Given:

Compensated n-type silicon

Conductivity (σ) = 16 S/cm

Acceptor doping concentration (Na) = 1017 cm-3

Temperature (T) = 300 K


To find:

Donor concentration (Nd)

Electron mobility (μn)


Solution:


Donor concentration (Nd):

Compensated n-type silicon indicates that it has both donor and acceptor impurities, which contribute to the carrier concentration. The net carrier concentration in compensated semiconductors is given by the difference between the donor and acceptor concentrations. Therefore, the donor concentration can be found as follows:

Nd – Na = n
where n is the electron concentration

Since the material is n-type, the electron concentration is higher than the hole concentration (p), so n = Nd. Therefore,

Nd – Na = n
Nd – 1017 cm-3 = 16 S/cm / 1.6 x 10-19 C/cm3 (charge density of electron)
Nd = 1.6 x 1022 cm-3

Therefore, the donor concentration is 1.6 x 1022 cm-3.

Electron mobility (μn):

The electron mobility can be found using the following equation:

σ = nqμn
where q is the electron charge (1.6 x 10-19 C)

μn = σ / nq
μn = 16 S/cm / (1.6 x 1022 cm-3 x 1.6 x 10-19 C)
μn = 625 cm2/Vs

Therefore, the electron mobility is 625 cm2/Vs.

Explanation:

Compensated n-type silicon has both donor and acceptor impurities. The acceptor impurities create holes and the donor impurities create electrons, which contribute to the carrier concentration. The net carrier concentration in compensated semiconductors is given by the difference between the donor and acceptor concentrations. The electron concentration is higher than the hole concentration in n-type materials, so the donor concentration can be found by subtracting the acceptor concentration from the net carrier concentration. The electron mobility describes how easily electrons can move through the material, and it can be found using the conductivity and electron concentration.