I'm having trouble finding a theoretical explanation about the transconductance photodiode behavior, the materials I find on the internet they talk about the connections, but not the behavior, in case someone could insert material or write here with the source please.
The expression does not make sense.
Transconductance is defined as:
The image shows the transfer characteristics for a photodiode (By Kennlinie_Photodiode_1.png: Gregor Hess (Ghe42)derivative work: Material scientist (talk) - Kennlinie_Photodiode_1.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15579778)
A transfer characteristic can be defined as:
as shown in the diagram.
The photodiode mode is also called the photoconductive mode.
You should question your source for the phrase!