26.2: The Simulation and its Limitations

The most obvious limitation of the simulation is its restriction to two dimensions. Surface diffusion on the screen thus only takes place along a line, and atoms are rather more likely to meet each other than in three-dimensional reality. A second less-obvious consequence is that the crystallography of real semiconductors is not reproduced on the screen (silicon and GaAs adopt the "diamond cubic" structure whereas our simulation implies a close-packed fcc structure). Thirdly we have not allowed you to change the rate of production of the deposited atoms. In an MBE reactor this would be controlled via the temperature of the (solid or liquid) sources of gas phase atoms. The simulation must be regarded as a "model" which demonstrates many (but certainly not all) of the behaviours of the real crystals. Another simplification is that the possible existence of impurity or dopant atoms is ignored. This is obviously of huge importance in the device industry, but makes very little difference to the behaviour simulated in this TLP.

However despite all these limitations the model is based soundly on the physics of atomic interactions, and incorporates key aspects of the movement of atoms across surfaces ("surface diffusion") including thermal activation. Atoms will therefore show a greater probability of moving from their original position, across the surface, at higher temperatures. It also takes into account the possibility that the relaxed lattice parameter of the deposited crystal might not be the same as that of the substrate crystal. This often occurs in heteroepitaxy, leading to the build-up of strain in the growing layer. The simulation correctly models many of the behaviours observed during the epitaxial growth of real crystals.

The three common growth modes have the following characteristics:

• Frank-van der Merwe: each layer of deposited atoms is completed before the next layer starts to form. The surface at any instant will be flat or will contain a few monolayer steps.
• Volmer-Weber (island growth): each deposited atom attaches to an island (or incipient particle); islands grow appreciably before joining up to cover the substrate completely. The surface at any instant will not be flat, and the substrate may not be entirely covered.
• Stranski-Krastanov: initially the deposited atoms form one or more perfect layers but this is followed by island growth. The surface is therefore initially flat but develops to become less flat.

Click on this link to launch the epitaxial growth simulation in a new window.

Please note that the simulation is for educational purposes only, and the accuracy of the data contained within it is not guaranteed.

Note: This animation requires Adobe Flash Player 9 and later, which can be downloaded here.

An effective way of using this TLP is to experiment for a few minutes with the simulation, in order to familiarise yourself with its operation, before attempting to answer the following questions, many of which will require that you experiment with the effect of specific variables on the simulated growth, in order to explore different growth regimes. The simulation offers you by default 100 atoms to deposit (three to four atomic layers), but if you need more to see how the film develops, simply increase the number using the slider control.

Notes about the simulation parameters:

• Temperature is shown as Tm, the temperature of the substrate expressed as a fraction of its melting temperature.
• Bond strengths are in arbitrary units on a scale from 0 to 100, where zero implies no bonding and 100 is a strong bond which is unlikely to be broken except at high temperatures.
• Lattice parameter difference is the percentage difference between the natural lattice parameters of the substrate material and the deposit material. If this is non-zero then for epitaxy to occur the deposit must be strained to fit the substrate and therefore strain energy will accumulate as growth occurs.