Problem: Silicon has a face-centered cubic crystal structure with unit cell edge length of 5.43 Å and four atoms per unit cell.Suppose you dope that 1 - cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

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We’re asked to determine how many milligrams of 1 ppm phosphorus, P is required to dope (fill in the gaps) a 1 cm3 sample of silicon, Si having a face-centered cubic (FCC) crystal structure and unit cell edge length of 5.43 Å and four atoms per unit cell.


To do so, we need to do these steps:

Step1: Calculate the mass and volume one unit cell of Si to determine its densityRecall that the density  cube is given by the equation:

density=massvolume

Step 2: Calculate the mass of 1 cm3 sample of Si

Step 3: Determine mass (in mg) of 1 ppm P needed to dope the 1 cm3 sample of Si.  Recall that ppm is given by the equation: 


ppm=g soluteg solution×106

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Problem Details

Silicon has a face-centered cubic crystal structure with unit cell edge length of 5.43 Å and four atoms per unit cell.

Suppose you dope that 1 - cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?