Question

Estimate the temperature (in Kelvins) at which GaAs has an electrical conductivity of 4.0 x 10^-3 (?-m)^-1, assuming a temperature dependence for ? as shown in Eq. 18.36. For GaAs, use a band gap of 1.42 eV, and a room temperature (298K) conductivity of 1.0 x 10^-6 (?-m)^-1.

Answer 1

temperature dependence equation for ?

conductivity of the intrinsic material =

temperature independent constant =

temperature =

band energy gap = = 1.42 eV

Boltzmann constant = 8.62 x 10^-5 eV/K

Electrical conductivity =

Band gap energy =

Now solve for T

ln(4*10^-3) = 22.37 - 1.5*ln(T) - 1.42/(2*8.62*10^-5*T)

-5.52 - 22.37 = - 1.5*ln(T) - 8236.65/T

27.89 = 1.5*ln(T) + 8236.65/T

By trial and error method

T = 439 K