SEMITIP V6, Uni1, Example 2: n-type GaAs(110) at 0 K, comparison to theoretical expectation
Click here for input/output files for Example 2
As a check on the SEMITIP version 6 results, we can take a situation similar to
example 1,
but perform the simulation at 0 K so that the results can be directly compared to an expected parabolic potential profile. This comparison is shown below.
The green curve shows the result from SEMITIP version 6, whereas the blue curve is the version 4 or 5 result (using an approximate form for the
numerical derivatives in the variable-spaced grid). The red circles give the theoretical expectation, (2πe2N/ε) (L - z)2 where N is the doping concentration, ε is the relative dielectric constant of the semiconductor, and L is the depletion width, with L = -εs + sqrt(ε2s2+(εeV/2πe2N)) for sample voltage V and tip-sample separation s (using electrostic units throughout). The theoretical depletion width is 27 nm and magnitude of the band bending at the surface is 0.510 eV, in good agreement with the version 6 results. The version 4 or 5 results are somewhat lower than the theoretical expectation, with this discrepancy increasing when the computation exends into higher grid points (with greater nonlinearity in their spacing) due to the approximate form used for
numerical derivatives in versions 4 and 5.