To enter the sample structure manually, follow the instructions given below.

To run the simulation for a superlattice structure, enter the number of layers within the repeating superlattice in the first field. Then enter the parameters for each layer in the repeating superlattice from top to bottom and enter the total number of superlattice layers.

Otherwise, to run the simulation for a non-repeating structure, enter the total number of layers in the first field. Then enter the parameters for each layer in the sample and in the 'number of repeating superlattice layers' field enter 1 to specify that the structure is not repeating.

To plot the lattice sum, complete the form as explained and then complete the last two fields regarding the range of angles and discretization of the plot and click 'Lattice Sum'.

Example Structures

SiGe/Si (title image)

This pattern is the reflection between the Si (004) Bragg peak at θ = 27.41 degrees and the strained SiGe (004) Bragg peak at θ = 26.95 degrees.

Angle of incidence: 27.2 degrees

2 layers

Material: SiGe & Si

Out of plane lattice constant SiGe: 5.4719 Å

Out of plane lattice constant Si: 5.387 Å

SiGe 200 unit cells thick

Si 50 unit cells thick

Strained SiGe

This pattern is the reflection of the strained SiGe (004) Bragg peak.

Angle of incidence: 26.947 degrees

1 layer

Material: SiGe

Out of plane lattice constant: 5.4719 Å

100 unit cells thick

AlGaAs/GaAs Superlattice

This pattern is the reflection of the AlGaAs/GaAs (008) Bragg peak.

Angle of incidence: 61.265 degrees

2 layers in each superlattice

Material: AlGaAs & GaAs

Out of plane lattice constant AlGaAs: 5.6572 Å

Out of plane lattice constant GaAs: 5.6533 Å

AlGaAs 20 unit cells thick

GaAs 10 unit cells thick

Superlattice repeated 20 times

SrTiO3/PbTiO3

This pattern is the reflection between the SrTiO3 (004) Bragg peak and the PbTiO3 (004) Bragg peak. The brightening of the fringes from left to right are the thickness fringes approaching the SrTiO3 Bragg peak.

Angle of incidence: 28.38 degrees

2 layers

Material: SrTiO3 & PbTiO3

Out of plane lattice constant SrTiO3: 3.89 Å

Out of plane lattice constant PbTiO3: 3.97 Å

SiGe 150 unit cells thick

Si 30 unit cells thick

Sample Parameters

An explanation of each of the input parameters to run the diffraction simulation are listed below along with parameters for two example structures.

Number of Layers - The sample is made of layers of different materials stacked in the out of plane direction, each with different thickness. This field asks for how many of these different layers are in the sample. If the structure is a superlattice, enter the number of layers of materials within the repeating superlattice layer. The value entered must be a positive integer.

Angle of Incidence - The angle that the center of the incoming beam makes with the surface of the sample. As this angle is varied, only the l value in reciprocal space is changed. That is, as the angle is varied, the simulation observes along the (00l) direction in reciprocal space. The value entered must be a positive number between 0 and 90 degrees. For the lattice sum simulation, this will be the center of the range of angles in the plot.

Material - In order of depth, from top to bottom, select the material for each layer in the sample or the repeating superlattice.

Out of Plane Lattice Constant - In order of depth, from top to bottom, enter the value of the lattice constant in the direction of the surface normal in Angstroms for each layer in the sample or repeating superlattice. The value entered must be a positive number. Typical lattice constant values for all the materials in this simulation will be ~5 Å.

Number of Unit Cells - In order of depth, from top to bottom, enter the thickness of each layer in number of unit cells in the out of plane direction. The value entered must be a positive integer.

Number of repeating superlattice layers - In a superlattice, a pattern of layers of different materials are repeated one or more times. This field asks for the total number of these repeating cells in the sample. If the structure you are entering is not a superlattice, enter 1 to specify that the strucutre does not repeat. The value entered must be a positive integer.

A schematic of a simple two layer structure is shown at right.
For this structure, the input parameters with the information given would be:

Number of layers: 2

Material for Layer 1: A

Number of Unit Cells for Layer 1: 6

Material for Layer 2: B

Number of Unit Cells for Layer 2: 9

Number of Repeating Superlattice Layers: 1^{*} (* 1 here indicates that it is not a superlattice structure)

A schematic of a simple superlattice structure is shown at right.
For this structure, the input parameters with the information given would be: