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note
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At 4 K, well below the donor ionization energies, it is possible to perform a simple calculation from Kittel chapter 8, of the carrier concentration (n) in the silicon using the formula n= (n0 Nd) 1/2 exp (- Ed /2 kB T), dependent on the impurity concentration Nd, ionization energy of the impurities Ed and n0 =2 (me kB T/2π) 3/2. Using a simple Drude fit of our complex permittivity in Fig. 5, we estimate that the charge carrier concentration in the silicon is approximately 1021 at room temperature; the temperature dependence indicates that this concentration should decrease to nearly nil at 4.2 K.
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