Hi,

I am wondering if obtaining excess noise would be possible for an avalanche photodiode using Lumerical? What are your advices and suggested references for simulating this parameter?

Thanks!

# DEVICE Photodiode modeling - Excess Noise

**kghaffari**#1

**gbaethge**#3

Hi @kghaffari,

Sorry for the delay, we’ve been pretty busy recently! I’m not too familiar with this application, but from what I could read (for instance on Wikipedia), you can express the excess noise ratio as:

$$ F = \kappa M + \left( 2-\frac{1}{M} \right) \left( 1-\kappa\right) $$

Where \(M\) is the APD’s gain, \(\kappa\) is the ratio of the hole impact ionization rate to that of electrons.

The gain can be obtained from the DEVICE simulation. You can refer to this page for a some examples of avalanche photodiode simulations.

Regarding \(\kappa\), it depends on the material properties as well as the electric field in the multiplying region, so I’m not sure how it can be obtained. In DEVICE, we’re using the Selberherr model to describe the impact ionization:

$$ \alpha_{n,p} = \alpha_{n,p}^{\infty}exp \left[ -\left( \frac{E_{n,p}^{crit} }{\vert E \vert } \right)^2 \right] $$

where \(\alpha_{n,p}\) is the impact ionization rate for electrons or holes. As \(E\) can be spatially dependent (but can be obtained from the simulation), a possibility could be to integrate \(\alpha_{n,p}\) over the material area/volume and then calculate \(\kappa\) from that.

I will try and see if my colleague who wrote the APD examples can have a look at your question. In the meantime, I hope this will help!

**kghaffari**#4

Hi @gbaethge

Thank you for your response.

In Selberherr model, do you have any suggestions about how to account for the non-uniformity of electric field when determining |E|? Also do you have any references for alpha_n and E_crit values used in the software (particularly for silicon)?

**gbaethge**#5

Hi @kghaffari,

In DEVICE, you can use a monitor to record the electric field distribution. Then you could use this information and integrate \(\alpha_{n,p}\) over the area of the material.

Regarding the model, there is some references here. More specifically, Selberherr, S. Analysis and Simulation of Semiconductor Devices, Springer Verlag, Vienna (1984), includes tables of coefficients for some semiconductors (including Si). That said, the data is taken from the literature, so this book will also list the various sources.