R prime E values for Semiconductor PN juctions @25°C.

             r'e             Formulas for Vbe
            
1N914       0.0502      Log(Ic) × 0.11562 + 0.27230
2N3904      0.0268      Log(Ic) × 0.06167 + 0.48667  Fairchild MMPQ
2N3906      0.0272      Log(Ic) × 0.06271 + 0.47457  Fairchild MMPQ
2N2222A     0.0270      Log(Ic) × 0.06219 + 0.42500
2N2907A     0.0284      Log(Ic) × 0.06550 + 0.42400
2N4401      0.0297      Log(Ic) × 0.06837 + 0.41966
2N4403      0.0310      Log(Ic) × 0.07167 + 0.39829
MPSA18      0.0278      Log(Ic) × 0.06410 + 0.40260
MPSH10      0.0284      Log(Ic) × 0.06545 + 0.49400
MPSH81      0.0331      Log(Ic) × 0.07619 + 0.52789
HFA3101     0.0261      Log(Ic) × 0.01000 + 0.55800 
AU5517      0.0282      Log(Ic) × 0.06485 + 0.55240
                                  Factor     Bias

r'e = ∆V/dec. ÷ Ln(10) ⇒ 2.302585093

Current (Ic) is in µa.
Formaulas were extrapolated from
the graphs to generate the values. 

These were obtained from Vbe log graphs in the
datasheets. Use Vbe On and not Vbe Sat. Take
accurate voltage measurements from graphs over
as many whole decades where the line is straight.
Divide the vLow and vHigh (voltage) difference
by the number of decades spanned. This is ∆V/dec.
and also the Factor. For the Bias subtract one
∆V/dec. for every decade above 1µa from vLow.
A vLow for 1µa is the Bias.