Scipy Curve_fit Coefficient Does Not Align With Expected Value (physics Relevant?)

I am currently processing experimental data for my thesis and am running into a problem with scipy curve_fit. Background This is a study of LED emission with the following model de

Solution 1:

Apparently the trouble is due to a non convenient criteria of fitting.

LMSE (Least Mean Square Error) in probably implemented in your software. This is not a good choice of criteria of fitting in case of data extended on several decades.

LMSRE (Least Mean Square Relative Error) is recommended in the case of your data.

See below the comparison of results.

NOTE: The expected value of about a=0.0005 is absurd compared to the range of the data from 1. to 240. This would be with no effect, just like a=0. May be a muddle in scales or units ?