# Young's Modulus as a function of temperature

Is there a formula that relates Young's Modulus as a function of temperature? From Wikipedia, there is this formula in section 3.3:

https://en.wikipedia.org/wiki/Young%27s_modulus

I tried my best to understand the formula, but I am still lost when I try to apply it. If any one can explain the formula to me or know off the top of their heads another formula that relates Young's Modulus to temperature, that would be amazing.

Specifically, I am designing a MEMS resonator and I wanted to see how the resonance frequency of my structure will change based on ambient temperature. to my understanding, Young's Modulus and density of polysilicon are the main factors that will contribute to a shifting in resonance frequency. Thus, I am trying to find Young's Modulus for polysilicon of lattice [110]. The standard Young's Modulus for polysilicon[110] is 170 GPa and density of 2330 kg/m^3 at a temperature of 25 deg Celsius I THINK.

Any help would be greatly appreciated.

• For completeness, consider adding the formula to the post using MathJax, leaving the link for reference.
– Urb
Nov 23, 2021 at 8:04
• If averaging over many grains, you should use a modulus averaged over all directions. Also realize that you likely have some rather high built-in stresses in at least a handful of grains, making any simple equation potentially questionable. Nov 23, 2021 at 14:35