Question

Using the data presented in Figure 19.16, determine the number of free electrons per atom for intrinsic germanium and silicon at room temperature (298 K). The densities for Ge and Si are 5.32 and 2.33 g/cm³, respectively.

Now explain the difference in these free-electron-per-atom values.

Answer 1

Figure 19.16 is not provided, but typically germanium has more free electrons than silicon at room temperature due to its smaller bandgap energy, which allows more thermal excitation of electrons.

Step-by-step explanation:

Since the data from Figure 19.16 is not provided here, we cannot calculate the exact number of free electrons per atom for intrinsic germanium and silicon at room temperature (298 K).

However, typically for intrinsic semiconductors at room temperature, germanium (Ge) has approximately 2.2 x 1013 free electrons per cm³, and silicon (Si) has about 1.5 x 1010 free electrons per cm³.

The difference in the number of free electrons per atom between germanium and silicon is largely due to the difference in energy required to excite an electron from the valence band to the conduction band, known as the bandgap energy.

Germanium has a smaller bandgap energy, which allows more electrons to be thermally excited to the conduction band at a given temperature compared to silicon.