6.1 How to simulate semiconductor layers without electrodes

\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} SIMsalabim}}\) can also be used for cases that have no electrodes. For example, a transient photoluminescence experiment on a perovskite layer on a substrate. In this case, the semiconductor is not attached to any electrodes and there can be no current flow into or out of the semiconductor. All that is needed, is a means to block any such current. A robust way to implement this is to include two very thin layers next to either electrode with suitable band offset and small effective densities of states. Especially the use of small effective densities of states is highly effective: if you set \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} N\_ c}}\) to 1 (per cubic metre), then \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} SIMsalabim}}\) will put at most a single electron or hole per cubic metre in that layer. ¹

As tunnelling is not including in \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} SIMsalabim}}\) there is no physical mechanism that allows current to flow through a well chosen—thin—blocking layer. Very low charge carrier mobilities are not needed and, in fact, best avoided. Figure 6.1 shows an example band diagram. Please note, it is counterproductive to make this blocking layers very thin as 1) this limits the number of grid points available in the region of interest—the perovskite—reducing numerical accuracy and 2) it affects the optics if, for example, a reflective back surface is used. Table 6.1 lists a number of convenient parameters for such a simulation.

To facilitate simulations without electrodes, \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} pySIMsalabim}}\) (as of version 1.05) includes two functions that implement the blocking layers as described above. Function \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} create\_ contactless\_ device}}\) simply takes the input files and add two carefully designed blocking layers between the electrodes and the other layers. The simulation can then be run as usual. Function \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} process\_ output\_ contactless}}\) removes any output that relates to two blocking layers, if desired. There is an example notebook that illustrates how to use these function.