Semiconductors: P-N junction and carriers density confusion

[PizzaCake]

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 length 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.

 

[KataKoniK]

Thank you for sharing your lab experience with us. From your post, it seems like you are trying to understand the concept of band gaps and how they relate to the diode equation. Let me try to provide some clarification and help you towards finding a solution.

First, the energy of the band gap (Eg) is the energy difference between the top of the valence band and the bottom of the conduction band in a semiconductor material. This energy gap is what determines the conductivity of the material and is an important factor in understanding the behavior of a diode.

Now, in order to calculate Eg, you will need to know the concentrations of the majority carriers (electrons in the N region and holes in the P region) as well as the effective densities in the conduction and valence bands. These values can be determined experimentally or can be estimated using equations (3) and (4) that you have provided.

Equation (5) is also important in understanding the relationship between band gap and concentration of carriers. It states that the product of the concentrations of electrons and holes (majority carriers) is equal to the square of the intrinsic carrier concentration (ni). This value can also be calculated using equation (5) if you have the values for Nc and Nv.

In order to find Eg, you will need to rearrange equation (5) to solve for Eg. This can be done by taking the natural logarithm of both sides and then solving for Eg. Once you have Eg, you can use it in equation (1) to calculate the constant e/K.

I hope this helps you towards finding a solution for your lab. If you have any further questions, please do not hesitate to ask. Good luck!