Analysis of the 3-dimensional electron distribution in silicon using directional Compton profile measurements

A method of reconstructing the electron momentum density (p), and its Fourier transform,B(t), from a series of directional Compton profiles is described. It is based on a double Fourier inversion technique and an expansion in lattice harmonic functions. The effect of random errors has been analysed, and the implications for the data collection discussed. We have used the reconstruction technique to obtain (p) andB(t) for silicon from six directional Compton profiles measured with 412 KeV gamma-radiation. The experimental result is in good agreement with earlier measurements and with available solid state theories. A recent Wannier function calculation for silicon using orthogonalised bond orbitals provides a useful tool for identifying the physical origins of the observed anisotropies. A comparison between the information presented in position and momentum space shows that the ease of interpretation depends upon the degree to which the various interactions give rise to localised features in each representation.