Manual curve fitting

1. Preparation

This document practically introduces the procedure of “Manual Fitting.” The term “fitting” here means that the parameters of a model are varied until the best match between the simulated and experimental reflectivity curves is achieved. The parameters of a multilayer model are the thickness, density, and roughness of individual layers. Before Fitting, the initial model must be created, and the experimental reflectivity data must be loaded into the program. The creation of a model is described in How to create a model and calculate XRR, so details of this step are omitted here. The project file mo-b_demo.xrcx is located in the examples folder.

1. Create an initial model. The model's parameters should be based on some preliminary information, such as materials used for deposition and their sequence thickness of layers based on deposition rates and times. Cross-sectional TEM might help with the initial step. In this case, a thick Mo sublayer was first deposited on the Si wafer. Then, 250 pairs of Mo and B were deposited. A thick B layer was deposited on the top.

2. To load the experimental XRR curve, click Load on the Data pane and select file mo-b_demo.tet.

3. Press F5 to compute the theoretical XRR curve. After finishing the computation, the Calculation tab will be activated. There, you can see both experimental and calculated curves. The curves did not match because the initial model did not represent the real structure well.

4. Use Spinedits for every layer's parameter to adjust the model's parameters to match the curves quickly. Step combobox in the bottom of the fitting window allows changing of the variation step from 0.001 to 5 (1 by default).

2. Fitting

1. Roughly adjust the period of the structure. Use the spin button to quickly change the thickness of the second B layer until the position of the main diffraction peaks matches. Also, reduce the roughness of the B layer to increase the intensity of the last peak.

2. Roughly adjust the ratio of B and Mo thickness. This ratio affects the relative intensity of the diffraction peaks. For instance, the second peak is now too high, and the third peak is too low. Because Mo and B layers are inside the main stack, and the total thickness of the main stack defines their angular position (see Bragg’s equation), the ratio adjustment should not change the stack. To keep the total thickness of the stack fixed, check B and Mo layers as shown here:

3. Adjust the roughness of the layers to match the intensity of peaks further.

4. Modify the model to approach the real structure and to get a better Fitting. For instance, interlayers between B and Mo might be introduced. Some low-density carbon contained layer could be on the surface, etc.