Electronic structure in the crossover regimes in lower dimensional structures

• Electronic structure calculations in the dimensional crossover regimes.
• Evolutions of DOS, Fermi energy and DOS at Ef have been calculated.
• Free electron model calculations in all dimensional crossover regimes.
• Experiments were performed in Ag islands on Si(1 1 1) surfaces for 0D to 2D crossover.
• The trend of variation of DOS at Ef agrees well with the theoretical calculation.

Modern growth and fabrication techniques can produce lower dimensional structures in the crossover regimes. Such structures in the crossover regimes can provide tunability of various properties of materials. For example, a zero-dimensional (0-D) structure (quantum dot) evolving towards a 3-D structure (bulk) shows electronic structure, which is neither 0-D-like, nor 3-D-like in the dimensional crossover regime. Within the crossover regime the electronic density of states (DOS) at Fermi level (Ef) keeps on changing as the size of the system changes. DOS at Ef determines many properties of materials, such as electronic specific heat, spin susceptibility, etc. Such properties can be tuned by controlling the size of the system in the crossover regimes. Keeping the importance of DOS at Ef in mind, we determine their values and other details of electronic structure of lower dimensional structures, in the 0-D to 1-D, 1-D to 2-D, 2-D to 3-D, 0-D to 2-D, 0-D to 3-D and 1-D to 3-D crossover regimes, in a simple free electron model. We compare our results with analytical theory and experimental results, wherever available. We also present some results obtained by scanning tunneling spectroscopy measurements on Ag islands on Si(1 1 1) substrates evolving from a 0-D to a 2-D structure. This simple model is quite useful in understanding lower dimensional structures in the crossover regimes and, in general, in nanoscale science. Fabrication of such structures would provide control on materials properties.

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