Forbidden Zones Research Articles

Theory of Forbidden Zones in the Flow of a Magnetized Plasma

The theories of Alfvén and Karlson on the two-dimensional flow of a magnetized plasma are discussed. An analog mathematical model is introduced to clarify the various features of Karlson's exact theory of forbidden zones. It is shown that the boundary of the forbidden zone is a contour of constant magnetic field strength. Karlson's theory is generalized to include an arbitrary energy distribution in the plasma, and it is shown that the size of the forbidden zone is not unique. The physical processes which give rise to charge separation and the creation of high electric fields in the plasma are examined in detail, and an elementary derivation of the appropriate Poisson's equation is given.

In Re Lippert.

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Photoelectric Emission and Contact Potentials of Semiconductors

In spherical photo-tubes with interchangeable emitters, energy distributions of external photoelectrons from the semiconductors, Te, Ge, and B, were compared with those of several metals. Contact potentials were determined from the saturation points of current-voltage characteristics. For the semiconductors, as contrasted with metals of the same work function, there was a pronounced sparsity of electrons with energies near the Einstein maximum. In general form, the distributions could be described by the expression, $N(\ensuremath{\nu},E)dE\ensuremath{\propto}q(\ensuremath{\nu})E{(h\ensuremath{\nu}\ensuremath{-}\ensuremath{\phi}\ensuremath{-}\ensuremath{\delta}\ensuremath{-}E)}^{m}\mathrm{dE}$based on simplified assumptions analogous to those previously applied in the case of metals. Here $\ensuremath{\phi}$ is the work function; $\ensuremath{\delta}$ is the energy difference between the Fermi level and the top of the occupied band of energy states; $m$ is a parameter depending both on the form of this band and on the energy dependence of the photoelectric excitation probability; $q$ is a slowly varying function of $\ensuremath{\nu}$. The photoelectric properties of the semiconductors could also be specified conveniently by plotting measured values of $\frac{N(\ensuremath{\nu},E)}{E}$ as functions of $h\ensuremath{\nu}\ensuremath{-}\ensuremath{\phi}\ensuremath{-}E$. Spectral distributions of the photoelectric yields varied more rapidly with $\ensuremath{\nu}$ than those for metals and were not measurable unless $h\ensuremath{\nu}$ exceeded $\ensuremath{\phi}$ by several tenths of an electron volt.Near the Einstein maximum, energy distributions deviated from the simple relation given above. The experiments failed to disclose sharply defined stopping potentials corresponding to upper edges of occupied bands of energy states in the semiconductors. Thus $m$ and $\ensuremath{\delta}$ were not defined uniquely. Typical values of $m$ obtained both from energy and spectral measurements were $\frac{3}{2}$ and 2; illustrative values of $\ensuremath{\delta}$ were 0.10 to 0.18 ev for evaporated $\mathrm{Te}(\ensuremath{\phi}\ensuremath{\sim}4.76 \mathrm{ev})$, 0.2 to 0.3 for evaporated $\mathrm{Ge}(\ensuremath{\phi}\ensuremath{\sim}4.8)$, and 0.3 to 0.5 for pyrolytic films of $\mathrm{B}(\ensuremath{\phi}\ensuremath{\sim}4.6)$. Thermoelectric measurements showed that all samples were $P$ type. For Te the results were in agreement with available data on electrical properties.Using the above values of $\ensuremath{\delta}$, upper limits were found for photo-currents originating in the forbidden zones (as defined by $Egh\ensuremath{\nu}\ensuremath{-}\ensuremath{\phi}\ensuremath{-}\ensuremath{\delta}$. For the surface states that were assumed as possible sources of these currents, estimated densities were of the order of magnitude, ${10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}2}$.

Soft X-Rays from (100) and (111) Faces of Copper Single Crystals

Between 90 and 220 volts 14 critical potentials were found for both the (111) and the (100) faces. Each break is the same within 1.5 volts for the two targets. Agreement with published results for polycrystalline copper is fair, although there are fewer discontinuities than for the ordinary metal, as in other experiments with single crystals. The critical potentials may be grouped to show level differences, attributed by Richardson to structure electrons in the crystal lattice. Comparison with other results for metals of similar structure casts doubt on this theory. Kronig's theoretical interpretation of fine structure in x-ray absorption presents a possible explanation of soft x-ray critical potentials. Assuming 4 to 7 volts inner potential, 10 of the 14 observed critical potentials agree with Kronig's calculated energy discontinuities and only one calculated discontinuity was not observed. A strong break at 104 volts, not predicted by this theory, is within 2 volts of Kurth's value for the $N$ series convergence frequency. Similar good agreement exists between Thomas' critical potentials for polycrystalline iron and nickel and the energy discontinuities calculated from Kronig's theory. From these results it appears that the theory of forbidden energy zones may account for soft x-ray critical potentials.