Epitaxial Growth

Molecular Beam Epitaxy

Figure 1: Schematic illustration of the fundamental processes involved in MBE. From [1]
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In this text we propose a detailed computational study of several of the processes present in Molecular Beam Epitaxy (MBE). Before we can proceed with modeling this type of system we must understand the experimental setup involved. MBE provides us with the ability to easily grow complex multilayered semiconductor structures with taylor made characteristics

In an MBE growth experiment, we start with a flat surface of material that constitutes the substrate that we bombard with a flux of particles. In order to avoid contamination and unwanted reactions, the chamber that is used in this process is submitted to an ultrahigh vaccum ( $ P<10^{-8} Pa$). This is represented schematically in Fig. 1. The particles that collide with the substrate become bound to its surface, but are still able to diffuse until they find an adequate crystallographic site where they can be incorporated in to the growing surface. Temperature fluctuations can also cause particles to evaporate and join the vapour inside the chamber. The experimental setup is described in more detail in Sec. 3.

Growth can occur in three different modes. The so called Frank-van der Merwe, in which growth occurs layer by layer, and where a layer only forms after the previous one is complete. The Stranskki-Krastanov mode, where after the completion of a few complete layers we observe the growth of three dimensional clusters of particles. Finally, we can observe the growth of three dimensional clusters right from the begining, in which case we are in the presence of the Volmer-Weber growth mode. These three types of growth as represened in Fig. 2 are due to the presence of growth instabilities as described in Sec. 0.2.

Figure 2: Surface growth modes
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Instabilities

During the growth process there are several instabilities that can affect the final characteristics of the experiment. These instabilities must be well studied, understood and controled if we are to be able to manipulate the MBE process.

  • Chemical Instability If we don't choose the chemical elements used criteriously, this instability can lead to the apperance of spontaneous composition modulations, non-uniformities in the band-gap of the final material. This instability can also be used to spontaneously obtain structures that are strained on nano-scales.

  • Lattice Mismatch A mismatch in the lattice parameter of the material tha constituted the substrate and of the depositing particles leads to the formation of a thin pseudo-morphic layer. This layer is expected to grow uniformily and commensurably with the strain energy increasing linearly with the thickness up to a threshold. It also posesses a modified band-struture which can be useful for a wide range of practical applications. The lattice mismatch results in an effective elastic interaction between the adatoms.

  • Ehrlich-Schwoebel This type of instability causes the behaviour of the adatoms on the vicinity of steps to behave differently by introducing an energy gain (or loss) for specific events such as climbing up (or descending from) a step. This leads to the formation of the three dimensional clusters characteristic of Volmer-Weber and the Stranskki-Krastanov growth modes.


Experimental Setup

Figure 3: Photograph and schematic representation of the experimental setup used for MBE studies.
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Typically, the elements that will be used to grow the epitaxial layer are stored in the Effusion Cells. These cells are responsible for maintaining a steady flux of material and are independently heated. Since their output flux is temperature dependent, there is a chilled panel separating the cells to prevent thermal crosswalk.

The MBE system that we have represented schematically in Fig. 3 consists of three main vacuum chambers: a growth chamber, a buffer chamber, and a load lock. The growth chamber is where the actual growth of the material occurs. The buffer chamber is used for preparation and storage of samples, but in some cases they are equipped for material characterization as well. Finally, the load lock is used to bring samples into and out of the vacuum environment without compromising the vacuum integrity of the other chambers.

Samples are placed in the growth chamber sample holder with the use of a magnetically coupled transfer rod. The sample holder has two axes on which it can rotate as represented in Fig. 3. If layer uniformity is a concern, the sample can be rotated using the Continual Azimuthal Rotation ($ CAR$) assembly of the sample holder. Usually there is a sensor for chamber pressure monted in the CAR facing opposite of the sample to monitor the vaccum conditions of the chamber. This sensor can also be rotated so that it faces the effusion cells in order to measure the Beam Equivalent Pressure (BEP) and assure that the effusion cells are operating within the expected parameters.

The criopanels located between the chamber walls and the CAR acts as an effective pump for many of the residual gasses in the chamber. This arrangement can keep the partial pressure of gasses, such as $ H_20$, $ CO_2$, and $ CO$ to less than $ \approx10-11$ Torr. Materials such as Ta, Mo, and pyrolytic boron nitride (PBN) which do not decompose or outgas impurities even when heated to 1400^oC are used to fabricate all the parts that are heated.

Bibliography

1
P. Politi et al.
Instabilities in crystal growth by atomic or molecular beams.
Physics Reports, (324):271-404, 2000.


 

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