6.2 From Bulk to Zero-Dimensional Structures
189
Fig. 6.1 a Sketch of the dimensionality reduction from bulk to zero-dimensional (from left to right).
Red objects within the black box indicate the lower-dimensional structures, which confine particles
in one, two or even three directions, resulting in quantum wells, wires and dots, respectively. The
latter one is the equivalent of an atom-like entity often referred to as artificial atom, or quantum
box. b Sketch of an electronic particle’s phase-space states for the different confinement scenarios
indicating the reduction of available states to a selection of allowed confinement states in the (3D)
k space. Discretisation of k vectors is indicated. For simplicity, only the lowest k vector state
for the respective confinement direction is sketched for wires and dots. Note that a modification of
translational energy E T and potential energy E V from free (massive) particle (E kinetic = 2 k 2 /2m ∗ )
to fully confined particle occurs. c Schematic diagrams of the energy-dependent density of states
D 3/2/1/0D (E) for the respective confinement situation from a, b. The proportionality is displayed.
Thus, it can be easily evidenced that tailoring the dimensionality of a structure can have a serious
impact on a system’s energetics
189
Fig. 6.1 a Sketch of the dimensionality reduction from bulk to zero-dimensional (from left to right).
Red objects within the black box indicate the lower-dimensional structures, which confine particles
in one, two or even three directions, resulting in quantum wells, wires and dots, respectively. The
latter one is the equivalent of an atom-like entity often referred to as artificial atom, or quantum
box. b Sketch of an electronic particle’s phase-space states for the different confinement scenarios
indicating the reduction of available states to a selection of allowed confinement states in the (3D)
k space. Discretisation of k vectors is indicated. For simplicity, only the lowest k vector state
for the respective confinement direction is sketched for wires and dots. Note that a modification of
translational energy E T and potential energy E V from free (massive) particle (E kinetic = 2 k 2 /2m ∗ )
to fully confined particle occurs. c Schematic diagrams of the energy-dependent density of states
D 3/2/1/0D (E) for the respective confinement situation from a, b. The proportionality is displayed.
Thus, it can be easily evidenced that tailoring the dimensionality of a structure can have a serious
impact on a system’s energetics