Qualifier

Executive Summary

Molecular Beam Epitaxy (MBE) holds the key to the formation of materials structured on the nanoscale, such as Quantum Dots, that can have technological applications in Quantum Computing and several other fields of interest. In this proposal we try to improve the understanding and possibilities of control of this type of system by describing in some detail a large-scale computer simulation to reproduce and possibly extend the experimental results reported by Moison et at [15,38,39] regarding MBE growth of clusters (Quantum Dots) of on the surface of at $500{}^\circ C$ . The clusters that are formed have a height of Å, a half-base of Åand are separated by an inter-dot distance of Å. This specific set of experiments is important because it defined, for the first time, a region where we could consistently obtain clusters that fulfill the requirements for QD manufacture. Also, the large lattice mismatch between the materials used makes it the ideal system to study the relative importance of this and other factors in the growth process.

The experimental technique used, Molecular Beam Epitaxy (MBE), consists of growth by the means of solid-source evaporation in an ultra-high vacuum environment. Current technology allows up to eight individual materials individually controlled. The process permits a high degree of control and flexibility and results in intricate alloy and superlattice structures that can be fabricated under computer control with a high degree of repeatability. The observed growth was consistent with the Stranski-Krastanow growth mode that is characterized by the growth of both a wetting layer and islands. The existence of a relatively large lattice mismatch of about $7\%$ between the deposited clusters of InAs and the GaAs substrate is believed to be responsible for the straining of the substrates lattice that results in the long distance interaction between the clusters that results in patterning of their growth. An Ehrlich-Schwoebell barrier is also believed to be present as an important contributor to the shaping of the clusters by privileging upward or downward motion along the edges of the clusters. One of the main objectives that we hope to achieve by the successful completion of this numerical simulation is to clarify the importance of the substrate mediated interaction and of edge barrier.

The 2D lattice geometry of the substrate surface can be accurately reproduced in the simulations by simply defining a local system of axis. The lattice formed by the deposited atoms can also be reproduced, but it poses a slightly bigger challenge to model. The long range interaction has been put into a form that is computationally viable and physically realistic without introducing any artificial cut-offs due to computational limitations. With the memory resources commonly available we are capable of simulating domains of enough size to accurately reproduce some of the long range organizational characteristics of the deposited material.

Table 1.1: Brief comparison between experiments and simulations

Measurement

Moison et al[38]

Simulation

Growth Rate

Calibrated using RHEED measurements on homoepitaxy with a $2\%$ accuracy.

We can easily reproduce any growth rate with arbitrary accuracy.

Statistics

Dot volume , height , half width at half height were estimated using just a fraction of available dots.
Interdot mean distance , was estimated from the square root of dot density.

Physical observables like , , and could be measured directly using much more information than what is available experimentally.
Statistics can be greatly improved.

Evolution

3D Crystal growth starts at $\Theta_{th}=1.75\pm 0.1ML$
3D single crystal dots are described to ``suddenly appear'' at $\Theta_{th}$
$\Theta_{th}$ is reported to be well defined and reproducible
Experimental techniques provide us a very limited view of surface evolution
The symmetry of the surface is roughly estimated in real time using RHEED. Detailed surface imaging requires stopping the growth.

Powerful professional and freely available graphics packages such as can be used to produce step by step or real time animations.
Simulation can potentially reproduce the observed threshold $\Theta_{th}$
The formation of the single crystal dots could be carefully observed.
The conditions that originate the threshold could be identified and understood.

We describe how the simulation computations can be compared with the experimental results (See Table 1.1). The way in which the simulations can be used to fill the gaps in our understanding of this process and how it supplements experimental imaging techniques such as RHEED, AFM, TEM, XPS and AES is also explained. We elaborate on the ways in which each of the mechanisms that underlie the growth process is believed to affect it and how it would be incorporated in the simulation effort. The possibility of parallelizing the simulation in order to increase the available domain and the number of runs thereby improving the accuracy of the results is also discussed and several implementation possibilities are addressed that would make this a viable choice.