An intrinsic semiconductor has a band gap of (1.9870Times10^0) eV. The hole and

Question

An intrinsic semiconductor has a band gap of (1.9870Times10^0) eV. The hole and electron mobilities are (7.12Times10^-1) and (2.6090Times10^0) m^2/V-s, respectively (assume that the mobilities do not change with temperature). This material has 10^19 molecules/cm^3 and there is at most 1 electron per molecule. Find the temperature (in K) at which the semiconductor acts like an insulator, that is it has an electrical conductivity of 10^-8 (ohm-m)A-1. where k = 8.62 Times 10^-5 eV/atom-K, and n_0 is the total number of electrons/m^3. As always, use scientific notation in the form X.YZ Times10^n.

Explanation / Answer

Conductivity, = e + h = nee + peh

                       = Ne (e + h)

   =>   10-8 = N * 1.6 * 10-19 * (0.712 + 2.609)

   =>     N = 0.188 * 1011   molecules/m3

=>   0.188 * 1011 = 1025 * exp(-1.987/(2 * 8.62 * 10-5 * T))

=>     0.188 * 10-14   =   exp(-1.987/(2 * 8.62 * 10-5 * T))

=>     ln(0.188 * 10-14 ) = -1.987/(2 * 8.62 * 10-5 * T)

=>     33.907 = 1.987/(2 * 8.62 * 10-5 * T)

=>      T = 339.91 K

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