# A Boundary Conductance in nanomaterials

1. Nov 2, 2016

### MSM

Greetings,

I hope this is the right place to ask.

I have been working with modeling of thermal conductance, G [W/K] of semi-conductor nanowires as a function of temperature.
To start, thermal conductivity of a nanowire is modeled using BTE (Boltzmann Transport Equation). Then the conductance is calculated based on the following relation:

$G= k * A/L$
where L is the length of the nanowire and A is the cross sectional area of the nanowire (πr2) and k is the thermal conductivity

Now I have a plot of thermal conductance vs temperature for a specified diameter and length of a silicon nanowire.

Now the next step I want to model the thermal boundary conductance, Gb[W/m2 K], which is the reciprocal of thermal boundary resistance, Rb [m2K/W]. I used DMM (diffuse Mismatch Model) to model this as a function of temperature.

The main goal of doing this is to have a plot showing how boundary conductance is compared to sample conductance over a wide temperature range (5 K to 800 K) (where is it more critical at low temperatures). I am confused because we have different units so I can't simply make 2 y-axis and make the comparison and to my understanding multiplying by area does not seem right..whats the right approach?

2. Nov 4, 2016

### CaptainJonathanNorth

You might try to think about electron flux through any given space. There is a very useful result, I forget the name. If you take any shaped bag, no matter how convoluted, the total flux through the area encompassed by the bag is equal to the current around the opening. Does that help?