Silicon atom density is 5 x 1022 cm-3 (i.e., number of silicon atoms per cubic c

Question

Silicon atom density is 5 x 1022 cm-3 (i.e., number of silicon atoms per cubic centimeter of silicon).

If the boron dopant concentration is 1015 cm-3, (i.e., in one cubic centimeter of that same silicon sample, there is 1015 boron atoms), how far are the boron atoms away from each other? Hints: As an approximate calculation: Assume a single silicon atom occupies a sphere; calculate the volume of the sphere as a function of its radius.

Assume the spheres pack into a cubic centimeter (with about a 70% packing efficiency); i.e.,

how many single-atom silicon spheres fit into 1 cubic centimeter.

This is already given as an empirical fact: 5 x 1022.

Repeat the same analysis for boron at the concentration given.

Explanation / Answer

I need to know what the doping concentrations in PPM would be for N-Type, Phosphorous doped silicon.

That's a question open to interpretation. Assuming you mean doping concentration as in electrons or holes the answer is directly related to the ppm of silicon. First we need some values:

Atomic weight of silicon: 28.0855
Density (near r.t.) 2.329 g/cm-3
Avogadro's number = 6.0221415E+23

Divide the atomic weight by the density:
28.085/2.329 = 12.059 cm-3 of Si per mole

Divide Avagadro's number by the result:
6.0221415E+23/12.059 = 4.994E+22 atoms of Si per cm-3

1ppm carriers = 4.994E+22/1E-6= 4.99388E+16 atoms/cm-3 of Phosphorus. Or Arsenic or Boron etc.

Now if you are trying to get the ppm in grams, you'll need to take into account the weight of the dopant. Again we'll need some values. Some of those we already have, now we need the atomic weight of Phosphorus and... oh let's take the P-type dopant Boron. And we'll need the AMU:

Atomic weight of phosphorus: 30.974
Atomic weight of boron: 10.81
Reciprocal of Avagadro's number (AMU) = 1.6605E-24

Divide the density by the product of the atomic weight of the element and the atomic mass unit, AMU.

For Phosphorus: 2.329/(30.974 x 1.6605E-24) = 4.530E+22

1ppm Phosphorus = 4.530E+22 x 1E-6 = 4.530E+16 atoms/cm-3

For Boron: 2.329/(10.81 x 1.6605E-24) = 1.297E+23

1ppm Boron = 1.297E+23 x 1E-6 = 1.297E+17 atoms/cm-3

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