Solve Quasi Fermi Levels: Separation of Fn-Fp

Fn-Fp)/KT)Taking the natural logarithm of both sides and solving for (Fn-Fp), we get:Fn-Fp=KT*ln(10^13/10^15)=KT*ln(10^-2)=KT*(-2.30)Therefore, the separation of the quasi Fermi level is -2.30KT. To find the change in conductivity, we can use the formula:Δσ=μn*ΔnWhere:- Δσ: The change in conductivity.- μn: The electron mobility.- Δn: The change in electron concentration.To find Δn, we can use the formula:Δn=np-ni^2Plugging in the values
  • #1
EE_or_Bust
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Can someone please help with this problem. I've been looking at it for a week!
I can figure out what equation to use.

A si sample with 10^15/cm^3 donors is uniformly optically excited at room temperature such that 10^19 EHPs (Electron Hole Pairs) are generated per second. Find the separation of the quasi Fermi level and the change of conductivity upon shinig the light. Electron and hole lifetimes are both 10μs. =12. {Hint: to find Fn-Fp , use the relation relating (np) and nd (ni, Fn, Fp). μn=1300[cm^2/ V-s].

I know that Fn and Fp are the quasi fermi electron and hole levels. And I know the common quasi formulas are
n=(ni)(e^-(ei-Fn)/KT)
p=(ni)(e^-(Fp-Ei)/KT)

How do I use these equations to find the separation of the quasi fermi level?
 
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  • #2


Hello,

Thank you for sharing your problem. I understand that you have been struggling with this for a week and I am here to help you. Let me break down the problem for you and guide you through the steps to find the separation of the quasi Fermi level and the change in conductivity upon shining light on the sample.

First, let's define some terms and variables:

- Si sample: This is the silicon sample that is being studied.
- Donors: These are the impurities in the silicon sample that donate extra electrons to the sample.
- EHPs: These are the electron-hole pairs that are generated when the sample is optically excited.
- Quasi Fermi level: This is the energy level at which the probability of finding an electron or hole is equal.
- Conductivity: This is the measure of a material's ability to conduct electricity.
- Electron and hole lifetimes: These are the average times that an electron or hole stays in the sample before recombining with its opposite charge.
- μn: This is the electron mobility in the sample.

Now, let's look at the given information:

- The sample has 10^15/cm^3 donors.
- 10^19 EHPs are generated per second.
- The electron and hole lifetimes are both 10μs.
- μn=1300[cm^2/ V-s].

To find the separation of the quasi Fermi level, we need to use the relation between (np) and nd (ni, Fn, Fp) as mentioned in the hint. This relation is:

np=ni^2*e^((Fn-Fp)/KT)

Where:
- np: The product of the electron and hole concentrations in the sample.
- ni: The intrinsic carrier concentration.
- K: Boltzmann constant.
- T: Temperature in Kelvin.

To use this relation, we need to find the values of np and nd. We can find np by using the given information:

np=10^19 EHPs/s*(10μs)=10^13/cm^3

To find nd, we can use the formula for the donor concentration in a p-type semiconductor:

nd=(ni^2)/np=10^15/cm^3

Now, we can plug in the values of np, nd, and ni into the relation and solve for (Fn-Fp):

10^13/cm^3=10^15/cm^3*e^((
 

What is the concept of quasi Fermi levels?

The concept of quasi Fermi levels refers to the energy levels in a material that are occupied by electrons or holes as a result of non-equilibrium conditions, such as the presence of an external electric field or the injection of carriers. These levels are not true Fermi levels, but rather represent the energy levels at which the electron and hole concentrations are equal.

What is the importance of separating Fn and Fp in solving quasi Fermi levels?

Separating the quasi Fermi levels for electrons (Fn) and holes (Fp) is important because it allows us to quantify the non-equilibrium distribution of carriers in a material. By understanding the individual quasi Fermi levels, we can better understand the behavior of electrons and holes within the material and how they contribute to the overall electrical properties.

How do you calculate the separation of Fn-Fp?

The separation of Fn-Fp can be calculated by using the formula: ΔF = kT ln(Ne/Nh), where ΔF is the separation, k is the Boltzmann constant, T is the temperature, and Ne and Nh are the electron and hole concentrations, respectively. This formula is based on the principle of charge neutrality, where the total number of electrons and holes in a material must be equal.

What factors can affect the separation of Fn-Fp?

The separation of Fn-Fp can be affected by various factors, including temperature, doping concentration, and the presence of defects or impurities in the material. Additionally, external factors such as applied electric fields or light can also influence the separation of quasi Fermi levels.

How does understanding the separation of Fn-Fp contribute to semiconductor device design?

Understanding the separation of Fn-Fp is crucial in the design of semiconductor devices, as it allows us to control the flow of electrons and holes within the material. By manipulating the separation, we can engineer the properties of the device, such as its conductivity and optical properties. This knowledge is essential for creating efficient and high-performing semiconductor devices for various applications.

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