Fig 1.
A quantum wire that is 100 Angstroms long and 10 Angstroms or less in diameter.
Fig 2.
The problem space for the simulation of a cylindrical quantum wire.
The cells are one Angstrom cubed. The entire three-dimensional space is 30x30x120 cells. (The Y direction is not shown.)
Fig 3.
Illustration of the difference between the two methods of specifying the potential.
Green represents a potential of 4.6 eV while red represents zero potential. The shades of orange represent weighted averages between the two. (a) The “in or out” method; (b) Averaging method.
Fig 4.
A test function is initialized in the problems space.
As the FDTD simulation proceeds, the waveform spreads out.
Fig 5.
(a) The stored time-domain data; (b) the Fourier transform. Frequency has been converted to energy.
Fig 6.
Comparison of the FDTD method vs. Bessel function in calculating ground state energies of the 100 Angstrom cylinder as a function of the radius of the cylinder.
Table 1.
Ground state energies for the cylindrical wire illustrated in Fig 1 for various radii as determined by the FDTD method and the Bessel function method.
Fig 7.
The first two eigenfunctions corresponding to the first two eigenenergies for the cylinder of Fig 1 with a radius of 5 Angstroms.
(a) 1st eigenstate at 0.6378 eV; 2nd eigenstate at 0.6488 eV.
Fig 8.
A 100 Angstrom quantum wire with a small perpendicular wire attached; (a) Diagram of the wire; (b) Diagram of the problem space; (c) The ground state eigenfunction.
Fig 9.
(a) A tapered 100 Angstrom cylindrical wire. (a) Diagram of the tapered wire; (b) Diagram of the problem space; (c) The ground state eigenfunction. Fig 8C shows that there is some probability that a particle exists in the small perpendicular appendage of the wire illustrated in Fig 8A. The eigenfunction in Fig 9C illustrates that a particle at the ground state energy is equally likely to be found at each end of the wire of Fig 9A, but very unlikely to be found in the middle.