temperatures to achieve total ionization of impurities. The deionization of impurities is most significant for low temperatures and high impurity densities.
4.3 Resistivity of p-Type Silicon
The resistivity of p-type silicon is given by
p (4.7)
epICp
where PC is the hole conductivity mobility calculated from equation (3.23) and p is the hole density discussed in Section 4.2. Equation (4.7) was used to calculate the hole resistivity for silicon doped with boron, gallium, and indium as a function of dopant density and temperature, for 1014 - N 1018 cm-3 and 100 T ! 400 K. The results are displayed in Figures 4.4 through 4.9. In the calculations of resistivity in silicon doped with gallium and indium, as was done for conductivity mobility, it was assumed that boron impurities were also present.
1313 -3
Boron densities of 10l3 and 5xlO1 cm were assumed to exist in the gallium- and indium-doped samples, respectively. The values of these background densities were deduced from a best fit of the experimental data. As the dopant density and temperature increase, the assumed background densities of shallow impurities becomes insignificant compared to the density of ionized dopant atoms, and Figures 4.4 through
4.9 accurately depict the influence of the particular type of impurity on the resistivity of holes in p-type silicon. The figures also show that for the case of the shallower ionization energies, resistivity depends more strongly on temperature for the lightly doped case where lattice scattering is dominant and become less temperature dependent as the dopant density increases.