How to simulate undercut heater?

Hi,

I am trying to simulate a doped silicon heater with substrate silicon removal. The cross-section is as follows. Silicon substrate under SiO2 box is removed.

The simulation file is attached here.
Undercut_heater.ldev (6.0 MB)

The air is filled in the removal space. In previous topics, I found that Lumerical could not simulate heat transport in fluid like air. Air can only be the thermal boundary condition. I tried to set the convection boundary. But it still failed to converge with error 9002. Could anyone help check the simulation file and solve the problem ?

Hi @lishifeng,

I was able make your simulation converge, by applying the following changes:

a) Increasing the “max update” limit to 10000 K (shown below); this attribute sets the maximum possible change in temperature at each step. Given the high temperature here, simulation fails to converge using the default values (100K “max update” and 40 “iteration limit”)

b) Adding voltage steps to decrease the interval (shown below); one volt is a large step especially given the significant change in your system as a result of applied voltage.

voltage_sweep

Edited Simulation File: Undercut_heater_converged.zip (4.4 MB)

Reading this article, which similarly addresses convergence in HEAT simulations can be insightful (pictures temporarily unavailable).

As mentioned earlier results indicate high temperatures. This might be due to convection being the only outlet for temperature in the simulation. You can try changing the convection coefficient to see if using a higher value leads to a better approximation.

Kind regards

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Hi Kghaffari,

Thank you very much for your help. Now the simulation converges.

A further question about the simulation result, the temperature at Vin=1V almost reaches 1.62*10^5K, which seems a bit unreasonable. I am not sure whether some parameters are set wrong.

As mentioned, convection is the only process by which heat is being dissipated here which contributes to the high temperature. Try adding radiation boundary condition to your simulation as well, which would be especially relevant given the high temperature.

Also, I suggest trying to change your contact positioning; placing them in front of the silicon heater instead of top of it (shown below). This might result in a more accurate electric simulation in HEAT solver given the original current direction.

Here is a useful discussion which addresses a similar issue.

Kind regards

Hi @kghaffari

I have added radiation boundary condition as you suggested. The temperature did become lower, but it is still around 3000K at 1V. Temperature below 1000K should be a reasonable value.

Thank you for sharing the improvement.

Did you have the chance to try the other recommendations mentioned (tuning the convection coefficient and adjusting the contact positioning in simulation)?

It would be helpful if you could share the reference or analytical calculations referring to your expected behavior from the structure.

Kind regards

Hi @kghaffari

I had increased the convection coefficient to 10000 (W/m^2*K), here is the temperature map. It is around 800K at 1V. But the typical air convection coefficient is 1-1000 (https://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html).
I am wondering whether there is something missed in the simulation model and is it a reasonable method to get a value just by adjusting the air convection coefficient ?

Hi @lishifeng,

Like you mentioned, increasing the coefficient to such a high value wouldn’t be reasonable.

Further studying your structure there are two attributes in your simulations which concerns me:

  • Electrical Conductivity: this value for the doped silicon heater is set to 100000 as opposed to the 0.00043 default value for intrinsic silicon. I expect this value to be lower which would in turn lead to a lower heat generated.
    Also note that you can enable the dependency of a conductivity as a function of temperature (shown below).

  • Length of the device: This attribute will also impact the result of your simulation (here set to 20um). Another factor is if in your application the length of the silicon heater would (roughly) match the length of the structure and waveguide as it does here.

As I mentioned earlier, it would be helpful if you could share a reference to a study/structure similar to what you intend to model or an analytical calculation referring to your expected behavior (e.g. 1000K temperature).

Kind regards

Hi @kghaffari,

  1. The electrical conductivity of doped silicon heater can be found in this paper. oe-27-8-10456.pdf (4.3 MB)

  2. I tried to increase the heater length to 200 um, and the temperature at 1V is about 730K which sounds reasonable.

Dear @lishifeng,

Thank you for the update and the information.

Kind regards

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