To calculate silicon carrier concentration values, we use carrier mobility values derived from Thurber, Mattis, Liu, and Filliben, National Bureau of Standards Special Publication 400-64, The Relationship Between Resistivity and Dopant Density for Phosphorus-and Boron-Doped Silicon (May 1981), Table 10, Page 34 and Table 14, Page 40.

To calculate germanium carrier concentration values, we use carrier mobility values derived from D. B. Cuttriss, Bell System Technical Journal (March 1961) Page 509

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Note: N type silicon concentrations derived from resistivities less than 1e-3 are approximated, and will not agree with those from Thurber's formulas. At low concentrations, near the intrinsic level, no consideration is made for the effect of minority carriers.