---
title: "Minority charge suppression in extrinsic semiconductors"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:minority-charge-suppression"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/minority-charge-suppression
site: BCT Engineering
---

# Minority charge suppression in extrinsic semiconductors

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2078 Bhadra, 4 marks; 2071 Shrawan, 4 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/minority-charge-suppression
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

What is minority charge suppression in extrinsic semiconductor?

## Short answer

Doping increases majority carriers; by the mass-action law np = ni², minority concentration is suppressed. For example, in Si with Nd = 10^16 cm^-3, holes drop from 1.45×10^10 to 2.1×10^4 cm^-3; conductivity becomes almost entirely due to majority carriers.

## Answer

**Minority carrier suppression** is the reduction of the minority carrier concentration far below $n_i$ when a semiconductor is doped. Adding donors increases electrons and at the same time decreases holes (and vice versa for acceptors).

#### Reason
In thermal equilibrium, the **mass action law** holds for a non-degenerate semiconductor:

$$
np = n_i^2
$$

$n_i^2$ depends only on the material and temperature, not on doping. So if doping raises the majority concentration, the minority concentration must fall by the same factor. Physically, the large number of electrons increases the recombination rate with holes, so fewer holes survive.

#### Example
Si at 300 K, $n_i = 1.45\times10^{10}$ cm$^{-3}$, doped with $N_d = 10^{16}$ cm$^{-3}$:

$$
\begin{aligned} n &\approx N_d = 10^{16}\ \text{cm}^{-3} \\ p &= \frac{n_i^2}{n} = \frac{(1.45\times10^{10})^2}{10^{16}} = 2.1\times10^{4}\ \text{cm}^{-3} \end{aligned}
$$

The hole concentration falls from $1.45\times10^{10}$ to $2.1\times10^4$ cm$^{-3}$, nearly a million times smaller.

#### Consequences
- Conductivity is due almost entirely to majority carriers: $\sigma \approx eN_d\mu_e$.
- Minority carriers, though few, control pn junction reverse saturation current and transistor action.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is minority carrier suppression?
   A. Doping lowers the majority concentration
   B. Doping raises both n and p equally
   C. Doping removes all minority carriers completely
   D. Doping reduces the minority carrier concentration far below ni
   Answer: D. Adding donors increases electrons and at the same time decreases holes far below ni. (Key point: Definition)

2. Which law explains the suppression?
   A. np = ni^2, with ni^2 independent of doping
   B. n + p = ni
   C. n/p = ni
   D. np = Nd
   Answer: A. Since ni^2 depends only on material and temperature, raising n lowers p in proportion. (Key point: Mass action law)

3. For Si with Nd = 10^16 cm^-3 and ni = 1.45 x 10^10, what is p?
   A. 1.45 x 10^10 cm^-3
   B. 2.1 x 10^4 cm^-3
   C. 10^16 cm^-3
   D. 2.1 x 10^26 cm^-3
   Answer: B. p = ni^2 / n = (1.45e10)^2 / 1e16 = 2.1e4 cm^-3, about a million times smaller than ni. (Key point: Numerical example)

## Related in Electrical Engineering Material

- [p-type minority carrier suppression and conductivity](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aptype-minority-suppression) — Electrical Engineering Material, chapter 6
- [Minority suppression and donor-defined conduction](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aminority-suppression-impurity-donor) — Electrical Engineering Material, chapter 6
- [Electron concentration in an extrinsic semiconductor](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aextrinsic-electron-concentration) — Electrical Engineering Material, chapter 6
- [Minority carriers suppressed in n-type](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Antype-minority-suppressed) — Electrical Engineering Material, chapter 6
- [Degenerate semiconductors; direct vs indirect bandgap](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adegenerate-direct-indirect) — Electrical Engineering Material, chapter 6
- [Importance of Fermi energy in semiconductors](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-energy-importance) — Electrical Engineering Material, chapter 6, asked 3×