Charge Densities in Semiconductor

Electrical Neutrality

Definition: A condition where the total positive charge equals the total negative charge in a material.
Example: Copper wire
- Copper is a good conductor.
- When a potential difference is applied, there is a flow of charge.
- Copper wire remains electrically neutral as the number of electrons entering equals the number of electrons leaving.
- If the balance is disturbed (e.g., 100 electrons enter, but only 50 electrons leave), the wire becomes charged.

Concept: The total positive charge (donor ions and holes) must equal the total negative charge (acceptor ions and electrons).
Equation:
- Total Positive Charge: (n_D + p)
- Total Negative Charge: (n_A + n)
- For neutrality: (n_D + p = n_A + n)

Doping: Adding impurities to a semiconductor to change its electrical properties.
n-type Semiconductors:
- Doped with pentavalent impurities.
- Acceptors ((n_A)) are zero.
- Charge neutrality equation simplifies to: (n_D = n - p \approx n) (since (n > p)).
- (n_n \approx n_D): Electron concentration in n-type material is approximately the donor density.
- Using Mass Action Law: (np = n_i^2)
- For n-type: (n_nn_p = n_i^2)
- Hole concentration: (p_n = \frac{n_i^2}{n_D})
p-type Semiconductors:
- Doped with trivalent impurities.
- Donors ((n_D)) are zero.
- Charge neutrality equation simplifies to: (p = n_A - n \approx n_A) (since (p > n)).
- (p_p \approx n_A): Hole concentration in p-type material is approximately the acceptor density.
- Using Mass Action Law: (np = n_i^2)
- For p-type: (n_pp_p = n_i^2)
- Electron concentration: (n_p = \frac{n_i^2}{n_A})

Electrical neutrality plays a critical role in understanding charge densities.
These fundamental equations and concepts are crucial for solving numerical problems involving semiconductors.