Constant, lattice

Figure A3.10.5 An fcc(l 11) monolayer (fiill circles) overlaid onto a bcc(l 10) substrate (open circles), (a) fee [Oil] parallel tobcc[001]. (b) 5.26° rotation relative to (a). The lattice constants were chosen to produce rowmatching in (b) [12].

Another example of epitaxy is tin growdi on the (100) surfaces of InSb or CdTe a = 6.49 A) [14]. At room temperature, elemental tin is metallic and adopts a bet crystal structure ( white tin ) with a lattice constant of 5.83 A. However, upon deposition on either of the two above-mentioned surfaces, tin is transfonned into the diamond structure ( grey tin ) with a = 6.49 A and essentially no misfit at the interface. Furtliennore, since grey tin is a semiconductor, then a novel heterojunction material can be fabricated. It is evident that epitaxial growth can be exploited to synthesize materials with novel physical and chemical properties. 

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

Figure B3.2.7. A perspective view of the cetineite (Na Se). The height of the figure is tluee lattice constants c. The shaded tube is included only as a guide to the eye. (From [88].)...

Figure B3.2.11. Total energy versus lattice constant of gallium arsenide from a VMC calculation including 256 valence electrons [118] the curve is a quadratic fit. The error bars reflect the uncertainties of individual values. The experimental lattice constant is 10.68 au, the QMC result is 10.69 (+ 0.1) an (Figure by Professor W Schattke).

III-V compound semiconductors with precisely controlled compositions and gaps can be prepared from several material systems. Representative III-V compounds are shown in tire gap-lattice constant plots of figure C2.16.3. The points representing binary semiconductors such as GaAs or InP are joined by lines indicating ternary and quaternary alloys. The special nature of tire binary compounds arises from tlieir availability as tire substrate material needed for epitaxial growtli of device stmctures. 

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.

Figure C2.16.4. A plot of the energy gap and lattice constant for large-gap nitrides. These materials have wairtzite stmcture.

Temary and quaternary semiconductors are theoretically described by the virtual crystal approximation (VGA) [7], Within the VGA, ternary alloys with the composition AB are considered to contain two sublattices. One of them is occupied only by atoms A, the other is occupied by atoms B or G. The second sublattice consists of virtual atoms, represented by a weighted average of atoms B and G. Many physical properties of ternary alloys are then expressed as weighted linear combinations of the corresponding properties of the two binary compounds. For example, the lattice constant d dependence on composition is written as ... 

This approximation, known as Vegard s laM>, accurately describes the average lattice constant (but not the microscopic stmcture ) of most ternary compounds. However, the expression for the gap must be modified by the inclusion of a quadratic tenn... 

Quaternary Ga In j.As jPj, grown on InP is of major importance to fibre-optic communications. In quaternary compounds, both the gap and the lattice constant can be tailored by changing the chemical composition. In thick layers, in order to avoid the generation of strain-induced defects, care must be taken in adjusting the ratio of x and v to maintain the lattice-matched composition x = 2.2v. The available gaps range from 1.34 eV in InP to -0.75 eV in... 

Wlrile quaternary layers and stmctures can be exactly lattice matched to tire InP substrate, strain is often used to alter tire gap or carrier transport properties. In Ga In s or Ga In Asj grown on InP, strain can be introduced by moving away from tire lattice-matched composition. In sufficiently tliin layers, strain is accommodated elastically, witliout any change in the in-plane lattice constant. In tliis material, strain can be eitlier compressive, witli tire lattice constant of tire layer trying to be larger tlian tliat of tire substrate, or tensile. 

Figure C2.16.2 shows tire gap-lattice constant plots for tire III-V nitrides. These compounds can have eitlier tire WTirtzite or zincblende stmctures, witli tire wurtzite polytype having tire most interesting device applications. The large gaps of tliese materials make tliem particularly useful in tire preparation of LEDs and diode lasers emitting in tire blue part of tire visible spectmm. Unlike tire smaller-gap III-V compounds illustrated in figure C2.16.3 single crystals of tire nitride binaries of AIN, GaN and InN can be prepared only in very small sizes, too small for epitaxial growtli of device stmctures. Substrate materials such as sapphire and SiC are used instead.

Epitaxial crystal growth methods such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) have advanced to the point that active regions of essentially arbitrary thicknesses can be prepared (see Thin films, film deposition techniques). Most semiconductors used for lasers are cubic crystals where the lattice constant, the dimension of the cube, is equal to two atomic plane distances. When the thickness of this layer is reduced to dimensions on the order of 0.01 )J.m, between 20 and 30 atomic plane distances, quantum mechanics is needed for an accurate description of the confined carrier energies (11). Such layers are called quantum wells and the lasers containing such layers in their active regions are known as quantum well lasers (12). 

Fig. 6. Band gap versus lattice constant for Group 13—15 (III—V) semiconductors where (—) denotes direct gap and (-) iadirect. Liaes joining the...

Fig. 8. A plot of band gap versus lattice constant for Groups 2—16 and 12—16 (II—VI) semiconductors used for the preparation of green and blue lasers.

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