4.3 Internal variables

The internal variables (\(x, V, n, p, J_n, J_p\), etc.) are stored in \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} varFile}}\) so they may be plotted to further analyse the results. A band diagram can readily be plotted as the vacuum level, conduction and valence bands, and quasi-Fermi levels are all included. The parameter \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} outputRatio}}\) determines at which voltages or times these variables are stored. Note, that writing many such variables to file—for example, at every voltage—can slow down the simulation simply due to I/O operations. The number of digits in the output can be limited (which is usually desirable) by setting parameter \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} limitDigits}}\) to 1. If the number of digits is not limited, and depending on the size of the floating point type used, ¹ the number of digits can be too large for some graphing software to read.

Most of the internal variables are self-explanatory. A few, however, may not be so obvious: \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ntb}}\) lists the density of electrons trapped by bulk traps (summed over all levels) in m\(^{-3}\). The density of electrons trapped in interface traps (so in m\(^{-2}\)) is denoted by \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} nti}}\). In steady-state, when electrons and holes recombine via a bulk trap (SRH recombination in the bulk), then the recombination rates for electrons and holes are equal in every grid point (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} BulkSRHn/p}}\)). In transient simulations, this is no longer true and they can have different values. Recombination via interface traps (see section 2.6) can also lead to different rates for electrons and holes: the overall rates (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} JIntSRH}}\) in \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} JVFile}}\) or \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} tJFile}}\)) should be the same, but they need not be the same in every grid point. Hence, the rates for electrons (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} IntSRHn}}\)) and holes (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} IntSRHp}}\)) are also shown separately. The generation rates of electron-hole pairs (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} G\_ ehp}}\)) and of free electrons and holes (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Gfree}}\)) are also listed. These will be the same unless the Onsager-Braun model is used, see section 2.5.