-:      40


3.8 Mobility in the Combined Valence Band

     The conductivity mobility in each individual band is calculated from equation (3.1), and the combined conductivity mobility in the valance band is then evaluated as a weighted average of the single-band mobilities over the population of holes in each band, thus

               m~l 3/2      l- 13/2      m*3 3/2
       iD= lLm         + P2{m   3   + 13 {m]                     (3.23)



    Using equation (3.23) and the parameters listed in Table 3-1, we

have calculated the hole mobility for silicon doped with boron, gallium, and indium as functions of dopant density and temperature, for 1014  NA s 1013cm-3 and 100   T   400 K. The results are displayed in Figures 3.1 through 3.6. In the calculations of mobility and resistivity in silicon doped with gallium and indium, it was assumed that boron impurities were also present. Since very pure silicon has a resistivity on the order of 1000Q-cm, it was assumed that boron densities of 1013 and 5x1013cm-3 existed in the gallium- and indium-doped samples, respectively. The values of these background densities were deduced from a best fit of the experimental data. For this reason, especially in the case of indium-doped silicon, the actual role of the impurities at low temperatures and/or low dopant densities is masked by the action of the always present boron impurities. As the dopant density and temperature increase, the assumed background densities of boron impurities become insignificant compared to the density of ionized dopant atoms, and Figures 3.1 through 3.6 accurately depict the influence of the particular type of impurity on the resistivity and mobility of holes in p-type silicon. The figures also show that for the case of the