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Modeling >> Semiconductor Devices >> Self-heating simulation
https://designers-guide.org/forum/YaBB.pl?num=1291911046

Message started by McSim on Dec 9^th, 2010, 8:10am

Title: Self-heating simulation
Post by McSim on Dec 9^th, 2010, 8:10am

Dear colleagues!

I deal with SPICE models for SOI MOSFETs. Self-heating effect is one of the most important problems for the designer because it's difficult to obtain the values of cth0 and rth0 parameters.

My objective is to study or develop the methodology for the extraction procedure for these parameters.

Unfortunately I actually don't know how this effect is modeled by simulator. BSIMSOI model has a separate pin "t" for the "intrinsic" temperature, but how is this information used by simulator?

I found the following formula:
P=ΔT/rth + cth*δ(ΔT)/δt,
where ΔT is the difference between "intrinsic" temperature and ambient, t is time, P is the power dissipation.

How this "P" is used for recalculation of Ids?

In another words, it's unclear for me how a simulator solve the equations for SHE. Let's consider the simple example:
1) Ids is calculated.
2) P=Ids*Vds.
3) A simulator "knows" rth and cth.
4) As far as I understand the simulation process, Ids is to be recalculated to obtain a negative output resistance (static IV). The first question is how to recalculate Ids? The second is the following: does "P" is also recalculated after the Ids changing? So, when will the recalculation process stop?

Thanks in advance.

Title: Re: Self-heating simulation
Post by sheldon on Dec 9^th, 2010, 6:54pm

McSim,

In general, the rth/cth are used to model self-heating. The external
node is used when you want to model thermal coupling between devices.
For details of the model, you may want to look at the BSIMSOI
manual,

http://www-device.eecs.berkeley.edu/~bsimsoi/archive/bsimsoi4p2/BSIMSOI_4.2_Manual.pdf

Best Regards,

Sheldon

Title: Re: Self-heating simulation
Post by McSim on Dec 10^th, 2010, 1:30am

Dear Sheldon!

There is unfortunately no answers for my questions in the manual... Let me explain. If we look at the Fig. 5.1 (page 34) we would see that there is power dissipation (P=Ids*Vds) and thermal resistance and capacitance, but how is decrease of the drain current simulated? There is only few words about "T" terminal:
"The T node is treated as a voltage node and is connected to ground through a thermal resistance Rth and a thermal capacitance Cth"

No any words about thermal coupling between devices, no information about Ids recalculation... It is probably evident for the community, but I really don't understand the simulation process... :(

Title: Re: Self-heating simulation
Post by Frank Wiedmann on Dec 10^th, 2010, 4:04am

The T node is a current source with a current that is propotional to the power that is dissipated in the transistor. The voltage at the T node corresponds to a temperature increase of the transistor with respect to ambient temperature. This increased temperature modifies the properties of the transistor. You can see how this works in the code for the VBIC model at http://www.designers-guide.org/VBIC/release1.2/vbic1.2.va.html (search for ElectroThermal). The network connected to the T node can model both thermal coupling and a thermal environment that is more complex than a simple RC combination.

Title: Re: Self-heating simulation
Post by Geoffrey_Coram on Dec 13^th, 2010, 1:29pm

... and, during the model evaluation for BSIMSOI, many of the parameters of the device are re-adjusted for the self-heating temperature, and Ids (etc) is computed using the re-adjusted parameters.

(BSIM3/BSIM4 etc adjust parameters once at the beginning of the simulation for the ambient temperature.)

Title: Re: Self-heating simulation
Post by McSim on Dec 16^th, 2010, 5:01am

As far as I understand in BSIMSOI Ids is computed using the re-adjusted parameters and this formula:
Pwr(t) <+ -Ids * Vds + ddt(ΔT * cth) + ΔT / rth,
where Pwr(t) is power dissipation at T node, ddt is time derivative, ΔT is additional device temperature, cth and rth are thermal capacitance and resistance respectively.
But unfortunately the process of Ids recalculation is unclear for me.

I suppose the following process is going on (let's consider the case with Cth=0):

1) ΔT=0 ("initial condition")
1.1 Ids=Ids without SH
1.2 ΔT1=Ids*Vds*Rth (is it used for Ids recalculation or transfered for the next step of simulation?)
1.3 Ids=Ids (ΔT1) (is there recalculation?)
1.4 ΔT2=Ids(ΔT1)*Vds*Rth (is there recalculation of ΔT?)

What temperature are parameters re-adjusted at: at ΔT2 or at ΔT1?

2) (the next step of simulation) ΔT=ΔT2
2.1 Ids=Ids(ΔT2)
2.2 ΔT2’=Ids(ΔT2)*Vds*Rth
2.3 Ids=Ids(ΔT2’)
2.4 ΔT3=Ids(ΔT2’)*Vds*Rth

If I'm not mistaken, the main parameter for SH is ΔT, not Pwr(t). So what is Pwr(t) needed for?

Title: Re: Self-heating simulation
Post by Geoffrey_Coram on Dec 16^th, 2010, 2:18pm

In BSIMSOI, the T node acts just like a regular electrical node: the "voltage" on that node is solved for, just like all the other voltages in the circuit (Spice's modified nodal analysis).

The T node has a "current source" (Ids*Vds) and a resistor (using your case Cth=0), and Spice has to solve such that KCL is satisfied, which usually means Ids*Vds = ΔT/rth.

The way you've written it looks like Verilog-A syntax, specifying that Pwr(T) is the current into the T node, which has to be zero by KCL -- unless you connect a thermal conductor to model heat transfer to a neighboring device.

Title: Re: Self-heating simulation
Post by McSim on Dec 17^th, 2010, 3:00am

Thank you for the answer!

The only thing I've not understood yet is following. OK, we solve the KCL equation to obtain ΔT and Ids. But there are 2 unknowns and 1 equation (KCL). What is the second equation? KVL with ΔT as node potential? But we have only one node in case when T isn't connected, don't we?

Title: Re: Self-heating simulation
Post by Geoffrey_Coram on Dec 20^th, 2010, 5:19am

Ids isn't an "unknown" -- once you know the node voltages, it's directly computable.

There are more than 2 unknowns -- V(d), V(g), V(s), etc. are all unknown. I guess if you start with a non-self-heating model and assume that all the equations and unknowns work out (which they do), then when you go and add self-heating you're adding 1 unknown (ΔT) and one equation (KCL for the T node).

Title: Re: Self-heating simulation
Post by McSim on Dec 27^th, 2010, 3:11am

Thanks for the answers! :)

Merry Christmas and Happy New Year!