Crystal structure tetrahedral semiconductors

Sphalerite (p-ZnS) has a cubic crystal structure in which both Zn and S occur in regular tetrahedral coordination. Pure sphalerite is a diamagnetic semiconductor with a large band gap (—3.6 eV Shuey, 1975). On the basis of the observed structure and properties, the simple MO energy-level diagram shown in Fig. 6.1 can be proposed to describe the bonding in a ZnS4 cluster molecular unit. Overlaps between outermost s and p... 

The copper, copper-iron, and the silver sulfides are more complex than the sulfides discussed previously, containing several cations or cation sites in their structures. Thus chalcopyrite (CuFeSj), although having a fairly simple structure based on that of sphalerite, but with Cu and Fe alternately replacing Zn atoms, contains both Cu+ and Fe + in regular tetrahedral coordination (as indicated by neutron diffraction and Moss-bauer studies see Vaughan and Craig, 1978). A family of more than thirty synthetic compounds with the chalcopyrite structure is known, and their properties have been studied because of potential applications as semiconductors. Miller et al. (1981) have reviewed the crystal structures, vibrational properties, and band structures of these materials. 

The choice of the diamond cubic structure (FC-2) as the initial configuration to be randomized is a natural one. It is the most common structure for group IV elements and related semiconductors with tetrahedral bonding and it is the one of highest symmetry. It has periodicity built in from the outset and it allows for the possibility that the randomized structure can in principle return to the initial crystal structure. Indeed, with insufficient randomization, the nearly-randomized structure will sometimes return to the perfect FC-2 crystal structure [34]. Without exactly N = Sn atoms this option is precluded. 

The above systematic trend of the catalytic activity of various spinel compositions may be explained on the basis of crystal structure, electronic activation energy and distribution of metal ions between the tetrahedral and octahedral sites. A radical mechanism was suggested by Deren etal for the decomposition of hydrogen peroxide on semiconductor surfaces. According to this mechanism, for the surface of a compound to be active, both donor and acceptor centres should be present. 

This approach has been successful in rationalizing the melting points, heats of formation and mixing, and various optical and electrical phenomena of tetrahedral semiconductor crystals (e.g., see Ref. 173). It is not clear how far it may be extended to other types of materials in the light of the complexities of bonding which many experiments demonstrate—also few experimental results may be related directly to a fractional ionicity for comparison. Levine, however, has generalized the dielectric model in terms of individual bond properties to several different structures. The critical ionicity ft = 0.785) between octahedral and tetrahedral coordination is not always appropriate for example PbS, PbSe, and PbTe (with rock-salt structures) have ft 0.6, and for LiH (also rock-salt)yi 0.1. This latter value would seem to be in... 

It has been shown that not only the elemental semiconductors of group IV and binary compounds which are their analogs crystallize in tetrahedral structures in fact, a whole series of ternary compounds of various types with an average of four valence electrons per atom have the same property. Thus, the formation of covalent bonds based on the sp hybrids is not peculiar to elemental semiconductors and binary semiconducting compounds, but is also found in ternary semiconducting compounds. 

Figure 9A Two-dimensional representation of crystal structure of an intrinsic semiconductor such as Si crystal. The original tetrahedral structure is oversimplified to a square one for clarity. Dark spots in the sketch illustrate shared valence electrons among Si atoms and form covalent bonds, (a) Simation at 0 K where no ionization takes place, (b) At higher temperature, valence electrons gain sufficient energy and are delocalized, which form the holes in the VB. (c) Energy diagram for the intrinsic semiconductor crystal. Mobility of holes in VB and the electrons in CB imparts conductivity to the intrinsic semiconductor crystal.

Interestingly, zinc sulfide (p-ZnS) may also crystallize in a cubic lattice, which consists of a fee array of S , with Zn occupying 1/2 of the available tetrahedral sites. This structure is known as sphalerite or zincblende, and is shared with other compounds such as a-AgI, p-BN, CuBr, and p-CdS. When the same atom occupies both the fee and tetrahedral interstitials of the sphalerite structure, it is described as the diamond lattice, shared with elemental forms (allotropes) of silicon, germanium, and tin, as well as alloys thereof. Important semiconductors such as GaAs, p-SiC, and InSb also adopt the sphalerite crystal structure. 

For example, consider silicon, the most prevalent semiconductor. Figure 9.9 shows two representations of a pure silicon lattice using Lewis dot structures. Each silicon atom has four valence electrons and is therefore tetrahedrally bonded to four neighboring Si atoms. This repeated structure forms the silicon lattice its crystal structure is identical to diamond. The diagram in the middle shows a perfect Si lattice at absolute zero. In this case, all the electrons are covalently bonded between a given pair of silicon atoms. At 0 K, silicon has no mobile charge carriers it is insulating. 

Mercuric sulfide (HgS) is dimorphic. The more common form, cinnabar (red a-form), has a distorted RS, trigonal structure which is unique among the monosulfides, for the crystal is built of helical chains in which Hg has two nearest neighbors at 2.36 A, two more at 3.10 A, and two at 3.30 A. Bulk a-HgS is a large-gap semiconductor (2.1 eV), transparent in the red and near IR bands. The rare, black mineral metacinnabarite is the 3-HgS polymorph with a ZB structure, in which Hg forms tetrahedral bonds. Upon heating, 3-HgS is converted to the stable a-form. The ZB structure of HgS is stabilized under a few percent admixture of transition metals, which replace Hg ions in the lattice. 

II-VI semiconductors, such as CdSe and CdS, normally have the wurtzite structure (see Chapter 1) where each element is tetrahedrally coordinated. Under high pressures (2 GPa), these transform to the six-coordinate NaCl (rock salt) structure. However, if pressure is applied to a CdSe nanocrystal of about 4 nm in diameter, it now takes much more pressure, about 6 GPa, to transform it to the rock salt structure. It is thought that this may be a resistance to the exposure of high-index crystal planes... 

The parameter is obtained by relating the static dielectric constant to Eg and taking in such crystals to be proportional to a - where a is the lattice constant. Phillips parameters for a few crystals are listed in Table 1.4. Phillips has shown that all crystals with a/ below the critical value of0.785 possess the tetrahedral diamond (or wurtzite) structure when f > 0.785, six-fold coordination (rocksalt structure) is favoured. Pauling s ionicity scale also makes such structural predictions, but Phillips scale is more universal. Accordingly, MgS (f = 0.786) shows a borderline behaviour. Cohesive energies of tetrahedrally coordinated semiconductors have been calculated making use... 

The diversity in structure and bonding possible for phosphides is effectively demonstrated by the monophosphides. Monophosphides MP of the group 1 and 2 elements (El, E2) are polyphosphides with i(P ) chains and P2" dumbbells, respectively. Ell and E12 monophosphides are not known. The E3 and E13 monophosphides are the so-called normal compounds with 3x = (M) (see Section 2). With El3, they form the zinc blende structure with tetrahedral heteroatomic bonds. Ternary derivatives such as MgGeP2 and CuSi2P3 have a random distribution of the M atoms, whereas CdGeP2, crystallizes in the ordered chalcopyrite type with a TO[GeP4/2] tetrahedral net (see Section 6.4). The E3 monophosphides form the NaCl structure. CeP is remarkable because of its physical properties (metal-semiconductor transition heavy-fermion behavior). The E14 monophosphides show the break usually observed when passing the Zintl border. Binary lead phosphides are not known SiP and GeP... 

---