SEMITIP V6, Uni3, Example 1: n-type GaAs(110)
Click here for input/output files for Example 1
This example illustrates a simple band bending computation for n-type GaAs doped at 1018 cm-3, assuming a tip radius of 10 nm, contact potential of 0 eV, and a sample-tip voltage of 1 V. The semiconductor is thus in depletion. Intrinsic surface states that are present just above the conduction band edge (lines 21-24 of the FORT.9 input file), but they play little role in the solution. Output to FORT.11 gives the electrostatic potential energy (column 2) along the central axis vs. the z-distance through the vacuum and semiconductor (column 1). Output to FORT.12 gives the electrostatic potential energy on the surface (column 2) vs. the radial distance along the surface (column 1), for an azimuthal angle 0. When plotted, these potentials appear as:
We see that only about a quarter of the applied voltage bias is dropped in the semiconductor, considerably smaller than occurs for the analogous one-dimensional case as in
Example 1 of Uni1 and in reasonable agreement with the computation assuming azimuthal symmetry in
Example 1 of Uni2 (this agreement could be made even better with tighter convergence parameters for the solution).
Also note that the electrostatic potential at the surface does not fall to zero even for large radial distance from the central axis. This is because intrinsic surface states are included; those distributions are located predominantly above the conduction band edge, but with weak Gaussian tails extending down into the band gap region. The density of surface states in those talks is sufficient to produce a small amount of depletion of the semiconductor even far from the tip. (If these states are removed, e.g. by setting the state density on line 21 of FORT.9 to be zero, then this depletion is eliminated and the potential falls to zero far from the tip).