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How to solve the Equilibrium band diagram by using Semiconductor module?
Posted 23.02.2023, 18:14 GMT-5 Semiconductor Devices Version 5.5 3 Replies
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Hi, I am now learning COMSOL and have done some practices by using the semiconductor module. The system for testing is a classical P-N junction. I found COMSOL offers two methods for solving the band diagram. One is a preset study for Semiconductor Equilibrium and the other is Stationary.
In the Semiconductor Equilibrium, COMSOL only solve Poisson’s equation and assuming charge carriers are in thermal equilibrium. This study can perfectly solve the equilibrium band diagram at zero bias but failed to find a solution with a biased metal contact. I think it doesn't make sense because such a model should work in the presence of bias.
The governing equation in COMSOL uses Ef0 to handle the external bias as V0,bias.
I have tried a Piecewise function of V0,bias inserted into the Semiconductor Equilibrium setting or using another Semiconductor Material Model for a applied bias voltage but both don't work. Maybe I lost something. The related COMSOL files were attached. I would be grateful for any suggestions.
On the contrary, the Stationary study not only solve Poisson’s equation but also solve drift-diffusion equation. Note that it also gets rid of the Boltzmann approximation for carriers. By this way, I have successfully obtained an equilibrium band diagram under bias that is consistent with the textbook. And I understand an Equilibrium study should be done before a Stationary study then a correct qusi-Fermi level can be obtained in the Stationary study.
Besides, I found the behavior of the Insulator Interface is weird, which sets a semiconductor/insulator interface to n⋅(D1-D2)=0. But as we know for a MOSFET structure, there is certain charge accumulated at interface. Should not define a Surface Charge Density boundary condition?
I would appreciate any suggestions or hints.
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I found the behavior of the Insulator Interface is weird, which sets a semiconductor/insulator interface to n⋅(D1-D2)=0.
This is a device physics question. The inversion layer is distributed over space, so this is correct if the boundary condition is imposed very close to the interface.
Interface state charge is often considered to be AT the interface, so if this charge is included this boundary condition needs to the modified.
I don't have the semiconductor module, so I can't look at your model. However- in other simulators- convergence is often better if applied voltages are ramped starting with the zero bias condition (and using a previous solution for initial values).
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I found the behavior of the Insulator Interface is weird, which sets a semiconductor/insulator interface to n⋅(D1-D2)=0.
This is a device physics question. The inversion layer is distributed over space, so this is correct if the boundary condition is imposed very close to the interface.
Interface state charge is often considered to be AT the interface, so if this charge is included this boundary condition needs to the modified.
Thank you for the clear clarification! I got it.
I don't have the semiconductor module, so I can't look at your model. However- in other simulators- convergence is often better if applied voltages are ramped starting with the zero bias condition (and using a previous solution for initial values).
It is possible that in the physics of COMSOL, a forward/backward bias configuration cannot be considered in equilibrium within the framework of Ideal Ohmic Contact.
However, it is possible to accomplish it successfully by buliding a electrostatic model following the procedure outlined in this link. https://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/advanced/t2_3_3.html
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It is possible that in the physics of COMSOL, a forward/backward bias configuration cannot be considered in equilibrium within the framework of Ideal Ohmic Contact.
This is not making sense to me and appears to also be a device physics question.
There is only one equilibrium and one equilibrium band diagram. And that is zero bias, zero illumination, no temperature gradients, no illumination.