Electrical Properties of Silicon Containing Arsenic and Boron

TLDR

Electrical conductivity and Hall effect were measured from 10 K to 1100 K on single‑crystal silicon doped with arsenic and boron, and extrinsic carrier concentration and Hall mobility were derived from the Hall coefficient and conductivity, with theoretical Hall‑mobility‑versus‑resistivity curves at 300 K compared to experiment. The study found arsenic donor and boron acceptor ionization energies of 0.049 eV and 0.045 eV, identified Fermi degeneracy between 10^18 and 10^19 cm⁻³, determined lattice‑scattering mobility to vary as T⁻²·⁶ for electrons and T⁻²·³ for holes, derived the carrier‑concentration relation np = 1.5 × 10³³ T³ exp(–1.21/kT) for T < 700 K, and characterized the temperature dependence of the Hall‑mobility to conductivity‑mobility ratio for both carriers.

Abstract

Electrical conductivity and Hall effect have been measured from 10\ifmmode^\circ\else\textdegree\fi{} to 1100\ifmmode^\circ\else\textdegree\fi{} Kelvin on single-crystal silicon containing arsenic and boron. Extrinsic carrier concentration is computed from Hall coefficient. Analysis of extrinsic carrier concentration indicates the ionization energy of arsenic donor levels to be 0.049 ev and of boron acceptor levels to be 0.045 ev for low impurity concentrations. Fermi degeneracy is found to occur in the range ${10}^{18}$ to ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ impurity concentration. Extrinsic Hall mobility is computed from Hall coefficient and conductivity. Curves of Hall mobility against resistivity at 300\ifmmode^\circ\else\textdegree\fi{}K are computed from theory and compared with experiment. The temperature dependence of lattice-scattering mobility is found from conductivity to be ${T}^{\ensuremath{-}2.6}$ for electrons and ${T}^{\ensuremath{-}2.3}$ for holes. From conductivity mobility and intrinsic conductivity, it is found that carrier concentration at any temperature below 700\ifmmode^\circ\else\textdegree\fi{}K is given by the expression: $np=1.5\ifmmode\times\else\texttimes\fi{}{10}^{33}{T}^{3}\mathrm{exp}(\ensuremath{-}\frac{1.21}{\mathrm{kT}})$. The temperature dependence of the ratio Hall mobility/conductivity mobility is determined for holes and electrons.