(h,k,l,) Miller IndicesĪll lattice planes and lattice directions are described by their associated Miller Indices. These primary planes are those that form the sides and diagonals of the unit cell. However, there are several primary planes and lattice directions that are associated with the unit cell of Figure 1. Bulk Si is an ideal lattice comprised of an infinite number of repetitive unit cells and an infinite number of cross-sectional planes and lattice directions. For SiGe, the lattice constant can be approximated using a simple linear interpolation as a function of composition. The lattice constant for Si is 5.43 A, and the lattice constant for Ge is 5.66 A. The unit cell and diamond lattice structure for Si, SiGe, and Ge. Si, SiGe, and Ge have a cubic lattice structure known as the diamond lattice structure, and the unit cell is actually two interpenetrating fcc lattices separated by a/4 along each axis of the cell.įigure 1 shows the unit cell, diamond structure, lattice constant, and the four nearest neighbor atoms bonding the Si lattice.įigure 1.
The length dimension of the unit cell defines the lattice constant (a). For example the common simple-cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) are all cubic lattice systems. Any lattice system having a cubic volume as a unit cell belongs to the cubic family. Single-crystal Si, SiGe, and Ge used in the microelectronics industry are all members of the simplest three-dimensional lattice system referred to as the cubic lattice system.
Therefore the discussion, lattice diagrams, and stereographic projections provided below are applicable to all three material systems. The general lattice characteristics of Si, SiGe, and Ge are effectively identically with the only difference being the lattice constant or spacing. This is particularly true in the case of micromachined Si devices used in MicroElectroMechanical Systems (MEMS). Different orientation wafers are typically used to produce performance advantages within electronic devices, as well as to illuminate critical anisotropic etch and growth characteristics during device and circuit processing. In this article we describe the basic nomenclature, equations, diagrams, and graphs that are used to describe crystallographic orientation. Two of the more fundamental parameters characterizing Si, SiGe, and Ge substrates are the crystallographic orientation of the wafer surface, and the crystallographic direction perpendicular to the wafer flat.
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