banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Determining a complete three-dimensional set of eigenfunctions for nanoscale structure analysis
Rent this article for


Image of FIG. 1.
FIG. 1.

The structure to be modeled. (a) The overall diagram. (b) The profiles in each direction along the center axes. The oxide is modeled as an infinite potential at and . Notice the profile next to these walls on the far right plot.

Image of FIG. 2.
FIG. 2.

Diagram of the problem space used to simulate the structure of Fig. 1. (a) is the XY plane and (b) is the YZ plane. Dimensions are in cells. Each cell is . The perfectly matched layer (PML) is seven cells wide at each border in the and directions.

Image of FIG. 3.
FIG. 3.

(a) Fourier analysis of the time-domain data taken at a point source in the middle of the problems space of the structure in Fig. 1. (b) The eigenfunction at is clearly the fundamental function. (c) The eigenfunction at is a superposition of rectangular functions.

Image of FIG. 4.
FIG. 4.

(a) A two point test function. (b) The eigenfunction found using the test function of (a).

Image of FIG. 5.
FIG. 5.

Repeat of the Fourier analysis of Fig. 3(a) using the phase detection method. Notice that the same fundamental frequency was found with only 5000 iterations.

Image of FIG. 6.
FIG. 6.

Three of the different source functions.

Image of FIG. 7.
FIG. 7.

The three eigenfunctions generated from the source functions of Fig. 6. [Remember that the (323) function is antisymmetric with respect to the XZ plane, and has a value of zero on the XZ plane.]

Image of FIG. 8.
FIG. 8.

Six of the eigenfunctions in the complete set. Only the XY plane is shown, so functions with cannot be displayed.

Image of FIG. 9.
FIG. 9.

(a) A propagating function is initiated on the left side of the channel and moves left to right [(b) and (c)]. The amplitude and phase of the coefficients of the eigenfunction decomposition for each wave form are shown directly below it. As the pulse propagates, the amplitudes of the coefficients remain the same, but the phases change.


Generic image for table
Table I.

List of the complete set of eigenfunctions for the structure in Fig. 1.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Determining a complete three-dimensional set of eigenfunctions for nanoscale structure analysis