Germanium lattice structure

Figure 5.1. Illustration of a unit cell of the diamond cubic lattice. The arrows designate the [001], [010], and [100] directions. Both silicon and germanium crystallize into the diamond cubic lattice structure, where each atom is bonded to four neighboring atoms in a tetrahedral geometry. Figure reproduced from Ref. [30] with permission.

In its crystalline state, germanium, similar to silicon, is a covalent solid that crystallizes into a diamond cubic lattice structure. Like for Si, both the (100) and (111)... 

Modern electronic devices use the semiconductor properties of materials such as silicon or germanium. The atoms of pure silicon or germanium are arranged in a lattice structure, as shown in Fig. 3.81. The outer electron orbits contain four electrons known as valence electrons. These electrons are all linked to other valence electrons from adjacent atoms, forming a covalent bond. There are no free electrons in pure silicon or germanium and, therefore, no conduction can take place unless the bonds are broken and the lattice framework is destroyed. 

Lead has only one form, a cubic metallic lattice. Thus we can see the change from non-metal to metal in the physical structure of these elements, occurring with increasing atomic weight of the elements carbon, silicon, germanium, tin and lead. 

Silicon and germanium as elemental substances are found only in the diamond-type form. The reluctance of Si and Ge to enter into pre-p bonding prohibits a graphite-type structure as a plausible allotrope. These are rather more reactive than diamond the weaker Si-Si and Ge-Ge bonds make disruption of the lattice kinetically easier. Tin occurs in both a metallic form (white tin) and a covalent (diamond-type) form the latter is slightly more stable at low temperatures. Lead forms only a metallic elemental substance. 

This is a specialised technique which has been applied in field emission and field ion microscopy (see Section 2.1.5c). It is achieved by giving the tip a positive potential. Tungsten can then be removed at liquid helium temperatures with an applied field of 5.7 x 10 V.cm Perfectly regular surface structures are exposed containing many different lattice planes. Clean surfaces have been produced on tungsten, nickel, iron, platinum, copper, silicon and germanium. It is potentially applicable to a wide range of materials, but the area of clean surface exposed is only about 10 ° cm . 

Note that diamond and a metal like copper have quite dissimilar structures, although both are based on a face-centered cubic Bravais lattice. To distinguish between these two, the terms diamond cubic and face-centered cubic are usually used. The industrially important semiconductors, silicon and germanium, have the diamond cubic structure. 

In the case of semiconductors, it was first shown in this laboratory that the arrangements of the atoms in the surface monolayers of (100) and (111) germanium and silicon are not the same as those for these planes in the bulk (25). The altered arrangements were revealed by the presence of fractional order beams for the surface gratings in certain azimuths. This was later found to be the case for all crystals tested which have a diamond-type lattice, including semiconducting diamond and several of the intermetallic compounds. The surface structure of silicon was observed to be much more complex than that of germanium. In some azimuths, several fractional orders less than one-half were observed. 

Fig. 3.4. Band structure of germanium calculated from empirical pseudopotentials including s-o coupling as a function of the electron wave vector along selected directions of the reciprocal lattice. The s-o splitting Aso is the energy difference between Ts+ and IV. The light- and heavy-hole VBs are the IV1" to Le and IV1" to L4 +L5 bands, respectively. The energy reference is the VB maximum at the T point after [21]...

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