This calculator determines the fraction of dopants that are ionised at a given temperature, dopant concentration and excess carrier concentration in crystalline silicon.

The dopant ionisation calculator utilises the procedure outlined in the band gap calculator to determine carrier concentrations and Fermi levels as a function of dopant concentration and temperature.

The ionised dopant concentration depends on the relationship between the dopant energy and the Fermi energy [Alt06a, Alt06b]. Several iterations of band gap, carrier concentration and dopant ionisation calculations are performed to simultaneously satisfy charge neutrality (p + N_D⁺ = n + N_A^–) and the law of mass action (p⋅n = n_i²). The calculator allows one or two dopant concentrations, thus providing the opportunity to analyse the ionisation behaviour in compensated silicon, but be careful: the model instituted here is valid for uncompensated or weakly componensated silicon; for strongly compensated silicon, refer to Section IV of [Alt06b]. (Screening properties change with strong compensation, as do the dopant energies, the metal–insulator transition, and the width of the dopant band.)

Note that the parameterisation of Altermatt et al. reproduces measurements between 30 and 300 K only. As temperature increases, the ionisation ratio approaches unity (and reaches unity for many relevant dopant concentrations). We therefore allow temperature inputs as high as 500 K, though we warn against reliance on calculations at T > 300 K.

Neither PV Lighthouse nor any person related to the compilation of this calculator make any warranty, expressed or implied, or assume any legal liability or responsibility for the accuracy, completeness or usefulness of any information disclosed or rendered by this calculator.

[Alt06a]	P.P. Altermatt, A. Schenck and G. Heiser, "A simulation model for the density of states and for incomplete ionization in crystalline silicon. I. Establishing the model in Si:P," Journal of Applied Physics, 100 113714, 2006.
[Alt06b]	P.P. Altermatt, A. Schenck, B. Schmithüsen and G. Heiser, "A simulation model for the density of states and for incomplete ionization in crystalline silicon. II. Investigation of Si:As and Si:B and usage in device simulation," Journal of Applied Physics, 100 113715, 2006.

We thank Fiacre Rougieux (ANU) and Maxime Forster (Apollon Solar) for helpful discussions on dealing with the intricacies of compensated Si.

Please email corrections, comments or suggestions to support@pvlighthouse.com.au.