItem TargetFileName=" $fileinputname$<#=thisDslEditorFileExtension#>diagram"> <#=thisDslEditorFileExtension#>diagram </ProjectItem> <ProjectItem ReplaceParameters="true" TargetFileName="$fileinputname$tt"> <#=thisDslEditorFileExtension#>ttfile </ProjectItem> </TemplateContent> </VSTemplate>

Estimates are the rst step in the customer transaction cycle for companies that provide them. The estimate feature is available only in the Pro, Premier, and Enterprise Solutions editions. An estimate is a document that establishes certain expectations between you and the customer within an agreed-upon range of certainty. Estimates differ from nal bills because they are not intended to re ect the nal amount that will be billed, only to inform the customer of an approximation of this amount. To create an estimate, you must rst make sure the QuickBooks estimate feature is turned on. Only the administrator can do this. To activate the estimates feature, perform the following steps: 1. From the Edit menu, choose Preferences. Select Jobs & Estimates in the scroll box, and then click the Company Preferences tab. The Preferences dialog box shown in Figure 14-2 appears.

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