Dear Labib Labib ,

I treated this problem since long time.

The LED equation is similar to any single junction diode following the Shockley equation

I = Is( exp (V- IRs)/nVt -1)with the usual meanings of the parameters in the equation.

As for the emitted light flux phi It is proportion to the current I such that:

phi= consatnt I

The consatnt can be obtained from the data sheet.

It can be that the relation between the current and the flux is not linear.

I studied this subject in full details for many years ago and you can get the paper at the link:Conference Paper A comprehensive study of an optical transceiver

Best wishes

Hello,

You need to consider the quantum efficiency of the LED, which dictates the amount of radiative output power of the LED in response to diode current and is affected by the generation-recombination processes in the material. In short, merely supplying current to the LED does not guarantee perfect emission. There's a power-law correlation. The chapter on LEDs is a good starting point Chapter 6: Light‐Emitting Diodes - CUHK Physics

Abdelhalim abdelnaby Zekry Thank you very much for the response. It seems both I-V characteristics and luminous intensity both are temperature dependent.

Is the temperature dependent equation of phi?

I got the constant from the datasheet for the luminous intensity vs forward current.

It would be really helpful if you share your research paper.

Thanks

Dear Labib Labib ,

I am happy that you found my answer useful for you. When you read my attached paper you will find a complete solution to your problem.

As for the temperature of the emitted it follows the temperature dependence of the DC current of the diode with temperature.

To see how the diode current varies with temperature please follow the book:Book Electronic Devices

Abdelhalim abdelnaby Zekry Although we do not normally include our own work as references unless it is absolutely necessary, in this case, I agree that the reference that you provided is good. I have been reading it and equation (1.8) on page 211, in particular, summarises the answer. In short, the photon emission flux is proportional to the applied current but also depends on the external quantum efficiency, n_EQE. The latter also depends on other parameters https://www.sciencedirect.com/topics/engineering/external-quantum-efficiency