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# 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?

###### FREE Expert Solution

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:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

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:

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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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Unit Cell concept. You can view video lessons to learn Unit Cell. Or if you need more Unit Cell practice, you can also practice Unit Cell practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Billman's class at Abilene Christian University.