Consider a silicon semiconductor doped with 3 phosphorus ato

Consider a silicon semiconductor, doped with 3 phosphorus atoms per 10^6 silicon atoms. If the semiconductor contains 5x10^21 silicon atoms per cubic meter, how many negative charge carriers (per cubic meter) do you expect to be present at room temperature? Give your answer to 3 significant figures.

Solution

3 phosphorus atoms are present in 10⁶ silicon atoms.

There are 5*10²¹ silicon atoms per cubic meter.

So number of phosphorus atoms per cubic meter is 3* 5*10²¹/(10⁶)=15*10¹⁵

Each phosphorous atom one free electron. So total number of electrons donated by phosphorus atoms=15*10¹⁵ .

At room temperature, relatively few electrons have enough thermal energy to become free electrons. In fact,
approximately one electron per 6.9×1012 silicon atoms does. So the intrinsic carrier concentration in silicon
at room temperature is approximately
ni = 1.45 × 10¹⁰ per cm³ silicon, 300 K.

=1.45*10¹⁶ per m³

So  total negative charge carriers=1.45*10¹⁶+15*10¹⁵=1.95*10¹⁵