SEMITIP V6, Film2, Example 3: semiconducting film on top of semiconducting substrate, contact to film, no interface states

Click here for input/output files for Example 3

In contrast to Example 1, this example shows the effect of having the contact made to the film. In other words, the Fermi level for the film+substrate system is taken to be that within the film (region 1 in the FORT.9 file). In this example, with the film having a gap of 2 eV, the Fermi level is thus located at +1 eV. With the substrate being n-type doped, then in order for its Fermi level to match that of the system, a negative electrostatic potential deep inside the substrate is required, amounting to -1 eV. With a sample voltage of -1 V (tip Fermi level at -1 eV relative to the sample Fermi level), perfectly flat bands are obtained everywhere. That is, the electrostatic potential energy is -1 eV everywhere:

This result is obtained, despite the boundary conditions (for SEMITIP in general) corresponding to zero potential at large values of the radius and large values of z deep inside semiconductor. The reason that these boundary conditions are not effective in this example is that they are applied at points spaced very far, in radii and/or z value into the semiconductor, from the grid on which the potential values are solved for. Hence, in this example where an electrostatic potential must be applied to the semiconductor substrate in order to achieve zero charge density there, the nominally zero boundary conditions are completely overwhelmed by the need for the nonzero electrostatic potential.