The Symmetrical Laue Case Measurement of the ‘Forbidden’ (222) Reflection in Silicon

Abstract

The purpose of this thesis is to determine, as accurately as possible, the electron charge density distribution situated at the center of each atomic bond length in a diamond-type silicon structure. Accurate information regarding the magnitude of this bonding charge is an urgent requirement in substantiating and directing the extension and refinement of atomic wave functions. At the present time, agreement between theoretical and experimental determination of this charge density for covalently bonded structures is far from satisfactory. For the few elements that allow its accurate assessment, a direct means of estimating the electron bond charge distribution is available in the measurement of the (222) structure factor of diamond-type elements of low atomic number. Such experiments have been limited to X-ray diffraction methods, although recent electron diffraction experiments (Cowley, 1970) have indicated that improved accuracy may be inherent in the latter method. Of the many experimental X-ray evaluations of (F₂₂₂)_si’ previous methods have employed Bragg geometry, whereby 1.44 ≤ (F₂₂₂)_si ≤ 1.78. However, the experimental result of this thesis work, in which Laue geometry has been used, has given a mean value of (F₂₂₂) = 0.90 (Hewat, Prager, Stephenson, Wagenfeld, I969).

Theoretically, Lelicur and Leman (1966) using an approximated tight binding computation, obtained a value (F₂₂₂)_si = 0.91, in good agreement with the Laue result, but much lower than the Bragg results. Similar calculations by these same authors for diamond and germanium have yielded values of (F₂₂₂)_c = 1.19 and (F₂₂₂)_Ge = 0.97 whereas experimentally (F₂₂₂)_c = 1.15 end 1.08 ≤ (F₂₂₂)_Ge ≤ 1.18.

In contrast to these results, the original value of (F₂₂₂)_c = 0.27, determined theoretically by Ewald and Honl (1936) using a tight binding approach, appears too low.

Thus the general unsatisfactory situation, existing between theoretical and experimental F₂₂₂ values, has prompted the following Laue method of approach in contrast and as an alternative to the usual Bragg method. Preliminary work by Hewat (1967), employing symmetrical Laue geometry and MoKa X-radiation, resulted in an approximate value of (F₂₂₂)_si ≈ 1.0. The purpose of this thesis was to repeat the experiment of hewat using Cuba ' X-radiation and to confirm or disprove his low F₂₂₂ value. Having confirmed this low value, it was then necessary to search for the possible source(s) of error inherent in either the Bragg or Laue methods.

Experimentally, a relative value of (F₂₂₂)_si = 0.90 was computed from the ratio of the (222) and (333) integrated intensities. This final result not only confirmed the low value obtainable by this method, but also involved the complete re-determination of the X-ray atomic absorption cross sections for elements whose atomic numbers range from Z =11 to Z = 84. The latter computation was found necessary due to some doubt in the accuracy of published quadrupole terms (Guttman and Wagenfeld, 196?) used in the evaluation of the (333) integrated intensity. Results indicated that significant errors were present in the quadrupole terms of high Z value, although those used in our calculation were essentially unchanged.

In measuring an extremely weak reflection, such as the (222) reflection in diamond-type structures, it is shown that significant intensity contributions, due to long range multiple reflections, may seriously effect the measured (222) intensity. In normal practice, it is usual to avoid short range multiple reflections by rotating the crystal about the (222) scattering vector and to identify and evade them by careful comparison-with a theoretically computed, azimuthal scan chart. In this work, Wagenfeld (1970), has proposed that long range multiple reflections, (involving reciprocal lattice points situated at distances one hundred times the normal excitation error), can contribute an intensity comparable to the true (222) intensity. Intensities of this magnitude, Which accompany the true (222) intensity, are thought to be the cause of the high F₂₂₂ values that have been reported in both symmetrical Bragg and Laue case measurements. Experimental support in favour of lower silicon F₂₂₂ values have recently been reported by Cowley (1969) using electron diffraction methods.