Lattice-Mismatch Effects on Semiconductor Epitaxial Growth

This is a continuation from the previous tutorial - what is molecular-beam epitaxy (MBE)?

A defect-free epitaxial growth of one crystal lattice over another takes place if the lattice constants of the two materials are nearly identical.

In the presence of a small lattice mismatch (less than 0.1%), growth occurs with an approximate match of the lattice sites in the interface region of two lattices.

This approximate match is possible if there is an elastic strain at the interface, that is, each atom is slightly displaced from its original position at the boundary layer.

Although a small amount of strain can be tolerated for thin layers and can even be beneficial in the case of quantum-well lasers, in general the strain energy stored in the crystal is reduced by the formation of a misfit dislocation (a missing row of atoms in one of the lattices).

This is schematically illustrated in Figure 4-15.

**Figure 4-15**. Schematic illustration of a misfit dislocation formed during the epitaxial growth in the (100) plane of a cubic lattice. The two semiconductors have slightly different lattice constants.

If \(a\) is the lattice constant of the substrate and \(a'=a-\Delta{a}\) is that of the grown layer, the separation between each row of missing atoms is approximately given by

\[\tag{4-6-1}L\approx{a^2}/\Delta{a}\]

At the interface between the two crystal lattices, the rows of missing atoms exist along two perpendicular directions. The separation between the rows along a principal crystallographic axis (e.g., 100) is approximately given by Equation (4-6-1).

This type of imperfection at the interface is called a dislocation; and since it arises from lattice mismatch (or misfit), it is called misfit dislocation.

Near a misfit dislocation, the lattice is imperfect, containing many dangling bonds that cause nonradiative recombination of electrons and holes. Thus misfit-dislocation-free layers are needed to fabricate high-quality electro-optical devices.

The generation of misfit dislocation depends on both the lattice mismatch and the thickness of the epitaxial layer grown. Oe. et al. found that misfit dislocations did not form in InGaAsP-InP double-heterostructure layers (0.4 μm thick) grown on (100) InP if the lattice mismatch \(\Delta{a}/a\) was in the range of \(-5\times10^{-3}\) to \(5\times10^{-3}\).

Nakajima et al. have studied the occurrence of misfit dislocations as a function of lattice mismatch for InGaAs layers of different thicknesses grown on (100) InP at \(650^\circ\text{C}\). The measured data are shown in Figure 4-16.

**Figure 4-16**. Occurrence of misfit dislocations as a function of lattice mismatch for different layer thicknesses of InGaAs grown by LPE on (100) InP. No misfit dislocations were observed in the region bounded by solid lines.

The solid lines represent the boundary where no misfit dislocations were observed. For the growth of thick, dislocation-free InGaAs layers, the tolerable room-temperature lattice mismatch is found to lie between \(-6.5\times10^{-4}\) and \(-9\times10^{-4}\).

The reason for this negative lattice mismatch is due to different thermal-expansion coefficients of InGaAs and InP that introduce a negative room-temperature lattice mismatch for perfectly matched layers at the growth temperature of \(650^\circ\text{C}\).

Since misfit dislocations are formed near the growth temperature, lattice matching at the growth temperature is important to produce dislocation-free layers.

The next tutorial discusses about the material parameters of InGaAsP quaternary alloy grown on InP.

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