1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Pure silicon mystery!

  1. Feb 11, 2012 #1
    I noticed that the temperature coefficient of resistivity of pure silicon is a rather high negative number, so just out of curiosity I wanted to see at what temp the resistivity would drop to zero.

    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*10^3 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

    I have been told that this can't possibly be right, but no one will tell me exactly why.
    I have been told that what I'm doing wrong is "assuming that resistivity does not change with temp", even though I obviously am taking that into consideration, since I am using an equation that says approximately how resistivity changes with temp.
    I have also been told that the linear approximation equation I am using holds only for a limited range with respect to the reference temp, and I also know that it won't hold for huge temps, but 307 K is not too far from room temp. (and actually, according to my book, this equation holds "over a rather large temperature range")

    Could someone please point out exactly what I am doing wrong?
    There must be something wrong because I dont think silicon is a conductor at some 35-ish degrees Celsius..
  2. jcsd
  3. Feb 11, 2012 #2
    The equation you have quoted is a version of the variation of resistance/resistivity equation for a material ( metal) with a + ve temp coefficient ( resistance increases with temp)

    R = Ro(1+αt) ( t is temp in C)
    This equation is only an approximation for reasonably low temps and shows that resistance increases uniformly with temp.
    A fuller form of the equation is R = Ro(1+αt+βt^2+.........)
    one thing for sure.... It is not the equation to use for semiconductors ( silicon)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Pure silicon mystery
Density of pure chromium
Spinning disk, friction and pure roll