Question

Show that for intrinsic semiconductors, the correct alternative expression for n and p are

n = n₁e​⁽ᴱᶠ ⁻ ᴱᶦ⁾ᵏᵏ¹ᵀ and p= n₁e​⁽ᴱᶠ ⁻ ᴱᶦ⁾ᵏᵏ¹ᵀ

Answer 1

These expressions describe the concentration of electrons
`(\(n\))` and holes
`(\(p\))` in an intrinsic semiconductor at thermal equilibrium, and they are based on the relationship between the Fermi level, intrinsic energy level, and temperature.

Step-by-step explanation:

The expressions you provided seem to be related to the intrinsic carrier concentration
`(\(n_i\))` in intrinsic semiconductors, where
`\(n_i\)` is the product of the electron concentration
`(\(n\))` and hole concentration
`(\(p\)).`

In intrinsic semiconductors at thermal equilibrium, the product of the electron concentration and hole concentration is a constant, and it is given by:

`\[ n_i^2 = n \cdot p \]`

Now, let's express
`\(n\)` and
`\(p\)` individually:

1. **Expression for \(n\):**

`\[ n = n_i \cdot e^((E_f - E_i)/(k \cdot T)) \]`

2. **Expression for \(p\):**

`\[ p = n_i \cdot e^((E_i - E_f)/(k \cdot T)) \]`

where:

-
`\(E_i\)` is the intrinsic energy level,

-
`\(E_f\)` is the Fermi level,

-
`\(k\)` is the Boltzmann constant,

-
`\(T\)` is the temperature, and

-
`\(n_i\)` is the intrinsic carrier concentration.

These expressions describe the concentration of electrons
`(\(n\))` and holes
`(\(p\))` in an intrinsic semiconductor at thermal equilibrium, and they are based on the relationship between the Fermi level, intrinsic energy level, and temperature.

If you have specific parameters and values for the intrinsic energy level
`(\(E_i\))`, Fermi level
`(\(E_f\))`, and temperature
`(\(T\))`, you can substitute these values into the expressions to get numerical values for
`\(n\)` and
`\(p\).`