Fuse current of silicon nanowire

[tresgog]

Hello,

I'm studying for a project a rectangular-cross sectionned suspended silicon nanowire.

My question is very simple: at which current will my nanowire break?

The melting point is 1687K and I start at 300K

I don't really know where to start since the resistance, the thermal conductivity and many physical depend upon the temperature and my temperature range is wide.

I've tried the following:

Provided that the heat of fusion of Silicon is: 50.6kJ.mol-1

I have the heat generated by the electrical power = R*I*I*t
R=electrical resistance
I=current
t=time

I must match the heat generated by the electrical power and heat of fusion

(Heat of fusion)*(Volume*density/molar mass)=R*I*I*t

And I can have my current I

However this model is stupid because I don't take to account the dissipation by convection, conduction and scattering.

how to do it properly?

 

[f95toli]

how to do it properly?

My guess is that you don't; you will have to perform the experiment.
That said, you might be able to get some qualitative understanding by performing a numerical simulation using Comsol, ANSYS or similar. But even that is tricky because there are so many parameters involved, some of which might be very difficult to find in the literature (e..g the boundary resistance between the nanowire and the substrate).

Note that I assuming here that you can use "classical" thermal conductivity; if the conductivity is quantized (as it can be in nanowires) it becomes even more complicated.

Thermal conductivity in nanowires is a "hot" topic at the moment, and it is far from trivial.

 

[tresgog]

Thank you for your answer.

At some point I was thinking to just go ahead and simulate my nanowire and ANSYS.

Before doing so, I would like to have a rough idea of the current I should put in my wire.

The thing is, I have the nanowire, I don't want to break it just right away so I just want to have an upper limit of the current.

The value I found with the above model is very low (in one hour I should only put 62pA)

 

[f95toli]

Yes, but the tricky bit here is to figure out how well the nanowire is cooled via conduction to the substrate. There are ways to estimate this using some fairly simple formulas, but these formulas are only useful if you know the numerical values for all relevant parameters; and these need to be determined experimentally...

Try googling (Google scholar) for information about e.g. hot-electron or transition-edge bolometers and similar devices; they all rely on efficient cooling of a mesoscopic device (sometimes fabricated on a suspended substrate) so you should be able to find quite a lot of information about cooling; some of which should be relevant to your case.