Chemical analysis of a silicon crystal reveals gallium at a level of 3.091×10−8 atomic percent. Assuming that the concentration of thermally excited charge carriers from the Si matrix is negligible, what is the density of free charge carriers (free carriers/cm3) in this Si crystal?
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(6.023*10^23)/(12.05)=m
m*(3.091*10^-8)*(10^-2)=
To calculate the density of free charge carriers in the silicon crystal, we need to use the information provided about the gallium impurity.
1. First, we need to convert the atomic percent of gallium (3.091×10−8 atomic percent) into a fraction. Since atomic percent is a relative measure, we divide it by 100 to convert it into a decimal fraction:
Gallium fraction = 3.091×10−8 / 100
2. Next, we need to determine the number of gallium atoms per unit volume. To do this, we need to know the atomic density of silicon (ρ_si) and the molar mass of gallium (M_ga). The atomic density of silicon is the Avogadro's number (6.022×10^23) divided by the molar volume of silicon (~28.09 cm^3/mol):
Number of silicon atoms / cm^3 (ρ_si) = 6.022×10^23 / 28.09
The molar mass of gallium is 69.72 g/mol, and to convert it into atoms/cm^3, we divide it by Avogadro's number:
Number of gallium atoms / cm^3 = 69.72 / (6.022×10^23)
3. Now, we multiply the gallium fraction and the number of gallium atoms per unit volume to get the density of gallium atoms in the silicon crystal:
Density of gallium atoms / cm^3 = Gallium fraction * Number of gallium atoms / cm^3
4. Since each gallium atom contributes one free charge carrier, the density of free charge carriers in the silicon crystal is equal to the density of gallium atoms. Therefore, the density of free charge carriers (free carriers/cm^3) in the Si crystal is:
Density of free charge carriers / cm^3 = Density of gallium atoms / cm^3
Now you can substitute the values mentioned above into the equations to calculate the density of free charge carriers in the silicon crystal.