Effective absorption coefficient of gold nanoparticles

[Luke137]

TL;DR

I am using COMSOL to model the optical properties of gold nanoparticles when laser light is incident on them. I am unsure about how to correctly calculate the effective absorption coefficient for a sample of these nanoparticles.

I am currently undertaking a research internship where I am modelling the heating of silicon wafers with a 515 nm femtosecond laser. In order to increase the absorption of the laser into the oxide layer on top of the wafer it was suggested we use gold nanoparticles. I was tasked with modelling the optical properties of a 5nm gold nanoparticle, in particular the absorption cross section, using COMSOL Multiphysics. My model seems to be getting correct values for the absorption coefficient and they agree with solutions to Mie Theory for the scattering around nanoparticles.

In my laser heating model I need the absorption coefficient of the different material in order to model the propagation of the laser in each layer. The plan was to find the effective absorption coefficient of the nanoparticles using the EM model and then apply that to a 100nm thick layer in the laser heating model (this is roughly the thickness we estimate the nanoparticles will take up). The problem I am having is with finding this absorption coefficient. I have seen in the literature it is common to use the following formula to calculate the absorption coefficient:

$$\mu=\sigma_{abs}n$$

where $\mu$ is the absorption coefficient, $\sigma$ is the scattering cross section and $n$ is the number density of nanoparticles. From my model I am getting an absorption cross section of $\sim 8e-18\ m^2$ and from the nanoparticle supplier website I am getting the concentration to be $5.5e19\ particles/m^3$. Multiplying these gives a value of $\mu \approx 440\ 1/m$. This seems very low, especially since the absorption coefficient for bulk gold at 515 nm is $\sim 1.14e6\ 1/m$. Is there something wrong with the formula I am using? I was thinking that maybe all I have done is calculate the absorption coefficient for a single "layer" of nanoparticles that is 5nm thick. If that is the case my value is off by a factor of 20 if I am modelling a 100nm layer. However, I am not sure if that is a valid way to go about this.

Any advice would be appreciated!

 

[sbrothy]

I really have no business "answering" this question and I suspect it should've been marked with an 'A'. Also, I intended to wait until views (and no replies) reached 100, but your question will probably drown. I also know that bumping threads is strongly discouraged, but maybe it'll catch the attention of a real solid state physicist. I know they have a nest here somewhere...

Until then I assume you've read this:

Enhanced absorptance of gold following multipulse femtosecond laser ablation.

It's behind a paywall or something, but then again I have no business reading papers like that anyway.

 

[tech99]

The particles are only 1/100 wavelength in size and the 100nm layer is only 20 particles thick, so scattering might be rather small.

 

[hutchphd]

TL;DR Summary: I am using COMSOL to model the optical properties of gold nanoparticles when laser light is incident on them. I am unsure about how to correctly calculate the effective absorption coefficient for a sample of these nanoparticles.

I am currently undertaking a research internship where I am modelling the heating of silicon wafers with a 515 nm femtosecond laser. In order to increase the absorption of the laser into the oxide layer on top of the wafer it was suggested we use gold nanoparticles. I was tasked with modelling the optical properties of a 5nm gold nanoparticle, in particular the absorption cross section, using COMSOL Multiphysics. My model seems to be getting correct values for the absorption coefficient and they agree with solutions to Mie Theory for the scattering around nanoparticles.

In my laser heating model I need the absorption coefficient of the different material in order to model the propagation of the laser in each layer. The plan was to find the effective absorption coefficient of the nanoparticles using the EM model and then apply that to a 100nm thick layer in the laser heating model (this is roughly the thickness we estimate the nanoparticles will take up). The problem I am having is with finding this absorption coefficient. I have seen in the literature it is common to use the following formula to calculate the absorption coefficient:

$$\mu=\sigma_{abs}n$$

where $\mu$ is the absorption coefficient, $\sigma$ is the scattering cross section and $n$ is the number density of nanoparticles. From my model I am getting an absorption cross section of $\sim 8e-18\ m^2$ and from the nanoparticle supplier website I am getting the concentration to be $5.5e19\ particles/m^3$. Multiplying these gives a value of $\mu \approx 440\ 1/m$. This seems very low, especially since the absorption coefficient for bulk gold at 515 nm is $\sim 1.14e6\ 1/m$. Is there something wrong with the formula I am using? I was thinking that maybe all I have done is calculate the absorption coefficient for a single "layer" of nanoparticles that is 5nm thick. If that is the case my value is off by a factor of 20 if I am modelling a 100nm layer. However, I am not sure if that is a valid way to go about this.

Any advice would be appreciated!

TL;DR Summary: I am using COMSOL to model the optical properties of gold nanoparticles when laser light is incident on them. I am unsure about how to correctly calculate the effective absorption coefficient for a sample of these nanoparticles.

Any advice would be appreciated!

I think you likely need to be more carefull in your definition of "absorbance". One cannot necessarilly conflate "scattering" with "absorbance". I do not know what your particular calculations provide.

 

[Cthugha]

Is there something wrong with the formula I am using? I was thinking that maybe all I have done is calculate the absorption coefficient for a single "layer" of nanoparticles that is 5nm thick.

No, your calculation seems about right. There is no layer thickness involved in this calculation. Usually you get the transmitted intensity I through a system of thickness d by calculating: $$I=I_0 e^{-\mu d}$$.

However, you mentioned that your nanoparticle supplier gave you some particle number density. The suppliers usually give this as a density per ml because nanoparticles are usually sold as a stable suspension in some liquid medium. What you calculated is then the absorption coefficient of this liquid suspension.

Is that the case and if so are you interested in the properties of the suspension or do you want a dry layer of gold particles forming at some surface? If so, it might be more appropriate to assume a more realistic density of particles for the dry layer without any liquid. Probably, as a first educated guess, you can just model the gold nanoparticles as spheres that form some hexagonal closed packing ordering, estimate the particle density of that and reduce the density by a few percent to take some stacking faults into account.

 

[sbrothy]

I knew you were around here somewhere! Let’s hope the OP checks back so you haven’t all wasted your time. I’m aware I didn’t contribute anything but a thread-bump.

Perhaps he solved it himself or with the help of a IRL homework-helper.