Dear Jasper,
Thank you very much for this question.
Indeed, the WKB module does have some limitations.
In the particular case of a triangular structure, I doubt that the approximations made in the WKB module would be valid.
Indeed, reading from the WKB theory section and tutorial, an important assumption made in the WKB module is that the potential for the lead is separable:
While this may be approximately the case for a lead with a box geometry, I strongly doubt that this would apply for a lead with a triangular shape. Indeed, assuming that the transport direction is x, the triangular shape imposes a sharp potential barrier which is given by an equation that involves both y and z.
Your idea seems reasonable, but unfortunately this solution is not directly available in our WKB module to my knowledge.
However, depending on your objective, alternative approaches may be attempted.
I imagine that you are interested in the current flowing through this FinFET geometry? And, since you are using the WKB solver, I am guessing that you are ultimately interested in the charge stability diagram of the device?
If this is the case, then please let me suggest an alternative approach that may allow you to circumvent the current limitations of the WKB module.
Outside the Coulomb blockade regime, our NEGF module enables computing the current and should work well in your geometry which is a mesh that was extruded along the transport direction. You may want to try following the steps given in our NEGF tutorial and compute the current I flowing through the transistor. You should then be able to compute the current as a function of gate bias for the first (one-electron) Coulomb peak, but because the NEGF method does not deal with Coulomb interactions between individual electrons (it uses a mean-field approach), you should not be able to get other peaks correctly from NEGF alone.
However, you may then try computing the same Coulomb peaks using the master equation approach within the featureless approximation, in which the absolute value of the current for all peaks is parameterized by a single broadening function Gamma.
By taking the ratio of the amplitude of the first Coulomb peak in the featureless approximation and NEGF approaches, you may be able to find the value of Gamma to be used for the first peaks to have equal amplitudes in the NEGF and master equation approaches. Using this value of Gamma in the master equation approach with the featureless approximation would then give you Coulomb peaks and charge stability diagram with absolute current values that are hopefully reasonable for all biases, including for transitions involving more than 1 electron.
Please let me know if I am understanding your problem correctly. It will be a pleasure to help you with this interesting problem!
Best regards,
Félix
