Consider intrinsic Si at room temperature. Intrinsic refers to pure Si, an ideal single crystal with impurity concentrations below ppb (parts per billion). There is an equilibrium concentration of electrons and holes at room temperature, due to thermal excitation. This is the intrinsic carrier concentration (ni) given by
Nc and Nv, the eﬀective density of states at the band edges, are dependent on temperature and the eﬀective mass of the electron and holes respectively. For Si, m^∗ e is 1.08 me and m^∗ h is 0.60 me. From this the eﬀective density of states can be calculated using
At room temperature the values of Nc and Nv for Si are 2.81 × 10^25 m^−3 and 1.16 × 10^25 m^−3. These are the total number of available states at the band edges for the electrons and holes to occupy. Hence, the intrinsic carrier concentration at room temperature can be calculated using equation 1 with the band gap value of 1.10 eV . This gives ni equal to 10^16 m^−3 or 10^10 cm^−3. Thus, pure Si at room temperature has 10^10 cm^−3 electrons in the conduction band and a equal number of holes in the valence band. To place this number in context, the number of Si atoms per unit volume can be calculated from the density (2.3 g cm^−3) and the atomic weight (28 g mol^−1). This works out to be 5 × 10^22 atoms cm^−3. So there is approximately 1 electron/hole for every 5 × 10^11 Si atoms! This is a very low concentration compared to metals, where the electron concentration is the comparable in magnitude to the atomic density and explains why semiconductors have a poor conductivity compared to metals. The conductivity is given by
For Si, µe and µh are 13^50 cm^2 V ^−1 s^−1 and 450 cm^2 V ^−1 s^−1 respectively. So, the room temperature conductivity is 3×10^−6 Ω^−1cm^−1 or a resistivity of 3.5 × 10^5 Ωcm. The room temperature conductivity of Cu is 16 × 10^−7 Ωcm, nearly 12 orders of magnitude lower than Si and the diﬀerence is directly related to the diﬀerence in concentration of the charge carriers.