SEMITIP, VERSION 5, Example 1: n-type GaAs(110), with no surface states

Click here for input/output files for Example 1

This example shows a theoretical spectrum for GaAs in the physically incorrect situation of no surface states, where a substantial accumulation current is seen for all negative voltages. The result should be compared with example 1 of VERSION 4 which is the physically correct situation, with a band of surface states resonant with the conduction band acting to restrict tip induced band bending and hence preventing any significant accumulation of the electrons at the surface. (Of course, for other surfaces, that type of band may not exist or it may be higher in energy, so that surface accumulation will indeed occur). Output for the conductance goes to FORT.93, FORT.94, and FORT.15, for the valence band (VB), conduction band (CB), and their sum, respectively. When plotted these appear as:

where the black circles show the sum of the VB and CB, the green x-marks show the VB, and the red x-mark show the CB. This result is very similar to Fig. 2(a) of Phys. Rev. B 80, 075320 (2009), except that this example was run with a number of energy steps (line 42 of FORT.9) of only 500, rather than the 5000 used in that publication. The energy of the accumulation states can be plotted from column 3 vs. column 1 of FORT.60,
As a minor comment, we note that the voltage values in the above plot are the ones computed from the FORT.9 file including voltage modulation, i.e. the specified voltage values plus or minus sqrt(2) times the specified modulation voltage. To make a similar plot but only at the specified voltage values, just set the modulation voltage to zero in the FORT.9 file.

A more significant comment concerns the set of accumulation states with principal quantum number n=2 seen above, located within a few meV of the conduction band minimum and extending from about -1.1 to -1.4 V. Similarly some of the n=3 states also fall very near the conduction band minimum. If the number of energy steps in increased to 5000, all of these states vanish. They are thus spurious localized states, not actually localized but appearing so in the computation when the number of energy steps is too small (in any case, these spurious states do not impact the computed tunnel current, at least for the cases tested). A few similarly spurious states are also found very near the valence band edge in this problem, as can be seen in the FORT.40 file. Again, these disappear if the number of energy steps is increased to 5000.