# Semiconductor Carrier Concentration Basics

• Master J
In summary, the relationship n.p = (n_i)^2 always holds for an un-doped semiconductor, but may cause confusion when dealing with doped semiconductors. This is because for an n-doped material, the electron concentration is approximately equal to the donor concentration, which is much larger than the intrinsic concentration for silicon. However, this relationship still holds true in doped semiconductors, with n representing the donor concentration and p representing the hole concentration in the valence band. This information can be found in the book "Simon M. Sze, 3rd, Physics of Semiconductor Devices."

#### Master J

I have been told that the relationship

n.p = (n_i)^2

always holds, where n_i is the intrinsic carrier concentration. This makes sense to me for an un doped semiconductor (sc.). However, for a doped sc., I'm a tad confused.

For an n-doped material say, the electron conc. is approximately (a very good approx. at normal temperatures) the donor concentration, since almost all of them are ionised. This conc. is usually of order say 10^17 cm^3, where as the intrinsic conc. for silicon is about 10^10 cm^3.
How is it that this still holds now for a doped sc?

We have n as the donor conc., and p as the hole conc. (incidentally, this is the hole conc. from hols left when the donor is ionized right?). Yet how is this still equal to the tiny in comparison intrinsic conc., as in the equation?

Cheers for any input!

Master J said:
incidentally, this is the hole conc. from hols left when the donor is ionized right?

No, it's the hole concentration in the valence band.

Please refer to the book "Simon M. Sze, 3rd, Physics of Semiconductor Devices"

## 1. What is a semiconductor?

A semiconductor is a material that has electrical conductivity between that of a conductor and an insulator. This means that it can conduct electricity, but not as well as a conductor such as copper, and not as poorly as an insulator such as rubber.

## 2. What is carrier concentration?

Carrier concentration refers to the number of charge carriers (electrons or holes) in a semiconductor material. It is typically measured in units of carriers per cubic centimeter (cm^-3).

## 3. How is carrier concentration determined?

Carrier concentration can be determined using various techniques such as Hall effect measurements, capacitance-voltage measurements, or optical measurements. These methods involve applying an external electric field to the semiconductor and measuring the resulting current or voltage.

## 4. What factors affect carrier concentration in a semiconductor?

The carrier concentration in a semiconductor is affected by the type of material, temperature, and the presence of impurities or dopants. For example, adding a dopant with more or less valence electrons than the semiconductor material can increase or decrease the carrier concentration.

## 5. Why is carrier concentration important in semiconductor devices?

The carrier concentration in a semiconductor plays a crucial role in determining its electrical properties and performance in devices. It affects parameters such as conductivity, resistance, and mobility, which are essential for the functioning of electronic devices such as transistors, diodes, and solar cells.