Parabolic Edge Research Articles

Electrical Conductivity in Heavily Dopedn-Type Germanium: Temperature and Stress Dependence

Investigations of the piezoresistance of heavily doped $n$-type germanium were made to determine (1) the nature of the carrier scattering mechanisms in degenerate materials and (2) any modification of the conduction-band edge resulting from the large number of impurity states. Stresses large enough to alter the resistivity well beyond the range of linear piezoresistance were applied; saturation of the resistivity at the larger stresses was attained in samples with as many as ${10}^{19}$ carriers per cc. Resistivity was measured with extensive parametric variation of dopant, carrier concentration, temperature, and applied stress. The Hall coefficient was also measured as a function of stress for several concentrations. The data are interpreted qualitatively by a four-valley model with a parabolic conduction-band edge, and deviations from this model are discussed. Electron-electron interactions and the temperature dependence of screening contribute significantly to the temperature dependence of the resistivity. The variation of the screening with the relative population of the valley must be considered in interpreting the results of the piezoresistance experiments; in the case of arsenic doping, intervalley scattering is also significant. The mobility anisotropy for screened Coulomb scattering in one valley, as determined from resistivity measurements on antimony-doped samples with large $〈111〉$ stress, varies with concentration from 5.5 at 1\ifmmode\times\else\texttimes\fi{}${10}^{18}$ per cc to 3.8 at 1\ifmmode\times\else\texttimes\fi{}${10}^{19}$ per cc. Evidence for the existence of tail states extending \ensuremath{\approx}0.04 eV below the conduction-band edge is presented.

The rolling of spring strip with parabolic edges

The rolling of spring strip with parabolic edges