I am attempting to comprehend the performance of graphene/n-type semiconductor Schottky diodes in photodetector applications.
Given that silicon (Si) and germanium (Ge) have similar electron affinities, 4.05 eV and 4 eV respectively, it might be expected that their Schottky barrier heights with graphene would be nearly identical.
However, the dark current in graphene/Ge contacts is significantly larger, as evidenced by both literature data and my experimental observations.
Beyond Schottky barrier height, what additional factors should be considered to understand this discrepancy in dark current?
The conductivity of a device is determined by both bulk and interface properties of the materials.
When we're talking about a Schottky barrier height, that is an interface property, but the bulk properties may still be affecting the conductivity: Ge has a smaller bandgap by 0.42eV, so for intrinsic material the expectation is "more bulk charge carriers" and that matches "higher currents".
In the equation for the Schottky diode I-V curves, see
https://ieeexplore.ieee.org/document/7074349
(to my extent of knowledge, that should be the first reference which includes the series resistance), you find the Richardson constant which is material-specific. In the formula for it,
A*= (4 pi e m* k2)/h3
you find the effective mass m* and that's related to the band gap, see
https://web.mst.edu/~juliaem/topics/TCOeffective-mass.pdf
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