I know in IGBTs while operating, parameters Ic (collector current) and Vce (collector-emitter voltage) are Tj (junction temperature) and Vge (gate-emitter voltage) dependent. Is there anything else that Ic and Vce are dependent on them? Is there any formula for these two parameters based on Tj, Vge, ...?
You obviously want a physics based model for IGBTs. Most of us are happy with much less. Web searches show that there exists at least Allen Hefner's IGBT physics model. Here's a link to an academic work which applies it:
Check, if you can understand it.