# Temperature coefficient of resistance - size effects vs bulk

• Hyo X
In summary, the conversation discusses the effects of resistor size on alpha, the temperature coefficient of resistivity. The linear equation R=R0*(1+alpha*(T-T0)) is mentioned, with alpha being a material constant for bulk-type resistors. The question is raised whether alpha will change as the size of the resistor shrinks to tens of nanometers. A reference is requested, and a link to an article is shared, discussing the effects of surface roughness on resistivity in thin films. The article also mentions the study of temperature coefficient, with no significant effect on alpha observed. It is suggested that differences in the scattering of electrons and phonons could potentially contribute to changes in alpha. The article also provides an equation relating surface
Hyo X
I am looking for a reference to discuss the effects of resistor size on alpha, the temperature coefficient of resistivity.
If we use the linear R=R0*(1+alpha*(T-T0))
alpha is a material constant, presumably for bulk-type resistors. Will alpha change as size (cross sectional area) of the resistor shrinks to tens of nanometers in one dimension? any reference on this? thanks

Alpha is a material constant that is independent of the dimensions.

Baluncore said:
Alpha is a material constant that is independent of the dimensions.

I concluded something different, based on literature.

http://iopscience.iop.org/1347-4065/9/11/1326there is also the fuchs-sondheimer theory but i don't think it dicusses alpha

I cannot access that article because it is behind a pay-wall.

The abstract refers to resistivity as being determined by surface roughness in thin films. I would interpret that as a “virtual thickness” parameter, not as a change in the bulk material resistivity.

Although the abstract mentions the temp-co was also studied, it reveals no temp-co effect due to thickness. That might suggest that there was no significant effect on alpha observed.

I can't attest to the quality of the article but it has the suggestion that alpha may have some dependence on the physical dimensions of the sample.

I think a difference in the effect of surfaces and grains on the scattering of electrons and scattering or localization of phonons could conceivably contribute to changes in alpha as a function of surface:volume ratio or some other size parameter.

for completeness, from the article
Here h is the amplitude of oscilations describing the surface roughness and lambda is the mean-free-path of electrons.

if you are really interested in the article let me know and i can send you a dropbox link or something

## 1. What is the temperature coefficient of resistance?

The temperature coefficient of resistance is a measure of the change in resistance of a material with respect to a change in temperature. It is typically expressed as a percentage change in resistance per degree Celsius.

## 2. How is the temperature coefficient of resistance calculated?

The temperature coefficient of resistance is calculated by taking the change in resistance (in ohms) divided by the change in temperature (in degrees Celsius) and multiplying it by the original resistance value. This gives a unitless value that represents the percentage change in resistance per degree Celsius.

## 3. What is the difference between size effects and bulk effects in terms of temperature coefficient of resistance?

Size effects refer to changes in the temperature coefficient of resistance that occur in materials at the nanoscale, while bulk effects occur in larger materials. Size effects are more pronounced in smaller materials due to a higher surface-to-volume ratio, which can cause changes in the electronic and atomic properties of the material.

## 4. How do size effects and bulk effects affect the temperature coefficient of resistance?

In general, size effects cause the temperature coefficient of resistance to increase, while bulk effects cause it to decrease. This is due to the changes in electronic and atomic properties mentioned earlier. However, the exact effect can vary depending on the specific material and temperature range being studied.

## 5. What applications are affected by the temperature coefficient of resistance?

The temperature coefficient of resistance is an important factor to consider in the design and performance of electronic devices, as changes in temperature can affect the overall resistance and functionality of the device. It is also relevant in industries such as aerospace, where accurate temperature measurements are crucial for proper functioning of equipment. Additionally, understanding the temperature coefficient of resistance can aid in the development of new materials with specific thermal properties for various applications.

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