# Boundary Conductance in nanomaterials

• A
• MSM
In summary, the speaker has been working on modeling the thermal conductance of semi-conductor nanowires as a function of temperature. They have used the BTE to model the thermal conductivity and have calculated the conductance using a specific equation. They now have a plot of thermal conductance vs temperature for a silicon nanowire. The next step is to model the thermal boundary conductance using the DMM and compare it to the sample conductance over a wide temperature range. However, the units are different and the speaker is unsure of the correct approach. They are considering the concept of electron flux to help understand the relationship between thermal boundary conductance and sample conductance.
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?

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?

## 1. What is boundary conductance in nanomaterials?

Boundary conductance in nanomaterials refers to the ability of a material to conduct electricity at its boundaries, which are the interfaces between two different materials. In nanomaterials, these boundaries are particularly important because of the high surface-to-volume ratio, which can significantly affect the overall conductance of the material.

## 2. How is boundary conductance measured in nanomaterials?

Boundary conductance in nanomaterials is typically measured using a technique called scanning thermal microscopy (SThM). This method involves scanning a heated probe over the surface of the material and measuring the thermal resistance at the boundaries. The thermal resistance can then be used to calculate the boundary conductance.

## 3. What factors affect boundary conductance in nanomaterials?

Several factors can affect the boundary conductance in nanomaterials, including the type of materials at the interface, the roughness of the surface, and the temperature. Other factors such as the presence of impurities or defects can also impact the boundary conductance.

## 4. Why is boundary conductance important in nanomaterials?

Boundary conductance is essential in nanomaterials because it can significantly affect their thermal and electrical properties. Understanding the behavior of boundaries is crucial for the design and development of nanomaterials for various applications, such as electronics, thermoelectrics, and energy storage.

## 5. How can boundary conductance be manipulated in nanomaterials?

There are several ways to manipulate boundary conductance in nanomaterials, including modifying the materials at the interface, controlling the roughness of the surface, and introducing defects or impurities. Changing the size and shape of the nanomaterials can also affect the boundary conductance. Additionally, external factors such as temperature and applied electric or magnetic fields can also influence the boundary conductance in nanomaterials.

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