Parameters

In this instance, the geometry of the nanodot is similar to that of a ``droplet''; we consider the shape to be split into two parts -- the lower part follows a ``bounding sphere'' to some fraction, at which point it is cut off to form a part-sphere. This is then provided with an ellipsoidal top, giving the geometry a dome-topped appearance, which can be seen more clearly in figure 5.4, in order to approximate the experimentally grown droplets (figure 5.1) as well as possible..

For these simulations, we define the height of the geometry thus (as figure 5.4, right):

$$l_{z(s)} = 2/7d$$ (5.1)

$$l_{z(e)} = 1/7d$$ (5.2)

$$\therefore l_z = 3/7d$$ (5.3)

$$< 1/2d$$ (5.4)

$l_{z(s)}$The physical size of the $z$ component of a sphere in a constructive solid geometry, see equation (5.1) $l_{z(e)}$The physical size of the $z$ component of an ellipsoid in a constructive solid geometry, see equation (5.2) where $l_{z(s)}$ is the part which follows the outline of some bounding sphere of diameter $d$, and $l_{z(e)}$ is the upper ellipsoidal dome part. These parameters most closely reflect the geometry of droplets resulting from the partial filling of templates with spherical voids. We study the results of simulations performed on such nanodots with $d$ between 50nm and 500nm.