Electrical resistivity and Hall measurements have been made over the temperature range from 87° to 900°K on pure silicon and on silicon alloys containing from 0.0005 to 1.0 percent boron ($p$-type impurity) or phosphorus ($n$-type impurity). X-ray measurements indicate that both elements replace silicon in the lattice. It is shown that each added boron atom contributes one acceptor level, and it is likely that each added phosphorous contributes a donor level.

The temperature variation of the concentrations of carriers, electrons and holes, and of their mobilities, are determined from the resistivity and Hall data for the different samples. In the intrinsic range, at high temperatures, conductivity results from electrons thermally excited from the filled band to the conduction band. The energy gap is about 1.12 ev. The product of electron and hole concentration at any temperature is $n_e{n}_h=7.8\mathrm{}\times {10}^{32}{T}^3\exp \left(\frac{-12,900\mathrm{}}{T}\right)$

In the saturation range, which occurs just below the intrinsic range, the concentrations are independent of temperature. All donors (or acceptors) are ionized and the concentration of carriers is equal to the net concentration of significant impurities ($P$ or $B$).

The energy, $E_A$, required to ionize an acceptor by exciting an electron from the filled band, as determined from the temperature variation of concentration at lower temperatures, decreases with increasing impurity concentration and vanishes for concentrations above 5×${10}^{18}$/${\mathrm{cm}}^3$. The value of $E_A$ at high dilution, 0.08 ev, is about what is expected for a hole moving in a hydrogen-like orbit about a substitutional $B^{-}$ ion. The decrease in $E_A$ with increase in concentration is attributed to a residual potential energy of attraction between the holes and impurity ions. The ionization energy of donors is less than that of acceptors, probably because conduction electrons have a smaller effective mass than holes. In samples with large impurity concentrations the carriers form a degenerate gas at low temperatures, and the resistivity and Hall coefficient become independent of temperature.

At high temperatures the mobilities of electrons and holes approach the values ${\mu }_e=3.0\mathrm{}{\mu }_h=15\mathrm{}\times {10}^5{T}^{-\frac{3}{2}}\left(\frac{{\mathrm{cm}}^2}{\mathrm{volt}sec.}\right).\mathrm{}$

These values are determined by lattice scattering and are independent of impurity concentration. At lower temperatures scattering by both ionized and neutral impurity centers contribute, and the mobility is largest for the more pure samples. Impurity scattering increases rapidly with decrease in temperature and the mobility passes through a maximum which depends on impurity concentration. Theories of impurity scattering of Conwell and Weisskopf, of Johnson and Lark-Horovitz, and of Mott give mobilities which agree as to order of magnitude with the observed.

• Received 29 November 1948

DOI:https://doi.org/10.1103/PhysRev.75.865