This NPL simulation is designed to show the effects of various parameters on the resistivity/conductivity of selected semiconductors and an insulator (Diamond).
The left side of the simulation shows the controls.
The temperature can be varied between 10 and 1000 °K.
There is a choice of three substrates, Silicon, Germanium (semiconductors) and Diamond (insulator).
The two semiconductors can be doped to provide either n type or p type materials by the use of donor impurities or acceptor impurities respectively. There are mulitple choices for each type of impurity, each of which will have an associated ionization energy for the particular substrate it is in. It is also possible to have no impurities and just look at the intrinsic properties of the semiconductor.
The impurity concentration can also be varied, using a logarithmic slider.
On the right hand side is shown the outputs from the simulation. The top two bar graphs show the number ratio of majority carriers and resultant resistivity/conductivity using logarithmic scales, a necessity because of the large range of these parameters. The label for the number ratio graph shows the majority carrier (where Ne = number of electrons, Nh = number of holes and Ntot = the total number of valence electrons). To change from a resistivity display to a conductivity display press the button below the bar graph.
The lower figure is a band gap diagram showing the effect of the substrate on the band gap and the effect of adding impurities. The colour of the two bands indicates the number of carriers present in each band using the same colour scale as the graph above. The filled or empty circles represent a logarithmic scale showing the number of electrons/holes that are still to be ionized. When all the circles are full it means that 100% of the donor impurity atoms have electrons. For every circle that becomes empty then this means that the 0.1, 0.01, 0.001 etc. of the donor impurity atoms are ionized. The converse is true for acceptor impurities, i.e. when all the circles are full then all the electron vacancies are filled, this is as if all the holes have ionized.
By varying the temperature it is very easy to see how the impurity atoms become completely ionized. And by adding impurities it is easy to see the large effect this makes on the resistivity of the material.