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AMI Infrar ed Crystalline Materials    239


                 1   2  3 4 5 6 7891  2  3 4 56 7891  2  3 4 56 7891  2  3 4 56 7891  2  3 4 56 7891
                1
                9
                8
                7
                6
                5
                4
                3
                2
             100  9
                8
                7
                6
                5
                4
                3
                2
              10  9 8 7 6 5 4
           Absorption at 10.6 mm (cm –1 )  1.0  3 2 9 8 7 6 5 4 3





             0.1
                8 2 9
                7
                6
                5
                4
                3
                2
            0.01  9
                8
                7
                6
                5
                4
                3
                2
            0.001
               0.001      0.01       0.1        1.0       10        100
                                     Resistivity (Ω·cm)
        FIGURE 9.20  Free carrier absorption at 10.6 µm in N-type gallium arsenide as a
        function of resistivity.

              a decrease in resistivity front to back of 1 to 0.35 Ω·cm in the 8-in plate
              length. Such a fall is consistent with an increase in dopant concentra-
              tion as a melt is slowly frozen down the length of the plate, such as
              found in the zone refining purification process of high-purity materials.
                 Classical methods 22,23  may be used to calculate the absorption by
              infrared, the long wavelengths of microwave and radio frequencies. Such
              methods have been used before by the author  in dealing with the depth
                                                  18
              of mechanical damage in GaAs. The classical expressions all show the
              absorption process increasing with the wavelength squared. However, for
                                   24
              GaAs the value is reported  to be 3 not 2; the effect is much stronger than
              predicted with classical expressions. When our measured values were
              reexamined, we found our calculated power value was 2.8, not quite 3.
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