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Introduction

A single crystal of either an elemental (e.g., silicon) or compound (e.g., gallium arsenide) semiconductor forms the basis of almost all semiconductor devices. The ability to control the electronic and opto-electronic properties of these materials is based on an understanding of their structure. In addition, the metals and many of the insulators employed within a microelectronic device are also crystalline.

Group iv (14) elements

Each of the semiconducting phases of the group IV (14) elements, C (diamond), Si, Ge, and α-Sn, adopt the diamond cubic structure ( [link] ). Their lattice constants ( a , Å) and densities (ρ, g/cm 3 ) are given in [link] .

Unit cell structure of a diamond cubic lattice showing the two interpenetrating face-centered cubic lattices.
Lattice parameters and densities (measured at 298 K) for the diamond cubic forms of the group IV (14) elements.
Element Lattice parameter, a (Å) Density (g/cm 3 )
carbon (diamond) 3.56683(1) 3.51525
silicon 5.4310201(3) 2.319002
germanium 5.657906(1) 5.3234
tin (α-Sn) 6.4892(1) 7.285

As would be expected the lattice parameter increase in the order C<Si<Ge<α-Sn. Silicon and germanium form a continuous series of solid solutions with gradually varying parameters. It is worth noting the high degree of accuracy that the lattice parameters are known for high purity crystals of these elements. In addition, it is important to note the temperature at which structural measurements are made, since the lattice parameters are temperature dependent ( [link] ). The lattice constant ( a ), in Å, for high purity silicon may be calculated for any temperature (T) over the temperature range 293 - 1073 K by the formula shown below.

a T = 5.4304 + 1.8138 X 10 -5 (T - 298.15 K) + 1.542 X 10 -9 (T – 298.15 K)

Temperature dependence of the lattice parameter for (a) Si and (b) Ge.

Even though the diamond cubic forms of Si and Ge are the only forms of direct interest to semiconductor devices, each exists in numerous crystalline high pressure and meta-stable forms. These are described along with their interconversions, in [link] .

High pressure and metastable phases of silicon and germanium.
Phase Structure Remarks
Si I diamond cubic stable at normal pressure
Si II grey tin structure formed from Si I or Si V above 14 GPa
Si III cubic metastable, formed from Si II above 10 GPa
Si IV hexagonal
Si V unidentified stable above 34 GPa, formed from Si II above 16 GPa
Si VI hexagonal close packed stable above 45 GPa
Ge I diamond cubic low-pressure phase
Ge II β-tin structure formed from Ge I above 10 GPa
Ge III tetragonal formed by quenching Ge II at low pressure
Ge IV body centered cubic formed by quenching Ge II to 1 atm at 200 K

Group iii-v (13-15) compounds

The stable phases for the arsenides, phosphides and antimonides of aluminum, gallium and indium all exhibit zinc blende structures ( [link] ). In contrast, the nitrides are found as wurtzite structures (e.g., [link] ). The structure, lattice parameters, and densities of the III-V compounds are given in [link] . It is worth noting that contrary to expectation the lattice parameter of the gallium compounds is smaller than their aluminum homolog; for GaAs a = 5.653 Å; AlAs a = 5.660 Å. As with the group IV elements the lattice parameters are highly temperature dependent; however, additional variation arises from any deviation from absolute stoichiometry. These effects are shown in [link] .

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Source:  OpenStax, Physical methods in chemistry and nano science. OpenStax CNX. May 05, 2015 Download for free at http://legacy.cnx.org/content/col10699/1.21
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