# Semiconductor problem: how much Boron is required to establish a certain amount of charge carrier density

The problem description is as follows:

Boron is used to dope 1 kg of germanium (Ge). How much boron (B) is required to establish a charge carrier density of 3.091 x 10^17 / cm^3. One mole of germanium has a volume of 13.57 cm^3 and weighs 72.61 gram. Give answer in grams of boron.

I'd like some advice on how this problem should be solved. I've tried finding the conductivity first, but it seems that this practice exam did not have a graph for the Hole Mobility (I suppose a Hole Mobility vs. Impurity Concentration graph), so I assumed there must be another way of solving this.

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How many ‘charge carriers’ are there if you dope a given amount of Germanium with one Boron atom? How does this translate to a ‘charge carrier densitiy’ if you dope one mole of Germanium with one Boron atom? –  Claudius Dec 13 '12 at 21:22
It's too late now perhaps but the answer can be found here: dspace.mit.edu/bitstream/handle/1721.1/35863/99/3-091Fall-2002/… –  Hasan Nov 26 '13 at 10:31

Lets assume the concentration of Boron is uniform throughout Ge (which is never the case).

You can calculate the volume of 1 kg of Ge with the information given, then you can calculate number of charge carriers by using the given carrier density. Assuming one B atom generates one charge carrier, you can calculate the number of moles of boron needed to generate the number of carriers. Multiply the number of moles with the molar mass of boron and you got your answer.

I don't know why there is a need to calculate conductivity. Its late but I hope you did well in your exam.

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