Epitaxial layers critical thickness

Experimentally, we can introduce a built-in strain in an epitaxial layer by growing it on a lattice mismatched substrate. As long as the mismatched epitaxial layer is below the critical thickness, the produced strain is uniform and no dislocations are induced. As a result, the in-plane lattice constant of the epitaxial layer is fitted to that of the substrate, and the out-of plane lattice constant is adjusted to a new lattice constant according to the Hook law. Then, the subband structure is modified by introducing a built-in strain, and the strain has a dramatic influence on the electronic properties of the system. Theoretically, we can easily include the strain effect in the k.p theory. 

The mechanical interaction between the different epitaxial layers may result in the formation of misfit dislocations. Nucleation and propagation of cracks can ensue if the mismatch in thermal expansion coefficient is relatively large. The defects significantly influence the physical properties of the thin films. Examples from different material combinations and models of how to predict the numbers for critical thicknesses are provided in Section 14.4. 

SLS thickness is thicker than the critical thickness [12]. It is suggested from the experimental results that the dislocations generated at SLS are bended by TCA2, resulting in the low dislocation density. Until now, the low etch pit density on the order of 10 cm has been obtained using SLS and TCA for the total epitaxial layer thickness of more than 3.5 pm [40-43]. Few papers have been reported on the growth of GaAs on Si, with the dislocation density of 10 cm at the epitaxial layer thickness of less than 3 pm. 

Early observations of elastic strain relaxation during growth of epitaxial layers led to paradoxical results. An attempt to interpret the observations on the basis of the critical thickness theory in its most elementary form suggested that, once the thickness of a film exceeded the critical thickness, the final elastic strain of the film should be determined by the thickness of the film alone, independent of the original, or fuUy coherent, mismatch strain. This is implied by the result in (6.27), which states that that the mean elastic strain predicted by the equilibrium condition G(/if) = 0 is completely determined by hf beyond critical thickness, no matter what the value of Cni- However, it was found that the post-growth elastic strain as measured by x-ray diffraction methods did indeed vary with the initial elastic mismatch strain, and it did so in different ways for different film thicknesses (Bean et al. 1984). As a consequence, the critical thickness theory came under question, and various alternate models were proposed to replace it. However, further study of the problem has revealed the relaxation process to be much richer in physical phenomena than anticipated, with the critical thickness theory revealing only part of the story. 

Suppose that a strained layer with uniform mismatch strained Cm is deposited on a substrate to a thickness h i that exceeds the critical thickness her for the layer itself. Then, an unstrained layer of uniform thickness is deposited on the surface of the strained layer. For example, suppose a SiGe alloy film is deposited epitaxially on a Si substrate to a thickness beyond its critical thickness, and then a Si capping layer is deposited on the surface of the alloy layer. The total thickness of the composite film is /if = /igi + /i i. The case of a Si capping layer is the simplest case that can be considered because, in the absence of a dislocation within a strained layer, the epitaxial capping layer is free of mismatch stress this particular system was studied experimentally by Nix et al. (4990). The case of a capping layer that is not matched to the substrate can be handled in essentially the same way, but with slightly greater complexity in the details an example is included as an exercise. 

The epitaxial emitter structure was fabricated, as shown in Figure 6.26 [23]. In this case, only 1,000-A-thick, p-type base layer doped at 2 x 10 cm is grown. This is followed by an epitaxial growth of 3,000-A-thick n emitter layer. The emitter layer is etched using RIE to stop at the base layer. The rest of the process details are similar to those described in Section 6.4. The most difficult step in this process is the etching of the emitter layer and stopping at the base layer. The uniformity of the RIE is critical at this step. 

The main issue involving GaN substrates for nitride epitaxy concerns obtaining optoelectronic devices without mismatch dislocations. The critical conditions for misfit-dislocation creation include lattice mismatch between the layer and the substrate, layer thickness, growth conditions and substrate quality. 

The increase in the TD density in the films grown on relatively thick (6-8 pm) PSC is most probably caused by a specific plastic relaxation process, occurring as a reaction to a particular state of strain that appears in these epitaxial films. This can be stated on the basis of strain inversion in the films grown on PSC, as well as on the increase in compressive stress with the thickness of the PSC layer increasing. These effects show that apart from the stress caused by the GaN/SiC lattice mismatches, an additional built-in stress arises in the films. Obviously, the additional stress is caused by the presence of (0001) PDs, because one can expect that a part of GaN film within the faulted region may have altered its mechanical properties as compared with unfaulted material [72]. Then the increase in dislocation density in GaN grown on relatively thick PSC can be explained by a plastic relaxation process, which relieves the built-in stress and occurs because this internal stress/(0001) PD density reaches a certain critical value. 

Third, and finally, it has been established that the lanthanide magnetism is in general remarkably robust, and in particular is insensitive to the interfaces, even in crystals only a few atomic layers thick. A reservation of critical importance in this regard is the central role of the state of strain in the description of the magnetic behavior. Specifically it has been established for Dy that epitaxial strains 2% are sufficient to double the Curie temperature or completely suppress the ferromagnetic phase. The twin assets of robustness and strain sensitivity make these materials at one time both ideal systems with which to explore epitaxial effects, and attractive models with which new states of magnetic order may be designed and synthesized. 

Fritz, I. J. (1987), Role of experimental resolution in measurements of critical layer thickness for strained-layer epitaxy. Applied Physics Letters 51, 1080-1082. 

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