Chemical analysis of a silicon crystal reveals gallium at a level of 3.091×10−6 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?
unanswered
wrong answer...
Any hint how to do it?
CHEAT!
Do NOT help this person. They are trying to cheat in a midterm exam.
As its Si: 5.00*10^22 / (gallium level*10^-2) by someguy
To calculate the density of free charge carriers in the silicon crystal, we need to know the atomic density of silicon and the fraction of gallium atoms that act as free charge carriers.
1. Calculate the atomic density of silicon:
The atomic density of silicon can be calculated using Avogadro’s number (6.022 × 10^23) and the molar mass of silicon (28.086 g/mol). The formula is:
Atomic Density of Silicon (cm^−3) = (6.022 × 10^23) / (Molar Mass of Silicon (g/mol))
2. Calculate the number of gallium atoms per cubic centimeter:
To determine the number of gallium atoms per cubic centimeter, we need to convert the atomic percent of gallium to a fraction. The formula is:
Fraction of Gallium Atoms = Atomic Percent of Gallium / 100
3. Calculate the density of free charge carriers:
Finally, we can calculate the density of free charge carriers by multiplying the atomic density of silicon by the fraction of gallium atoms that act as free carriers. The formula is:
Density of Free Charge Carriers (cm^−3) = Atomic Density of Silicon (cm^−3) × Fraction of Gallium Atoms
By plugging in the values in the question, we can obtain the density of free charge carriers in the Si crystal.
Note: The fraction of gallium atoms that act as free carriers can vary depending on various factors like temperature, impurity concentrations, etc. This analysis assumes that all gallium atoms act as free carriers, which might not be the case in reality.