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Lachlan Black

Including bulk doping when simulating QM accumulation capacitance in Schred V1

Through examination of the source code I have figured out that I need to use the “accumula=yes” flag in the “calc” section of the input file to get Schred V1 to include quantum mechanical effects when calculating the capacitance in accumulation (it is my understanding that Schred V2 does not support this feature). Inclusion of this flag results in a lower capacitance in accumulation compared to the semiclassical case, as expected. However, it also appears to result in the neglect of the bulk doping, with the capacitance minimum in depletion sitting close to zero. Is there any way around this, short of modifying the source code?

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    Gokula Kannan

    Hi lachlan, I am assuming you are simulating a MOS cap and not an SOI. I wrote the part for the Schred V2.0 and yes, you are right the V2.0 supports only 1D SWE for electrons, so it does not solve for holes in the accumulation for the MOScap. I went through the code and what i found is that the code by default solves for electrons in inversion and holes in accumulation automatically when you enable the QM mode .(it checks for the potential energy(fi) at the si-oxide interface(fi_sc) and if the value is greater than fi(end) then does the QM for electrons else if less, it does the QM for holes.(in each case the suitable PARITy bits are assigned 1,2 for electrons and holes resp., and this determined whether we solve for electrons or for holes in the QM_BODY_CHARGE subroutine) The flag for accumulate that you indicated actually enables the SOI mode of calculation and I guess thats why at zero vg you get a capacitance minimum which should be close to zero. Enabling the flag only sets flag_doping =0 which actually sets bulk doping of the gate-oxide-bulk-oxide-gate SOI structure. It does not set the bulk doping to zero,if that is what you meant.

    If you want to exclude the hole calculation in QM mode, and see how it varies with just semiclassical in accumulation in QM mode, just set the parity bit to 1 in that case as well so it does solve for electrons in inversion and solves semiclassically in accumulation.

    Gokul

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      Lachlan Black

      Thanks for the quick response Gokul. Indeed I am simulating a MOS rather than SOI. Unfortunately the behaviour I am seeing is different to what you describe. When simulating a MOS capacitor in QM mode clearly only the inversion capacitance is being handled quantum mechanically, and is lower than the semiclassical case. The capacitance in accumulation is virtually identical (within 3 significant digits) to the semiclassical case. This is true both for n- and p-type base doping. Examining the part of the code which you refer to, it appears that this is due to a pair of additional conditional statements which occur prior to setting the parity bit and calling the QM_BODY_CHARGE subroutine (lines 648 and 663 of main.f). These statements appear to allow electron quantisation to be used only if the doping is p-type, (ie, in inversion) (min_doping.ge.body_doping_min), and hole quantisation only if the sample is n-type (min_doping.le.-body_doping_min). I have tried commenting out these lines to remove the doping check, but then I receive a convergence error when solving in accumulation and the program aborts. Unfortunately it is the quantum mechanical behaviour in accumulation that I am interested in. I am trying to find a way to include it, not exclude it. Setting the accumula=yes flag results in capacitance output that looks like correct QM capacitance output in both accumulation and inversion, and matches the QM output of the simulation run without this flag in inversion. It may be intended for use in SOI simulation as you say, but so far it is the closest I have been able to come to QM simulation of the accumulation capacitance with Schred. In the source the section where the flag is checked is labelled “CV calculation with QM treatment in acculation regime”, which lead me to believe it was for this purpose. Please tell me whether you are able to replicate my results or not and whether you have any further suggestions on how to get around this issue.

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        Gokula Kannan

        Oh My bad, dint see that. You are right, in the MOScap simulation, what happens is that you either calculate electrons in inversion in p-type OR holes in inversion in n-type.(Because if you look in the QM_BODY subroutine depending on the parity the Conduction band potential is calculated from the Fi(Ef-Ei potential energy) values. So if you comment it out it will be unable to solve for hole density in negative bias on p-type and thus give you convergence error. I think the only option is probably to play around with the structure a bit in the SOI mode, like try decreasing t_ox2 and see if that probably calculate a higher and much closer value of capacitance in minimum region of it. But I would have to look deeper into the code as the boundary conditions for the potential and charge density would vary. Because right now the SOI device does a p-type bulk simulation and calculates electrons in inversion near the top gate and holes in accumulation in the bottom gate for a positive bias and vice versa in a negative bias, so i guess removing the bottom oxide would mean a totally different set of conditions for the QM solver in terms of the potential , charge density. But as such, unfortunately I do not think the code offers you the ability to calculate the accumulation in MOScap directly. It does so only in SOI mode with the bulk sandwiched between 2 oxides and 2 gates.

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