Chemical analysis of a germanium crystal reveals indium at a level of 0.03091 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?

1.3724*10^19

To calculate the density of free charge carriers in the germanium (Ge) crystal, we need to use the concept of atomic percent and the number of free carriers per atom.

Here are the steps to calculate it:

Step 1: Find the concentration of indium atoms in the Ge crystal.
The concentration of indium is given as 0.03091 atomic percent. Atomic percent represents the ratio of the number of atoms of the element to the total number of atoms in the crystal. So, 0.03091 atomic percent means there are 0.03091 indium atoms for every 100 germanium atoms.

Step 2: Find the number of indium atoms per unit volume.
To do this, we need to know the density of Ge crystal (ρ). Assume that the density is known, typically in grams per cubic centimeter (g/cm3). Then, we can convert it to the number of indium atoms per cubic centimeter.

Step 3: Convert the number of indium atoms to the number of free charge carriers.
In an n-type semiconductor like Ge, each indium atom contributes one free electron. Therefore, the number of free charge carriers is equal to the number of indium atoms.

Step 4: Calculate the density of free charge carriers.
Divide the number of free charge carriers by the volume of the Ge crystal to obtain the density of free charge carriers in units of carriers/cm3.

Note: The thermal excitation of charge carriers is assumed to be negligible in this case.

Please provide the density (ρ) of the Ge crystal in g/cm3, and then we can proceed with the calculation.