Pn junction in solar cell case

[Rossomingus]

HI. I got some question about the derivation of the I-V characteristic in a solar cell.
The first step is to solve the minority carrier diffusion equation with appropriate boundary conditions: at the edges of the cell and at the edges of the depletion zone.
At the edges of the d.z. the conditions for the concentrations p_N and n_P can be found using quasi-Fermi levels...

1) Suppose to be in case of forward applied voltage V. In the quasi neutral regions, far from the d.z, and into the d.z., the quasi-Fermi levels are constant. This means that here currents J_p and J_n equal to 0. How is it possible to have currents just in teh little spaces out of the d.z. when a votage is applied?

2) Why qV= F_n - F_p ?

In thee next step of the derivation, they integrate the electron continuity equation over the d.z. ,

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dJ_n/dx = q[ R(x) - G(x)]
with R recombinatio rate ad G generation.
For R they consider just midgap single level trap mechanism. They keep a point X_m inner the d.z. at which p(x_m)=n(x_m) and then consider R(x_m) for the whole d.z.

3) Does is exst a point xm where p=n?

If someone would like to answer id be really glad. Bye

 

[eljose79]

Hello,

Thank you for your questions about the derivation of the I-V characteristic in a solar cell. I will do my best to explain and answer your questions.

1) In the case of forward applied voltage, the quasi-Fermi levels are constant in the quasi-neutral regions and in the depletion zone. However, this does not mean that there is no current in these regions. The constant quasi-Fermi levels indicate that the majority carriers (electrons in n-type material and holes in p-type material) are evenly distributed throughout the material, creating a potential barrier at the junction. When a voltage is applied, this potential barrier decreases, allowing majority carriers to flow from one side of the junction to the other. This flow of majority carriers creates a current in the material.

2) The equation qV = F_n - F_p is known as the voltage equation and is a result of the quasi-Fermi level approximation. The quasi-Fermi levels (F_n and F_p) represent the energy levels at which the electrons and holes are distributed in the material. When a voltage is applied, the quasi-Fermi levels shift, and the difference between them is equal to the applied voltage.

3) Yes, there does exist a point Xm where p=n. This point is known as the intrinsic point and occurs within the depletion zone. At this point, the concentration of electrons and holes are equal, creating a neutral region within the depletion zone.

I hope this helps to answer your questions. If you have any further inquiries, please don't hesitate to ask.

 

[charng]

I can provide some clarification on the content you have shared about Pn junctions in solar cells. The first step in deriving the I-V characteristic of a solar cell is to solve the minority carrier diffusion equation with appropriate boundary conditions. This equation describes the movement of minority carriers (electrons or holes) in a semiconductor material. The boundary conditions at the edges of the cell and at the edges of the depletion zone determine the concentration of minority carriers at these points.

Now, let's address your first question. In the case of forward applied voltage, the quasi-Fermi levels are constant in the quasi-neutral regions and into the depletion zone. This means that the currents Jp and Jn are equal to zero in these regions. However, when a voltage is applied, there is a potential difference across the depletion zone, creating an electric field. This electric field allows for the movement of minority carriers, resulting in a non-zero current in the little spaces outside of the depletion zone.

Moving on to your second question, qV = Fn - Fp represents the difference between the quasi-Fermi levels of the electrons (Fn) and holes (Fp). This equation is derived from the Boltzmann distribution, which describes the energy distribution of particles in a system. The difference in quasi-Fermi levels is a result of the applied voltage and the built-in potential of the Pn junction.

In the next step of the derivation, the electron continuity equation is integrated over the depletion zone, taking into account the recombination and generation rates (R and G). The point Xm where p=n represents the point of charge neutrality, where the concentration of electrons is equal to the concentration of holes. This point may vary depending on the material and doping levels of the Pn junction.

In summary, the derivation of the I-V characteristic of a solar cell involves solving equations that describe the movement of minority carriers, taking into account the boundary conditions and the effects of applied voltage and built-in potential. I hope this helps to clarify your questions.