Simple layer

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Simple layer

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Simple layers are used in most cases to represent a thick or thin layer of a material in the stack. Simple layers have a thickness (always specified in microns) and you must assign a material to it. In addition, you can choose between two modes of handling the contributions from multiply reflected partial waves, as discussed below.

Some considerations about wave propagation through layer stacks are discussed in [Harbecke 1986A], in particular the superposition of partial waves. In the case of thin layers, the partial waves reflected at the top interface and those that travel through the layer and are reflected back at the bottom interface must be superimposed to the total reflected wave by summing up their amplitudes, taking into account the phase. This may lead to constructive or destructive interference, depending on the wavelength of light. This kind of superposition is called 'coherent'. The interference fringes observed in reflection or transmission spectra get very narrow if the thickness of the layer becomes larger and larger.

Eventually the narrow structures are not resolved experimentally due to the limited resolution of spectrometers, or due to thickness inhomogeneities over the investigated sample spot which may lead to a cancellation of the interference structures. In these cases the measured spectra are quite smooth as the red one shown below, whereas the simulated blue spectrum shows interference fringes. As can be seen the sharp structures are not resolved completely in the simulation, either.

Measured transmission spectrum (red) of an ITO layer (90 nm) on top of a glass substrate (990 micron thickness). The blue curve shows a computed spectrum with coherent superposition of partial waves for the glass layer.

 

Instead of doing the tedious task to compute a lot of spectra for various thicknesses and take the average to remove the interference fringes in the simulation one can follow a shortcut and drop the phase terms in the superposition of the partial waves, as suggested in [Harbecke 1986A]. This is called the incoherent superposition which leads to multiple reflection, but no multiple interference effects. As shown below the agreement between computed and measured spectra can be excellent if the layer thickness is really much larger than the wavelength of light:

Same as above, but now with incoherent superposition of partial waves for the glass layer.

 

To switch between coherent and incoherent superposition mode for a layer, select the cell labeled 'coherent' or 'incoherent' in the layer stack list and press the function key F4 or F5. This will change from coherent to incoherent treatment or the other way round.

 

Warning: if you choose incoherent superposition for thin layers your computed spectrum will be wrong!