Fig. 3. Cross-section TEM of pure Si grown by Solid Phase epitaxy under externally imposed elastic stress. (a) Initial corrugated interface, fabricated by X-ray lithography, amplifies (b) under compressive stress and decays (c)under tensile stress.
(Fig.
1: VCSEL, from National Nanotechnology Initiative literature) are revolutionizing
communications technology. This device can be made only because of the
very precise control scientists have obtained over the synthesis, organization,
and uniformity of nanometer-thick films. Future optoelectronic devices
will rely on the synthesis, organization, and uniformity of nanoscale materials
in two and three dimensions. An example of such a material is the array
of "quantum dots" of Ge on Si shown in Fig. 2a. A blow-up of a single such
quantum dot is shown in Fig. 2(b). We are currently trying to understand
the configurational forces and fundamental materials transport laws governing
the formation, and stability of nanoscale features such as these, and much
work remains to be done before we can make such features with sufficient
precision and reliability for technological applications in mass production.
Fig.
2. (a) Ge on Si Nanodot array, topographical image from G. Medeiros-Ribeiro
et al., Phys. Rev. B 58, 3533 (1998). (b) Single quantum dot image
from HP research labs, G. Medeiros-Ribiero et al.,via National Nanotechnology
Initiative literature.
One complicating feature in the formation of most semiconductor quantum
dots is the currently unpredictable interaction of chemistry (i.e. the
dots and the substrate have different chemical compositions) and elasticity
(i.e., the elastic strain energy that inevitably arises when one tries
to grow a material with one characteristic interatomic spacing on top of
a material with a slightly different spacing). We have now succeeded in
uniquely isolating, and attacking separately, the effects of chemistry
and of elasticity by externally loading pure Si mechanically, thereby eliminating
the "chemistry" contribution (see publication #106
and #124).
We find that tensile and compressive stress affect growth differently:
compression makes dots grow and tension makes them flatten out (Fig. 3),
contrary to previously published theories.
Fig. 3. Cross-section TEM of pure Si grown by Solid Phase epitaxy
under externally imposed elastic stress. (a) Initial corrugated interface,
fabricated by X-ray lithography, amplifies (b) under compressive stress
and decays (c)under tensile stress.
A new model for the stress effect alone, which does not yet incorporate
the effects of chemistry, has been developed (see publications #123
and #128)
to predict the conditions under which dots will grow or flatten out, depending
on the magnitude and sign of the strain (e );
the deviation from equilibrium (G-tilde), and a material-specific parameter
called the activation strain (V-tilde) (Fig. 4). This model is expected
to be able to predict the initial stages of quantum dot growth or shrinkage
for a wide variety of materials grown by a wide variety of methods.
Fig. 4. Predicted stability map of nanoscale surface features. Boundaries
between regimes of stable planar growth and unstable nanodot amplification
(due to either what we call the "AT mechanism" or the "BC mechanism", see
publication
#128), shift with increasing driving free energy G-tilde for growth.
For 
big
enough in magnitude (W is the atomic volume
and the activation strain V*11 is a measure of the stress effect
on the interface mobility, see links at bottom), the elastic strain energy
effect commonly studied is insignificant compared to the effect we have
discovered of stress on mobility. T-tilde is the normalized temperature.
Related research descriptions:
The
activation strain tensor: explanation, experiment, and theory (1997)
Self-organization
of nanoscale features (2000)