Semiconductor Basics. George Domingo

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      where C is a constant, Eg is the energy difference between the conduction and valence bands (that is, the energy gap), k is the Boltzmann constant, and T is the temperature in degrees Kelvin. Notice that C, Eg, and k are all constants. The only variable in this equation is the temperature, T. In an intrinsic semiconductor – that is, one without any impurities whatsoever – the number of electrons must be identical to the number of holes:

      (2.4)

      Therefore,

      (2.5)

      that is, the product of the number of free electrons and free holes in a material is always the same at a given temperature.

      The number of intrinsic charges in a semiconductor changes drastically with the temperature because the temperature appears in the denominator of the exponential function. Figure 2.9 shows how much the number of free charges in a pure, intrinsic semiconductor like silicon or GaAs changes with temperature. Note that the y axis is logarithmic.