SEMITIP, VERSION 5, Example 2: n-type GaAs(110), viewing charge density images
Click here for input/output files for Example 2
This example uses nearly the same input values as example 1, but evaluated at only a single voltage (-0.7 V) and with no modulation voltage so that only that single voltage point is computed (and, the number of energy steps is 5000). The output parameter is set to 2, so that various quantities are output including the charge density images img1.PGM, img2.PGM, and img3.PGM. These images have one pixel for each grid point within the semiconductor. The horizontal scale is radial distance r, and the vertical scale is perpendicular distance into the semiconductor z as indicated below. Since these two scales are linear in the grid index, they are nonlinear in the distance since the grid spacing increases as the grid index increases as described in the
Version 2 Documentation.
The gray scale in the images is logarithmic in the magnitude of the charge density, thus allowing viewing of the charge densities over a reasonably large range.
The left-hand image shows the charge density of the localized states. The solution to Schrödinger's equation is performed line by line, for each discrete value of r. In this example, a single state is found along the central axis (i.e. r=0). This state persists out to some particular value of r, after which it vanishes since the confining potential becomes too small at that particular r value. Hence the image is black for larger r values. (A small oscillation in the presence/absence of the localized state occurs around this r value, due to numerical noise). The middle image show the extended states. Near the r value where the localized state vanishes, the extended states also show a significant change. The right-hand images shows the total charge density (sum of localized and extended states). This total now has relatively smooth, continuous behavior (albeit with a small oscillation around the r value where the localized state vanishes).