The Diamond Lattice: Structure of Diamond

Introduction:

The basic crystal structure for many important semiconductors is the fee lattice with a basis of two atoms, giving rise to the diamond structure, characteristic of Si, Ge, and C in the diamond form.

The Diamond Lattice:

• In many compound semiconductor atoms are arranged in a basic diamond structure, but are different on alternating sites. This is called a zinc blende structure and is typical of the III-V compounds.
• One of the simplest ways of stating the construction of the diamond structure is the following:

The diamond structure can be thought of as an fee lattice with an extra atom placed at a/4 + b/4 + c/4 from each of the fcc atoms.

• The construction of a diamond lattice from an fee unit cell. We notice that when the vectors are drawn with components one-fourth of the cube edge in each direction, only four additional points within the same unit cell are reached.
• Vectors drawn from any of the other fee atoms simply determine corresponding points in adjacent unit cells.
• This method of constructing the diamond lattice implies that the original fee has associated with it a second interpenetrating fcc displaced, by 1/4, 1/4, 1/4.
• The two interpenetrating fee sublattices can be visualized by looking down on the unit cell of Fig.(a) from the top (or along any (100) direction).
• In the top view of Fig. (b), atoms belonging to the original fee are represented by open circles, and the interpenetrating sublattice is shaded.
• If the atoms are all similar, we call this structure a diamond lattice; if the atoms differ on alternating sites, it is a zinc blende structure.
• For example, if one fee sublattice is composed of Ga atoms and the interpenetrating sublattice is As, the zinc blende structure of GaAs results.
• Most of the compound semiconductors have this type of lattice, although some of the II-VI compounds are arranged in a slightly different structure called the wurtzite lattice.
• We shall see here to the diamond and zinc blende structures, since they are typical of most of the commonly used semiconductors.
• A particularly interesting and useful feature of the III-V compounds is the ability to vary the mixture of elements on each of the two interpenetrating fcc sublattices of the zinc blende crystal.
• For example, in the ternary compound AlGaAs, it is possible to vary the composition of the ternary alloy by choosing the fraction of Al or Ga atoms on the column III sublattice.
• It is common to represent the composition by assigning subscripts to the various elements.
• For example, Al_xGa_1-xAs  refers to a ternary alloy in which the column III sublattice in the zinc blende structure contains a fraction x of Al atoms and 1-x of Ga atoms.
• The composition Al_0.3Ga_0.7As has 30 percent Al and 70 percent Ga on the column III sites, with the interpenetrating column V sublattice occupied entirely by As atoms.
• It is extremely useful to be able to grow ternary aUoy crystals such as this with a given composition.
• For the Al_xGa_1-xAs example we can grow crystals over the entire composition range from x = 0 to x = 1, thus varying the electronic and optical properties of the material from that of GaAs (x = 0) to that of AlAs (x = l).
• To vary the properties even further, it is possible to grow four-element (quaternary) compounds such as In_xGa_1-xASP_1-y having a very wide range of properties.