The LCAO, or Bloch, or tight binding, approximation for solids is discussed as an interpolation method, to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants, so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made, and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given, including tables of matrix components of energy for simple cubic, face-centered and body-centered cubic, and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni, and Howarth on Cu, as illustrations of the fcc case. In discussing the bcc case, the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out, as well as a distribution of energy states for the case of no antiferromagnetism. For diamond, comparisons are made with the calculations of Herman, using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed, and it is shown that their properties fit in with the energy band picture.

Simplified LCAO Method for the Periodic Potential Problem

Character tables for the "group of the wave vector" at certain points of symmetry in the Brillouin zone are given. The additional degeneracies due to time reversal symmetry are indicated. The form of energy vs wave vector at these points of symmetry is derived. A possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure will be presented.

Spin-Orbit Coupling Effects in Zinc Blende Structures

Boron doses of 1×1012–5×1015/cm2 were implanted at 60 keV into 1‐μm‐thick polysilicon films. After annealing at 1100 °C for 30 min, Hall and resistivity measurements were made over a temperature range −50–250 °C. It was found that as a function of doping concentration, the Hall mobility showed a minimum at about 2×1018/cm3 doping. The electrical activation energy was found to be about half the energy gap value of single‐crystalline silicon for lightly doped samples and decreased to less than 0.025 eV at a doping of 1×1019/cm3. The carrier concentration was very small at doping levels below 5×1017/cm3 and increased rapidly as the doping concentration was increased. At 1×1019/cm3 doping, the carrier concentration was about 90% of the doping concentration. A grain‐boundary model including the trapping states was proposed. Carrier concentration and mobility as a function of doping concentration and the mobility and resistivity as a function of temperature were calculated from the model. The theoretical and ex...

The electrical properties of polycrystalline silicon films

The data given on the optical properties of InSb are analysed and precise values for the position and temperature dependence of the absorption edge are given. The variation of the position of the absorption edge with impurity concentration is explained by the very low effective mass of the conduction electrons, which is estimated by three methods to be about 0.03 of the free electron mass.

https://iopscience.iop.org/article/10.1088/0370-1301/67/10/306/pdf

The Interpretation of the Properties of Indium Antimonide

The available data on solid solubilities of impurity elements in germanium and silicon are summarized in the form of solidus or solvus curves. New solubility data are presented for the lead-germanium, zinc-germanium, indium-germanium, antimony-silicon, gallium-silicon and aluminum-silicon systems. The correlation of the solid solubilities with the heats of sublimation and the atom sizes of the impurity elements is considered.

Solid solubilities of impurity elements in germanium and silicon

Electrical resistivity and Hall measurements have been made over the temperature range from 87\ifmmode^\circ\else\textdegree\fi{} to 900\ifmmode^\circ\else\textdegree\fi{}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 ${n}_{e}{n}_{h}=7.8\ifmmode\times\else\texttimes\fi{}{10}^{32}{T}^{3}\mathrm{exp}(\frac{\ensuremath{-}12,900}{T})$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\ifmmode\times\else\texttimes\fi{}${10}^{18}$/${\mathrm{cm}}^{3}$. 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 ${B}^{\ensuremath{-}}$ 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 ${\ensuremath{\mu}}_{e}=3.0{\ensuremath{\mu}}_{h}=15\ifmmode\times\else\texttimes\fi{}{10}^{5}{T}^{\ensuremath{-}\frac{3}{2}}(\frac{{\mathrm{cm}}^{2}}{\mathrm{volt}sec.}).$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.

Electrical Properties of Pure Silicon and Silicon Alloys Containing Boron and Phosphorus

Modulation of Conductance of Thin Films of Semi-Conductors by Surface Charges

This paper describes an extensive study of the magneto-resistance effect in germanium as a function of crystal orientation. Experimental measurements establish the constants involved in the dependence of the effect on orientation of magnetic field and electric current relative to the crystal axes. The measurements are internally consistent with existing phenomenological theory based on cubic crystal symmetry, in which terms involving the magnetic field to higher than the second order are neglected. It is shown that such deviations as do occur arise from higher terms in the field, since an extension of the phenomenological theory to the fourth order predicts their symmetry. Relations are established between the experimentally observed phenomenological constants and those constants appearing in existing magneto-resistance electronic theories. It is concluded that no electronic theory yet worked out is entirely consistent with experiment. The present electronic theories are special cases of a very general theory recently proposed by Shockley, and it is possible that agreement can be obtained as soon as the computational difficulties of the latter theory are overcome.

G. L. Pearson

Papers

Electrical Properties of Pure Silicon and Silicon Alloys Containing Boron and Phosphorus

Modulation of Conductance of Thin Films of Semi-Conductors by Surface Charges

The Magneto-Resistance Effect in Oriented Single Crystals of Germanium

Spin Resonance of Donors in Silicon

Theory and Experiment for a Germanium p − n Junction