What does negative resistivity mean

[kahwawashay1]

silicon has a negative temperature coefficient of resistivity. So that means that it's resistivity decreases as temperature increases. How is that possible? Also, would that mean that at some certain temperature higher than room temp, silicon would act as superconductor? It has a very high melting point..1687 K..so plenty of room to increase temp so as to decrease resistivity..

 

[kahwawashay1]

i just calculated the temp at which resistivity of pure silicon would drop to zero and got 307 K...

 

[Gordianus]

Silicon's resistivity changes with temperature following an exponential law. Therefore, using a linear trend is a fair assumption only within a limited range. 307 K is room temperature and silicon's resistivity is far from zero at this temperature.

 

[kahwawashay1]

Silicon's resistivity changes with temperature following an exponential law. Therefore, using a linear trend is a fair assumption only within a limited range. 307 K is room temperature and silicon's resistivity is far from zero at this temperature.

then what am I doing wrong?
The formula is ρ-ρ₀ = ρ₀α(T-T₀)
where ρ is the final resistivity, ρ₀ is the reference resistivity, α is the temperature coefficient of resistivity, T is the final temp and T₀ is the reference temp

My book gives the α at a reference temp of 293 K. At this temp, ρ₀ is 2.5*10³ and α is -70*10^-3. Therefore, if we set the final resistivity (ρ) to 0:

-ρ₀ = ρ₀α(T-T₀)
-1/α = T-T₀
T = -1/α + T₀
= -1/(-70*10^-3) + 293
= 307 K

Like you said, 307 K is nearly room temp, so the linear equation still holds for that temp...

Also, my question was not answered about why it is that resistivity decreases as temp increases for pure silicon (ie, why it is that it has a negative temp coefficient of resistivity)

 

[kahwawashay1]

using a linear trend is a fair assumption only within a limited range

According to my book, "The relation between temperature and resistivity is fairly linear over a rather broad temperature range", and it shows a graph of a curve that is indeed somewhat exponential but very close to linear for a temperature up to 1400 K...which is not a very limited range...

 

[technician]

On the atomic scale there are 2 competing processes that effect resistivity.
1) Atomic vibrations increase as temperature increases and this makes resistivity increase... A positive coefficient of resistivity. This is the case for metals
2) as temperature increase the concentration of charge carriers ( electrons) tends to increase and this makes resistivity decrease
For metals there is a very high concentration of charge carriers and temperature has no effect on this. The predominant process affecting metals is therefore the increased atomic vibrations and metals have a positive temp coeff of resistivity.
Silicon is a semiconductor and has a very low concentration of charge carriers. As temperature increases the concentration of charge carriers increases and this is the predominant process and. Out weighs any effect due to increased atomic vibrations. Semiconductors therefore have a negative temp coeff of resistivity.
You could picture that at some high temp the effect of increased atomic vibrations will begin to show in semiconductors and could be greater than the effect of increased concentration of charge carriers.
Hope this simplified description helps

 

[kahwawashay1]

On the atomic scale there are 2 competing processes that effect resistivity.
1) Atomic vibrations increase as temperature increases and this makes resistivity increase... A positive coefficient of resistivity. This is the case for metals
2) as temperature increase the concentration of charge carriers ( electrons) tends to increase and this makes resistivity decrease
For metals there is a very high concentration of charge carriers and temperature has no effect on this. The predominant process affecting metals is therefore the increased atomic vibrations and metals have a positive temp coeff of resistivity.
Silicon is a semiconductor and has a very low concentration of charge carriers. As temperature increases the concentration of charge carriers increases and this is the predominant process and. Out weighs any effect due to increased atomic vibrations. Semiconductors therefore have a negative temp coeff of resistivity.
You could picture that at some high temp the effect of increased atomic vibrations will begin to show in semiconductors and could be greater than the effect of increased concentration of charge carriers.
Hope this simplified description helps

Thanks! this helped explain the negative coefficient...but still...what is wrong with my calculations? 307 K is not too far from room temp...so I'm assuming at that temp, the atomic vibrations aren't as important yet and so the above linear approximation equation holds...