Fermi Level of intrinsic and extrinsic semiconductor

[kidsasd987]

(1)

(2)

(3)

(4)

(5)

we can find Equation (5) by dividing po by n0, and write an equation with respect to Ei.
However since equation (3) is a special form of (1) and (2), [when Ef=Ei] we can obtain equation (5) from
any arbitrary Ef.

However, since eq (5) consists of constants only, it will give a result Ef=Ei which contradicts to eq(4).
I know I am wrong, but from which step did I get this wrong?

 

[Achy47]

I would like to address this issue and clarify the steps that may have led to this incorrect conclusion.

Firstly, it is important to note that equations (1) and (2) are general equations that describe the relationship between energy (E) and frequency (f). These equations take into account all the variables that affect the energy of a system, such as Planck's constant (h) and the speed of light (c).

Equation (3), on the other hand, is a special case of equations (1) and (2) where the final energy (Ef) is equal to the initial energy (Ei). This means that there is no change in energy and therefore the frequency remains constant.

When we divide po by n0, we are essentially canceling out the variables and simplifying the equation. This does not mean that equation (5) is a special case of equations (1) and (2). In fact, equation (5) is derived from equations (1) and (2) by setting Ef equal to Ei and simplifying the equation.

However, it is incorrect to assume that equation (5) will always give a result of Ef=Ei. This is because equation (5) only considers the constants and does not take into account other variables such as the energy levels of the system. Therefore, when we substitute the values of the constants into equation (5), it may give a result of Ef=Ei, but this does not mean that this will always be the case.

In conclusion, the mistake was made when assuming that equation (5) will always give a result of Ef=Ei. This is not always true and it is important to take into account all the variables and their effects on the system when using equations (1) and (2).