by Professor Federico Rosei
Semiconductor nanostructures have been studied extensively over the last two
decades. Under proper processing conditions, the fabrication of heterogeneous
junctions between different semiconductor materials results into three
dimensional nanostructures with lateral dimensions in the 1-100 nm length scale.
A notable example is the case of Group IV semiconductors such as silicon (Si)
and germanium (Ge).
The deposition of Ge on a Si substrate just a few atomic layers thick induces
self organization of a high density nanostructure with physical and chemical
properties different to their neighboring environment. For instance, one
peculiar trait of their electrical behavior is the ability to trap discrete
amounts of opposite charge (electrons and electron holes), similarly to the case
of natural atoms. As a result, these nanostructures are often referred to as
'quantum dots' (QDs) and 'artificial atoms'. Likewise, mutual interactions
within functional architectures of QDs may give rise to artificial analogues of
molecules and crystals, leading to a gamut of new opportunities.
The potential applications of QDs are enormous. Technological fields
where the use of QDs may exert the highest impact include light emitting diode
(LED) and laser technologies, single photon sources, new transistors, cellular
automata and quantum computers, advanced catalysts, photovoltaic devices,
environmental and biomedical diagnostics, imaging and therapeutics, biosensing,
etc. In particular, the development of processes compatible with silicon
technology holds potential for immediate integration of QDs in state of the art
semiconductor fabrication processes.
The fabrication of germanium / silicon nanostructures using the bottom-up
approach could become a viable option to realize arrays of epitaxially grown
QDs. The prototypical experiment consists involves the slow deposition of
germanium atoms on a silicon substrate (e.g. fractions of monatomic layers per
second), which may be realized by a variety of chemical and physical methods
already in use in semiconductor processing.
At high temperatures, Ge atoms replicate the crystal lattice geometry of the
Si substrate, due to similarities between these elements. However the lattice
parameter of Ge is about 4% larger than that of Si, which causes excessive
strain accumulation at the heterogeneous interface.
Beyond a certain thickness, spontaneous mechanisms intervene to accomplish
partial relaxation of this strain. One of these mechanisms is the creation of
roughness, which ultimately leads to the emergence of three dimensional
nanostructures. Other mechanisms include the nucleation of misfit dislocations
and intermixing of Ge and Si atoms, which reduces the effective lattice mismatch
at the interface. The geometrical, strain and elemental profile within and
around the three dimensional nanostructures governs fundamental characteristics
of these QDs.
While the principal concept at the origin of the self organization of
semiconductor nanostructures is a thermodynamic instability, over recent years a
novel paradigm has been proposed, which refers to a leading role of kinetic
parameters and energy barriers against atomic diffusion. Thermodynamic
stability, which is one of the most ubiquitous concepts in physics, does not
explain a number of physical and chemical properties observed under typical
experimental conditions, including e.g. strain and elemental profiles.2
To achieve thermodynamic stability all material within and around the three
dimensional nanostructures should sustain massive rearrangements and great
multitude of competitive configurations. However this is obstructed by energy
barriers against atomic diffusion and exchanges. Under typical experimental
conditions, there is a large unbalance between the probability of surface
diffusion and bulk diffusion.2
In practice, surface diffusion proves extremely rapid and is essentially
governed by Brownian motion (random movement) and only partially directed by the
thermodynamic landscape of the surface.
In contrast bulk diffusion is negligible, i.e. atoms below the topmost atomic
layer are frozen as soon as overlaid by new atoms. Moreover when temperature is
quenched soon after deposition, the overall configuration of the sample
comprising e.g. size and shape statistics, strain and elemental profiles and
mutual separations of the QDs cannot undergo significant evolution, which gives
the highest importance to the dynamic processes realized during growth.
An important feature which is defined early in the deposition process is the
mutual positions of the resulting three dimensional nanostructures. The
probability of nucleation of an individual nanostructure increases with the
local concentration of available atoms, whose diffusion and clustering may
generate stable nuclei.
This probability suddenly drops as soon as one nucleus appears and begins to
enlarge by capture of nearby atoms essentially driven by Brownian motion.3 This explains why nuclei tend to keep a certain distance
apart, which correlates with the atomic surface diffusion length.4 Surface diffusion also mediates nanostructure growth, size
and shape by capture of mobile atoms.3
Under the simplest assumption of Brownian motion, this is an intuitive
competitive process between coexisting nanostructures, whereby the closer their
mutual proximity the smaller their relative size.4
The correlation between size and shape is a solid concept.1 Finally, surface diffusion determines the elemental
profile within the nanostructures, whose principal features may be explained in
terms of Brownian motion once again, the different mobility of germanium and
silicon and its dependence on temperature.2
At moderate temperatures for example (say approximately 500 Celsius) the
mobility of germanium is much higher than that of silicon, which causes Si atoms
to accumulate at nanostructure edges and perimeters,5,6 whereas thermodynamic stability would require the
opposite, i.e. Si rich cores and Ge rich peripheries.
While oversimplified, the picture described above is a reasonable start to
understand individual and collective properties of semiconductor nanostructures
as observed in experimental data. A variety of additional thermodynamic
components, including e.g. strain interactions between nanostructures and
substrate, between coexisting nanostructures and within individual
nanostructures, may induce effective perturbations in the definition of
preferential nucleation sites, the transfer of mass and modulation of size and
shape (see e.g. Ostwald ripening which promotes the growth of large over small
nanostructures), and the exchange of germanium and silicon atoms.
Both diffusive dynamics and additional thermodynamic components may become
modulated by integration of suitable top-down interventions, which may be
designed and implemented in keeping with the spontaneous behavior described
above, which cannot be suppressed. This is a hybrid approach to achieve
semiconductor nanostructures with enhanced control over their position, size,
shape and elemental composition.
In this context the notion of 'surface cues' is a powerful concept,7 whereby a preliminary modification of the substrate alters
the kinetic and thermodynamic landscape at the surface, thus guiding adsorption
and diffusion of atoms and molecules. Examples of 'surface cues' may be arrays
of steps,8 dislocations and chemical inhomogeneities
introduced onto the silicon substrate prior to germanium deposition.
In conclusion, over recent years there has been significant progress in the
fundamental understanding and fabrication of QDs based on semiconductor
nanostructures. While there are still many critical issues ahead, the potential
for radical innovation behind these concepts provides strong motivation for
future investigations of semiconductor nanostructures.
1. F. Rosei, J. Phys.: Cond. Matt. 16, S1373 (2004).
2. F. Ratto, G. Costantini, A. Rastelli, O.G. Schmidt, K. Kern, F.
Rosei, J. Exp. Nanosci. 1, 279 (2006).
3. M. Fanfoni, M.
Tomellini, J. Phys.: Cond. Matt. 17, 571 (2005).
4. F. Ratto,
A. Locatelli, S. Fontana, S. Kharrazi, S. Ashtaputre, S.K. Kulkarni, S. Heun, F.
Rosei, Phys. Rev. Lett. 96, 096103 (2006).
5. G. Katsaros, G.
Costantini, M. Stoffel, R. Esteban, A.M. Bittner, A. Rastelli, U. Denker, O.G.
Schmidt, K. Kern, Phys. Rev. B 72, 195320 (2005).
6. F. Ratto,
A. Locatelli, S. Fontana, S. Kharrazi, S. Ashtaputre, S.K. Kulkarni, S. Heun, F.
Rosei, Small 2, 401 (2006).
7. F. Cicoira, F. Rosei, Surf. Sci.
600, 1 (2006).
8. A. Sgarlata, P.D. Szkutnik, A. Balzarotti, N.
Motta, F. Rosei, Appl. Phys. Lett. 83, 4002 (2003).
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