3 Improved formatting and corrected the incorrectly copied the numerical values from the textbook example

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$10^{13}$$ cm$$^{-3}$$$$10^{13}\ \mathrm{cm}^{-3}$$ per $$\mu s$$$$\mu$$s in a sample of Siliconsilicon.

The equilibrium concentration of electrons in the sample is $$n_0 = 10^{14}$$ cm$$^{-3}$$$$n_0 = 10^{14}\ \mathrm{cm}^{-3}$$.

Also, it gives $$\tau_n = \tau_p = 2\,\mu s$$$$\tau_n = \tau_p = 2\ \mu\mathrm{s}$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n = 2.0 \times 10^{14}$$ ($$n_0 = 1.0 \times 10^{14}$$)

$$p = 2.0 \times 10^{14}$$ ($$p_0 = 2.25 \times 10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i = 0.233$$ eV$$F_n-E_i = 0.233\ \mathrm{eV}$$

$$E_i-F_p = 0.186$$ eV$$E_i-F_p = 0.186\ \mathrm{eV}$$

The equilibrium fermi level ($$E_F)$$$$E_F$$) being at $$E_F-E_i=0.228$$ eV $$E_F-E_i=0.228\ \mathrm{eV}$$

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$10^{13}$$ cm$$^{-3}$$ per $$\mu s$$ in a sample of Silicon.

The equilibrium concentration of electrons in the sample is $$n_0 = 10^{14}$$ cm$$^{-3}$$.

Also, it gives $$\tau_n = \tau_p = 2\,\mu s$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n = 2.0 \times 10^{14}$$ ($$n_0 = 1.0 \times 10^{14}$$)

$$p = 2.0 \times 10^{14}$$ ($$p_0 = 2.25 \times 10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i = 0.233$$ eV

$$E_i-F_p = 0.186$$ eV

The equilibrium fermi level ($$E_F)$$ being at $$E_F-E_i=0.228$$ eV

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$10^{13}\ \mathrm{cm}^{-3}$$ per $$\mu$$s in a sample of silicon.

The equilibrium concentration of electrons in the sample is $$n_0 = 10^{14}\ \mathrm{cm}^{-3}$$.

Also, it gives $$\tau_n = \tau_p = 2\ \mu\mathrm{s}$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n = 2.0 \times 10^{14}$$ ($$n_0 = 1.0 \times 10^{14}$$)

$$p = 2.0 \times 10^{14}$$ ($$p_0 = 2.25 \times 10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i = 0.233\ \mathrm{eV}$$

$$E_i-F_p = 0.186\ \mathrm{eV}$$

The equilibrium fermi level ($$E_F$$) being at $$E_F-E_i=0.228\ \mathrm{eV}$$

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?
2 Improved formatting and corrected the incorrectly copied the numerical values from the textbook example

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$2*10^{13} cm^{-3}$$$$10^{13}$$ cm$$^{-3}$$ per $$\mu S$$$$\mu s$$ in a sample of $$Si$$Silicon.

The equilibrium concentration of electrons in the sample is $$n_0=10^{14}cm^{-3}$$$$n_0 = 10^{14}$$ cm$$^{-3}$$.

Also, it gives $$\tau_n=\tau_p=2\mu S$$$$\tau_n = \tau_p = 2\,\mu s$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n=1.2*10^{14}$$$$n = 2.0 \times 10^{14}$$ ($$n_0=1.0*10^{14}$$$$n_0 = 1.0 \times 10^{14}$$)

$$p = 2.0*10^{14}$$$$p = 2.0 \times 10^{14}$$ ($$p_0=2.25*10^6$$$$p_0 = 2.25 \times 10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i=0.233eV$$$$F_n-E_i = 0.233$$ eV

$$E_i-F_p=0.186eV$$ $$E_i-F_p = 0.186$$ eV

The equilibrium fermi level ($$E_f)$$$$E_F)$$ being at $$E_f-E_i=0.228eV$$$$E_F-E_i=0.228$$ eV

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$2*10^{13} cm^{-3}$$ per $$\mu S$$ in a sample of $$Si$$.

The equilibrium concentration of electrons in the sample is $$n_0=10^{14}cm^{-3}$$.

Also, it gives $$\tau_n=\tau_p=2\mu S$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n=1.2*10^{14}$$ ($$n_0=1.0*10^{14}$$)

$$p = 2.0*10^{14}$$ ($$p_0=2.25*10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i=0.233eV$$

$$E_i-F_p=0.186eV$$

The equilibrium fermi level ($$E_f)$$ being at $$E_f-E_i=0.228eV$$

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$10^{13}$$ cm$$^{-3}$$ per $$\mu s$$ in a sample of Silicon.

The equilibrium concentration of electrons in the sample is $$n_0 = 10^{14}$$ cm$$^{-3}$$.

Also, it gives $$\tau_n = \tau_p = 2\,\mu s$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n = 2.0 \times 10^{14}$$ ($$n_0 = 1.0 \times 10^{14}$$)

$$p = 2.0 \times 10^{14}$$ ($$p_0 = 2.25 \times 10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i = 0.233$$ eV

$$E_i-F_p = 0.186$$ eV

The equilibrium fermi level ($$E_F)$$ being at $$E_F-E_i=0.228$$ eV

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?
1

# Why are there two quasi Fermi levels and only one Equilibrium Fermi level?

I am reading a book and I'm trying to understand the concept of quasi Fermi levels.

For example,

A steady state of Electron Hole pairs are created at the rate of $$2*10^{13} cm^{-3}$$ per $$\mu S$$ in a sample of $$Si$$.

The equilibrium concentration of electrons in the sample is $$n_0=10^{14}cm^{-3}$$.

Also, it gives $$\tau_n=\tau_p=2\mu S$$. I am not sure what this is but I think this is the average recombination time.

The result is that the new levels of carrier concentrations (under the described steady state) are

$$n=1.2*10^{14}$$ ($$n_0=1.0*10^{14}$$)

$$p = 2.0*10^{14}$$ ($$p_0=2.25*10^6$$)

I follow until here but I get a bit confused after this.

The book goes onto say that this results in two different virtual Fermi levels which are at:

$$F_n-E_i=0.233eV$$

$$E_i-F_p=0.186eV$$

The equilibrium fermi level ($$E_f)$$ being at $$E_f-E_i=0.228eV$$

My question:

1. Why are there two different quasi fermi levels now created?
2. Why do we not consider two different ones at equilibrium conditions?
3. Why is it that due to a steady state input of electron hole pairs that we now consider two quasi Fermi levels?
4. What is the relevance of these new quasi fermi levels?