FWIW, this is what I have for the 1N4007 in CircuitMaker:
IS: Saturation current 2.550n
RS: Ohmic resistance [0,] 42.00m
N: Emission coefficient 1.750
TT: Transit-time [0,] 5.760u
CJO: Zero-bias junction capacitance [0,] 18.50p
VJ: Junction potential 750.0m
M: Grading coefficient 333.0m
EG: Activation energy 1.110
XTI: Saturation-current temperature exponent 3.000
KF: Flicker-noise coefficient 0.000
AF: Flicker-noise exponent 1.000
FC: Foward-bias depletion coefficient 500.0m
BV: Reverse breakdown voltage 1.000k
IBV: Current at breakdown voltage 98.60u
TNOM
aramameter measurement temperature 27.00
CM doesn't have a model/subcircuit for the ICM7556. But I see from the
datasheet at
http://www.madlabo.com/mad/edat/spice/ex1/icm7555.pdf
obtained by the google search
spice "ICM7556"
that it's virtually identical to the NE556.