Temperature dependence of conductivity An n-type Si sample has been doped with 1

Question

Temperature dependence of conductivity An n-type Si sample has been doped with 1015 phosphorus atoms per cm3. The donor energy level for P in Si is 0. 045eV below the conduction band edge energy. Calculate the room temperature conductivity of the sample. Estimate the temperature above which the sample behaves as if intrinsic Estimate to within 20% the lowest temperature above which all the donors are ionized Sketch schematically the dependence of the electron concentration in the conduction band on the temperature as log(n) versus 1/T, and mark the various important regions and critical temperatures. For each region drawn an energy band diagram that clearly shows from where the electrons are excited into the conduction band. Sketch schematically the dependence of the conductivity on the temperature as log (sigma ) versus 1/T and mark the various critical temperatures and other relevant information.

Explanation / Answer

the electrical resistivity of most materials changes with temperature. If the temperature T does not vary too much, a linear approximation is typically used: where is called the temperature coefficient of resistivity, is a fixed reference temperature (usually room temperature), and is the resistivity at temperature . The parameter is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, is different for different reference temperatures. For this reason it is usual to specify the temperature that was measured at with a suffix, such as , and the relationship only holds in a range of temperatures around the reference. When the temperature varies over a large temperature range, the linear approximation is inadequate and a more detailed analysis and understanding should be used.

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