Disentangling Neighbors and Extended Range Density Oscillations in Monatomic Amorphous Semiconductors

High energy x-ray diffraction measurements of pure amorphous Ge were made and its radial distribution function (RDF) was determined at high resolution, revealing new information on the atomic structure of amorphous semiconductors. Fine structure in the second peak in the RDF provides evidence that a fraction of third neighbors are closer than some second neighbors; taking this into account leads to a narrow distribution of tetrahedral bond angles, $(8.5\pm 0.1)°$. A small peak which appears near 5 Å upon thermal annealing shows that some ordering in the dihedral bond-angle distribution takes place during structural relaxation. Extended range order is detected (in both $a$-Ge and $a$-Si) which persists to beyond 20 Å, and both the periodicity and its decay length increase upon thermal annealing. Previously, the effect of structural relaxation was only detected at intermediate range, involving reduced tetrahedral bond-angle distortions. These results enhance our understanding of the atomic order in continuous random networks and place significantly more stringent requirements on computer models intending to describe these networks, or their alternatives which attempt to describe the structure in terms of an arrangement of paracrystals.

Figure 1

Schematic representation of bonding in fourfold-coordinated amorphous semiconductors. Only eight connected atoms are depicted with arrows indicating possible tetrahedral and dihedral bond-angle variations.

Figure 2

Second peak in the $a$-Ge (annealed) RDF for different values of $Q_{\max }$. (Curves have been offset for clarity.) Straight segments in top right corner indicate theoretical resolution for each of the $Q_{\max }$ values. Two straight and parallel vertical lines illustrate increased visibility of fine structure in the second peak.

Figure 3

Radial distribution function of relaxed $a$-Ge. Measurement shown as dots (relaxed $a$-Ge) and dashed line (as-implanted $a$-Ge). The solid lines correspond to a simple theory where the red line is the sum of a Gaussian centered at the nearest neighbor (not separately shown), a Gaussian centered at the second nearest neighbor distance is shown as a green line, a distribution of third nearest neighbors as discussed in the text (blue line with two peaks near 4 and $6\AA$), and a dash-dotted black curve which is a convolution of the average density with an error function.

Figure 4

Extended range ordering. Pair distribution functions for $a$-Ge (as-implanted and relaxed), $a$-Si (relaxed only) [5], and for a theoretical model [15]. Curves have been vertically offset for clarity. Thin lines through each of the experimental curves correspond to nonlinear fits and were used to deduce the periodicity and decay length of the PDFs.