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Precision in evaluating space charge density (semi.rho)

Posted Apr 14, 2021, 9:23 a.m. EDT Semiconductor Devices 4 Replies

Kresten Yvind
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I am curious: The space charge density is calculated from the difference in doping and carrier densitites which are of the order of 1E24/m^3 with a resulting space charge density at least in some areas being 1E4/m^3 or similar. How is this implemeted in the COMSOL semiconductor module (as far as I know the general calculations are double precision?).

Can this issue affect the convergence for high doping densities or high injection of both electrons and holes into a region (e.g. optoelectronic heterostructure).

Thanks, Kresten

4 Replies Last Post Apr 18, 2021, 6:25 p.m. EDT
Robert Koslover Certified Consultant
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Posted: 4 years ago Apr 14, 2021, 11:05 a.m. EDT

Are you sure that the net space charge density is actually being computed in the way you described? (I, for one, would not attempt to code it that way.) See https://www.comsol.com/semiconductor-module for more info.

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Scientific Applications & Research Associates (SARA) Inc.
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Are you *sure* that the *net* space charge density is actually being computed in the way you described? (I, for one, would not attempt to code it that way.) See https://www.comsol.com/semiconductor-module for more info.
Kresten Yvind
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Posted: 4 years ago Apr 14, 2021, 2:06 p.m. EDT

That is what they write in the documentation and how it is evaluated in the model so when plottet it gives a limited "dynamic range".

However, looking at the equation view in more detail it looks like the space charge density itself is actually not used for the further calculations so it is just computed for plotting. In that case things make sense.

That is what they write in the documentation and how it is evaluated in the model so when plottet it gives a limited "dynamic range". However, looking at the equation view in more detail it looks like the space charge density itself is actually not used for the further calculations so it is just computed for plotting. In that case things make sense.
Dave Greve
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Posted: 4 years ago Apr 14, 2021, 10:31 p.m. EDT

Often (usually?) the semiconductor equations are formulated in terms of the quasi-Fermi levels, not the charge densities.

I don't have the semiconductor module, but you can see what variables Comsol solves for by looking under Solver Configurations > Solution > Dependent Variables. All other quantities will be computed from these variables.

Often (usually?) the semiconductor equations are formulated in terms of the quasi-Fermi levels, not the charge densities. I don't have the semiconductor module, but you can see what variables Comsol solves for by looking under Solver Configurations > Solution > Dependent Variables. All other quantities will be computed from these variables.
Kresten Yvind
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Posted: 4 years ago Apr 18, 2021, 6:25 p.m. EDT

I am using the quasifermilevel formulation but that doesn't change the problem of evaluating Poissons equation.

I am using the quasifermilevel formulation but that doesn't change the problem of evaluating Poissons equation.

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