Using a modified Gaussian approximation to the depth distribution of the energy dissipation function for electron bombardment, an analytical expression was derived for electron-beam-induced current (EBIC) at a Schottky barrier parallel to the bombarded surface. Comparison of theory and experiment for the voltage dependence of EBIC for 14 specimens (including p- and n-type GaAs and Si) provided values for the diffusion length of excess carriers, the thickness of the metal layer of the Schottky barrier diode, and the average energy ℰ required to generate a hole-electron pair. Diffusion lengths ranging from 0.41 to 55 μ were determined with an estimated accuracy of ±20%. The values of ℰ were found to be 3.75±0.11 eV for Si and 4.68±0.14 eV for GaAs. The unique advantages of this method for measuring small diffusion lengths are emphasized.
In semiconductors having high efficiency for radiative recombination, the voltage dependence of cathodoluminescence may be used to determine the diffusion length and to estimate the surface recombination velocity of excess carriers. Theoretical calculations are based on a knowledge of the Laplace transform of the distribution of excitation with depth as determined from the target absorption correction in electron probe microanalysis or, alternatively, on a Gaussian approximation to the distribution of excitation with depth. Experimental results with accelerating voltages of 5–50 kV indicate values of diffusion length in n-type GaAs ranging from 3.0 μ at low-carrier concentration (5.1×1016 cm−3) to 0.65 μ at high-carrier concentration (3×1018 cm−3). The estimated accuracy for diffusion lengths between 0.5 and 4 μ is ±30%. Information is also obtained on the surface recombination velocity and the thickness of a ``dead layer'' at the surface.
The x-ray continuum from thick elemental targets was investigated from 1–10 Å using a crystal spectrometer and electron energies of 10–50 keV in an electron probe microanalyzer. Experimental results corrected for absorption, atomic number, and stray radiation agreed well with theoretical calculations based on Sommerfeld's cross section and Bethe's retardation law. The calculations used an improved version of the empirical formula of Kirkpatrick and Wiedmann for the cross section. Theory and experiment agreed best for J = 11.5Z in Bethe's law, but taking account of known inaccuracies in the Sommerfeld cross section, the Berger-Seltzer values are recommended. Results did not verify the linear atomic number dependence of the Kulenkampff-Kramers equation; for fixed electron energy E0 and photon energy Ev the intensity varied as Zn, where n ranged from 1.18 to 1.38 depending on Z, E0, and Ev. For fixed Z and Ev the intensity varied approximately as (E0 − Ev). Agreement of theory and experiment indicated that the correction procedures commonly used for characteristic lines can be applied to the continuum but the atomic number correction using Duncumb and Reed's procedure differed for the continuum compared to that for characteristic lines. Absorption correction using f(χ) of Andersen and Wittry gave good results for f(χ)≥0.4 but lower values could not be conclusively tested because of errors due to stray radiation which is shown to be caused by electrons backscattered from the specimen. Nevertheless, it was possible to use the Z dependence of the continuum to estimate certain mass absorption coefficients.
A simple homogeneous-field magnetic prism spectrometer is described for use below the camera chamber of a conventional transmission electron microscope. The prism is designed for point-to-point focusing from the exit pupil of the electron microscope to the exit slit of the spectrometer. Energy spectra are scanned by varying the accelerating voltage to minimize chromatic effects in the microscope. Scanning coils are used to deflect an image or a diffraction pattern across an area-selecting aperture which also serves as the aperture stop for the spectrometer. A phase-sensitive periodic differential integrator is used to record the output from the scintillation counter detector.
Calculations of the x-ray optics of four types of doubly curved diffractors are described and the results are compared with similar results for singly curved diffractors (Johann and Johansson geometry). In these calculations the locus of points on a curved diffractor’s surface is determined for a given deviation from the Bragg angle when the diffractor is used at Bragg angles ranging from 15 to 75 degrees. The six cases discussed include cylindrical, spherical, and toroidal geometries. The calculations are used as a basis for comparing the collection efficiency and the spectral resolution when these diffractors are used in scanning monochromators. It is shown that doubly curved diffractors are superior to singly curved ones and that a diffractor with spherical planes and toroidal surface provides the best performance of all of the diffractors considered if a wide range of Bragg angles must be covered.
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