Find out Emitter Saturation and Collector Saturation Current

Question

An n-p-n transistor contain the given properties are as follows::

Doping Concentrations: N_e = 10¹⁸ cm^-3, Nb = 10¹⁷ cm^-3, Nc = 10¹⁵ cm^-3. 

Diffusion Coefficients: D_e = 15cm²s^-1, D_b = 7cm²s^-1, D_c = 5cm²s^-1.

Diffusion Lengths: L_e = 5 µm, L_b = 10 µm, L_c = 12.5 µm .

 Base Width: W_b = 1µm.

Cross Sectional Area as: A = 2 x 10^-4 cm². And Forward Active Transfer Ratio is as given below: α_F = 0.985 as well as Reverse Active Transfer Ratio: α_R = 0.5

Find out the Emitter Saturation Current I_ES and the Collector Saturation Current I_CS within the Ebbers-Moll model of such transistor. Therefore evaluate the Emitter, Base and Collector currents I_E, I_B, I_C while the transistor is operating as given conditions:

(a) Within the forward active mode along with V_BE = 0.7V as well as V_BC = -4.5V

(b) Within the saturation mode along with V_BE = 0.725V as well as V_BC = 0.655  

Remember that n_i = 1.5 x 10¹⁰ cm^-3 and q = 1.6 x 10^-19 C as well asV_T = 26 mV.