Chemical analysis of a germanium crystal reveals indium at a level of 0.0003091 atomic percent. Assuming that the concentration of thermally excited charge carriers from the Ge matrix is negligible, what is the density of free charge carriers (free carriers/cm3) in this Ge crystal?

To calculate the density of free charge carriers in the Germanium (Ge) crystal, we need some additional information.

One crucial piece of information is the number density of germanium atoms in the crystal. Let's denote it as n_Ge (number of germanium atoms per cm^3).

The atomic percent of indium in the Ge crystal is given as 0.0003091 atomic percent. It means that there are 0.0003091 indium atoms for every 100 germanium atoms. Since the concentration of thermally excited charge carriers from the Ge matrix is considered negligible, we can assume that all the indium atoms contribute to the density of free charge carriers.

We can calculate the concentration of indium atoms (n_In) in the Ge crystal using the following formula:

n_In = n_Ge * (0.0003091 / 100)

Now, assuming that each indium atom contributes one free charge carrier (i.e., one electron), the density of free charge carriers (n_free) can be calculated as:

n_free = n_In

Therefore, the density of free charge carriers in the Ge crystal is given by:

n_free = n_Ge * (0.0003091 / 100)

Please provide the number density of germanium atoms (n_Ge) in order to calculate the density of free charge carriers accurately.