Lattice matching

The oriented overgrowth of a crystalline phase on the surface of a substrate that is also crystalline is called epitaxial growth [104]. Usually it is required that the lattices of the two crystalline phases match, and it can be a rather complicated process [105]. Some new applications enlist amorphous substrates or grow new phases on a surface with a rather poor lattice match. 

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.

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. 

Emission L, nm Active layer material Stmcture Window layer material Substrate Lattice matched Growth technique Other... 

Eig. 6. Plot of band gap energy vs lattice parameter for (a) common III—V materials employed for LEDs where (—) corresponds to direct and (—) to indirect band gaps. Both Al Gaj As and (Al Gaaj )q lattice matched to GaAs, whereas In Gaj As P can be matched to InP. (b)... 

Quantum well lasers ia this system typically use ternary Iuq 53GaQ 47AS wells and biaary InP barriers. AH quaternary lasers, ie, lasers ia which both the wells and barriers are formed by quaternary compounds, are also being developed. These stmctures can be lattice matched or strained. 

Fig. 3. The lattice-matched double heterostmcture, where the waves shown in the conduction band and the valence band are wave functions, L (Ar), representing probabiUty density distributions of carriers confined by the barriers. The chemical bonds, shown as short horizontal stripes at the AlAs—GaAs interfaces, match up almost perfectly. The wave functions, sandwiched in by the 2.2 eV potential barrier of AlAs, never see the defective bonds of an external surface. When the GaAs layer is made so narrow that a single wave barely fits into the allotted space, the potential well is called a quantum well.

Fig. 4.12 (a) CdSe wurtzite unit cell (b) schematic illustration of a hexagonal (wurtzite) CdSe basal plane on a (111) section of the gold lattice, emphasizing the 2 3 lattice match. Note the [111] Au//(0001)CdSe orientation, with the CdSe a-directions aligned along the (llO)Au. The outlined rhombus indicates the projection of a CdSe unit cell. (Adapted from [112])... 

Here, we show three differences in the interface between the nucleus, N, and the original crystal, A. We find that in the first case, the lattices match fairly closely and are coherent. In the second case, there is some correspondence between the lattices. But the incoherent case shows little matching of the two lattices. 

There are many deposit-substrate combinations where the basic lattice mismatch is very large, such as when a compound is formed on an elemental substrate, but where excessive strain does not necessarily result. Frequently a non one-to-one lattice match can be formed. If a material can match up every two or three substrate surface unit cells, it may still form a reasonable film [16]. In many cases the depositing lattices are rotated from the substrate unit cells, as well. In a strict definition of epitaxy, these may not be considered, however, it is not clear why high quality devices and materials could not be formed. 

The majority of deposits formed in this group have been on Au electrodes, as they are robust, easy to clean, have a well characterized electrochemical behavior, and reasonable quality films can be formed by a number of methodologies. However, Au is a soft metal, there is significant surface mobility for the atoms, which can lead to surface reconstructions, and alloying with depositing elements. In addition, Au it is not well lattice-matched to most of the compounds being formed by EC-ALE. 

Some Cu substrates have been used, including Cu foils, etched foils, and vapor deposited Cu on glass. There does not appear to be a significant difference in the quality of deposits formed on Cu vs. Au, beyond those expected from considerations of lattice matching. 

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