I examined the forward voltage of the diode (depend on current) in EveryCircuit.
I:nA V:mV
1~10 V=360 I^0.0668 (I:nA)
10~100 V=367 I^0.0579
100~1000 V=379 I^0.0510
1E+3~1E+4 V=394 I^0.0456
1E+4~1E+5 V=410 I^0.0142
1E+5~1E+6 V=425 I^0.0399
1E+6~1E+7 V=414 I^0.0399
10mA~10A V=1.0161I+846 (I:mA)