Semiconductors: P-N junction and carriers density confusion

Homework Statement

Hello PF, this is my first post (however I lurked here a few times).
This comes from a lab I recently did.

In this lab, we measure the current and voltage at a fixed temperature, in order to make an I(V) graph of a diode. Then, from this data and equation (1), we managed to find out the constant e/K, for a set temperature (where e is the elementary charge and K the Bolztmann constant). The second objective was to find Eg, the energy of the band gap (?).

To sum up, the data we have is voltage and associated current, at one temperature, and we measured for 10 different temperatures.

This is where I am confused; I don't know what Eg is or what it does and this is all the written information I have. Please refer to the other equations for more info.

Homework Equations

(1) Diode equation, forward bias
$$I_F =I_0 e^\frac{eV}{KT}$$

(2) Equation provided for ##I_0##:
$$I_0=Ae [n_{p0} \frac{D_n}{L_n} + p_{n0} \frac{D_p}{L_p}]$$
where:
A is the area of the junction (I have no idea how to figure this out);
##D_n## et ##L_n## are respectively the coefficient and lenght of diffusion for electrons;
##D_p## et ##L_p## same for holes; (again, I kinda understand what this is, but I do not know how to get values for these)
##n_{p0}## and ##p_{n0}## are the concentrations of the minority carriers (which I understood to be electrons in the P region, and the opposite for p)
e is the electron charge

(3) and (4), equations for the concentrations of majority carriers
(3) ## n_0 = N_d = N_c e^{-\frac{E_C-E_F}{KT}}##
(4) ## p_0 = N_a = N_v e^{-\frac{E_F-E_V}{KT}}##

where:
##N_d##: the concentration of donator atoms in the N region (?)
##N_a##: the concentration of acceptor atoms in the P region (?)
##n_0##: the concentration of free electrons in the N region (?)
##p_0##: the concentration of holes in the P region (?)
##N_C##: the effective density in the conduction band (?)
##N_V##: the effective density in the valence band (?)

(5) ## n_0 p_0 = N_C N_V e^{-\frac{E_G}{KT}} = n_i^2 ##

The Attempt at a Solution

First, my problem. I have a hard time understanding where do all these concentrations come from, specificially, how can I calculate/know them?
In equations (3) and (4), ##E_F##,##E_C## and ##E_V## seem to stand for energy at fermi level, conduction level and valence level. I know these refers to an energy level, but while I have a vague idea of what the fermi level is I don't know what's it used for. What I'm looking for is ##E_G##. (and I'm not quite sure what it is)

I tried reading lots of material however I seems I was only able to find things that were loosely related to my problem, and got me confused some more.

Any general help or clarification would be highly appreciated. Do not hesitate to ask for clarifications; I will happily deliver.