Diffusion current in a MOSFET device can be calculated using Fick's Law per \$J=-qD\frac{d \rho}{dx}\$. It is often taken that the charge carrier configuration (\$\rho\$) across the MOSFET channel is linear, which produces a straightforward diffusion current calculation (see here for instance). What I am wanting to know however is how to calculate the diffusion current if the charge concentration is not linear? This can happen for instance if charges become trapped in the gate oxide, which shifts the threshold voltage higher in the region of the channel under the trapped charge. In this non-linear charge configuration case, the calculated current density appears to vary across the channel, which makes it difficult to interpret what the drain-source diffusion current is, and appears to violate conservation properties like KCL. Is there a resolution to this apparent conundrum? Any insight would be greatly appreciated.
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Yes. oxide charges would influence the electric field in the channel- which would no longer be uniform laterally- and would to first order introduce a sort of percolation path for conduction. This is something which could be simulated in a device simulation using a model charge distribution(s). The current would be then influenced by both drift and diffusion, instead of (approximately) diffusion only.
I have no idea what KCL has to do with this. All you do to find drain current is to integrate the (now maybe nonuniform) current density.
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\$\begingroup\$ The KCL is because the current entering a point (x-\$\Delta\$x) is different than the current leaving a point (x+\$\Delta\$x). Is the current integration as easy as something like \$dJ=\int\frac{dQ}{dx}dx\$ (the units aren’t working out so I probably need to play with it more)? If you could provide any links or point me to any literature that would be fantastic! \$\endgroup\$Schoppe– Schoppe2024-04-30 01:24:30 +00:00Commented Apr 30, 2024 at 1:24
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\$\begingroup\$ No, the divergence of current will be zero always. The current will be nonuniform, as it will flow through a nonuniform energy landscape that's all. Imagine a river flowing through a natural riverbed. Water amount in is the same as water amount out. @Schoppe \$\endgroup\$tobalt– tobalt2024-04-30 04:00:46 +00:00Commented Apr 30, 2024 at 4:00