Epitaxial layers relaxation

TABLE 1 Lattice parameters of III-N compounds (hexagonal-wurtzite and cubic-zincblende structures). For GaN bulk crystals, the errors indicate variations between various samples, as the measurement accuracy was of about 5 parts per million. For cubic AIN and InN, the given lattice parameters are estimated from bond-lengths of the wurtzite phase. For all epitaxial layers, the given values are relaxed lattice parameters calculated from the measured ones using EQN (1),... 

For epitaxial layers, it is essential to measure LPs both parallel and perpendicular to the surface. The relaxed values can be evaluated using the following formula [13] ... 

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. 

Cullis, Sprectroscopic eliipsometiy characterization of strained and relaxed Sil-xGex epitaxial layers,. Appl.Phys.73 (1993)239-250. 

In this chapter we discuss the measurement and analysis of simple epitaxial stractures. After showing how to select the experimental conditions we show how to derive the basic layer parameters the composition of ternaries, mismatch of quaternaries, misorientation, layer thickness, tilt, relaxation, indications of strain, curvature and stress, and area homogeneity. We then discuss the hmitations of the simple interpretation. 

Calculate the strains and that would be applied if the lattice parameters in the interface plane of the layer were forced to conform to the substrate (full coherent epitaxy). Multiply these by (1-i ) where R is the (fractional) relaxation of the layer. (See the discussion of measurement of relaxation in Chapters.)... 

A ,Ga)As buffer layer is grown before epitaxy of (Ga,Mn)As. To control strain in the film, strain-relaxed thick (In,Ga)As ( 1 /zm) with the lattice constant a0 greater than the subsequent (Ga,Mn)As layer can be employed. The Mn composition x in the Gai - Mn As films can be determined from measurements of a0 by x-ray diffraction (XRD), once the dependence a0(x)is calibrated by other means, such as electron probe micro-analysis (EPMA) or secondary ion mass spectroscopy (SIMS). 

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. 

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