Hello everyone

I have a homework that needs me to calculate the depletion with of a PN junction under applied small forward bias voltage. I have difficulties understanding the units.

The question states that the PN junction is formed from material with 1*10^14 acceptors per cm^3 and 1*10^17 donors per cm^3. The bias applied is +0.4 V.

What I do not understand is the notation cm^-3 and cm^3... What is the difference between these? How can I convert from one to another? Basically, the formula for depletion width uses cm^-3, and I do not understand it at all. I hope you understand my issues...

The formula uses the intrinsic carrier concentration = 1.45*10^10 cm^-3. I have doping concentrations given at atoms per cm^3. Is there a difference? I cannot wrap my head around that. I know what the right answer should be, and I am not getting it.

I would appreciate an explanation. Thanks

 

Simple. Doping and carrier concentrations are quoted in units for a given volume. The volume is cubic metres or cubic centimetres in this case, cubic centimetres.

Hence the units are in numbers per cubic cm.
i.e. numbers per cm^3
i.e. numbers divided by volume

per cm^3 is the same as cm^-3

i.e. the units are the same.

The key word is"per", meaning "divide by" which translates into the negative exponent.

 

Thank you for the clear explanation! The problem was that I was getting the answer in cm, whereas I was thinking it was in m... what a shame.